Issue 72, Fall 2022

JOURNAL OF
TECHNICAL ANALYSIS

Issue 72, Fall 2022

jota cover 2022

Editorial Board

Bruce Greig CFA, CMT, CIPM, CAIA

Director of Research, Q3 Asset Management

Chris Kayser, CMT

Cybercriminologist Founder, President & CEO

Ryan Hysmith DBA, CMT

Assistant Professor of Finance, Freed-Hardeman University

Paul Wankmueller, CMT

Investment Solutions Specialist

Private: Jerome Hartl, CMT

Vice President, Investments, Wedbush Securities

Eric Grasinger, CFA, CMT

Managing Director, Portfolio Manager, Glenmade

CMT Association, Inc.
25 Broadway, Suite 10-036, New York, New York 10004
www.cmtassociation.org

Published by Chartered Market Technician Association, LLC

ISSN 2378-7295 (Print)

ISSN 2378-7341 (Online)

The Journal of Technical Analysis is published by the Chartered Market Technicians Association, LLC, 25 Broadway, Suite 10-036, New York, NY 10004.New York, NY 10006. Its purpose is to promote the investigation and analysis of the price and volume activities of the world’s financial markets. The Journal of Technical Analysis is distributed to individuals (both academic and practicitioner) and libraries in the United States, Canada, and several other countries in Europe and Asia. Journal of Technical Analysis is copyrighted by the CMT Association and registered with the Library of Congress. All rights are reserved.

Letter from the Editor

by Sergio Santamaria, CMT, CFA

Welcome to the 72nd issue of the Journal of Technical Analysis (JoTA), the global leading publication in the field of technical analysis since January 1978.

Inflation measured by headline Consumer Price Index (CPI) peaked at 14.8% in the United States in March 1980. In the issue 7th of the Market Technicians Association Journal (the predecessor of the JoTA) published a month earlier (February 1980), Stan Weistein discussed his bullish forecast for equities for the next decade in his “A Contrary Opinion” article. He found that the extreme readings in different sentiment indicators such as allocation to equities vs. bonds, number of secondary offerings and investor sentiment plus favorable relative strength were going to lead to “the best bull market in over a decade” despite of the economic stagflation and poor equity returns of the 1970s. Will history repeat? As Mark Twain famously said “History doesn’t repeat itself, but it often rhymes”.

As a CMT Association member, you might enhance your research using free of charge the historical archives of the JoTA, that include approximately 500 peer-reviewed articles (https://cmtassociation.org/development/journal-technical-analysis/). Furthermore, the CMT Association is developing a new platform to improve significantly the search capabilities not only for the JoTA publications but also for other valuable content of technical analysis such as videos.

This JoTA edition contains five original articles plus the 2022 Charles H. Dow Award winning paper. Covering a wide range of technical analysis topics including the highly controversial market efficiency, these manuscripts keep on adding to the technical analysis literature and might provide inspiration to develop successful trading and investing strategies. For example, Troy Trentham in his “Portfolio Management Using Long-Term Relative Strength and Long-Momentum Strength as the Only Criteria” proposes a S&P 500 sector rotation strategy using the relative strength index (RSI) that seems to outperform the market on a risk-adjusted basis.

Finally, as usual, I would like to recognize all the individuals that have contributed to a new edition of the JoTA. First, to the authors for sharing their knowledge and pioneering ideas with the broader investment community. Second, to my exceptional editorial board colleagues who provide their invaluable expertise and time to make sure that all the papers are subjected to a double-blind review process (the reviewers do not know the identity of the author and the author does not know the identity of the reviewers). All the submissions are reviewed by at least two experts who provide feedback regarding, among other things, the contribution to the body of knowledge of technical analysis as well as the suitability of the manuscript for publication in the JoTA. Third, to the terrific staff at the CMT Association in conjunction with external providers for making the production and distribution process possible. Additionally, our president Brett Villaume and our CEO Alvin Kressler provide vital leadership and support to the journal.

If you are interested in sharing your ideas with the JoTA readers, including about 5,000 CMT members in 137 countries, please feel free to contact me.

Sergio Santamaria, CMT, CFA

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Portfolio Management Using Long-Term Relative Strength and Long-Term Momentum as the Only Criteria

by Troy Trentham, CMT

About the Author | Troy Trentham, CMT

Troy Trentham currently works in operations for LINK Investment Management, which is a Calgary, Alberta based fintech company that specializes in investment management. He has worked in the Canadian financial services sector for the past seven years where he also had positions working on a retail trading floor and in business development.

 

Troy graduated from Mount Allison University in New Brunswick, Canada with a Bachelor of Commerce with a double minor in Economics and Environmental Studies. He was an Academic All-Canadian while at Mount Allison. He attained his CMT designation 2021 and specializes in statistical analysis.

Abstract

This paper will examine portfolio returns using long-term relative strength and long-term momentum as the only criteria for investment decisions. It will compare various portfolios using quarterly RSI readings as the sole gauge for long-term relative strength and will use the S&P 500 monthly RSI reading for its long-term momentum parameter. The results suggest that long-term relative strength and the S&P 500 long-term momentum are both useful for investment criteria.

 

Introduction

The academic literature is dominated by fundamental analysis. Fundamental analysis itself is built on a handful of foundational concepts. Seemingly most academics and academic institutions have accepted these concepts and their assumptions as fundamentally true. This, in turn, has affected the belief of most market participants. Many professional market participants aspire to beat passive “buy and hold” investing where investors will buy index funds with low management fees. It is quite challenging to beat indexing over the long term and many people believe this is due to the efficient market hypothesis (EMH), especially when accounting for management fees as outlined by Eugene Fama and Kenneth French.[1] Furthermore, many fundamentalists believe technical analysis has no merit as the efficient market hypothesis debunked all technical analysis theory decades ago. This paper will explore the foundational concepts of modern portfolio theory and whether using long-term relative strength and long-term momentum can provide superior returns compared to passive investing.

 

Foundational Concepts and Literature Review

 

Efficient Market Hypothesis

Eugene Fama mainstreamed the efficient market hypothesis into the financial literature. He hypothesized that there are three levels of market efficiency – weak form, semi-strong form, and strong form efficient markets. Many market participants believe that financial markets, especially liquid, information rich markets, are weak form efficient. Weak form efficient markets, in theory, accurately discount all historical stock pricing information. This means that all past stock prices are accurately reflected in a security’s current price and therefore no edge can be gained from using it to invest for the future.[2] As technical analysis uses mainly pricing historical information, it would not be useful for investing in markets that are weak form efficient. Much of the empirical evidence on the efficient market hypothesis was focused on finding serial correlation of a stock’s price over a time-series. The evidence showed there was little, if any, correlation between a stock’s past change in price and a future change in price; therefore, markets were weak form efficient. After conducting serial correlation research on stocks in the Dow Jones Index from the late 1950’s to the mid 1960’s, Fama concluded there was only very slight dependence or it was non-existent.[3]

 

Capital Asset Pricing Model

The capital asset pricing model (CAPM) is closely linked to the efficient market hypothesis. CAPM hypothesizes that markets have a security market line whereby securities will be accurately priced given their risk and the only way to beat the market is to take on more risk. CAPM identifies systematic and unsystematic risk as the two types of risk in the market. [4] This model implies that market participants cannot beat the market while taking on less risk or, said another way, market participants cannot beat the market on an absolute and risk-adjusted basis.

 

Modern Portfolio Theory

Modern portfolio theory (MPT) is the practical application of the above theories. MPT was also built on Harry Markowitz’s portfolio selection research. His research argued that investors should consider expected returns and variance which he outlined as the “E-V rule”.[5] The E-V rule implies that the right kind of diversification is needed in portfolio selection. The diversification outlined advocates for buying securities that aren’t highly correlated to an investors existing portfolio to reduce overall risk.[6] MPT is the practice of buying diversified market indexes in accordance with Markowitz’s portfolio selection criteria and CAPM to eliminate unsystematic risk.

The above frameworks tie together in their belief that markets are efficient, that active investing cannott beat passive investing over the long term, and that market participants cannot avoid systematic risk. Interestingly, one pillar of CAPM and modern portfolio theory is their reliance on correlation when selecting securities in a portfolio. This is interesting because correlation is a technical indicator since it does not consider intrinsic value. On one hand EMH and CAPM suggest that technical analysis is futile, and on the other hand, technical analysis is a foundational element in the application of both theories.

 

Correlations in Bear Markets

In recent years, more research has been done on systematic risk, or what this author colloquially refers to as “macro risk”. Longin and Solnik researched market correlations in 2000 and they concluded that correlations increase in bear markets, but that correlations don’t increase in bull markets which partially nullifies the potential benefit of diversification.[7] Correlations approaching one are what caused this author to refer to the risk as macro risk because the macro environment was evidently poor making it so that harsh bear markets are a poor time to be invested in any stocks. Longin and Solnik’s research suggest that a market timing system could be useful for investors as market timing and avoiding bear markets could provide more downside protection than diversification as the benefit of diversification is greatly reduced in a bear market.

 

Relative Strength

Robert Levy, adding to the work of Benjamin F. King Jr.’s unpublished PhD dissertation, was the first person to bring the concept of relative strength into the mainstream literature. He didn’t dispute serial correlation, which EMH, CAPM, and MPT all rely on, however, he researched if relative strength could provide investors an edge and therefore show that the above frameworks, while useful, might not be entirely robust. Relative strength, also known as cross-sectional momentum, compares two securities or sectors and notes which one was stronger than the other over a given timeframe.

Robert Levy researched stocks according to recent strength and put them in groups based on their relative strength. His research examined stocks over a 26-week period. He concluded that stocks among the top decile far outperformed stocks that were in the bottom decile over the same period. The stocks in the top decile averaged a 9.6% increase over the 26-week period while stocks in the bottom decile averaged 2.9% over the 26-week period. His empirical testing suggested the concept of relative strength had merit and could serve as a tool for outperforming the market. Levy also implied that examining serial correlation alone might not preclude the existence of underlying dependencies in the stock market.[8] This suggests that even though stocks abide by a random walk movement, it does not invalidate certain forms of technical or statistical analysis, in particular relative strength. Levy’s research and assertions were the basis for this paper.

 

System Design and Results

This system was designed to further explore Levy’s findings and to examine if a simple technical system could beat passive investing. This paper will also briefly explore one long-term momentum parameter and whether it can be used as a type of macro (systematic) risk gauge. Modern portfolio theory states that investors should rebalance their portfolios on a quarterly basis so that excess growth from one index is sold and invested in index funds that didn’t appreciate as much (rebalancing) – the opposite will be done for this system. Depending on which type of portfolio is being tested, the system will concentrate funds every quarter in the weakest or strongest sectors. The quarterly relative strength index (RSI) readings will be used to rank each of the original nine SPDR sectors from strongest to weakest starting from the 2nd quarter of 2002 through the end of September 2021. This paper focused on the original nine sectors because they were created in late 1998 and had the most quarterly RSI data. The nine sectors that were included in the testing are materials (XLB), energy (XLE), financials (XLF), industrials (XLI), technology (XLK), consumer staples (XLP), utilities (XLU), health care (XLV), and consumer discretionary (XLY). Their first quarterly RSI readings were available at the end of June 2002 and the final recording was taken at the end of September 2021. The sectors will be ranked according to the previous quarter’s RSI reading meaning the RSI reading at the end of Q1 will determine the sectors selected for Q2 of that year and so on.

In all, eight different portfolios will be tested. The first six portfolios will not include the long-term momentum parameter (macro/systematic risk gauge). The long-term momentum parameter will be added to the last two portfolios to gauge its effect on performance. The long-term momentum parameter will be used to gauge the health of the broad market. The long-term momentum parameter is the monthly RSI reading on the S&P 500. When the S&P 500 finishes a month below the 50 level on the monthly RSI, the entire portfolio will be sold and moved into bonds. Vanguard’s Total Bond Market Index Fund, VBMFX, was used as the bond security for the portfolios. When the monthly RSI closes a month above 50, the portfolio will stay or be invested in the prescribed sectors. The long-term momentum parameter is a simple, practical approach to mitigate damage done in bear markets where correlations move to one and diversification has limited benefit. This system only uses one indicator and applies it into two different ways.

The results for the eight portfolios are below. The timeframe for all portfolio’s will be from July 2002 until the end of September 2021, except for portfolio SPY-LTM which will have its timeframe in its explanation. The funds will be reallocated at the close of the last trading day in every quarter.

 

Portfolio 1-WK

Allocating all portfolio funds in the single weakest SPDR sector according to the quarterly RSI reading. Reallocating is done every quarter to allocate in the weakest sector.

Metric 1-WK SPDR S&P 500 ETF Trust
CAGR 1.51% 10.04%
Beta 1.40 1.00
Annualized Alpha -10.02%
Standard Deviation 25.81% 14.54%
US Market Correlation .80 1.00
Sharpe Ratio .14 .65
Sortino Ratio .20 .96
Treynor Ratio 2.65 9.47

 

Investing in the single weakest sector vastly underperformed passive investing on an absolute and risk-adjusted basis. All risk measures were well below passive investing’s risk measures and 1-WK’s CAGR trailed by over 8%. The Sharpe ratio of .14 showed significant underperformance as the portfolio didn’t have much upside to make up for its standard deviation while the Sortino ratio of .20 shows 1-WK had significant drawdowns compared to passive investing. The Treynor ratio also trailed passive investing significantly coming in at 2.65. Evidently, it does not always pay to be a contrarian.

 

The below tables compare the annual returns for 1-WK and SPY.

Returns Jul-Dec 02 2003 2004 2005 2006 2007 2008
1-WK -19.10% 28.16% 6.99% -0.32% 12.16% 15.45% -51.09%
SPY -10.01% 28.18% 10.70% 4.83% 15.85% 5.14% -36.81%

 

Returns 2009 2010 2011 2012 2013 2014 2015
1-WK 17.61% 11.90% -17.15% 28.42% 35.52% 15.05% -21.47%
SPY 26.36% 15.06% 1.89% 15.99% 32.31% 13.46% 1.25%

 

Returns 2016 2017 2018 2019 2020 Jan-Sep 21
1-WK 28.02% -0.90% -18.21% 11.73% -32.51% 42.03%
SPY 12.00% 21.70% -4.56% 31.22% 18.37% 15.91%

 

Portfolio 1-WK had eight negative years and 12 positive years over the tested period. In contrast, SPY had 3 negative years and 17 positive years. Portfolio 1-WK’s average negative year was -20.09% while its average positive year was 21.09%. SPY’s average negative year was -17.12% and its average positive year was 15.90%. Portfolio 1-WK outperformed SPY in seven years and underperformed SPY in 13 years.

 

Portfolio 2-WK:

Allocating all portfolio funds in the two weakest SPDR sectors according to the quarterly RSI reading. The portfolio will be allocated in two equal parts at the start of each quarter based on last quarter’s reading.

Metric 2-WK SPDR S&P 500 ETF Trust
CAGR 7.02% 10.04%
Beta 1.20 1.00
Annualized Alpha -3.88%
Standard Deviation 20.50% 14.54%
US Market Correlation .86 1.00
Sharpe Ratio .38 .65
Sortino Ratio .55 .96
Treynor Ratio 6.43 9.47

 

The addition of diversifying into the 2nd weakest sector markedly improved results compared to being entirely allocated in the weakest sector, however, it still underperformed passive investing on an absolute and risk-adjusted basis. Investing 50% each in the two weakest sectors improved all risk measures compared to portfolio 1-WK. The Sharpe ratio improved from .14 to .38, the Sortino ratio improved from .20 to .55, and the Treynor ratio improved from 2.65 to 6.43. This amount of improvement from the last portfolio suggests that the weakest sector can significantly impair an investors portfolio if they have too much exposure to it.

 

The below tables compare the annual returns for 2-WK and SPY.

Returns Jul-Dec 02 2003 2004 2005 2006 2007 2008
2-WK -21.70% 18.75% 17.10% 1.34% 13.55% 14.16% -44.63%
SPY -10.01% 28.18% 10.70% 4.83% 15.85% 5.14% -36.81%

 

Returns 2009 2010 2011 2012 2013 2014 2015
2-WK 28.47% 19.45% -1.64% 25.15% 32.90% 3.31% -4.17%
SPY 26.36% 15.06% 1.89% 15.99% 32.31% 13.46% 1.25%

 

Returns 2016 2017 2018 2019 2020 Jan-Sep 21
2-WK 31.17% 11.21% -13.08% 17.98% -7.51% 35.62%
SPY 12.00% 21.70% -4.56% 31.22% 18.37% 15.91%

 

Portfolio 2-WK had six negative years and 14 positive years over the tested period. Portfolio 2-WK’s average negative year was -15.46% while its average positive year was 19.30%. Portfolio 2-WK outperformed SPY in eight years and underperformed SPY in 12 years.

 

Portfolio 3-WK:

Allocating all portfolio funds in the three weakest SPDR sectors according to the quarterly RSI reading. The portfolio will be allocated in three equal parts at the start of each quarter based on last quarter’s reading.

Metric 3-WK SPDR S&P 500 ETF Trust
CAGR 7.95% 10.04%
Beta 1.17 1.00
Annualized Alpha -3.07%
Standard Deviation 18.73% 14.54%
US Market Correlation .92 1.00
Sharpe Ratio .44 .65
Sortino Ratio .65 .96
Treynor Ratio 7.02 9.47

 

Adding a third layer of diversification again improved the results. The portfolio’s CAGR improved to 7.95% compared to 7.02% for portfolio 2-WK. This portfolio, while it still underperformed passive investing, had improved risk measures across the board compared to portfolio 2-WK. The Sharpe ratio improved from .38 to .44, the Sortino ratio improved from .55 to .65, and the Treynor ratio improved from 6.43 to 7.02. Given all three portfolios where all funds were concentrated in some variation of the weakest 3 sectors underperformed passive buy and hold investing on an absolute and risk-adjusted basis over the near 20-year period, it is reasonable to conclude that relentlessly buying the weakest sectors is an inferior strategy compared to passive investing. It is also interesting that the results incrementally improved as more funds were allocated in relatively stronger, albeit still weak, sectors.

 

The below tables compare the annual returns for 3-WK and SPY.

Returns Jul-Dec 02 2003 2004 2005 2006 2007 2008
3-WK -11.04% 25.15% 12.33% 5.05% 16.23% 1.01% -43.26%
SPY -10.01% 28.18% 10.70% 4.83% 15.85% 5.14% -36.81%

 

Returns 2009 2010 2011 2012 2013 2014 2015
3-WK 27.52% 16.99% 6.46% 21.16% 29.39% 9.81% -3.02%
SPY 26.36% 15.06% 1.89% 15.99% 32.31% 13.46% 1.25%

 

Returns 2016 2017 2018 2019 2020 Jan-Sep 21
3-WK 22.76% 13.13% -12.18% 23.79% -2.15% 27.27%
SPY 12.00% 21.70% -4.56% 31.22% 18.37% 15.91%

 

Portfolio 3-WK had five negative years and 15 positive years over the tested period. Portfolio 3-WK’s average negative year was -14.33% while its average positive year was 17.20%. Portfolio 3-WK outperformed SPY in ten years and underperformed SPY in ten years.

 

Portfolio 3-STR:

Allocating all portfolio funds in the three strongest SPDR sectors according to the quarterly RSI reading. The portfolio will be allocated in three equal parts at the start of each quarter based on last quarter’s reading.

Metric 3-STR SPDR S&P 500 ETF Trust
CAGR 10.80% 10.04%
Beta .9 1.00
Annualized Alpha 1.8%
Standard Deviation 14.56% 14.54%
US Market Correlation .89 1.00
Sharpe Ratio .70 .65
Sortino Ratio 1.02 .96
Treynor Ratio 11.34 9.47

 

Portfolio 3-STR outperformed SPY by .76% per year on an absolute basis. Its risk-adjusted performance also outperformed passive investing. This is the first portfolio where it outperformed passive investing on an absolute and risk-adjusted basis. Accordingly, 3-STR was the first portfolio where annualized alpha was positive. 3-STR also outperformed in all risk-adjusted ratios. Portfolio 3-STR saw the Sharpe ratio increase from .44 to .70 compared to 3-WK. Also, the Sortino ratio increased from .65 to 1.02 and the Treynor ratio increased from 7.02 to 11.34.

 

The below tables compare the annual returns for 3-STR and SPY.

Returns Jul-Dec 02 2003 2004 2005 2006 2007 2008
3-STR -14.96% 23.62% 19.31% 9.95% 18.68% 18.70% -40.52%
SPY -10.01% 28.18% 10.70% 4.83% 15.85% 5.14% -36.81%

 

Returns 2009 2010 2011 2012 2013 2014 2015
3-STR 20.96% 16.33% 3.88% 10.67% 36.72% 16.70% 8.05%
SPY 26.36% 15.06% 1.89% 15.99% 32.31% 13.46% 1.25%

 

Returns 2016 2017 2018 2019 2020 Jan-Sep 21
3-STR -0.17% 25.54% 0.15% 29.45% 20.87% 13.70%
SPY 12.00% 21.70% -4.56% 31.22% 18.37% 15.91%

 

Portfolio 3-STR had three negative years and 17 positive years over the tested period. Portfolio 3-STR’s average negative year was -18.55% while its average positive year was 17.25%. Portfolio 3-STR outperformed SPY in 12 years and underperformed SPY in eight years.

 

Portfolio 2-STR:

Allocating all portfolio funds in the two strongest SPDR sectors according to their quarterly RSI readings. The portfolio will be allocated in two equal parts at the start of each quarter based on last quarter’s reading.

Metric 2-STR SPDR S&P 500 ETF Trust
CAGR 11.68% 10.04%
Beta .85 1.00
Annualized Alpha 3.13%
Standard Deviation 15.04% 14.54%
US Market Correlation .82 1.00
Sharpe Ratio .73 .65
Sortino Ratio 1.10 .96
Treynor Ratio 12.93 9.47

 

Portfolio 2-STR outperformed passive investing on an absolute and risk-adjusted basis. 2-STR’s CAGR was 1.64% more than SPY with superior risk-adjusted ratios. 2-STR had a positive annualized alpha of 3.13% and saw the Sharpe, Sortino, and Treynor ratios modestly improve from portfolio 3-STR. The Sharpe ratio improved from .70 to .73, the Sortino ratio improved from 1.02 to 1.10, and the Treynor ratio improved from 11.34 to 12.93. Interestingly, the standard deviation increased from 14.56% to 15.04% compared to 3-STR. This is the first portfolio that invested incrementally more in relative strength and had its standard deviation increase. All previous increments saw the standard deviation decrease.

 

The below tables compare the annual returns for 2-STR and SPY.

Returns Jul-Dec 02 2003 2004 2005 2006 2007 2008
2-STR -16.27% 23.53% 17.51% 15.03% 18.81% 22.19% -33.83%
SPY -10.01% 28.18% 10.70% 4.83% 15.85% 5.14% -36.81%

 

Returns 2009 2010 2011 2012 2013 2014 2015
2-STR 18.84% 16.57% 3.44% 2.78% 31.59% 20.40% 5.35%
SPY 26.36% 15.06% 1.89% 15.99% 32.31% 13.46% 1.25%

 

Returns 2016 2017 2018 2019 2020 Jan-Sep 21
2-STR 5.61% 28.50% -0.03% 28.20% 28.34% 13.84%
SPY 12.00% 21.70% -4.56% 31.22% 18.37% 15.91%

 

Portfolio 2-STR had three negative years and 17 positive years over the tested period. Portfolio 2-STR’s average negative year was -16.71% while its average positive year was 17.68%. Portfolio 2-STR outperformed SPY in 12 years and underperformed SPY in eight years.

 

Portfolio 1-STR:

Allocating all portfolio funds in the strongest SPDR sector according to the quarterly RSI reading. Reallocating is done every quarter to allocate in the strongest sector.

 

Metric 1-STR SPDR S&P 500 ETF Trust
CAGR 14.38% 10.04%
Beta .79 1.00
Annualized Alpha 6.55%
Standard Deviation 17.17% 14.54%
US Market Correlation .67 1.00
Sharpe Ratio .80 .65
Sortino Ratio 1.24 .96
Treynor Ratio 17.42 9.47

 

Portfolio 1-STR significantly outperformed SPY over the 19 year and 3-month period. 1-STR’s CAGR was an impressive 14.38% which was 4.34% higher than passive investing. 1-STR outperformed passive investing on all risk-adjusted ratios. Additionally, all risk-adjusted ratios improved compared to portfolio 2-STR – the Sharpe ratio improved from .73 to .80, the Sortino ratio improved from 1.10 to 1.24, and the Treynor ratio improved 12.93 to 17.42. Portfolio 1-STR had an annualized alpha of 6.55%. Portfolio 1-STR saw its standard deviation increase from 15.04% to 17.17% compared to portfolio 2-STR.

All six portfolios that strictly allocated according to the previous quarter’s relative strength index, which is historical information, incrementally improved as the allocation was increasingly concentrated in relative strength.

 

The below tables compare the annual returns for 1-STR and SPY.

Returns Jul-Dec 02 2003 2004 2005 2006 2007 2008
1-STR -14.74% 17.64% 19.26% 40.17% 18.08% 36.88% -29.82%
SPY -10.01% 28.18% 10.70% 4.83% 15.85% 5.14% -36.81%

 

Returns 2009 2010 2011 2012 2013 2014 2015
1-STR 20.25% 13.78% 2.92% 10.74% 27.73% 25.14% 5.44%
SPY 26.36% 15.06% 1.89% 15.99% 32.31% 13.46% 1.25%

 

Returns 2016 2017 2018 2019 2020 Jan-Sep 21
1-STR 4.98% 21.34% 1.59% 25.91% 41.20% 15.50%
SPY 12.00% 21.70% -4.56% 31.22% 18.37% 15.91%

 

Portfolio 1-STR had two negative years and 18 positive years over the tested period. Portfolio 1-STR’s average negative year was -22.28% while its average positive year was 19.38%. Portfolio 1-STR outperformed the SPY in half of the years.

 

Portfolio SPY-LTM:

Allocating all portfolio funds in SPDR’s S&P 500 ETF, SPY, if long-term momentum is positive (monthly RSI above 50). All funds will be moved to VBMFX, Vanguard’s bond index, when long-term momentum is negative (monthly RSI close below 50). For this comparison, the timeline will be from January 1999 to September 2021.

Metric SPY-LTM SPDR S&P 500 ETF Trust
CAGR 8.76% 7.58%
Beta .55 1.00
Annualized Alpha 4.44%
Standard Deviation 11.16% 14.92%
US Market Correlation .72 .99
Sharpe Ratio .66 .45
Sortino Ratio .99 .66
Treynor Ratio 13.49 6.77

 

Portfolio SPY-LTM outperformed SPY on an absolute and risk-adjusted basis. SPY-LTM had an annualized alpha of 4.44% and outperformed on all risk ratios.

Starting this comparison at the beginning of 1999 biases this timeframe toward portfolio SPY-LTM as the long-term momentum parameter will allow it to miss most the bear market from 2000-2002. This paper will also examine a timeframe that is biased towards passive investing compared to this timeframe.

 

The below tables compare the annual returns for SPY-LTM and SPY.

Returns 1999 2000 2001 2002 2003 2004
SPY-LTM 20.39% -7.64% -2.80% 8.26% 9.14% 10.70%
SPY 20.39% -9.73% -11.75% -21.59% 28.18% 10.70%

 

Returns 2005 2006 2007 2008 2009 2010
SPY-LTM 4.83% 15.85% 5.14% -2.94% 9.80% 3.87%
SPY 4.83% 15.85% 5.14% -36.81% 26.36% 15.06%

 

Returns 2011 2012 2013 2014 2015 2016
SPY-LTM 1.89% 15.99% 32.31% 13.46% 1.25% 6.72%
SPY 1.89% 15.99% 32.31% 13.46% 1.25% 12.00%

 

Returns 2017 2018 2019 2020 Jan-Sep 2021
SPY-LTM 21.70% -4.56% 22.72% 6.81% 15.91%
SPY 21.70% -4.56% 31.22% 18.37% 15.91%

 

Portfolio SPY-LTM had four negative years and 19 positive years over the tested period. Portfolio SPY-LTM outperformed SPY in four years, underperformed SPY in six years, and performed the same as SPY in 13 years.

 

Portfolio SPY-LTM:

The allocations will be the same as above except the timeframe will be from July 2002 to September 2021.

Metric SPY-LTM SPDR S&P 500 ETF Trust
CAGR 9.83% 10.04%
Beta .55 1.00
Annualized Alpha 4.12%
Standard Deviation 10.82% 14.54%
US Market Correlation .74 1.00
Sharpe Ratio .81 .65
Sortino Ratio 1.24 .96
Treynor Ratio 15.97 9.47

 

SPY-LTM underperformed SPY on an absolute basis but outperformed SPY on a risk-adjusted basis over this timeframe. As noted above, this timeframe begins near the end of 2000-2002 bear market so passive investing does not see a sizeable decline at the beginning of the timeframe. SPY-LTM was still invested in bonds at the beginning of this timeframe and didn’t invest in equities until the November 2003, so this timeframe is biased towards passive investing.

 

The below tables compare the annual returns for SPY-LTM and SPY.

Returns Jul-Dec 02 2003 2004 2005 2006 2007 2008
SPY-LTM 5.24% 9.14% 10.70% 4.83% 15.85% 5.14% -2.94%
SPY -10.01% 28.18% 10.70% 4.83% 15.85% 5.14% -36.81%

 

Returns 2009 2010 2011 2012 2013 2014 2015
SPY-LTM 9.80% 3.87% 1.89% 15.99% 32.31% 13.46% 1.25%
SPY 26.36% 15.06% 1.89% 15.99% 32.31% 13.46% 1.25%

 

Returns 2016 2017 2018 2019 2020 Jan-Sep 21
SPY-LTM 6.72% 21.70% -4.56% 22.72% 6.81% 15.91%
SPY 12.00% 21.70% -4.56% 31.22% 18.37% 15.91%

 

Portfolio SPY-LTM had two negative years and 18 positive years over the tested period. Portfolio SPY-LTM’s average negative year was -3.75% while its average positive year was 11.30%. Portfolio SPY-LTM outperformed SPY in two years, underperformed SPY in six years, and performed the same as SPY in 12 years.

 

Portfolio 1-STR-LTM:

Allocating all portfolio funds in the strongest SPDR sector according to the quarterly RSI reading while the S&P 500’s monthly RSI reading closes above 50. If the S&P 500’s monthly RSI reading closes below 50, the portfolio will be allocated in bonds. This comparison will use the timeframe of July 2002 to September 2021.

Metric 1-STR-LTM SPDR S&P 500 ETF Trust
CAGR 14.36% 10.04
Beta .45 1.00
Annualized Alpha 9.66%
Standard Deviation 13.79% 14.54%
US Market Correlation .47 1.00
Sharpe Ratio .96 .65
Sortino Ratio 1.64 .96
Treynor Ratio 29.57 9.47

 

Portfolio 1-STR-LTM utilizes the long-term momentum / macro risk parameter to signal when to invest in bonds. It was invested in bonds at the start of this timeframe and didn’t invest into equities until November 2003. 1-STR-LTM outperformed SPY by 4.32% per year on an absolute basis and significantly outperformed on a risk-adjusted basis. Although it is not displayed above, this portfolio had a skew of 0 which is atypical for a portfolio. 1-STR-LTM had significant annualized alpha at 9.66% with a lower standard deviation and only .47 correlation to the US market. Portfolio 1-STR-LTM had a lower annual return of .02% compared to 1-STR by itself, however, its risk-adjusted returns significantly improved compared to 1-STR – the Sharpe ratio improved from .80 to .96, the Sortino ratio improved from 1.24 to 1.64, and the Treynor ratio improved from 17.42 to 29.57.

 

The below tables compare the annual returns for 1-STR-LTM and SPY.

Returns Jul-Dec 02 2003 2004 2005 2006 2007 2008
1-STR-LTM 5.24% 7.05% 19.26% 40.17% 18.08% 36.88% -9.39%
SPY -10.01% 28.18% 10.70% 4.83% 15.85% 5.14% -36.81%

 

Returns 2009 2010 2011 2012 2013 2014 2015
1-STR-LTM 7.50% 3.63% 2.92% 10.74% 27.73% 25.14% 5.44%
SPY 26.36% 15.06% 1.89% 15.99% 32.31% 13.46% 1.25%

 

Returns 2016 2017 2018 2019 2020 Jan-Sep 21
1-STR-LTM 1.53% 21.34% 1.59% 22.91% 26.25% 15.50%
SPY 12.00% 21.70% -4.56% 31.22% 18.37% 15.91%

 

Portfolio 1-STR-LTM had one negative year and 19 positive years over the tested period. Portfolio 1-STR-LTM’s lone negative year was -9.39% while its average positive year was 15.73%. Portfolio 1-STR-LTM outperformed SPY in 11 years and underperformed SPY in nine years.

The long-term momentum parameter was added to all six original portfolios, but the data will not be included for the sake of brevity. The additional parameter improved the absolute and risk-adjusted performance for all portfolios outside of 1-STR where it only improved the risk-adjusted return. Portfolio 1-WK saw the largest improvement in absolute return as it moved to bonds and avoided a significant drawdown during the great financial crisis. The other four portfolios CAGR’s improved as well as they also moved to bonds and avoided much of the GFC. Most portfolios saw a noticeable improvement with risk-adjusted returns except for portfolio 1-WK which only saw modest improvements in its risk-adjusted returns. Portfolio 1-WK-LTM still had a 58% drawdown as XLE, which was the weakest sector and was therefore the sole investment in 1-WK-LTM, markedly declined during the 2020 covid crash as the long-term momentum parameter didn’t trigger before the Covid crash. This 58% drawdown in 2020 for 1-WK-LTM was the reason why the portfolio only had modest improvements in its risk-adjusted performance compared to portfolio 1-WK.

 

Implications and Discussion

Combined Portfolio Performance Metrics

All portfolios that invested exclusively in the weakest sectors as judged by their last quarter’s RSI reading underperformed SPY on an absolute and risk-adjusted basis. On the other hand, all portfolios that invested exclusively in the strongest sectors outperformed SPY on an absolute and risk-adjusted basis. The data shows that as the portfolios incrementally invested more in relatively strong sectors all risk ratios improved. It is reasonable to conclude that as the portfolios invested incrementally more in relative strength, they saw relatively smaller drawdowns and relatively larger rallies. The standard deviation is the only risk indicator that didn’t increase incrementally along with relative strength exposure portfolio, however, all portfolios that invested in relative strength had lower standard deviations than all portfolios that invested in relative weakness.

SPY-LTM outperformed passive investing from 1999 to the end of September 2021, however, it underperformed passive investing from July 2002 to the end of September 2021. SPY-LTM outperformed passive investing on a risk-adjusted basis on both timeframes. Additionally, when the broad market long-term momentum indicator was combined with 1-STR, it significantly increased risk-adjusted returns for 1-STR-LTM. The results were inconclusive as to whether long-term momentum can beat passive investing, however, the results suggest that monitoring and acting on the long-term momentum of the broad market is effective for reducing risk. This ties into Longin and Solnik’s conclusion that correlations in the stock market increase in bear markets so the risk-reward profile for most equities is poor in bear markets. Consequently, investors should avoid these periods of poor risk-adjusted returns and significant volatility.

 

Combined Annual Return Data

Portfolios that allocated more in relative strength saw a larger number of positive years and fewer negative years. The number of positive years increased sequentially as portfolios allocated more to the stronger sectors. Over and underperformance was a different story. The portfolios that allocated the most in relative weakness underperformed more during the tested period compared to SPY, but 1-STR didn’t outperform SPY during the majority of the tested period. Similarly, 1-STR-LTM only outperformed SPY in 11 of the 20 years. Portfolios 2-STR and 3-STR outperformed SPY in 12 of the 20 years, but they experienced more negative years than 1-STR and their average positive year’s return were also less than 1-STR’s average positive year.

The above data further shows that the long-term momentum parameter was useful for preventing large drawdowns. SPY-LTM and 1-STR-LTM had the lowest average negative returns of all portfolios tested. This is consistent with Longin and Solnik’s assertion that correlations approach 1 in bear markets; the long-term momentum parameter was effective at reducing drawdowns in bear markets where no sectors escaped the broad selling in equities. However, the long-term momentum parameter also forced portfolios to be invested in bonds during the early stages of new bull markets so portfolios that used the LTM parameter missed those periods of strong returns.

The data is clear in that investing in relative strength provides superior absolute and risk-adjusted returns compared to passive investing. This supports Robert Levy’s claim that serial correlation alone, or lack thereof, does not necessarily mean markets are weak-form efficient and that markets may still have underlying dependencies. These results suggest EMH, CAPM, and the security market line aren’t strictly accurate portrayals of markets even though they are useful, profound frameworks. The results have similar implications for modern portfolio theory in that the theory is useful and perhaps is the best investing method for the majority of market participants, but that it is beatable over the long term.

It is important to highlight the simplicity of this system. This system only uses one indicator in two different ways over two timeframes. Some readers might be skeptical of a portfolio management system that only uses one indicator to beat the market over the long term, especially one that has an annualized alpha of 9.66%; however, the relative strength index has been applied in ways that are consistent with existing research on relative strength, gauge the broad market strength, and quantify which sectors of the market have been the strong strongest. Essentially, it is not the indicator itself that provides superior returns, but the concept of relative strength that allows for superior returns. Many market participants believe technical indicators or trading rules are static and rigid. This is a flawed view of technical analysis as the foundational concepts are more important than rigid investing rules. This paper was written to test long-term relative strength and long-term momentum, but it also shows that technical indicators can be used in a multitude of ways and that they don’t have static, rigid applications.

 

Conclusion

The above evidence and near 20-year testing period show that using long-term relative strength and long-term momentum can significantly outperform passive investing on an absolute and risk-adjusted basis. Historical relative strength information provides investors with a measurable edge and can show investors where the best risk and reward opportunities lie. These results are consistent with existing research on relative strength.

The results of the six portfolios showed that investing more in relatively strong sectors improved results with each increment. Adding a long-term momentum parameter to gauge broad market health can also improve risk-adjusted performance by markedly decreasing drawdowns and volatility.

Lastly, the results showed a soundly applied, simple technical system could beat passive investing over the long-term; simplicity might be the ultimate form of sophistication.

 

References

Fama, Eugene F., Kenneth R. French, 2010, Luck Versus Skill in the Cross-Section of Mutual Fund Returns, Journal of Finance

Fama, Eugene F., 1969, Efficient Capital Markets: A Review of Theory and Empirical Work, Journal of Finance

Fama, Eugene F., 1965, The Behavior of Stock Market Prices, Journal of Business

Sharpe, William F., 1964, Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance

Markowitz, Harry M., 1952, Portfolio selection, Journal of Finance

Longin, François, Bruno Solnik, 2000, Extreme Correlation of International Equity Markets, Journal of Finance

Levy, Robert A., 1967, Relative Strength as A Criterion for Investment Selection. Journal of Finance

[1] Fama, Eugene F., Kenneth R. French, 2010, Luck Versus Skill in the Cross-Section of Mutual Fund Returns, Journal of Finance

[2] Fama, Eugene F., 1969, Efficient Capital Markets: A Review of Theory and Empirical Work, Journal of Finance

[3] Fama, Eugene F., 1965, The Behavior of Stock Market Prices, Journal of Business

[4] Sharpe, William F., 1964, Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance

[5] Markowitz, Harry M., 1952, Portfolio selection, Journal of Finance

[6] Markowitz, Harry M., 1952, Portfolio selection, Journal of Finance

[7] Longin, François, Bruno Solnik, 2000, Extreme Correlation of International Equity Markets, Journal of Finance

[8] Levy, Robert A., 1967, Relative Strength as A Criterion for Investment Selection. Journal of Finance

 

Appendix

  • Sector Strength as Judged by Their Previous Quarter’s Ending RSI, July 2002–September 2021

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A Theoretical Case for Technical Analysis: Testing Weak Form Market Efficiency in Pakistan

by Dr. Kelly Corbiere, CMT, CFA, CFP

About the Author | Dr. Kelly Corbiere, CMT, CFA, CFP

Kelly Corbiere, CFA, CMT, CFP has over 25 years of experience in financial services. She has worked in wealth management, as a global equity analyst and in institutional taxable fixed income.

Kelly holds both a Bachelor of Business Administration in Finance and a Bachelor of Arts in Language and International Trade from Eastern Michigan University. She has a Master of International Management with a concentration in Finance from Thunderbird School of Global Management and recently completed a PhD in International Development through the University of Southern Mississippi. She holds a Post-Graduate Certificate of Accounting from Simpson College and is also a graduate of Texas Trust Schools. Her experience in academia also includes teaching finance and investments courses as an adjunct instructor.

Kelly has served as the Chair of the CFA Societies of Texas (which has over 3,000 members) and is an active board member of several other professional and charitable boards, including the CMT Association board. She is also a Rotarian, an avid volunteer, and a frequent host parent to exchange students from around the world. Kelly has earned both the Chartered Financial Analyst (CFA) and Chartered Market Technician (CMT) designations and is also a CERTIFIED FINANCIAL PLANNER ™ professional. She has completed everything except the experience requirement toward the Certified Public Accountant (CPA) designation. Kelly speaks Spanish fluently, as well as some Danish and French.

Abstract

The dearth of empirical studies substantiating the merits of technical analysis limits the legitimacy of the field. This study seeks to address that by offering evidence that Pakistan does not conform to the assumptions of weak form efficiency and therefore offers opportunities to generate abnormal returns using historical data such as that employed by technical analysts. Results of three versions of the runs test, the Augmented Dickey Fuller test, the Phillips Perron test, and an autoregressive model of order one, point to a lack of randomness, and thus a lack of weak form efficiency, over the two periods studied.

 

Introduction

This study employs parametric and non-parametric tests to assess whether Pakistan’s KSE-100 Index is weak form efficient. Eugene Fama (1965, 1970) posited via the Efficient Market Hypothesis (EMH) that stock prices are unpredictable. The weak form of Fama’s EMH implies that stock prices include all past information. When that is the case, prices move randomly which suggests that tools used by technical analysts such as past prices, charts, and pattern recognition are not helpful in assessing the future direction of prices. Therefore, any attempt at routinely finding undervalued securities using these methods is futile. If, however, prices are not random, that condition violates weak form efficiency and provides a theoretical foundation for the value of technical analysis.

Pakistan’s benchmark index serves as the test case for this analysis. Daily closing prices, as well as price returns, for the Karachi Stock Exchange’s KSE-100 index between January 1, 2008 and December 31, 2010, as well as January 1, 2019 through 2021, are tested for randomness. Since published literature does not appear to include data on the latter period and little, if any, research evaluates market efficiency specifically during bear markets, this affords the opportunity to test the hypothesis that Pakistan’s benchmark index has become weak form efficient over time and remains so during market downturns when emotions may cause investors to act irrationally.

The results of statistical tests evaluated in this article suggest that returns in Pakistan’s main stock market are not random and not weak form efficient. This implies that investors can generate above-market returns using technical analysis. Following a review of the literature on Random Walk theory, the Efficient Market Hypothesis, and the Adaptive Market Hypothesis, the methodology is presented, and results are analyzed.

 

Literature Review

Among other functions, stock markets channel investment and act as a gauge of the financial environment of a country. When stock prices incorporate all available information and thus accurately reflect the value of listed companies, capital flows optimally based on risk-reward tradeoffs. In such an efficient market, where securities are always priced at fair value, attempts to predict market outcomes and identify undervalued assets are useless. Efficiency in the context of the EMH is therefore a reference to the information content of a security that links asset prices to their value.

The efficiency of developed markets is well documented. Market efficiency implies that prices fully incorporate all available information, are random, and are unpredictable. Investors are only able to earn above-market returns in these jurisdictions by assuming above-market levels of risk. Even in developed markets, however, a degree of ambiguity remains regarding the type of information that is included in stock prices, as well as the speed that constitutes instantaneous incorporation of information. Dsouza and Mallikarjunappa (2015) point out that some interval of time is necessary for the market to absorb new information, even if that period is only split seconds.

The situation is different in many developing markets where even the most basic form of market efficiency has not been empirically established and no consensus exists as to the validity of EMH. Developing countries often differ from those in developed markets in terms of liquidity, regulation, trading infrastructure, and information availability, among other things. To that point, past studies by Han Kim and Singal (2000) suggest that liberalization via opening markets to foreign capital can lead to market efficiency. Naidu and Rozeff (1994), as well as Jain (2005), show that electronic trading can also improve efficiency while Antoniou, Ergul, and Holmes (1997) demonstrate efficiency increases as the regulatory environment in a market improves. At the other extreme, one factor that can reduce market efficiency is the use of circuit breakers that place a ceiling or floor on prices, thus limiting price movements.

If markets are not efficient and prices and returns are not random, then opportunities exist for investors to profit by leveraging past information and chart patterns. Methods for evaluating weak form efficiency ascertain whether prices are predictable by testing their randomness.

 

Random Walk Theory

The random walk model was first evaluated by Bachelier (1900) with the hypothesis that generating above market returns is not feasible. By definition, a random walk lacks a pattern. As applied to stock markets, randomness implies that asset prices are a function of the prior period’s price plus or minus a zero-mean, random, independent quantity. Stated differently, tomorrow’s stock price is anyone’s guess and the likelihood of stocks increasing or decreasing on any given day is independent of what occurred the prior day or during any previous period.

 

Efficient Market Hypothesis (EMH)

Random Walk Theory and EMH have similarities. Fama (1965, 1970) suggested that because the information flows in efficient markets take place randomly, changes in stock prices should also occur randomly. Both theories suggest an inability to profitably predict stock prices. One key difference between the two theories, however, is the EMH assumption that investors act rationally. This implies that investors use information advantages to arbitrage away any price discrepancies, thereby ensuring that prices remain at their fair value and markets stay efficient.

EMH was independently pioneered by Paul Samuelson (1965) and Eugene Fama (1965, 1970). Fama used US stock market data from 1956 through 1962 to test the statistical dependence between stock prices. Finding none, he was the first to use the label “efficient” to denote this condition.

Fama (1970) conceptualized three stages of market efficiency, each of which build on the prior stage. Weak form efficiency predicts that all historical information is fully incorporated into stock prices, thereby negating the value of technical analysis. Semi-strong efficiency predicts all historical and publicly available information is incorporated into prices and suggests neither technical nor fundamental analysis is useful for generating abnormal returns according to the website myaccountingcourse.com (n.d.). Strong form efficiency occurs when even inside information cannot be leveraged to generate above market returns. In short, Fama described efficient markets as those where asset prices match their fair value and where no amount of proprietary information will allow for returns above those that are commensurate with the level of risk assumed.

 

Adaptive Market Hypothesis (AMH)

Not all evidence in all countries supports that markets are efficient. Lo’s Adaptive Market Hypothesis (2004) bridges the gap between EMH and evidence refuting it by implying that efficiency varies over time and among markets. This condition allows for the more realistic possibility that market efficiency varies on a spectrum between complete efficiency and complete inefficiency. It also implies certain markets may be predictable at certain times if EMH does not always hold. Myriad reasons may explain a lack of efficiency but one of them may be Fama’s exacting requirement for prices to “fully” incorporate all available information which establishes a high standard for complete efficiency.

The predictions of AMH are therefore consistent with a periodic lack of weak form efficiency. AMH also helps explain phenomena such as trends, bubbles, anomalies, and cycles, all of which are well known to technical analysts. AMH theory is aligned with scholarship such as that of Grossman and Stiglitz (1980) indicating that investors who expend effort to compile information regarding profitable trading opportunities require compensation for doing so. The logical follow-on is that, particularly in developing markets where information gathering can present a challenge, investors must be incentivized to pursue costly due diligence efforts. All of these issues point to possible gaps in EMH theory.

 

Pakistan’s Stock Market

Hussain and Qasim (1997) share that the KSE-100 index was launched and the Pakistani stock market was opened to foreign investors in 1991. This was followed by the implementation of electronic trading in 1998 and a series of other regulatory improvements over time to address governance, transparency, and investor protections.

Despite the steps to improve efficiency scholars such as Haque and Liu (2011), Irfan, Saleem, and Irfan (2011), Riaz, Hassan, and Nadim (2012), Mudassar and co-authors (2013), and Rizwan Qamar and Sheikh (2014) conclude that the KSE-100 index lacks weak form market efficiency. However, when using monthly data, Khan and Khan (2016) find the KSE-100 to be weak form efficient. The same is true for Mustafa and Nishat (2007) after adjusting for thin trading, while Chakraborty (2006) finds indications of weak form efficiency only during the most recent sub-periods of a longer study. The data are therefore inconclusive and merit further evaluation.

 

Methodology

Using closing prices for the KSE-100 obtained from Bloomberg (2022) for the periods January 1, 2008 through December 31, 2010 (“early data”) and January 1, 2019 through December 31, 2021 (“recent data”), this study evaluates the weak form efficiency of Pakistan’s stock index by testing for randomness.

 

Tests of Normality

Both parametric and non-parametric tests are employed to evaluate the study’s null hypothesis that returns are random. However, parametric tests are only valid when distributions are normal. In the absence of normality, inferences may be unreliable. Normality is therefore evaluated via the Shapiro-Wilk test (1965), the Shapiro-Francia test (1972), and the Kolmogorov-Smirnov test created by Kolmogorov (1933) and Smirnov (1948) and amended by Lilliefors (1967).

The Kolmogorov-Smirnov test measures the widest point between a sample distribution and a normal distribution and fails to reject the null hypothesis of normality when that distance is within tolerable levels. The Shapiro-Wilk and Shapiro-Francia tests are goodness of fit tests that resemble the Kolmogorov-Smirnov methodology in that they assess the relationship between the sample data and a normal distribution, but they do so by weighting differences of paired data.

For time series data, Wooldridge (2020) suggests that each collection of data represents one possible realization of a random draw that is determined by historical conditions. The same draw would be different in the face of different conditions. Therefore, it is acceptable to assume time series data are random which allows researchers to perform parametric tests such as the Augmented Dickey Fuller test below, created by Dickey and Fuller (1979, 1981), even when normality is not assured.

 

Tests for Randomness

Runs Test

Rather than testing raw prices for randomness, Fama’s seminal research (1965) uses returns. A price change of $5 on a $100 stock represents a 5% change, but that same 5% change constitutes a $50 move for a stock that is priced at $1,000. A method to neutralize the effect that rising prices have on variability is to employ logarithmic price returns as the unit of analysis. To do so, the data are transformed via the equation

where r is the price return, P equals price, t represents the current time period and t-1 represents the prior time period.

Data that are transformed per equation (1) above are used to test the null hypothesis that returns are random first by employing the non-parametric runs test as postulated by Wald and Wolfowitz (1940). Naghshpour (2016) defines a run as a string of consecutive trading days where one-day price returns are entirely positive or negative. Each consecutive string of positive days forms a single run, as does a string of negative days. This is somewhat similar to the strings of x’s and o’s used by point and figure technicians except that, instead of beginning a new column each time a change occurs, the runs test registers a reversal as an additional run. In the extreme case where the market increases (or decreases) every day over a test period, the data would contain a single run whereas alternating between positive and negative returns every day would entail a number of runs equal to the sample size.

The claim of the runs test is that returns are not random if the data contain too many or too few runs compared to the number that is expected by chance. In other words, according to Gibbons and Chakraborti (2011), returns that lack randomness are expected to have clusters of up or down days that produce fewer, longer runs than random returns. Additional runs tests, used to provide more conclusive results, compare the number of observations falling above and below the mean and the median. Weak form efficiency is assumed when a sufficiently high p-value causes the researcher to fail to reject the null hypothesis. This implies that returns follow a random walk and past returns, therefore, cannot be used for predictive purposes.

To obtain critical values when the number of observations exceeds 20 (the maximum covered by existing statistical tables), a continuity correction factor is recommended. In that instance, the mean expected number of runs (R) is calculated as:

where n1 is the number of observations that increase versus the prior trading day and n2 is the number of observations that decrease compared to the prior day. The expected standard deviation for the number of runs is:

while the Z statistic is computed as:

Finally, the continuity correction factor (h) is calculated with the formulas:

h = +0.5 if

h = -0.5 if

One drawback of the runs test is that it fails to account for the magnitude of price changes and, instead, considers only whether returns are positive or negative. Another limitation of this test is its low power. When power is defined as the potential for a Type II error, this implies that the runs tests has a somewhat poor record of properly rejecting the null hypothesis when it is incorrect.

 

Augmented Dickey-Fuller (ADF) Test

The parametric ADF test, created by Dickey and Fuller (1979, 1981), is a tool used in time series analysis to test for stationarity. As defined by Hill and his co-authors (2017), a process is stationary when it lacks trends or seasonality, is identically distributed across all time periods, and has an unchanging mean and variance over time. Stationarity can be tested by assessing whether the data contain a unit root, with a unit root being a necessary condition for randomness and therefore weak form efficiency. The precise methodology, which is beyond the scope of this study, uses an autoregressive model to evaluate whether a unit root is present. The null hypothesis for the ADF test is non-stationarity, meaning the data have a unit root. In practice, failing to reject the null hypothesis therefore implies a lack of randomness and a degree of predictability.

 

Phillips-Peron (PP) Test

The Phillips-Peron test (1988) also tests for randomness by evaluating whether the series contains a unit root. It modifies the Dickey Fuller methodology by correcting for any autocorrelation or heteroskedasticity. Like the ADF test, the null hypothesis is non-stationarity, indicating the presence of a unit root.

 

Autoregressive (AR) Models

With autoregressive time series models, lagged values of the dependent variable are used as explanatory variables to determine the statistical significance of the association between past and current values. An autoregressive model of order one (AR1) uses only a one-period lag as a predictor

Yt = ẞ0 + ẞ1Yt-1 + μt

In the above model, Y represents the logarithmic return while the coefficient ẞ1 represents the presence of a unit root when the absolute value of the coefficient is one. Again, the presence of a unit root indicates randomness and conformity with weak form efficiency.

 

Analysis

Descriptive statistics for both time periods studied are found in Table I. As can be seen in the table, both series are negatively skewed and leptokurtic.

Table I Descriptive Statistics of KSE-100 Daily Price Returns
  2008-2010 2019-2021
Mean -0.021 0.025
Median 0.000 0.030
Maximum 8.255 4.684
Minimum -5.135 -7.102
Standard Deviation 1.549 1.234
Skewness -0.084 -0.740
Kurtosis 5.403 7.780
Observations 743 745
Sources: Bloomberg for KSE-100 closing prices and STATA for statistical analysis.

This skewness and kurtosis are the reasons the data are not normal. P-values for all three normality tests in both time periods are 0.0000, offering evidence of the lack of normality.

The runs tests is a non-parametric test that does not assume normality. Its null hypothesis is randomness, meaning that a failure to reject the null hypothesis is consistent with weak form efficiency. Tables II-IV illustrate that returns are not random in either time period based on evidence from the standard runs test and from alternative runs tests using median and mean. Again, this indicates that the KSE-100 is not weak form efficient.

Table II Results of Runs Tests
  2008-2010 2019-2021
Runs (R) 331 347
Observations > 0 (n1) 361 382
Observations < 0 (n2) 382 363
P-value 0.00 0.05
P-value with Continuity Correction 0.00 0.06
Inference Not Random Not Random

 

 

Table III Results of Runs Tests Based on Median

  2008-2010 2019-2021
Runs (R) 331 343
Observations > median (n1) 361 373
Observations < median (n2) 382 372
P-value 0.00 0.03
P-value with Continuity Correction 0.00 0.03
Inference Not Random Not Random

 

Table IV Results of Runs Tests Based on Mean
  2008-2010 2019-2021
Runs (R) 321 341
Observations > mean (n1) 403 376
Observations < mean (n2) 340 369
P-value 0.00 0.02
P-value with Continuity Correction 0.00 0.02
Inference Not Random Not Random

 

The 2008-2010 data contain a 110-day period between August 2008 and December 2008 when the circuit breakers were implemented to limit price movements during the market uncertainties of the Great Recession. The total price return for the KSE-100 during this period was 0.46% due to negligible or zero price changes on most days. By comparison, the price return for the US market over the same time period was -31.8%. When circuit breakers were lifted in December 2008, the KSE-100 fell by 46.8% over 13 trading days, representing a particularly long run. This inability of prices to move freely clearly inhibits the efficiency of markets. Excluding the period during which circuit breakers were engaged, the longest string of runs for the early data occurred in June and July 2008 when the index fell by 19.8% over 15 trading days as is illustrated by the shaded area in in Figure I. The length alone suggests that prices may not immediately incorporate new information, although further empirical studies are needed to confirm that hypothesis.

 

Figure I Run Length versus Cumulative Returns During the Run

By contrast, the longest string of runs for the 2019-2021 data was a 13-trading day stretch when the market increased by 8.6%. While not conclusive evidence, this could suggest that a lack of randomness may not be a function that occurs only in bear markets.

The results of the ADF and PP tests using closing prices support the conclusions from the runs tests. Failing to reject the null hypothesis that prices have a unit root implies that prices lack randomness and are therefore inconsistent with weak form efficiency.

Table V P-Values for the ADF and PP Tests
2008-2010 2019-2021
ADF
 Using Closing Prices 0.6267 0.8283
 Using Price Returns 0.0000 0.0000
PP
 Using Closing Prices 0.5777 0.7534
 Using Price Returns 0.0000 0.0000

 

Finally, autoregressive models using a one-period lag of the dependent variable to explain the price return for the following period are significant. The p-value of the model is 0.0000 for the 2008-2010 data and 0.0003 for the 2019-2021 data. Again, this points to a non-random relationship between past and current values which is inconsistent with weak form efficiency.

 

Conclusions

Randomness is a feature of weak form efficiency of the Efficient Markets Hypothesis. The normative question of whether weak form efficiency is positive or negative is not debated here. Instead, the tested hypothesis, that Pakistan’s benchmark index has become weak form efficient over time and remains so during market downturns, is evaluated by examining whether prices and returns on the KSE-100 conform to the assumption of weak form efficiency by displaying a random distribution.

The relative dearth of academic studies regarding the merits of technical analysis is often mentioned as concerning in terms of the legitimacy of the field. This study sought to address that issue by offering empirical evidence that at least one emerging market, Pakistan, does not conform to the assumptions of weak form efficiency and therefore offers evidence of opportunities to generate abnormal returns using historical data such as that employed by technical analysts. Based on three versions of the runs test, the Augmented Dickey Fuller test, the Phillips Perron test, and an autoregressive model of order one, the evidence points to a lack of randomness over the two periods studied. This implies a lack of conformity with weak form efficiency and a degree of predictability in the market. However, because the results may not be generalizable to other developing markets, further research is merited.

While the findings are inconsistent with the Efficient Market Hypothesis, they conform to the predictions of the Adaptive Market Hypothesis. Numerous factors may impede market efficiency, but the EMH requirement for investors to act rationally represents a material hurdle that may not hold for myriad reasons. As this study demonstrated, investors may be slow to incorporate information in a market that is moving strongly in one direction or the other. In addition, institutional constraints may impede investors from acting rationally in the presence of circuit breakers. While not addressed in this study, factors such as fake news and behavioral biases, among other things, could also affect rational behavior. This message is encouraging for active investors and technical traders. Because prices are not random and the KSE-100 is not weak form efficient, the use of historical price information offers a way to systematically leverage profitable trades.

 

References

Antoniou, Antonios, Nuray Ergul, and Phil Holmes, 1997, Market Efficiency, Thin Trading and Non-Linear Behaviour: Evidence from an Emerging Market, European Financial Management 3, 175–190

Bachelier, L., 1900, Théorie de la Spéculation, Doctoral dissertation in mathematics, University of Paris, English translation by Cootnerr, P.H. (ed.), 1964

Bloomberg, 2022, Bloomberg L.P. Index Prices for the KSE-100 12/31/07 to 12/31/21

Chakraborty, Madhumita, 2006, Market Efficiency for the Pakistan Stock Market: Evidence from the Karachi Stock Exchange,  South Asia Economic Journal 7, 67–81

Dickey, David A., and Wayne A. Fuller, 1979, Distribution of the Estimators for Autoregressive Time Series With a Unit Root, Journal of the American Statistical Association 74, 427–31

Dickey, David A., and Wayne A. Fuller, 1981, Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root, Econometrica 49, 1057–1072

Dsouza, Janet Jyothi, and T. Mallikarjunappa, 2015, Does the Indian Stock Market Exhibit Random Walk?, Paradigm 19, 1–20

Fama, Eugene F., 1965, The Behavior of Stock-Market Prices, The Journal of Business 38, 34–105

Gibbons, Jean Dickson, and Subhabrata Chakraborti, 2011, Nonparametric Statistical Inference (Taylor & Francis, Boca Raton, FL)

Grossman, Sanford J, and Joseph E Stiglitz, 1980, On the Impossibility of Informationally Efficient Markets, The American Economic Review 70, 393–408

Han Kim, E., and Vijay Singal, 2000, Stock Market Openings: Experience of Emerging Economies, The Journal of Business 73, 25–66

Haque, Abdul, and Hung-Chun Liu, 2011, Testing the Weak Form Efficiency of Pakistani Stock Market (2000–2010), International Journal of Economics and Financial Issues 1, 153–62

Hill, R. Carter, William E. Griffiths, and G. C. Lim, 2017, Principles of Econometrics (Wiley, Hoboken)

Hussain, Fazal, and Muhammad Ali Qasim, 1997, The Pakistani Equity Market in 50 Years: A Review, The Pakistan Development Review 36, 863–872

Irfan, Muhammad, Muhammad Saleem, and Maria Irfan, 2011, Weak Form Efficiency of Pakistan Stock Market Using Non-Parametric Approaches, Journal of Social and Development Sciences 2, 249–257

Jain, P. K., 2005, Financial Market Design and the Equity Premium: Electronic versus Floor Trading, Journal of Finance 60, 2955–2985

Khan, Naimat U., and Sajjad Khan, 2016, Weak Form of Efficient Market Hypothesis – Evidence from Pakistan, Business & Economic Review 8, 1–18

Kolmogorov, A., 1933, Sulla Determinazione Empirica Di Una Legge Di Distribuzione, Inst. Ital. Attuari, Giorn. 4, 83–91

Lilliefors, Hubert W., 1967, On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown, Journal of the American Statistical Association 62, 399–402

Lo, Andrew, 2004, The Adaptive Market Hypothesis: Market Efficiency From an Evolutionary Perspective, Journal of Portfolio Management 30, 15–29

Mudassar, Muhammad, Arshad Ali, Maryam Nawaz, and Syed Muhammad Amir Shah, 2013, Test of Random Walk Behavior in Karachi Stock Exchange, Pakistan Journal of Commerce and Social Science 7, 70–79

Mustafa, Khalid, and Mohammed Nishat, 2007, Testing for Market Efficiency in Emerging Markets: A Case Study of the Karachi Stock Market, The Lahore Journal of Economics 12, 119–40

Naghshpour, Shahdad, 2016, A Primer on Nonparametric Analysis Volume I (Business Expert Press, New York, NY)

Naidu, G. N., and Michael S. Rozeff, 1994, Volume, Volatility, Liquidity and Efficiency of the Singapore Stock Exchange Before and After Automation, Pacific-Basin Finance Journal 2, 23–42

Phillips, Peter C B, and Pierre Perron, 1988, Testing for a Unit Root in Time Series Regression, Biometrika 75, 335–46

Riaz, Tabassum, Arshad Hassan, and Muhammad Nadim, 2012, Market Efficiency in Its Weak-Form; Evidence from Karachi Stock Exchange of Pakistan, The Journal of Commerce 4, 9–18

Rizwan Qamar, Muhammad, and Ali Nawaz Sheikh, 2014, Random Walk Behavior of Emerging Stocks Markets: Evidence from Karachi Stock Exchange, Studies in Business and Economics 9, 97–106

Samuelson, Paul A., 1965, Proof That Properly Anticipated Prices Fluctuate Randomly, Industrial Management Review 6, 41–50

Shapiro, S. S., and R. S. Francia, 1972, An Analysis of Variance Test for Normality, Journal of the American Statistical Association 67, 215–25

Shapiro, S. S., and M. B. Wilk, 1965, An Analysis of Variance Test for Normality (Complete Samples), Biometrika 53, 591–611

Smirnov, Nickolay, 1948, Table for Estimating the Goodness of Fit of Empirical Distributions, Annals of Mathematical Statistics 19, 279–81

Wald, A., and J. Wolfowitz, 1940, On a Test Whether Two Samples Are from the Same Population, The Annals of Mathematical Statistics 11, 147–62

What Is Semi-Strong Form Efficiency? n.d., myccountingcourse.com, Accessed June 16, 2022, https://www.myaccountingcourse.com/?s=semi-strong+efficiency.

Wooldridge, Jeffrey M, 2020, Introductory Econometrics: A Modern Approach, Seventh edition (Cengage Learning, Boston, MA)

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Are The Streets Still Smart? Evaluating Swing Trading Strategies in Modern Markets

by Davide Pandini, PhD, CMT, MFTA, CSTA

About the Author | Davide Pandini, PhD, CMT, MFTA, CSTA

Davide Pandini holds a PhD in Electrical and Computer Engineering from Carnegie Mellon University, Pittsburgh, USA.

He was a research intern at Philips Research Labs. in Eindhoven, the Netherlands, and at Digital Equipment Corp., Western Research Labs. in Palo Alto, CA. He joined STMicroelectronics in Agrate Brianza, Italy, in 1995, where he is a Technical Director and a Fellow of ST Technical Staff.

Dr. Pandini has authored and coauthored more than fifty papers in international journals and conference proceedings and served on the program committee of several premiere international conferences. He received the STMicroelectronics Corporate STAR Gold Award in 2008 and 2020, and the Corporate STRIVE Gold Award in 2022, for R&D excellence.

Since June 2015, Dr. Pandini is the Chairman of the ST Italy Technical Staff Steering Committee.

In the field of Technical Analysis, Dr. Pandini holds the Chartered Market Technician (CMT) designation from the CMT Association, is a MFTA (Master of Financial Technical Analysis) holder of IFTA (International Federation of Technical Analysts), and he is a Professional Member of SIAT (Societa’ Italiana Analisi Tecnica). In 2021 Dr. Pandini was the recipient of the prestigious XII SIAT Technical Analyst Award in the Open category. He was a speaker at SIAT Trading Campus in May 2022, and at the Investing and Trading Forum in June 2022.

Dr. Pandini served as Volunteer at the Universal Exhibition Expo2015 – Feeding the Planet, Energy for Life – in Milano, Italy.

Abstract

In 1995 Larry Connors and Linda Bradford Raschke published a book titled: “Street Smarts: High Probability Short-Term Trading Strategies” that soon became a reference milestone for many generations of traders. The book presented multiple strategies inherently discretionary and mostly focused on equities and futures. The strategies were based on three simple swing trading concepts: retracements, pattern breakouts, and climax reversals, which are among the fundamental pillars of Technical Analysis, and by which support and resistance levels are formed. Although several traders have used these strategies for many years, following some structural changes in the markets, and an increasingly adoption of mechanical trading systems, the strategies of Street Smarts lately ended up on a sidetrack, and were no longer considered as mainstream by an increasing number of technical analysts and systematic traders.

In this work, some of the most popular strategies described in Street Smarts are reviewed. Moreover, an exhaustive backtesting on historical data across a significant time period, from the year 2005 till September 2021, is presented. This time period includes the most important events in the markets, from the global financial crisis (2007-2008), till the more recent COVID-19 sell-off. The backtesting covered the principal stock indexes, the S&P 500 sectors, real estate, bonds, commodities, but also the most important FOREX currency pairs, which were not considered in the original book. Furthermore, a rigorous statistical hypothesis testing was performed on the Street Smarts strategies by means of inferential statistics multiple hypothesis testing and time series bootstrap. Such a comprehensive analysis of the Street Smarts strategies allows to assess their effectiveness on different asset classes and markets. Moreover, this thorough study also provides a deeper insight on swing trading techniques in changing market scenarios.

Keywords: technical analysis; swing trading; Donchian channels, breakout, volatility compression; volatility explosion; ADX, momentum, stochastic, equity indexes, S&P 500 sectors, FOREX, inferential statistics, hypothesis testing, confidence intervals, probability value, bootstrap.

 

Introduction

In the Cambridge English Dictionary, “street smarts” means the ability to manage or succeed in difficult or dangerous situations, especially in big towns or cities. Street smarts is having the experience and knowledge necessary to deal with the potential difficulties or dangers of life in an urban environment. Being street smarts requires practical intelligence, i.e., the ability to deal with daily tasks in the real world and shows how well a person relates to the external environment. When you are street smarts, you know your way around, you know how to handle yourself in tough situations, and you are able to “read” people.

Published in 1995 by Larry Connors (LC) and Linda Bradford Raschke (LBR) [3], Street Smarts is considered by many to be one of the best books on trading equities, commodities, and futures. The backbone of this book’s success is swing trading and the techniques which apply these methodologies. Moreover, strategies based on pattern recognition and volatility explosion are also presented, along with the use of popular technical indicators such as the ADX [13] and the stochastic oscillator [12]. Although most of the strategies described by LC and LBR were initially aimed at short-term swing trading, nevertheless they can also be used by longer-term swing traders, who could hold a position for days, weeks, and sometimes even months. The swing traders referred to in this book are those traders who ride a prolonged move within their trading timeframe. Hence, it is a book suitable for both day traders and longer-term traders.

In this work, we will review the most popular strategies presented in Street Smarts by performing a thorough backtesting over several different asset classes and across an exhaustive time window, covering more than sixteen years of historical data. The purpose of this comprehensive study is to assess the validity and robustness of these strategies, after more than 25 years since they were first published. Since then, most of the equities, commodities, futures, and FOREX markets have changed their structural behavior, and unfortunately, most methods do not always work in all market conditions, and market conditions never persist forever. Therefore, we believe that this work will provide a new and more in-depth insight on the effectiveness of the Street Smarts techniques. Moreover, a rigorous statistical hypothesis testing was performed on the Street Smarts strategies by means of inferential statistics multiple hypothesis testing and time series bootstrap. Even the most powerful strategies, or Technical Analysis rules, may deliver a highly variable performance depending on the time series of historical data tested. Statistical analysis is the only practical approach to distinguish strategies that have a predictive power from those that do not have an intrinsic merit.

The paper is organized as follows: the fundamental principles of swing trading and pattern breakout are reviewed in Section 2. Section 3 illustrates the historical period for backtesting the Street Smarts strategies and the asset classes considered for this analysis, while Section 4 describes the performance metrics used to assess the strategies. The Streets Smarts strategies considered in this work and the backtesting results are presented in Section 5. The statistical hypothesis testing procedures are thoroughly discussed in Section 6 and Section 7, while Section 8 summarizes some conclusive remarks.

 

Swing Trading

In order to better understand the strategies presented in Street Smarts, it is important to review the basic concepts of swing trading. This method of trading was first introduced by Charles Dow in 1908[1], to perform many trades in active markets and relying on stop-losses for protection. In swing trading, opportunities appear both on the long and short side, regardless of the underlying long-term trend. Swing trading attempts to anticipate the market’s next most probable outcome: when a market breaks a support level and has a sharp move down, then the strongest trade would be to sell (or short) the first pullback. In this case, the most likely event for the market would be at least to make a retest of the new low before it could be expected to reverse direction again. Swing trading effectiveness depends on retaining profits already gained. Trades should be exited either in the direction of the price movement or as the price reverses. Trailing stops will lock in profits already won.

The strongest pattern in swing trading is trading on tests of previous highs or lows. These tests would offer a good trade entry signal with a controlled risk of loss. The second type of trade enters on a reaction or retracement. A trend rarely follows a straight trendline, and usually includes a number of smaller countertrends, which are called retracements. Hence, retracements are always corrections to the principal trend. As an example, the prices rise in a strong uptrend is periodically interrupted by downward corrections. Thus, a retracement is a smaller trend itself that runs against the principal trend. From a more formal standpoint, it is worth pointing out that variations of retracements occurring after a breakout, usually from horizontal support or resistance zone, but sometimes also from a trendline, are called pullbacks or throwbacks, depending on whether the breakout is downward or upward. When the price retraces back to the breakout zone from an upward breakout it is called a throwback. In contrast, a retracement from a downward breakout is called a pullback, according to the definition proposed by Edwards and Magee [21]. This is “buying a higher low” in a sequence of higher lows and higher highs (or selling a lower high in a series of lower lows and lower highs). The third type of trade is a climax or exhaustion pattern. The most successful climax trades will occur in a high-volatility environment, and after the market has already reversed.

A price swing is a sustained price movement of a predetermined size. An upwards swing ends with a swing high, or peak, and a downward swing ends with a swing low, or valley. The distance from a peak to a valley is the swing. A swing can be small or large, depending on the sensitivity of the swing criterion. The only requirement is that each swing should be greater than a threshold value, which can be expressed as a percentage of the current price. This minimum value, called the swing filter, determines the frequency of the swings and therefore the sensitivity of the chart. A method to build a swing chart from a price time series was presented in [6]. The parameter that controls the height of the swing is the swing filter, where a new swing is recorded only if the distance from the previous swing exceeds a user-defined threshold (as a percent of the current swing). In this work, we use a similar approach to define the swing height. The basic rules for creating a swing chart can be summarized as follows:

When prices are in an upswing and the high of the new bar is higher than the current swing high, extend the swing higher to the point of the new high. Because prices are in an upswing, the lows are ignored;

Prices are in an upswing and the high of the current bar is not higher than the current swing high. If the current swing high minus the current bar low is less than the swing filter, then this new price data is ignored. If the current swing high minus the current bar low is equal to or greater than the swing filter, then reverse the current swing direction and update the swing level;

When prices are in a downswing and the low of the new bar is lower than the current swing low, extend the swing lower to the point of the new low. Because prices are in a downswing, the highs are ignored;

Prices are in a downswing, and the low of the current bar is not lower than the current swing low. If the current bar high minus the current swing low is less than the swing filter, then this new price data is ignored. If the current bar high minus the current swing low is equal to or greater than the swing filter, then reverse the current swing direction and update the swing level.

An advantage of swing trading is that no trade occurs when prices move sideways. In contrast, in a trend-following approach prices must continue to advance in the same direction if the trend is to remain intact. In a swing trading philosophy, prices can move sideways or stand still within a trend. Prices can move up and down in any pattern if they do not violate the previous swing highs (if in a downtrend) or swing lows (if in an uptrend). Risk will be measured as the difference between the entry point of a trade (the price at which the old swing high or low was penetrated) and the price at which a reverse trade would be entered. This risk can be as small as a swing reversal or much larger if prices move quickly without any intermediate reversals. If prices move out of their current trading levels to new highs or new lows, the swing method will trigger a new trade. This immediate response can be quite different from trend systems that use lagging indicators like moving average or other time series calculations. There are two sets of rules commonly used in swing trading to enter positions in the trend directions:

Buy when the high of the current upswing exceeds the high of the previous upswing. Sell when the low of the current downswing falls below the low of the previous downswing;

Buy as soon as a new upswing is recognized. Sell when a new downswing is recognized.

Both conditions occur when there is a reversal greater than the swing filter.

The strategies and methods described in Street Smarts can be framed within the concepts and rules of swing trading. One of the most important of these rules states that profits should be secured when they are gained. Therefore, it is required to have a reliable approach for a trailing stop-loss.

 

Backtesting: Historical Period and Asset Classes

 

Look-back Period

The choice of the time window for backtesting has always been of interest and concern to the technical analysts to assess the robustness and performance of a strategy, since different periods and sizes of the window can lead to different experimental results and conclusions. The study presented in [4] assessed the robustness of the performance of a strategy given the window size of the backtesting period. This study shows the impact that the chosen window can have on the results and as such, the authors argue that the window should not be arbitrarily selected. In [5] it was demonstrated that an active market timing strategy outperforms the passive buy-and-hold strategy during bear markets and vice versa during bull markets. To account for these results, the study in [5] concluded that the look-back period should include bear and bull markets to observe both these market conditions.

Therefore, the strategies of Street Smarts were tested across an historical data length covering the past sixteen years (from September 2005 to September 2021), because it includes multiple bull and bear markets, some of which were quite significant, like the global financial crisis (2007-2008) and the recent COVID-19 sell-off (March 2020), and the last bull market lasting over a decade.

 

Asset Classes

Usually, Technical Analysis strategies are not distributed and tested equally across all asset classes. It is frequent practice to find strategies that have been assessed only on some specific assets like the major stock market indexes, commodities, bonds, or currency pairs. It is well-known that the performance of a given strategy can vary significantly depending on the tested asset class. Therefore, for a thorough and comprehensive assessment, the Street Smarts strategies were evaluated on all the above-mentioned asset classes. The following ETFs were considered (Figure 1): the most important U.S. stock market indexes (SPY, QQQ, DIA), the S&P 500 sectors (XLP, XLY, XLE, XLV, XLF, XLI, XLK, XLB, XLU, IYZ), real estate (IYR), gold (GLD), 7–10 year Treasury bonds (IEF), and 20+ year Treasury bonds (TLT). Furthermore, to complete the assessment of the Street Smarts strategies, the major FOREX currency crosses were evaluated as well. All the ETFs historical data were downloaded from Yahoo! Finance [15] and the FOREX crosses from the site Investing.com [16]. The strategies analyzed in this work were implemented and tested with MS Excel, and all the historical data used were on a daily timeframe.

 

 

Figure 1. Asset classes and FOREX currency pairs

 

Performance Metrics

There are diverse ways to measure a portfolio performance [18], where the simplest and most common is the excess return. It measures the total return less the risk-free rate of return. However, it is not the best performance measure because it does not consider risk.

A risk-adjusted measure is more appropriate because investors and traders require compensation for risk. Among the popular methods that are commonly utilized and include the risk factor, there is the Sharpe Ratio [19], which is the ratio of return, adjusted for the risk-free return of T-bills, to the annualized standard deviation of returns, which is considered as a proxy for risk:

Although the disadvantages of the Sharpe ratio are known and have been discussed in the literature [7], in this study we used it because of its overwhelming popularity. Additionally, practitioners commonly use drawdown to assess the riskiness of any given strategy. The most common performance measure after the Sharpe ratio is the maximum drawdown, which in this work is measured as a percentage from a highest NAV (net asset value) to the subsequent lowest NAV. The maximum drawdown is important because, in a long performance record, a single and large drawdown can be lost in the standard deviation when there is an overwhelming number of “normal” drawdowns. A statistician might be satisfied saying that there is a small chance of that large drawdown occurring again, but an investor or trader might want to know that it did happen and understand why it happened and the extreme losses he/she should be able to digest to stay invested in the corresponding strategy. One measure that accounts for the maximum drawdown is the Calmar ratio [20]:

Therefore, both the Sharpe and Calmar ratios are used in this study, along with other popular metrics such as the total returns, the annualized volatility, and the CAGR (compound annual growth rate).

 

Street Smarts Strategies

The strategies of Streets Smarts were originally developed and evaluated mostly on U.S. equities and futures, and they were used for many years in those markets. However, a comprehensive and thorough backtesting, also encompassing the FOREX market and along a statistically significant look-back period, has never been published. Hence, given the structural differences between the FOREX and the equities markets, in this work a detailed analysis of some of the most popular Street Smarts strategies applied to equities, commodities, bonds, and the most important currency pairs listed in Figure 1 is presented. The purpose of this analysis is to evaluate the performance of Street Smarts strategies across structurally different markets and asset classes.

All the Street Smarts strategies discussed in this work were implemented considering both long and short trades, reversing the trade direction after closing the open trade when an opposite entry signal was triggered, and rolling over an open position when a new signal in the same direction of the current trade was generated. The strategies were backtested on all the ETFs and FOREX crosses listed in Figure 1, from September 2005 to September 2021 (sixteen years of historical data). The backtesting is based on daily candlesticks, where by definition only the OHLC (open, high, low, close) data are available. OHLC values are discrete data meaning that price is not represented in a continuous way, and we only have access to few specific values during the time period. Therefore, ideally both stop loss (SL) and take profit (TP) can be triggered during the same candlestick, which can show a low under the SL level and a high above the TP level. The fundamental question is: which one is hit first? There is no way to answer to this question. Although this case seldom happens, nevertheless it cannot be ruled out, and in general it can occur when the volatility is high[2]. Many traders would spontaneously assume that the TP is reached before the SL, thus only considering the most favorable outcome that would confirm the effectiveness of their strategy (i.e., confirmation bias). If the SL is tight, this phenomenon can occur more frequently, thus shifting the strategy’s performance towards a more favorable outcome. However, in this work the strategies were normally assessed with a risk-reward ratio of 1:2 or larger, thus significantly reducing the probability of the occurrence of such scenario. Moreover, to avoid the impact of the confirmation bias, a more conservative policy was implemented, and in case both the SL and the TP were triggered by the same candlestick (i.e., during the same time period) the SL was chosen. By being more conservative, we believe that this policy contributes to reduce the impact of type I errors discussed in Section 6.2.

 

Turtle

The Turtle Soup strategy proposed in [3] is based on the concepts of swing trading outlined in Section 2. However, before looking into the rules of the Turtle Soup, we first review its background. The Turtle Soup sets its roots into the famous strategy called Turtle [8], which was introduced by Richard Dennis [9] and William Eckhardt [10] in the 1980s to a group of novice traders called the Turtles. The Turtle is a trend-following strategy based on a 20-day breakout of prices. Richard Donchian earlier introduced a 4-week price breakout system [11]: cover short positions and buy long whenever the price exceeds the preceding full calendar 4-week highs; liquidate long positions and sell short whenever the price falls the preceding full calendar 4-week lows. Trend-following strategies typically have lower percentage of winning trades, but the profits gained by the winners should be sufficient to compensate for the losing trades. Like other trend-following techniques, even the Turtle strategy suffers from false breakouts. Instead of sustaining strong directional moves in the direction of the breakout, prices can trace back within the Donchian channel, originating whipsaws that result in losing trades. The backtesting of this strategy has demonstrated that to make it profitable, it is mandatory to implement a careful management of the stop-loss. Various stop-loss approaches were tested: a static trailing stop-loss and a dynamic trailing stop-loss. The methods considered were:

Trailing stop-loss with fixed amplitude (e.g., 1% and 2%);

Trailing stop-loss with variable amplitude at 2xATR[3] (other ATR multipliers were evaluated but generated inferior results with respect to the 2x multiplier);

Trailing stop-loss corresponding to the opposite limit of the Donchian channel with respect to the breakout (lower limit for a long breakup, and upper limit for a short breakdown).

The best performances were obtained with approach c) i.e., a trailing stop-loss tracking the opposite limit of the Donchian channel; hence, this was the method used to backtest the Turtle strategy.

Different take-profit targets were evaluated with respect to the maximum allowed loss. Furthermore, it was also assessed the typical approach of trend-following strategies, to let the profits run and use the trailing stop-loss as a dynamic take-profit level (i.e., to exit the trade when the trailing stop-loss is hit). The trailing-stop loss allowed to secure most of the gained profits, and for this trend-following strategy the backtesting evinced to be the best exit approach.

The monthly NAV (net asset value) for the indexes, equities, commodities, real estate, and bonds over the backtesting time window is reported in Figure 2, while Figure 3 shows the monthly drawdowns. The worst result was obtained for the 7‒10 years bonds (IEF), with a maximum drawdown of about 17%. In contrast, the best performances were achieved on QQQ (Nasdaq 100), XLK (technology), XLY (consumer discretionary), XLE (energy), and GLD (gold), with maximum drawdowns that did not exceed 10%. It is worth noting that XLK and QQQ, which are highly correlated with a correlation coefficient of 0.9598, consistently showed the best performances over the look-back period. The performances and the trade statistics of the Turtle strategy are reported in Table 1 and Table 2 respectively.

 

Figure 2 Turtle strategy asset classes monthly NAV

 

Figure 3 Turtle strategy asset classes monthly drawdown

 

Table 1 Turtle strategy asset classes trade results

 

Table 2 Turtle strategy asset classes trade statistics

The Turtle turned out to be less performing in the FOREX market. All the main crosses were considered, and the NAV results shown in Figure 4 did not reach the same values reported for the equity indexes and sectors in Figure 2. However, the drawdowns on the FOREX shown in Figure 5 were smaller than the drawdowns of the other asset classes (with the only exception of AUDUSD having a maximum drawdown of about 16%). The currency pair where the Turtle strategy’s overall performance was better than the other currency crosses was USDTRY, which should be considered more as an outlier, since the behavior of this currency pair over the backtesting period is significantly different from the typical behavior of the other currency pairs, as illustrated in Figure 6. In contrast, the worst performance was achieved on AUDNZD with CAGR of 0%.

Given the typical mean-reverting structure of the FOREX, the best approach to protect the gained profits was to close the trade after three trading days if the profit target had not been reached within this time window.

 

Figure 4 Turtle strategy FOREX monthly NAV

 

Figure 5 Turtle strategy FOREX monthly drawdown

 

Figure 6 AUDUSD and USDNZD vs USDTRY

The overall performances and the trade statistics in the FOREX market are reported in Table 3 and Table 4 respectively.

 

Table 3 Turtle strategy FOREX trade results

 

Table 4 Turtle strategy FOREX trade statistics

In summary, the Turtle strategy can deliver good performances on some S&P 500 sectors and equity indexes, with a particular focus on the technology stocks, if used with a trailing stop-loss set on the Donchian channel. In contrast, its performance was less effective in the FOREX market. This outcome is consistent with the strategy’s trend-following behavior and the structure of the FOREX, which essentially is mean reverting. A lower performance of a trend-following strategy in a typical mean-reverting market can be expected.

 

Turtle Soup

The Turtle Soup strategy attempts to identify a false breakout and to enter the trade trying to capture its reversal, since quite often when the market is in a strong trend, false breakouts may have a short duration. Over the years, the markets have changed their behavior and inherent structure, and the breaks instead of producing a strong movement in the direction of the breakout, sometimes generate rapid and sudden reversals. To take advantage of these changes of direction, LC and LBR proposed the Turtle Soup. The set-up for a long entry can be summarized as follows[4]:

Prices must have fallen to the lows of the last 20 days;

The previous 20-day low must have occurred at least 4 days before;

After the price has fallen below the previous low, an entry buy-stop is placed 5‒10 ticks above the level of the previous 20-day low;

When the order is filled, a stop-loss is placed one tick below the day’s low;

If the position becomes profitable, a trailing stop is used to protect the profits already gained.

The Turtle Soup was backtested on the same assets and FOREX crosses as the Turtle strategy. The same stop-loss techniques used for the Turtle were evaluated, and a trailing stop-loss on the Donchian channel limit where the false breakout occurred was set as soon as the position became profitable. Figure 7 and Figure 8 show the monthly NAV and the monthly drawdown of the Turtle Soup. The performance metrics numerical results and trade statistics are summarized in Table 5 and Table 6.

 

Figure 7 Turtle Soup strategy asset classes monthly NAV

 

Figure 8 Turtle Soup strategy asset classes monthly drawdown

 

Table 5 Turtle Soup strategy asset classes trade results

 

Table 6 Turtle Soup strategy asset classes trade statistics

Similar to the Turtle, even the Turtle Soup generated worse results on the FOREX, as illustrated in Figure 9, but with significantly less drawdowns, not exceeding 3%, as reported in Figure 10. It is worth remarking that in the FOREX market the overall performance of the Turtle Soup was comparable with the Turtle’s performance (with the exception of USDTRY). Since the Turtle Soup attempts to capture a reversal after a false breakout, this outcome confirms that a trend-following strategy like the Turtle does not outperform a reversal strategy such as the Turtle Soup in a mean-reverting market such as the FOREX.

 

Figure 9 Turtle Soup strategy FOREX monthly NAV

 

Figure 10 Turtle Soup strategy FOREX monthly drawdown

The performance metrics and the trade statistics for the Turtle Soup backtested on the currency crosses are reported in Table 7 and Table 8 respectively. Even the Turtle Soup is more effective in the FOREX market when the trades are closed after three days if the profit target has not been reached yet.

 

Table 7 Turtle Soup strategy FOREX trade results

 

Table 8 Turtle Soup strategy FOREX trade statistics

The Turtle and Turtle Soup are two strategies having an opposite behavior, and this is confirmed by the correlation analyses on all the asset classes and currency pairs, which are summarized in Table 9. Each table entry represents the correlation between the daily returns generated by the Turtle and Turtle Soup on a given asset. The correlation values are close to zero, which means that the two strategies are basically uncorrelated. The negative values of the correlations show a small intrinsic tendency (although not significant) of the strategies to be negatively correlated. The complete results of the correlations between the Turtle and the Turtle Soup among all asset classes are reported in Appendix 3, confirming that the two strategies are uncorrelated and can be used concurrently.

 

Table 9 Turtle vs. Turtle Soup correlations

 

 

Anti

The Anti strategy is an example of retracement pattern. It enters in the direction of the long-term trend after a retracement (either a throwback or pullback depending on whether the long-term trend is bullish or bearish) of the short-term trend towards the long-term trend. The basic principle of this strategy is that often a short-term trend tends to resolve in the direction of the long-term trend.

The oscillator used in Anti is the stochastic [12], which is set up with the same settings used in Street Smarts: 4-period %K-slow that smooths the 7-period %K line (stochastic “fast” line) and 10-period %D line (stochastic “slow” line). These settings are different from the default values normally defined for the stochastic oscillator (3-period %K-slow, 14-period %K, 3-period %D) in most trading platforms. The backtesting confirmed that the stochastic settings for the Anti recommended in Street Smarts give better results than other settings, thus in this work we kept the same stochastic values as in [3]. In Anti, the %D line is used as a momentum indicator to determine the direction of the trend (it makes sense to use a number of periods equal to or greater than 10). The %K-slow line (the original %K line calculated over seven periods and then smoothed by a 4-period moving average) moves in the opposite direction with respect to the trend and then “hooks” it by turning in the same direction of the trend (represented by the %D line). Anti tries to enter immediately after a trend reversal has failed, i.e., by (re-)entering in the direction of the main trend after a retracement, and then follows the direction of the primary trend. For a long entry, the buy-stop is placed one tick above the high of the candle that gave “the hook” in the direction of the main trend, and the initial stop-loss is placed one tick below the minimum of the set-up candle (for a short entry both the trend direction and set-up are reversed). The exit is determined either by a trailing stop-loss that follows the trend, or the trade is closed after a number of periods (in this work three days because Street Smarts recommends using the Anti strategy on a daily timeframe).

Anti worked better on the sectors XLF, XLE, XLB, and XLY, which outperformed the technology stocks (QQQ and XLK) and the other assets. The worst performances were obtained on IEF and XLU, as shown in Figure 11 and Figure 12. The drawdowns were less than 7% across the look-back period.

 

Figure 11 Anti strategy asset classes monthly NAV

Figure 12 Anti strategy asset classes monthly drawdown

The numerical results and the trade statistics for the Anti are reported in Table 10 and Table 11 respectively.

 

Table 10 Anti strategy asset classes trade results

 

Table 11 Anti strategy asset classes trade statistics

The same Anti set-up was used for the FOREX market. The monthly NAV and drawdown are illustrated in Figure 13 and Figure 14.

 

Figure 13 Anti strategy FOREX monthly NAV

 

Figure 14 Anti strategy FOREX monthly drawdown

The numerical results and the trade statistics are summarized in Table 12 and Table 13, with the worst drawdowns around 4%.

 

Table 12 Anti strategy FOREX trade results

 

Table 13 Anti strategy FOREX trade results

Even the overall performance of the Anti was better on the stock indexes and S&P 500 sectors than on the FOREX crosses, thus showing a consistent behavior with the other Street Smarts strategies. In particular, the performance of the Anti was comparable with the Turtle, even though on different asset classes.

 

ID-NR4

Swing trading can be profitable when there are price oscillations and a good amount of volatility. The ID-NR4 strategy attempts to identify a pattern where a period of volatility expansion follows a period of volatility contraction. When the volatility is cyclical, then the market can experience sequences of range contractions followed by range expansions, and usually after the market has been inactive (or in a period of range contraction), a trend period often follows [14]. Moving from a “swing trading” style looking for reactions, to a “breakout mode”, is not straightforward. The first step is to identify beforehand the conditions leading to a trend day. In a trend day, the market opens at one extreme of its range and then closes at the opposite extreme, covering a long distance. These days can be traded for volatility expansion.

Narrow-range bars indicate low volatility. Determining narrow-range bars is useful because the low volatility will eventually lead to high volatility, i.e., trend days. Toby Crabel [14] proposed one method to define and exploit narrow-range days. In his method, he determines whether the current day has a narrower range than a given number of past days. For example, if the current day has a narrower range than the past three days, it is an NR4 day (including the current day and the past three days); in other words, the current day represents the narrowest trading range of the four days. The entry signal is a breakout from the most recent narrow-range day. Thus, if today is an NR4 day, we place a buy and sell entry stop one tick above the high and one tick below the minimum of the NR4 bar. An inside day (ID) has a higher low than the previous day’s low and a lower high than the previous day’s high. An inside bar with the smallest range out of the last four bars is an ID-NR4 pattern. LBR was one of the leading proponents of using narrow-range days to determine low-volatility patterns. The buy and sell entry stops are placed at the high and low of the ID-NR4 bar. If the entry stop is executed, an additional exit stop is placed where the opposite entry stop was previously set. In the breakout mode, we cannot predict the direction in which the trade is going to enter. However, we can expect that there might be an expansion in volatility, after a phase of volatility compression. Therefore, we place both a buy-stop and a sell-stop at the same time and it will be the actual price movement entering the trade that will determine the direction of the trend. The rules for the ID-NR4 strategy are summarized as follows:

Identify an ID-NR4 bar;

Place a buy-stop one tick above and a sell-stop one tick below the ID-NR4 bar;

On entry day only, if we are filled on the buy side, enter an additional sell-stop one tick below the ID-NR4 bar. This means that if the trade is a loser, not only will be stopped out with a small loss, but it will reverse and go short (the set-up is reversed if initially filled on the short side).

Insert a trailing stop-loss to lock-in the accrued profits;

If the position is not profitable within few days and have not been stopped out, exit the trade.

The ID-NR4 strategy was backtested closing an open position after three days. The experimental results are shown in Figure 15 and Figure 16. GLD delivered the best performance along the backtesting period.

 

Figure 15 ID-NR4 strategy asset classes monthly NAV

 

Figure 16 ID-NR4 strategy asset classes monthly drawdown

The numerical results and the trade statistics are summarized in Table 14 and Table 15 respectively.

 

Table 14 ID-NR4 strategy asset classes trade results

 

Table 15 ID-NR4 strategy asset classes trade statistics

It is quite important to assess the effectiveness of stopping and reversing in a whipsaw (or trading range). This means that if the trade is a loser, not only it will be stopped out with a small loss, but it will reverse direction. The Stop & Reverse technique was part of the ID-NR4 set-up, and it was backtested with the strategy. The overall performance with respect to the implementation without Stop & Reverse has only slightly improved, as shown in Figure 17 and Figure 18. After a Stop & Reverse pattern, it is more likely to enter a trading range than a true trend reversal. The numerical results summarizing the performance and trade statistics of the Stop & Reverse technique are shown in Table 16 and Table 17.

 

Figure 17 ID-NR4 strategy asset classes monthly NAV with Stop & Reverse

 

Figure 18 ID-NR4 strategy asset classes monthly drawdown with Stop & Reverse

 

Table 16 ID-NR4 strategy asset classes trade results with Stop & Reverse

 

Table 17 ID-NR4 strategy asset classes trade statistics with Stop & Reverse

The ID-NR4 strategy was also tested on the FOREX currency pairs. The monthly NAV and drawdown are reported in Figure 19 and Figure 20. In the FOREX market, large volatility movements after a period of volatility compression are not likely to happen very often. Therefore, a better performance was obtained locking in the accrued profits by closing the positions after three days, instead of relying on a trailing stop-loss to exit the trade. The numerical results are outlined in Table 18 and Table 19, and they confirm that ID-NR4 is not suited for the FOREX.

 

Figure 19 ID-NR4 strategy FOREX monthly NAV

 

Figure 20 ID-NR4 strategy FOREX monthly drawdown

 

Table 18 ID-NR4 strategy FOREX trade results

 

Table 19 ID-NR4 strategy FOREX trade statistics

 

Holy Grail

This pattern is based on Welles Wilder’s ADX (Average Directional Index) [13] and is supposed to work in any market and in any time frame. The ADX measures the strength of a trend over a period: the stronger the trend in either direction, the higher the ADX value. More details about the construction and interpretation of the ADX can be found in [17]. When prices make new highs (lows) in a strong trend, we should buy (sell) the first throwback (pullback). The Holy Grail is a strategy that enters a position after a retracement. Once we are in the trade, we look for a continuation of the previous trend. For long entries, the Holy Grail can be summarized as follows (for short entries the set-up is reversed):

A 14-period ADX must initially be greater than 30 and rising. This will identify a strong trending market;

Look for a price retracement to the 20-period exponential moving average. Usually, the price retracement will happen along with a downturn in the ADX;

When the price hits the 20-period exponential moving average, set a buy-stop above the high of the previous bar;

After entering the trade, set a stop-loss at the newly formed swing low. A trailing stop-loss should be used to lock in the profits, and exit at the most recent swing high;

In case the market continues its move, close part of the position at the most recent swing high and tighten the stop;

After a successful trade, the ADX must once again turn up above 30 before another retracement to the exponential moving average can be traded.

In the Holy Grail, when prices retrace after a strong move, the 20-period exponential moving average acts as support/resistance for these retracements. By waiting for the market to move above the previous day’s high, there is a confirmation to resume the longer-term trend. The original strategy recommends that not only the ADX must be greater than 30, but it should also be rising. Our trials demonstrated that this second condition considerably reduces the number of entry signals. Hence, to have a significant backtesting, only the first condition (i.e., ADX greater than 30) was considered. The monthly NAV and drawdown are reported in Figure 21 and Figure 22. The numerical results of the Holy Grail for the equity indexes and sectors are summarized in Table 20 and Table 21. A trailing stop-loss with a fixed amplitude of 1% was used, and positions were closed after three days if the profit target had not been reached.

 

Figure 21 Holy Grail strategy asset classes monthly NAV

 

Figure 22 Holy Grail strategy asset classes monthly drawdown

 

Table 20 Holy Grail strategy asset classes trade results

 

Table 21 Holy Grail strategy asset classes trade statistics

Even on the FOREX crosses the performance of the Holy Grail was worse than on the other asset classes, as confirmed by the results shown below.

 

Figure 23 Holy Grail strategy FOREX monthly NAV

 

Figure 24 Holy Grail strategy FOREX monthly drawdown

 

Table 22 Holy Grail strategy FOREX trade results

 

Table 23 Holy Grail strategy FOREX trade statistics

 

Statistical Hypothesis Testing

“… There are three types of lies: lies, damn lies and statistics …”

Benjamin Disraeli (1804-1881), Prime Minster of Great Britain from 1874 to 1880.

 

The strategies of Street Smarts were backtested on several times series of historical data, and we used inferential statistics to have a better insight whether they can generate excess returns different than and above zero. The hypothesis testing is a rigorous inference procedure to decide whether a trading rule or a strategy has some intrinsic value, i.e., it can generate positive excessive returns, and so can help us to decide if it can be used for trading in the future. Statistical inference can apply different procedures for hypothesis testing and parameter estimation, like multiple hypothesis testing adjustments, time series bootstrap, Monte Carlo simulations, and walk-forward analysis. In this work, we considered multiple hypothesis testing adjustments and time series bootstrap. All the results presented in Appendix 1 and Appendix 2 were obtained with the statistical software R [30].

 

Multiple Hypothesis Testing

Multiple hypothesis testing consists of statistical inference by not rejecting or rejecting assumptions on an unknown population parameter such as mean, standard deviation, skewness, or kurtosis, from its representative or random samples associated statistics[5], with a specific degree of statistical significance or confidence. The statistical inference parameter for hypothesis testing considered in this work is the mean return by means of probability value assessment.

First, we calculate the multiple hypothesis testing probability values (i.e., p-values) and then we perform the corresponding adjustments. The p-value is the probability that the observed value of the test statistic could have occurred given that the hypothesis being tested (i.e., the null hypothesis) is true. The smaller the p-value, the greater is the justification to challenge the truth of the null hypothesis H0 and reject it in favor of the alternative hypothesis H1. When the p-value is less than a given threshold, then H0 is rejected and H1 is accepted. Therefore, a statistically significant result has a p-value low enough to justify a rejection of the null hypothesis H0.

The p-value adjustments are done through the family-wise error rate or Bonferroni procedure [22], and the false discovery rate or Benjamini-Hochberg procedure [23], and these two adjustments are compared with the corresponding original p-value calculations. Hence, the population mean multiple hypothesis testing consists of statistical inference by not rejecting or rejecting assumptions on an unknown population test statistic (like the mean) from its representative or random samples associated statistics, with a specific degree of statistical significance or confidence, by means of p-value estimations. The population mean p-value is assessed through following steps:

Define the unknown population mean null (H0) and alternative (H1) hypothesis. In the two-tail test hypothesis we define . In the one-tail (i.e., right-tail) test hypothesis we define . For both tests the unknown population mean is assumed ;

Define the unknown population mean multiple hypothesis testing degree of statistical significance or confidence with the associated non-rejection (where the null hypothesis cannot be rejected) and rejection regions. For the two-tail test, the critical values for the rejection vs. non rejection region are: , where α is the level of statistical significance, and  is the cumulative distribution function of the t-student probability distribution. Therefore, for the two-tail test, the null hypothesis non-rejection region is: . For the one-tail test the critical value is given by:  and the null hypothesis non-rejection region is:

Calculate the standardized representative or random samples mean statistics and test whether their values are within the multiple hypothesis testing non-rejection or rejection regions.

The standardized representative of a random sample mean statistic is the t-statistic, which is equal to the corresponding random sample mean  minus the null hypothesis mean  divided by the random sample standard error ( is the random sample standard deviation, while  is the number of observations within the random sample):

Therefore, the H0 two-tail test non-rejection region is: , while the H0 one-tail test non-rejection region is:  The t-statistic p-value is tested as follows:

 

If then do not reject the null hypothesis H0 with of statistical confidence;

 

If

then reject the null hypothesis H0 with of statistical confidence.

In the hypothesis testing, if α is the level of statistical significance, then (1 ― α) is the degree of statistical confidence. In this assessment, we use a level of statistical significance of 5%, which is translated into a 95% degree of statistical confidence. It is worth noting that when computing the  for a two-tail test, α is divided by two because we are considering both the lower and upper distribution tail.

 

Probability Value Adjustment

The population mean p-value adjustment consists of decreasing the expected rate of false positives in their individual statistical significance tests, when conducting multiple comparisons through the family-wise and the false discovery error rate filtering methods. The type I error (or false positive) consists of incorrectly rejecting an assumption on an unknown population mean parameter from its representative or random sample associated statistic. The statistical significance level α is the probability of making a type I error. A type II error (or false negative) consists of incorrectly not rejecting an assumption on an unknown population mean parameter from its representative or random sample associated statistic. Reducing the probability of making a type I error increases the probability of making a type II error and vice versa if the sample size remains constant.

The methods for multiple hypothesis testing adjust α, so that the probability of getting at least one significant result due to chance remains below a significance level α. Type I error leads to mistakenly reject the null hypothesis H0, thus investing in a worthless strategy, which exposes the capital to risk without the prospect of gain. The Bonferroni correction can be quite conservative, leading to a higher rate of false negatives (type II error). However, while the Bonferroni correction is considered too conservative in many fields, the higher bar to significance may be regarded as appropriate by many traders and investors for backtesting a trading strategy. Type II errors cause a potentially profitable strategy to be ignored, thus resulting in lost investing opportunities. From the investor’s or trader’s perspective a type I error is more serious, because lost capital is considered worse than lost investment opportunities. The family-wise error rate, or Bonferroni procedure, adjusts the population mean p-values by decreasing the expected rate of false positives (type I errors) in their individual statistical significance tests when conducting multiple comparisons. The Bonferroni procedure allows a stricter control than the false discovery rate (i.e., it is more conservative) and is calculated as follows:

Declare true positives all  when , where n is the number of trials.

The false discovery rate, or Benjamini-Hochberg procedure, consists of adjusting the population mean p-values by decreasing the expected rate of false positives in their individual statistical significance tests when conducting multiple comparisons through a more relaxed p-value adjustment than the Bonferroni procedure. The Benjamini-Hochberg procedure is calculated as follows:

Rank  from the smallest to the largest t-statistic p-values ;

Find the largest rank k for which , where n is the number of trials;

Declare true positives all random sample means  from.

With respect to the Bonferroni correction there is a slight increase in type I error rate, but at the same time a significant reduction in type II error rate.

 

Strategy Evaluation

The techniques of multiple hypothesis testing and probability value adjustments were applied to the Street Smarts strategies on the daily returns of all the asset classes and FOREX crosses for the length of the look-back period, from September 2005 to September 2021. The purpose of this evaluation was to assess whether the mean returns of the strategies were statistically significant with respect to the null hypothesis and could consistently bring some excess returns with respect to the zero return of the null hypothesis. The results for each strategy are reported in Appendix 1. The parameter chosen to evaluate the statistical significance was the p-value, and the tables summarize the p-values and their adjusted values according to the Bonferroni and false discovery rate (i.e., fdr) procedures. All the p-values greater than 0.05 (the level of statistical significance considered for this assessment), where the null hypothesis cannot be rejected, are marked in light red. The p-values show that the null hypothesis for most of the asset classes and currency pairs can be rejected, in favor of the alternative hypothesis.

Table 24 confirms that the Turtle does not generate statistically significant excess returns above zero on IEF and the null hypothesis (both for the two-tail and one-tail test) cannot be rejected. In the FOREX market, in agreement with the results shown in Figure 4, the null hypothesis cannot be rejected for the currency cross AUDNZD. Furthermore, the Bonferroni adjustment (to reduce the type I errors) does not reject the one-tail test null hypothesis for EURUSD, EURGBP, USDCAD, AUDUSD, AUDNZD, EURNZD, and EURAUD. This result may seem quite conservative since these currency crosses have a positive CAGR from the backtesting. However, it is worth noting that the returns generated by these currency pairs are smaller than the other returns and more likely to incur in type I errors. It is the investor’s or trader’s responsibility to decide whether this conservative filtering is consistent with her/his own risk profile. The Turtle Soup (Table 25) generated statistically significant excess returns on all asset classes after the fdr filtering procedure (the Bonferroni did not reject the null hypothesis only for the one-tail test of XLF).

Both the two-tail and one-tail test for the ID-NR4 (Table 26) showed a consistent statistical significance (confirmed by Bonferroni and fdr adjustments) on all the equity indexes and sectors, bonds, gold, and real estate. In contrast, the ID-NR4 results were less significant on the FOREX crosses, where only USDJPY, USDCAD, AUDUSD, and USDTRY delivered statistically significant excess returns according also to the p-value adjustments of both the Bonferroni and fdr procedures. This statistical result confirms the backtesting results shown in Figure 19 and reported in Table 18, where these currency pairs have the higher CAGR values. In summary, the multiple hypothesis testing supported the conclusion that ID-NR4 delivered a robust performance on the stock indexes and sectors, but it is not particularly suited for the FOREX market.

The Holy Grail strategy generated statistically significant excess returns on all the asset classes and most of the currency pairs (Table 27) also based on the Bonferroni and fdr procedures.

Even the Anti (Table 28) yielded statistically significant excess returns on all asset classes and many of the currency pairs, also confirmed by the Bonferroni and fdr adjustments. The only currency crosses where the null hypothesis could not be reject and did not generate robust statistically significant excess returns were AUDNZD and EURCAD, in agreement with the strategy backtesting results shown in Figure 13 and in Table 12, where AUDNZD and EURCAD delivered the worst CAGR and total returns over the backtesting period.

It is worth pointing out that the p-value adjustments obtained with the Bonferroni procedure are more conservative thus reducing the probability of type I errors, but also the trading opportunities.

In general, the backtesting results presented in Section 5 for the Streets Smart strategies were validated by the multiple hypothesis testing. The strategies generated excess returns on all the asset classes, except for ID-NR4 that on most of the FOREX currency pairs did not delivered statistically significant excess returns with respect to the null hypothesis.

 

The Bootstrap

The bootstrap method derives a sampling distribution’s shape of the test statistic[6] (or sample statistic) by randomly resampling with replacement from an original sample of observations. The test statistic is a point estimate (in our case the population mean) and is computed on each sample. Assuming that certain conditions are satisfied, the bootstrap technique converges to a correct sampling distribution as the sample size goes to infinity. In practice, this means that given a single sample of observations, bootstrapping can produce the sampling distribution needed to test the significance of a technical analysis rule, parameter, or strategy.

The time series bootstrap performs a probability distribution simulation of the population mean through repeated random resampling with replacement of representative or random sample means, tending towards an unbiased population mean as the number of resamples increases towards infinity. Resampling with replacement reuses the same data in the original sample [24]. The sample statistic probability distribution consists of statistical inference of the population unbiased parameter from the repeated representative or random samples statistics, assuming a theoretical or bootstrap probability distribution. For stationary data, random resamples are used [25], while for non-stationary data, random fixed-block resamples or random distributed block resamples are used [26]. In this work, the simulation of the population mean probability distribution is performed by means of random fixed-block resampling with replacement, with blocks of fixed length equal to 10, while the number of resamplings is equal to 1000. This corresponds to randomly re-shuffling the observations in blocks, with replacement in the original time series. At the end of the procedure, we calculate the test statistic for the bootstrap, which is the arithmetic mean, where B is the number of bootstrap estimates and  is the mean of each bootstrap resampling:

The bootstrap statistical inference parameter estimations are point estimates with their associated confidence intervals. The bootstrap population mean confidence interval estimation quantifies the population mean point estimate statistical inference accuracy, based on bootstrap population mean confidence interval simulation [27]. Such interval estimate is a range of values within which the (unknown) population mean lies with a given level of probability. The bootstrap population mean confidence interval is determined as follows:

In the two-tail test, the bootstrap confidence interval is from the lower tail bootstrap critical value to the upper tail bootstrap critical value:

The two-tail test critical values are calculated in this way: the lower tail bootstrap critical value is equal to the bootstrap cumulative distribution function: , where α is the level of statistical significance. Even for the bootstrap, we use α = 0.05, which translates into a level of statistical confidence of (1 ― α) = 0.95;

The upper tail bootstrap critical value is equal to the bootstrap cumulative distribution function: . In both calculations we consider α/2 because of the two-tail test;

With (1‒α) probability the unknown population mean lies within the bootstrap confidence interval.

 

Bootstrap Hypothesis Testing

The bootstrap statistical inference parameters hypothesis testing is given by the probability value estimations [28], and by not rejecting or rejecting assumptions on an unknown population mean from its representative or random sample associated bootstrap test statistic, with a specific degree of statistical significance or confidence. The bootstrap population mean p-value is obtained through the following steps:

Define the unknown population mean null (H0) and alternative (H1) hypothesis. For the two-tail test hypothesis: ; . In this work we consider ;

Define the unknown population mean bootstrap hypothesis testing degree of statistical significance α or confidence (1‒α);

Estimate the bootstrap population mean percentile probability value and test whether it is greater or less than the degree of statistical significance for hypothesis testing non-rejection or rejection, with a predefined degree of statistical confidence:

The two-tail test p-value for the null hypothesis is: ;

The lower tail test p-value for the null hypothesis is: , where B is the number of bootstrap resamplings and  are the bootstrap resamples means;

The upper tail test p-value for the null hypothesis is:

The H0 two-tails test for the bootstrap p-value is performed as:

If  then do not reject the null hypothesis H0 with  of statistical confidence;

If  then reject the null hypothesis H0 with  of statistical confidence.

 

Bootstrap Probability Value Adjustment

The bootstrap population mean p-value multiple test adjustment consists of decreasing the expected rate of false positives in the individual statistical significance test, when conducting multiple comparisons through the family-wise error rate, or the Sidak filtering method [29]. The Sidak procedure is calculated as follows:

The Sidak adjusted p-value for the null hypothesis H0 is given by: , where p(H0) is the previously calculated p-value and n is the number of trials;

The Sidak adjusted level of statistical significance is equal to: , where n is the number of trials;

Declare true positives all trials where the Sidak adjusted p-value is: ;

The Sidak procedure is linked to the Bonferroni procedure by the following relation:

The Sidak procedure assumes that the trials are independent, and the corresponding probability value adjustment is done for an individual time series bootstrap hypothesis testing. It is slightly less conservative than the Bonferroni procedure.

 

Bootstrap Strategy Evaluation

The bootstrap confidence intervals for the test statistic point estimates are reported in Appendix 2, for each Street Smarts strategy and for all the asset classes and currency pairs used for backtesting. The critical values marked in light yellow highlight when the confidence range includes the condition , where the null hypothesis cannot be rejected. Moreover, the tables in Appendix 2 also show the mean values of the original time series and the mean values obtained from the bootstrap sampling distribution. The bootstrap mean values are in good agreement with the original sample means.

It is possibile to observe that the statistical significance tests based on the two-tail test p-values obtained with the multiple hypothesis testing described in Section 6 and summarized in Appendix 1, are consistent with the p-values generated by the bootstrap procedure (two-tail test). The results obtained with the Sidak procedure are aligned with the adjusted p-values generated by the Bonferroni procedure, since both methods are family-wise error rate procedures. The numerical results summarized in Appendix 2 confirm that Sidak is slightly less conservative than Bonferroni.

Conclusions

In this work, some of the most popular strategies published in the book Street Smarts [3] by LC and LBR more than 25 years ago were backtested across stock indexes, S&P 500 sectors, real estate, commodities, bonds, and all the major FOREX currency pairs. The strategies of Street Smarts are inherently discretionary and were proposed for the stock and futures markets of a quarter of a century ago. Since then, most of the markets have changed their structure and behavior. Therefore, in this paper the addressed problem was to determine whether those strategies are still valid in the current markets and can be profitably traded. More in general, by answering such question, it would also be possible to have a deeper insight on the effectiveness of classical Technical Analysis methodologies such as swing trading and pattern breakouts.

The robustness of the backtesting results presented in this work is supported by the completeness of the asset classes considered, and by the length of the historical data look-back period, covering a time window from September 2005 till September 2021. It is worth pointing out that in [3] only a limited set of examples was presented, mainly with the purpose to describe to the reader how to set-up the strategies. From those few cases, it was not possible to thoroughly assess the overall performance of the strategies in different market scenarios.

In this paper, the settings of the strategies were kept substantially aligned with the original settings proposed by the authors. By keeping the strategies’ set-ups coherent with the original ones on one hand, and by testing the strategies on many different markets and for a very representative look-back period on the other hand, we believe that the results presented in this work are robust and not over-fitted. The backtests confirmed that the performance of the strategies can vary depending on the underlying assets and markets.

Another relevant contribution of this work has been a rigorous and comprehensive statistical assessment of the Street Smarts strategies. Unlike in several other fields, the data encountered in the markets and in the investment world are quite noisy from a statistical standpoint. Therefore, randomness can have a larger impact in the financial markets than in other sectors, and we believe that a complete evaluation and a deeper insight on a trading strategy and on its intrinsic value can be achieved through hypothesis testing with the techniques of inferential statistics. The backtesting results and the statistical assessment presented in this work confirm that the Street Smarts strategies have delivered statistically significant results across the look-back period on most of the asset classes. Only ID-NR4 did not produce statistically significant excessive returns on the currency pairs, given the typical mean-reverting structure of the FOREX.

After more than twenty-five years since they were presented, the Streets Smart techniques can still deliver good performances on several asset classes and in a changing market scenario, as it was confirmed by the extensive backtests and a rigorous statistical hypothesis testing. Even if these strategies are inherently discretionary, the robustness of the statistical assessment performed in this work makes some of the strategies’ underlying techniques, like swing trading and pattern breakouts, still effective options to be implemented in automatic trading systems.

In conclusion, the Street Smarts strategies can still be of interest to many traders and investors, both from an educational and a trading perspective. Reading Street Smarts is highly recommended to all traders. It probably remains one of the most valuable books on trading, and every trader should be familiar with the techniques proposed by Larry Connors and Linda Bradford Raschke.

 

References

William P. Hamilton, “The Stock Market Barometer: A Study of its Forecast Value Based on Charles H. Dow’s Theory of the Price Movement.” Harper & Bros., 1922.

 

Robert Rhea, “The Dow Theory: An Explanation of its Development and an Attempt to Define its Usefulness as an Aid in Speculation.” Fraser Publishing Company, (Reprint 1933).

 

Laurence A. Connors and Linda Bradford Raschke, “Street Smarts: High Probability Short-Term Trading Strategies.” M. Gordon Publishing Group, Los Angeles, CA, U.S., 1995.

 

Inoue A. and Rossi B., “Out-of-Sample Forecast Tests Robust to the Choice of Window Size,” Journal of Business & Economic Statistics, 30(3), 432-453, 2012.

 

Zakamulin V., “The Real-Life Performance of Market Timing with Moving Average and Time- Series Momentum Rules,” Journal of Asset Management, 15(4), 261-278, 2014.

 

Perry J. Kaufman, “Trading Systems and Methods 5th edition.” John Wiley & Sons, Inc., Hoboken, NJ, U.S., 2013.

 

Charles D. Kirkpatrick III and Julie R. Dahlquist, “Technical Analysis: The Complete Resource for Financial Market Technicians.” Pearson Education, Inc., Old Tappan, NJ, U.S., 2016.

The Original Turtle Trading Rules,http://www.tradingblox.com/originalturtles/

 

Jack D. Schwager, “Market Wizards.” John Wiley & Sons, Inc., Hoboken, NJ, U.S., 2006.

 

Jack D. Schwager, “The New Market Wizards.” John Wiley & Sons, Inc., Hoboken, NJ, U.S., 2008.

 

Richard D. Donchian, “Donchian’s 5- and 20-Day Moving Averages,” Commodities Magazine, Dec. 1974.

 

George C. Lane, “Lane’s Stochastics,” Technical Analysis of Stocks & Commodities (May/June 1984).

 

  1. Welles, Jr. Wilder, “New Concepts in Technical Trading.” Trend Research, Greensboro, NC, U.S., 1978.

 

Toby Crabel, “Day Trading with Short-Term Price Patterns and Opening Range Breakout.” Trader Press, Inc., Greenville, SC, U.S., 1990.

https://finance.yahoo.com/,

https://www.investing.com/

 

Charles LeBeau and David W. Lukas, “Technical Traders Guide to Computer Analysis of the Futures Market.” Mc Graw Hill, Boston, MA, U.S., 1992.

 

Cogneau, P. and Hübner, G., “The (More Than) 100 Ways to Measure Portfolio Performance, Part 1: Standardized Risk-Adjusted Measures,” Journal of Performance Measurement, 48, 56–71, 2009.

 

Sharpe, W. F., “The Sharpe Ratio,” Journal of Portfolio Management, 21 (1), 49–58, 1994

 

Young T. W.,”Calmar Ratio: A Smoother Tool,”, Futures, vol. 20, nr 1, 40, 1991.

 

Edwards R., Magee J., and Bassetti W. H. C., “Technical Analysis of Stock Trends 9th edition.” St. Lucie Press, Boca Raton, FL, U.S., 2007.

 

Bonferroni, C. E., “Teoria statistica delle classi e calcolo delle probabilita’,” Pubblicazioni del R lstituto Superiore di Scienze Economiche e Commerciali di Firenze,1936.

 

Benjamini, Y. and Hochberg, Y., “Controlling the false discovery rate: a practical and powerful approach to multiple testing,” Journal of the Royal Statistical Society, 1995.

 

Efron, B. and Tibshirani, R, “An Introduction to the Bootstrap.” Chapman and Hall, 1993.

 

Politis D. N. and Romano, J. P., “The Stationary Bootstrap,” Journal of the American Statistical Association, 1994.

 

Kuensch, H. R., “The Jackknife and the Bootstrap for General Stationary Observations,” The Annals of Statistics, 1989.

 

DiCiccio, T. J. and Efron B., “Bootstrap Confidence Intervals,” Statistical Science, 1996.

 

MacKinnon, J. G., “Bootstrap Hypothesis Testing,” Working Paper. Queen’s University Department of Economics, 2007.

 

Sidak, Z. K., “Rectangular Confidence Regions for the Means of Multivariate Normal Distributions,” Journal of the American Statistical Association, 1967.

https://www.r-project.org/

 

 

Appendix 1 Multiple Hypothesis Testing

Table 24 Turtle strategy p-values

 

Table 25 Turtle Soup strategy p-values

 

Table 26 ID-NR4 strategy p-values

 

Table 27 Holy Grail strategy p-values

 

Table 28 Anti strategy p-values

 

Appendix 2 Bootstrap

Table 29 Turtle strategy bootstrap confidence intervals and p-values

 

Table 30 Turtle Soup strategy bootstrap confidence intervals and p-values

 

Table 31 ID-NR4 strategy bootstrap confidence intervals and p-values

 

Table 32 Holy Grail strategy bootstrap confidence intervals and p-values

 

Table 33 Anti strategy bootstrap confidence intervals and p-values

 

Appendix 3 Turtle and Turtle Soup Correlations

 

Table 34 Turtle vs Turtle Soup correlations (FOREX currency pairs)

 

Table 35 Turtle vs Turtle Soup correlations (asset classes)

 

[1] Although named after Charles Dow, the theory was primarily developed by William Peter Hamilton (1922) [1] and then grew in popularity thanks to Robert Rhea (1932) [2].

[2] This situation could happen more frequently for asset classes with high volatility such as the cryptocurrencies, which are not considered in this work.

[3] Average True Range [6].

[4] The requirements for a short entry are reversed with respect to the set-up of the long entry.

[5] The term sample statistic refers to the parameter being used to test a hypothesis, like the average or mean return. The term sample statistic is interchangeable with the term test statistic.

[6] A test statistic is a statistic (i.e., a quantity derived from the sample) used in statistical hypothesis testing.

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The Tyche system: Application Of Physics For Stock Price Prediction

by Jayesh Chandra Gupta

About the Author | Jayesh Chandra Gupta

Jayesh Chandra Gupta is an Equity Product Specialist at Nomura International Wealth Management. His work involves recommending stock and structured product ideas, covering global equities (US,Europe, Japan, China, SEA), to Nomura Wealth Management Team. He is an MBA from Indian Institute of Foreign Trade, New Delhi and holds a B.Tech in Mechanical Engineering from Indian Institute of Technology, Mandi. He has also completed –The Henley Executive Hedge Fund Programme and is currently studying MSc in Financial Engineering from World Quant University.

Jayesh was introduced to Fundamental Equity Research & Technical Analysis during his MBA, where his team was the National Finalist of CFA Research Challenge. After MBA, Jayesh worked as a Sell-side Equity Research Analyst at JM Financial, covering Indian Auto & Auto Ancillaries.

Given his background in Engineering and love for Mathematics & Technical Analysis, he was always intrigued with likely application of Physics in Financial Markets. He authored this paper, as part of the same curiosity.

Abstract

In the book “The Man Who Solved the Market”[1], the author quotes Renaissance’s co-CEO Rober Mercer saying to a friend – “We’re right 50.75 percent of the time…but we are 100 percent right 50.75 percent of time…You can make billions that way”. This paper intends to provide a similar indicator or system, which is right a bit more than half the time. Drawing inspiration from physics, the paper investigates the applicability of basic principles of physics to arrive at a price prediction system (or indicator) for stocks. The system hence derived, named as “Tyche System”, shows strong performance during back-testing.  The current paper also demonstrates the usage of Tyche system for – a) Market technicians who would like to get a heads-up about an impending technical event in a stock without scanning through the charts of thousands of stocks; and b) Hedge Funds, who would like to use their long-only portfolio for additional leverage to generate higher and un-correlated returns using the Tyche system.

Keywords: Physics, Newton’s Law, Hooke’s Law, Price Prediction, Stocks, market timing, un-correlated, Nifty, back tests, Hedge Funds.

Introduction

Capital markets play a vital role in economic growth as they provide funding access to companies in the primary market (issuance of new bonds or shares). To arrive at the funding cost for a company, price discovery becomes an important aspect and market participants often rely upon business fundamentals like earnings growth, and outlook to value a company. However, post primary issuance, secondary market trading of stocks is influenced by multiple factors like liquidity, size, earnings report, news flow, daily volatility, positioning and speculation by market participants etc. While efficient market hypothesis states that asset prices reflect all available information (Fama, 1970), there is varying acceptance of the hypothesis and market participants have often relied upon fundamental / technical analysis for long-term investments / speculation, respectively.  Technical analysis is viewed as an art or science of planting the stock information like price movements, trading volume and market scenario in the form of charts for the purpose of forecasting the future price trends[2]. Increasingly, to improve trading edge, market participants are trying to create technical indicators based on simple physical systems. One such example is Elder Force (FI) which is calculated by multiplying the difference between the last and previous closing prices by the volume of the underlying, indicating a momentum shift towards strong buying or selling. At the same time, some researchers are also studying stock market’s physical properties description based on Stokes’ law[3], which is part of fluid mechanics and is a complex system. While physicist Jim Simons’ Medallion fund had posted c.39% CAGR returns (after fees) during 1988-2018 racing past peers[4], large part of investment community still struggles to grapple with physics in finance. As a result, some of the existing technical indicators which are based on physical systems are yet to demonstrate if their unit (read unit of measurement) has any dimensional similarity with Physics and if they can be right more than half the time? With this backdrop, we start the next section with the building blocks of Tyche System.

Brief overview from Physics: Dimensional analysis & Newton’s law 

Dimensional analysis offers a method for reducing complex physical problems to the simplest (that is, most economical) form prior to obtaining a quantitative answer[5]. In physics there are five fundamental dimensions in terms of which the dimensions of all other physical quantities may be expressed. They are mass [M], length [L], time [T], temperature [θ], and charge. The accepted units are, respectively, the kilogram, the meter, the second, and the Kelvin or degree Celsius. These fundamental dimensions are essential to understand principles of physics including Newton’s Laws of Motion.

Newton’s first law (law of inertia) states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force.Newton’s second law is a quantitative description of the changes that a force can produce on the motion of a body. If a body has a net force acting on it (in a direction – represented by vector in the equation), it is accelerated in accordance with the equation (in the direction of application of force). Conversely, if a body is not accelerated, there is no net force acting on it.

   or

Mass (m – assuming constant) has a dimensional unit of [M1]

Distance (x) has a dimensional unit of [L1]

Velocity has a dimensional unit of [L1 T-1]

Acceleration is the rate of change of the velocity of an object with respect to time, its dimensional unit is [L1 T-2] and has a vector (or direction of acceleration).

While the unit of Force is Newton, dimensional analysis helps in breaking down Newton into fundamental dimensions:

Further, any equation in Physics is only valid if the dimension on the LHS (Left Hand Side) and RHS (Right Hand Side) of the equation are similar. Let us see this with an example of the first equation of motion:

The first equation of motion gives the relation between Velocity and Time

Here, v is the final velocity, u is the initial velocity, a is the acceleration and t is the time.

Dimensional analysis of LHS and RHS of equation 3:

Multiplication of dimensions leads to sum of the powers

Only physical quantities of the same nature having the same dimensions can be added

Defining the dimensions for stocks

Before we can talk about applying principles of classic mechanics in stock price prediction, we need to define what is stock market equivalent of [M], [L] and [T].

For a particular stock, at a particular time [T], we get the following two major data points – a) Price and b) Volume. Yes, traders and investors can argue that one can get variation of prices (close, high, low, avg. etc) and volumes (open interest, one day volume, 1 month volume, 30-day average etc.). However, intrinsically, it is Price [P], Volume [V] and Time [T] that are the defining variable of a stock.

 

What is Mass for a stock?

In physics, mass is a quantitative measure of inertia, it is the resistance that a body of matter offers to a change in its speed or position upon the application of force. When we talk about mass of a stock, market cap might be the first thought in a person’s mind. However, like physics, in stock market, mass of a stock can be viewed as that property of a stock that makes it difficult to change its price.

And it would be wrong to assume that market cap resists price movement because – a) not all outstanding shares are traded in a day, b) not all free float of a stock is traded in a day and, c) big market cap stocks can also easily demonstrate price high volatility at times.

Then what is mass for a stock?  To answer this let us find out what are the properties of a stock that resist change in its price –

Daily traded volume of a stock – If daily average traded volume of a stock is 100,000 shares, then it would be very difficult to change the daily price of a share only by 1,000 shares etc.

Assuming daily traded volume of stock to be constant, what is the other factor that can resist price change of the stock? If a stock was trading at $20, 5 years ago, and is now trading at $25, then it would be more difficult to move the price of the stock now vs. 5 years ago as the investors will have to shell-out additional $5 to participate in the market. It also works the other-way round, if the stock is currently trading at $15 vs. $20 (5 years ago), it is easier to move the price of the stock as the investors will have to shell-out $5 less to participate in the market. So, price of a stock is also a property that resists further change in price of itself.

Since, we are using minimum unit of T = 1 day, we can define mass of a stock as daily turnover (i.e., average traded price * traded quantity in one day). As a result, dimensions of stock mass using Price [P], Volume [V] and Time [T] is:

Where  is the mass of a stock at the end of day t, is the average traded price of the stock on day t and is the traded volume on day t.

What is velocity and acceleration for a stock? In physics, velocity of an object is the rate of change of its position with respect to a frame of reference and is a function of time. Similarly, velocity of a stock can be viewed as rate of change of its price.

In Physics, acceleration is the rate of change of the velocity of an object with respect to time. Similarly, acceleration of a stock can be viewed as rate of change of its velocity.

 

Applying Newton’s second law of motion in stocks

Using equation 1 and 2 to find out the dimension of Force in the stock market.

Using equation 7 and 9:

Since multiplication of dimensions leads to sum of the powers:

The RHS of Force on a stock in calculus format (using equation 7 and 9):

Since we are focusing on predicting one day price movement of a stock, we can calculate the acceleration in equation 13 as rate of change of velocity:

As a result, after using equation 13 and 14, we will have the value of force on the stock at the end of day t.

 

Applying Hooke’s Law to determine the likely price of the stock on t+1

Market participants have often talked about stock prices behaving as spring and oscillating at a particular vibration. As per William Gann – “Through the Law of Vibration every stock in the market moves in its own distinctive sphere of activities, as to intensity, volume and direction; all the essential qualities of its evolution are characterized in its own rate of vibration. To speculate scientifically it is absolutely necessary to follow natural law”.[6]

Further, as per Hooke’s Law the force needed to extend or compress a spring by some distance is proportional to that distance. The same is expressed mathematically as:

Where F is the force applied on the spring and  is the displacement of the spring. And the negative sign indicating the displacement of the spring once it is stretched (k is spring constant).

We already have the value of Force from equation 13 and assuming that the force remains constant during t+1, we can find the likely change in price ( = of the stock using equation 15. Further, the only other calculus variation that would lead to same dimension of force is:

Where,  can be defined as (since we are focusing on one day movement):

 

As a result, we can use equation 13,14, 16 and 17 to find :

As a result, with the help of Equation 19, we can try to predict share price of a stock (for the next day) with a reasonable degree of accuracy. However, it is quite possible that the value of force during t+1 can be materially different than that derived from equation 13. As a result, one should use the current system to build position in a stock towards market close (i.e., t) only if the predicted price for tomorrow (i.e., t+1) is with 1SD range of today’s price movement. However, if an investor deploys strong computation power during market hours, she might be able to dynamically find force (choice of her time frame) as per equation 13 and predict stock price within 1 unit of chosen time frame.

 

Back-testing of Tyche System

As part of back testing, Tyche was run on historical data spanning 1Apr’05 to 19Mar’21, across 50 stocks which are currently part of Nifty 50 Index (India). Result of Tyche back testing can be seen in Table 1. It is worth noting that Tyche was able to achieve 53% hit rate i.e., 53 out of 100 share price predictions made on “t” was achieved during “t+1”. The hit rate is favourable and should improve further, as and when Tyche is deployed for computations during market hours (then t will not be 1 day but can even be hours, minutes etc.).  It is also important to note that on an average, Tyche generated only 166 trades per stock during the test period of 1Apr’05-19Mar’21.

Back testing conditions of Tyche for individual stocks:

Tyche has the flexibility to go both long and short individual stocks.

Tyche only looks for prediction of price movement greater than or equal to 1% or less than or equal to negative 1%.

If the stock opens in the opposite direction vs. the predicted direction, there is no provision for Stoploss and Tyche takes loss on a closing basis

If stock’s low during the day is above the predicted price (in case prediction was on the upside), Tyche does not book profit. Profit booking happens on a closing basis. Same is the case when Tyche predicted a decline and the high of the next day is lower than the predicted price, profit booking happens on a closing basis.

 

Table 1 Back testing result for Nifty 50 stocks (India) – Between 1Apr’05 to 19Mar’21

Underlying Tyche Total Return Tyche – Annualised CAGR % Stock Return CAGR% % Times the stock hit Tyche‘s TP Avg. Number of Day Trades
Average 21.0% 32% 17.5% 53% 166
WPRO IN -3.9% -7% 12% 51% 140
UPLL IN 169.1% 130% 18% 62% 299
UTCEM IN 16.5% 19% 21% 50% 225
TTAN IN 4.1% 4% 36% 54% 232
TECHM IN -11.1% -15% 15% 50% 177
TCS IN -46.9% -76% 20% 46% 110
TATA IN -31.6% -48% 5% 49% 146
TTMT IN 46.8% 65% 9% 59% 193
TATACONS IN 16.5% 17% 17% 54% 241
SUNP IN 18.1% 28% 18% 56% 169
SRCM IN 40.8% 33% 32% 52% 305
SBIN IN 31.5% 83% 12% 50% 113
SBILIFE IN -3.9% -26% 8% 44% 32
RIL IN -7.9% -22% 24% 55% 84
PWGR IN 37.3% 99% 6% 57% 115
ONGC IN -2.5% -4% 1% 57% 150
NTPC IN 67.2% 163% 3% 59% 133
NEST IN 6.7% 23% 19% 38% 77
MSIL IN 35.5% 68% 20% 53% 147
MM IN 110.1% 193% 18% 62% 173
LT IN -15.5% -33% 17% 45% 106
KMB IN -15.5% -19% 29% 56% 199
JSTL IN -0.4% 0% 17% 56% 238
ITC IN -19.5% -39% 14% 53% 110
IOCL IN 47.7% 55% 4% 55% 224
INFO IN -10.8% -33% 16% 47% 70
IIB IN -12.6% -12% 21% 52% 271
ICICIBC IN 37.0% 75% 14% 53% 141
HUVR IN 29.5% 88% 20% 55% 102
HNDL IN 13.9% 19% 7% 60% 185
HMCL IN 89.5% 146% 12% 61% 178
HDFCB IN -12.0% -27% 24% 49% 104
HDFC IN 66.0% 146% 20% 53% 141
HCLT IN 8.3% 11% 21% 54% 194
HDFCLIFE IN -0.6% -5% 19% 52% 29
GRASIM IN 34.8% 61% 15% 54% 158
EIM IN 56.0% 44% 32% 54% 308
DRRD IN 37.5% 71% 17% 54% 148
DIVI IN -27.1% -35% 30% 50% 184
COAL IN -9.4% -32% -8% 52% 64
CIPLA IN 64.3% 144% 14% 55% 139
BRIT IN 29.0% 42% 27% 56% 182
BPCL IN 9.5% 12% 13% 52% 199
BAF IN 81.2% 57% 45% 56% 332
BJFIN IN -1.3% -1% 24% 56% 220
BJAUT IN -9.1% -18% 22% 56% 124
AXSB IN 63.8% 113% 19% 52% 163
APNT IN 4.5% 7% 30% 42% 153
ADSEZ IN -3.0% -3% 11% 56% 214

 

Tyche performance vs. Long-only stock portfolio

In the back testing period, the long only equal weighted stock portfolio (stocks from table 1) generated a 24% return CAGR with a maximum drawdown of 13.1% on 23Mar’20. In the back testing, 100% capital deployment happened in long only equal weighted stock portfolio. On the other hand, Tyche generated 15.9% return CAGR with money deployed in the market only for 75% of the test duration. Also, the maximum drawdown faced by Tyche was 8.4% on 16Nov’07. Unlike long-only stock portfolio which declined c.35% between last week of Feb’20 and last week of Mar’20, Tyche posted a gain of c.27% (Figure 3). Also, during Global Financial Crisis (from Sep’07 to Mar’09), long-only stock portfolio declined c.35%. However, Tyche posted a gain of c.122% in the same period (Figure 2).

It is important to note that Tyche has benefits of choosing from a vast pool of stocks (can be beyond the 50 stocks used in back testing) and this 15.9% return CAGR is after Tyche switched between Longs / Shorts and gyrated between various stocks (albeit on an equal weighted basis). However, it is important to note that as per Pareto chart (Figure 4), 80% of the time Tyche had less than equal to 3 holding (long / short) and yet generated 15.9% CAGR returns. As a result, Tyche is a good alert system for market technicians who would like to get a heads-up about an impending technical event in a stock without scanning through the charts of thousands of stocks.

 

How can Tyche assist long-only portfolio?

While Tyche can be a standalone system, but it would be wise to use Tyche along with long-only investment portfolio. Hedge Funds usually enjoy a strong relation with their prime brokers. This allows Hedge Funds to get cheap stock financing. Even if one assumes that the haircut on financing is 50% and the same is deployed in Tyche, return CAGR improves from 24% to 33.8% (excluding financing cost). At the same time, maximum drawdown on a day reduces from 13.1% earlier to 10.3%.

 

Table 2 Comparison between Long-only portfolio, Tyche and Long-only+ Tyche (at 50% haircut)

Criteria Long-Only Tyche Long-only + Tyche
Maximum Drawdown (Daily) 13.1% 8.4% 10.3%
Return (% CAGR) 24.0% 15.9% 33.8%
% Of time Money was deployed 100% 75%

 

 

Figure 1 Portfolio value of Long only basket, Tyche System and Long only + Tyche System / portfolio (base of 100 as on 1Apr’05).

 

Figure 2 Tyche System / portfolio providing strong support to overall portfolio during the Global Financial Crisis (base of 100 as on 1Apr’05).

 

Figure 3 Tyche System / portfolio providing strong support to overall portfolio during Covid-19 market crash (base of 100 as on 1Apr’05).

 

Figure 4 Pareto Chart of Tyche: 80% of the time Tyche had less than equal to 3 holding (long / short) and yet generated 15.9% CAGR returns

References

Elder, Alexander (1993). Trading for a Living: Psychology, Trading Tactics, Money Management

H.C. Verma (2017). Concept of Physics

  1. Tony, The Law of Vibration: The Revelation of William D. Gann, UK, Harriman House, 2013.

Fama, E. F. (1970). Efficient Capital Markets: A Review of Theory and Empirical Work, Journal of Finance, 25(2), 383–417.

Gandia, Michael, “Modeling Financial Markets Using Concepts From Mechanical Vibrations and Mass-Spring Systems” (2014). HIM 1990-2015. 1638.

The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution by Gregory Zuckerman, New York, Portfolio/Penguin Random House, 2019

James Owen Weatherall, The Physics of Wall Street: A Brief History of Predicting the Unpredictable.

Peter L. Brandt, Diary of a Professional Commodity Trader: Lessons from 21 Weeks of Real Trading, 2011

Liang, B. (2000) Hedge Funds: The Living and the Dead. Journal of Financial and Quantitative Analysis, 35, 309-326.

1. [1] The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution by Gregory Zuckerman, New York, Portfolio/Penguin Random House, 2019

[2] International Journal of Development Research Vol. 5, Issue, 08, pp. 5410-5416, August, 2015

[3] Geoffrey Ducournau (2021) Stock market’s physical properties description based on Stokes’ law

[4] c.32% CAGR returns posted by Sorors (1969-2000), Steven Cohen (c.30%, 1993-2003), Peter Lynch (c.29%, 1977—1990), Warren Buffett (c.20.5%, 1965-2018) and Ray Dalio (c.12%, 1991-2018),

[5] Sonin, A.A. (2001) The Physical Basis of Dimensional Analysis. 2nd Edition, Department of Mechanical Engineering, MIT, Cambridge.

[6] Gandia, Michael, “Modeling Financial Markets Using Concepts From Mechanical Vibrations and Mass-Spring Systems” (2014). HIM 1990-2015. 1638.

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The Volume Factor

by Buff Dormeier, CMT

About the Author | Buff Dormeier, CMT

Buff Dormeier serves as the Chief Technical Analyst at Kingsview Wealth Management.  Previously, he was a Managing Director of Investments and a Senior PIM Portfolio Manager at the Dormeier Wealth Management Group of Wells Fargo Advisors.

In 2007, Dormeier’s technical research was awarded the prestigious Charles H. Dow Award. Also an award winning author, Buff authored “Investing with Volume Analysis“. Partnering with Financial Times Press, Pearson Publishing and the Wharton School, this book is the only one to win both Technical Analyst’s Book of the Year (2013) and Trader Planet’s top Book Resource (2012) to date.

Buff’s work has also been featured in a variety of national and international publications and technical journals. Now, with Kingsview Wealth Management’s affiliation, Buff’s expertise and proprietary work on technical and volume analysis shall become much more accessible to journalists and other media alike.

As a portfolio manager, Buff was featured in “Technical Analysis and Behavior Finance in Fund Management” – an international book comprised of interviews with 21 PM’s across the world who utilize technical analysis as a portfolio driver. In his new role with Kingsview Wealth Management, Buff’s unique performance driven strategies will be now be available to a wide audience of financial advisors and institutional clientele.

Buff has a Bachelor’s Degree of Science (B.S.) in Business and a Bachelor of Applied Science (B.A.Sc.) in Urban and Regional Planning from Indiana State University.

Abstract

Evidence of outperformance garnered through factor investing is abundant through many sources. Typically, these accepted factors have been shown to add alpha to an index. Although market volume is a crucial piece of investment information, the majority of the public ignores volume as an investment factor. This paper introduces a new factor exhibiting alpha generation: the volume factor.

 

Introduction

Presently baby boomers are piling money into the stock markets preparing for their upcoming retirements. According to Forbes Financial Council, over the course of the next decade, ten thousand baby boomers will retire per day on average. Meanwhile the highest earnings demographic, the millennial population, notorious for doing things ten years late, is just beginning to gear up their investment saving plans.  How are these new fund flows being allocated? According to CNBC, passive investing now accounts for 45% of all United States stock funds, up from 25% just a decade ago. Over the past few decades, capital weighted indexes have become America’s de facto investment option. It is not that passive investment strategies conducted primarily through capital weighting are a poor choice. To the contrary, capital weighting is a type of cross-sectional momentum investing that has shown excellent results. In a capital weighted index, as index members gain or lose relative momentum, they rise or fall in their weight rankings. With the vast allocation of these new net inflows being invested in this mindless strategy, holdings are becoming ever more concentrated. Currently (October 2021), the top five holdings of the S&P 500 (AAPL, MSFT, GOOGL/GOOG, AMZN, FB) account for over 22% of the index’s weightings.

Consequently, baby boomers, largely invested in the S&P 500, could be subjecting themselves to the risk associated with the sequences of returns or reverse dollar cost averaging when they begin selling their investment assets to supplement their lifestyle in retirement. According to Forbes, millennial investors despite being the youngest demographic, are actually the most risk averse group of all the generational demographics.  Thus, they are likely to be fickle investors in a less favorable investment climate. Far and away, these two demographics represent the largest percentage of the American investment population.  Combining these risks via the sequence of returns for baby boomers coupled with the risk aversion of millennials, multiplies the probability as well as the volatility associated with an S&P 500 unwinding event. Such an event would be especially devastating to those employing this passive index strategy and to those holding large concentrations of individual issues heavily weighted within the S&P 500.

As opposed to mindlessly following the movements of the herd, factor investing provides an alternative investment strategy to passive investing. Factor investing involves choosing or weighting investments based on their characteristics or attributes. Think about factor investing like screening a group of candidates. A hiring manager may desire candidates with certain levels of experience or education. Other options might be more subjective such as demonstrating leadership, being highly motivated and able to follow directions.

Likewise, equities attributes might be fundamental (the underlying company) in nature such as earnings, profitability, cash-flow and revenues. While other attributes are more technical (shareholder behavior) such as price momentum and volatility. Still other attributes may not be as easily characterized as either singularly fundamental or technical such as dividend and size characteristics. According to Blackrock, presently, five broad factor categories exist: value, size, quality, momentum, and low volatility.

Evidence of outperformance garnered through factor investing is abundant through many sources.  Typically, these accepted factors have been shown to add alpha to an index. Although these traditional factors may provide incremental improvement, this paper introduces a new factor exhibiting alpha generation. This paper is devoted to that factor – volume. When properly understood within the context of price trends, volume reveals the forces of supply and demand. When uncovered and applied correctly, this information could very well be the most prominent factor in price discovery to date.

In this paper, the reader is introduced to the Volume Price Confirmation Indicator (VPCI) and Capital Weighted Volume. The VPCI reveals the asymmetry between price trends and volume weighted price trends. The information derived from the VPCI indicator will empower us to rank securities according to their strength and persistence of volume confirmation. Capital Weighted Volume on the other hand reconciles price indexes with their corresponding volume flows. The accumulation of this flow data over time reveals the trends of capital in and out of their respective indexes. These capital flow trends may be useful in characterizing a given indexes investment forecast as being either favorable or unfavorable.

From the information presented from this paper, the reader will come to understand the power of volume as a truly unique investment factor. However, before we introduce the testing results, let us begin by reviewing the rationale of volume as an investment factor.  We begin our study by introducing volume and how it relates to its sibling price within market trends.

 

Price and Volume

In the exchange markets, price results from an agreement between buyers and sellers, despite their different appraisals of the exchanged item’s value. One opinion may offer legitimate fundamental grounds for evaluation, while the other may be pure nonsense. To the market, however, both are equal. Price represents the convictions, emotions, and volition of investors. It is not a constant, but rather changes and is influenced over time by information, opinion, and emotion.

Market volume represents the number of shares traded over a given period. It is a measurement of participation, enthusiasm, and interest in a security. Think of volume as the force that drives the market. Volume substantiates, energizes, and empowers price. When volume increases, it confirms price direction; when volume decreases, it contradicts price direction.

In technical analysis theory, increases in volume generally precede significant price movements. An intrinsic relationship exists within these two independently derived variables, price and volume. When examined together, price and volume give indications of supply and demand that neither could provide independently. This relationship is what the volume factor is all about.

 

Volume is the Force

“A Jedi’s strength flows from the force.”  -Yoda

Although market volume is a crucial piece of investment information, the majority of the public is ignorant of volume. Fundamental analysts often do not consider volume, while technical analysts underutilize it. Yet volume provides essential information in two critical ways: (1) by indicating a price change before it happens and (2) by helping the technician interpret the meaning of a price change as it happens.

 

Volume Leads Price

Although practitioners of technical analysis and academia have often been at odds, volume information is one area where they tend to largely agree. Volume can provide essential information by indicating a price change before it happens. The message is extremely telling, particularly when the volume reaches extreme levels. During such times, volume offers far superior information than price alone could ever provide.  Gervails, Kaniel, and Minglegrin authors of “The High Volume Return Premium,” a white paper from the University of Pennsylvania’s Rodney L.White Center for Financial Research, state, “We find that individual stocks whose trading activity is unusually large (small) over periods of a day or week, as measured by trading volume during those periods, tend to experience large (small) subsequent returns.” These researchers further state, “A stock that experiences unusually large trading activity over a particular day or a week is expected to subsequently appreciate.”

 

Figure 1 The High-Volume Return Premium

Source: “The High-Volume Return Premium,” The Wharton School of the University of Pennsylvania

 

Illustrated in Figure 1 are the testing results of Wharton’s 33-year study comparing stocks that experience relatively high-volume surges compared to normal and low-volume stocks. Similar conclusions were confirmed by Kaniel, Li, and Starks of the University of Texas. Their research paper, “The High Volume Return Premium and the Investor Recognition Hypothesis: International Evidence and Determinants,” concludes, “We study the existence and magnitude of the high-volume return premium across equity markets in 41 different countries and find that the premium is a strikingly pervasive global phenomenon. We find evidence that the premium is a significant presence in almost all developed markets and in a number of emerging markets as well.”

 

Volume Interprets Price

The second critical way in which volume provides information is by helping the technician interpret price. Volume enables the analyst to interpret the meaning of price through the lens of the corresponding volume. The authors Blume, Easley, and O’Hara (1994) reported in the Journal of Finance “Market Statistics and Technical Analysis: The Role of Volume”, “volume provides information on information quality that cannot be produced by the price static”. These researchers demonstrate how volume, information precision, and price movements relate, as well as how sequences of volume and prices can be informative. Moreover, they also show that traders who use information contained in market statistics do better than those trades who do not. Thus, technical analysis arises as a natural component of the agents learning process.

Nonetheless, price alone represents the vast majority of the work within technical analysis. Thus, this purpose of this paper is to grant the volume factor the significance volume is due as an essential element of investment analysis. However, doing so without also discussing price is also insufficient. Volume cannot be properly understood without price any more than price can be adequately assessed without volume. Independently, both price and volume convey vague market information. However, when examined together, they provide indications of supply and demand that neither could provide independently. Ying (1966), in his groundbreaking work on price-volume correlations, stated, “Price and volume of sales in the stock market are joint products of a single market mechanism; any model that attempts to isolate prices from volumes or vice versa will inevitably yield incomplete if not erroneous results.”  Two similar and related volume category types are tick based and volume weighted indicators.

 

Tick Based Indicators

An exchange market works much like an auction, where price is formed by two counter parties, each with a different opinion about the security’s future price direction, who agree to exchange a financial instrument. If the agreement occurs on an uptick, the buyer has applied more demand than the seller exerts to supply. Likewise, if the agreement occurs on a downtick, the seller’s actions wields greater force than those of the buyer. Through tick volume, one can decisively quantify the relationship between price and volume.

Don Worden, president and founder of Worden Brothers, developed the concept of Money Flow in the late 1950s under the name “Tick Volume.” Today, Money Flow is primarily popularized by Laszlo Birinyi. When investors use the term “tick,” they are referring to an individual trade. An uptick, or +tick, is a trade that occurs at a price higher than the previous trade. A downtick, or -tick, is a trade that occurs at a lower price than the previous trade. Tick volume refers to the volume of shares traded per tick. Tick volume analysis evaluates the change in price and volume on a tick-by-tick basis. Uptick volume is the volume that occurs on upticks. Likewise, downtick volume is the volume occurring on downticks. Where it gets muddy is in the common instance of trades that occur at the previous price – an unchanged tick. In such a scenario, the commonly accepted view is to treat the unchanged tick volume as if it were a part of the previous tick. Thus, if the previous tick was up, the unchanged tick’s volume would also be considered as uptick volume and vice versa.

Price-weighted tick volume uses tick data to weight each trade’s volume by its corresponding price. The upticks are subtracted from the downticks and accumulated over time.  In essence, Tick Volume/ Money Flow is volume weighted by the corresponding price accumulated on a tick-by-tick basis:

Tick Volume (aka Money Flow) = Cumulative Sum (Tick Price * Uptick’s Volume) – Cumulative Sum (Tick Price * Downtick’s Volume)

This calculation measures the supply relative to the demand on a per-trade basis and accumulates the difference over time. It reveals whether money is flowing into or out of the stock based on upticks being buys and downticks being sales. For example, we use two ticks to calculate Money Flow. The first tick goes through on an uptick of 100 shares at $100. Immediately, the next tick goes through on a downtick at $99.99 on 10,000 shares. The Money Flow is $10,000 (($100 *100 shares) – $999,900($99.99 * 10,000)), meaning that $989,900 (999,000 -10,000) more was sold than purchased in the stock. From this illustration, one can see how Money Flow wildly veers from the price direction by giving stronger weight to larger volume transactions. This information is used much in the same way as other volume indicators. When Tick Volume / Money Flow rises, it suggests demand is building, indicating the price might rise. When Tick Volume falls, it suggests that supply is building, an indication that the price might fall.

However, the increase in automation of the exchange markets combined with the decimalization of security prices has strongly reduced the reliability of this form of intraday analysis. Trades filled by scalpers and market makers are most often filled from existing inventories, making the concepts of accumulating up and downticks much more obscure. Additionally, institutions normally “work” their block trades throughout the course of the trading session making their activities less transparent to the public. Often this practice includes selling into upticks at the offer and buying into downticks at the bid further skewing the data.

The next development in tick based analysis was Volume-Weighted Average Price. The VWAP was first introduced to the trading community in the March 1988 Journal of Finance article, “The Total Cost of Transactions on the NYSE” by Stephen Berkowitz, Dennis Logue, and Eugene Noser.  VWAP is the average price at which investors have participated over a given time period, which is typically one trading day. This is calculated by multiplying and dividing the total by the number of shares traded: placing each price tick by the corresponding volume, and then summing the results of all these trades

VWAP = Sum of Trade’s Price * Trade’s Volume / Sum of Trading Volume

The VWAP is used more as a statistic than an indicator. It is the industry standard to determine a security’s accumulation or distribution throughout the trading session. VWAP is the benchmark utilized to compare the average price actually paid to the average price all investors paid for the stock throughout the trading day. Following the VWAP assists institutions in reducing the impact of their large trading operations.

The next innovation in this category of volume analysis is Volume Weighted Moving Averages or VWMAs. Volume weighted moving averages advance the concepts of both VWAP (tick based “reflections of time”) and Tick Volume (tick based accumulations) applying a much more flexible approach. Like tick volume and VWAP, VWMAs calculates average fund flows into and out of securities. Also, unlike tick-volume VMWA’s are not accumulation indicators. And unlike VWAP, VWMA’s are not reset in the beginning of a new trading period. Moreover, VWMAs can be either tick based or time based in its calculation, but more commonly time.

This example is in days but VWMAs can be set to any time frame (minutes, weeks, months), ticks or trading block sizes. The VWMA is calculated by weighting each frame’s (time, tick or block) closing price with the frame’s (time, tick or block) volume compared to the total volume during the range:

Volume-Weighted Average = Sum {Closing Price (I) * [Volume (I) / (Total Range)]}, where I = given action.

Because volume leads price, it makes sense to introduce volume into momentum indicators to make them even faster. Because volume confirms price trends, volume weighting can enhance trend indicator’s reliability. Likewise, because volume leads price, one can combine momentum with volume information to create indicators that provide quicker and more reliable signals. This leads us to the next innovation in volume weighting analysis, the Volume Price Confirmation Indicator or VPCI.

 

Volume Price Confirmation Indicator

Now what if there were a way to look deep inside price and volume trends to find out whether or not current prices are supported by volume? This is the objective of the Volume Price Confirmation Indicator (VPCI), a methodology that measures the asymmetry between price and volume trends.

Many technical indicators have been developed to decode the price volume relationship.  However, the key to grasping volume information is not the volume data alone or volume’s direct relationship with price movements. Rather, this interrelationship is best understood in the context of volume’s r

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MAC-V: Volatility Normalized Momentum

by Alex Spiroglou, CFTe, DipTA (ATAA)

About the Author | Alex Spiroglou, CFTe, DipTA (ATAA)

Alex Spiroglou is a quasi-systematic, cross-asset proprietary futures trader. His involvement with capital markets began in 1998, having worked for various proprietary trading and investment management firms in the UK and Greece. He is currently trading his own book, and is active in all major liquid futures markets, across all major asset classes (equity, interest rates, FX, commodities), while enjoying life with his family and the most amazing cat in the world (Greko), by the beautiful coast of South-East England.

Academic Background
Alex’s academic background began with a BSc in “Banking and International Finance” from City University Business School in London (1996). During those years he discovered technical analysis, which led him to specialize in that area. Eventually, this became his life-long passion. Since 2001 he holds the “Certified Financial Technician (CFTe)” accreditation by the International Federation of Technical Analysts (IFTA), and the “Diploma of Technical Analysis – DipTA (ATAA)”, administered by the Australian Technical Analysts Association (ATAA). Additionally, he holds the “Investment Management Certificate” (IMC) administered by the UK Society of Investment Professionals, as well as the “Market Maker/Trader” license administered by the Athens Derivatives Exchange and the “Investment Consultant license” administered by the Hellenic Capital Markets Commission.

Research Background
Alex over the years has built an extensive database of models and indicators, that includes inputs from Intermarket analysis, CoT, sentiment, and economic statistics, and thus developed a rules-based “Multiple timeframe, multiple factor” (MTMF) approach. His passion for research resulted in being an awarded Market technician, having received the NAAIM “Founders Award”, for advances in Active Investment Management (2022) and the CMT Association “Charles H. Dow Award”, for outstanding research in Technical Analysis (2022), for his paper “MACD-v: Volatility normalized momentum”.

Financial Industry
Alex enjoys being active in the Technical Analysis community. He was the founding Chairman of the London Chapter of the CMT Association (2010), one of the founding Co-Chairs of the Hellenic Chapter (2014), and continues to serve on the Advisory Board of the CMT Technical Analysis Educational Foundation. His involvement with CMT Association gave him the opportunity, to meet the greatest technicians of our time – Tom Demark, Ralph Acampora, John Bollinger, Larry Williams, Linda Raschke, and Martin Pring, to name a few.

Public Appearances
He has given presentations for various international Forums, Expos & Conferences, (London Money Show, London Traders Expo, etc). He has also done guest lectures/presentations for academic institutions in Britain and Europe, (City University, Macedonia University, etc) and interviews in local media TV, podcasts, magazines, and Journals

Latest Project
Finally, Alex is the Founder and CEO of SMART Trader Systems Ltd, London. A firm focused on the Training, Support & Development of Institutional Traders (primarily family office managers, emerging money managers, CTA’s) via a 15-step, rules-based Learning Path of quantified Technical and Macro strategies.  His Vision is to create a small, strong, Spartan-like, professional trader hub, whose members are willing to share ideas, techniques, and motivation because they realize that teamwork stands at the heart of great achievement.

He is a Happy husband and Family man, a caring cat dad, Global Macro Trader,  Awarded Market Technician & Energetic Entrepreneur – In that order…

He can be reached via his website www.AlexSpiroglou.com

Introduction

What is this topic about?

This paper will focus on the study of momentum using a very popular technical analysis indicator, the Moving Average Convergence Divergence (MACD), created by one of the most respected analysts of our time – Gerald Appel.[1]

This paper is comprised of 6 parts.

In the first section we will focus on the MACD itself. We will do a brief description of its construction, the most elementary ways to use it and then a review of the five limitations it has. This is a section that is familiar territory to all technicians.

In the second section, we will show a widely known suggestion to deal with these limitations, that does improve one, but does not solve all of them.

In the third and fourth sections we will present our own solution, which remedies the shortcomings, while creating unique advantages (edges) that would not be possible to obtain via the classic MACD.

In the last two sections, we will use our framework to improve existing tools in TA literature and explore new techniques.

 

Why does this topic matter to us?

Most price-based momentum indicators fall into -roughly- two camps:

Range Bound Oscillators

These operate within a finite range of values, usually 0 – 100 (e.g. RSI, Stochastics, Williams %R, etc.). They offer the advantage of having objectively defined momentum readings, while at the same time making these readings uniform across securities for cross market comparison purposes. On the other hand, the very fact that these tools can only obtain a limited range of values, presents problems during extended price trends, as their extreme readings (aka “overbought/overbought”) remain at high (or low) levels for a prolonged period of time, thereby giving many false signals. In fact some analysts have created some counterintuitive techniques, based on this phenomenon, whereby “overbought” is a sign of future strength, and “oversold” is a sign of future weakness.[2]  Oscillators are not trend friendly, and one could argue that these are not truly momentum measuring yardsticks, but range identification indicators. For example a 14 period stochastic oscillator states where you are, as a %, in a 14 period Donchian channel, and does not measure price momentum per se. Thus the terms “overbought, oversold” become a bit of a misnomer.

 

Trend-following Indicators

These measure price change over some period of time, and usually are boundless indicators (but not exclusively), as their readings can be increasing (or decreasing) along with price trends (eg. RoC, MACD, etc). Their very freedom makes it almost impossible to have objectively defined “overbought”, “oversold” levels, or have meaningful momentum comparisons between different asset classes (eg. individual equites vs currencies).

Of course the aforementioned categorization of indicators is not a fully detailed taxonomy, but a rather broad distinction for definitional purposes.

Irrespective of which family (category) of momentum tool is used, it would appear that in Technical Analysis literature, there is certainly no shortage of indicators.
One could even argue that there are more indicators than traders.

 

So, why attempt to build another tool?

It is not the author’s intention to simply design yet “another” indicator, that would provide approximately the same informational value as numerous ones already do so, thus resulting in a tool that exacerbates the already existent issue of indicator multicollinearity.

Our goal is to improve an existing tool (MACD), so that – by eliminating its shortcomings – we will be creating a unique type of hybrid “boundless oscillator”, that opens the doors for several pattern recognition opportunities which would not be definable using the classic MACD.

We are big believers in creating new techniques rather than new tools, thus we will use the improved MACD to define a general Momentum Lifecycle RoadMap (framework), new entry & exit techniques, and versatile cross asset (intermarket) strategies, among other uses, that would not be achievable via the venerable MACD.

 

MACD: A Measure of Momentum

Construction

One of the available tools to define momentum, is the Moving Average Convergence Divergence (MACD) indicator. The MACD was created by Gerald Appel in the late 1970’s. It is a trend-following momentum indicator that shows the relationship between two moving averages of prices.

The MACD is constructed in 4 steps:

Calculate a 12 bar Exponential Moving Average

Calculate a 26 bar Exponential Moving Average

MACD Line =  12 bar EMA – 26 bar EMA

Signal Line = 9 bar EMA of the MACD Line

Further to the MACD, Thomas Aspray in 1986 created the MACD Histogram, which is constructed as follows:

MACD Histogram = Signal Line – MACD Line

Thus in essence:

The 12 & 26 EMA’s are the 1st derivative of price

The MACD Line is the 2nd derivative of price

The Signal Line is the 3rd derivative of price

The MACD-H is the 4th derivative of price

The MACD is a versatile tool with many non-conventional uses, but it nevertheless has 5 key shortcomings.  Three of them are regarding the MACD values themselves and two have to do with signal line crossovers. Let’s see these in detail.

 

Limitation 1 – The MACD across time

By way of design, the MACD is an “absolute price indicator”, as it takes absolute price inputs (price MA’s), and produces an output (spread of raw price MA’s), without any kind of normalisation. This creates the following situation:

Although the MACD in 2020 has a bigger value than in 1957, that does not imply that the market has more momentum. That was simply a function of the underlying security having a larger absolute value when it was calculated in the second instance (2020) than the first (1978). The problem is exacerbated the further one goes back in time.

 

TABLE 1 MACD Ranges

S&P 500 1957- 1971 2019 – 2021
MACD Maximum  1.56 86.31
MACD Minimum   -3.3 -225.40

The implication of this is that MACD (and MACD Histogram) readings are not comparable across time for the same security, especially if the market in question has had substantial price appreciation or depreciation.

 

CHART 1 S&P 500 & MACD (1957 – 2021)

 

Limitation 2– The MACD across markets

The second limitation of the MACD and MACD Histogram is that they are not comparable across securities. Any differences in the indicator readings, are attributable to comparing securities that have different absolute values, rather than depicting varying levels of momentum strength.

For example, the MACD for the S&P 500 at the time of writing is 65
and for the Euro currency is -0.0070.

Again, this does not mean that the S&P has more momentum than the Euro, but its bigger MACD reading is a function of the bigger absolute price of the underlying security.

Cross market momentum comparisons are not possible, as it would be the case with -say- using a (0-100) scaled indicator. The RSI for the S&P and Euro in this instance would be directly comparable, but not for the MACD.

 

Limitation 3 – MACD Momentum LifeCycle

The MACD is an improved version of a moving average crossover system.
When a market is trending in a particular direction, the shorter term EMA responds quicker to price than the longer term EMA, moving away from (closer to) it, and consequently their difference / spread increases (decreases).  Thus, the MACD indicates the direction of momentum (bullish if above the signal line or bearish if below the signal line).  When this is viewed against the prevailing trend, it highlights momentum acceleration or deceleration, and the beginning and end of this process can be identified via signal line crossovers. Moreover the further away the MACD is from the equilibrium line, the stronger momentum is (please refer to Chart 4, bottom panel).

However, since MACD values are not comparable across time and across securities, it is impossible to standardize the intensity (strength) of (MACD-defined) momentum, into an objectively and quantitatively defined framework, where “High (fast) vs Low (slow)” and/or “overbought vs oversold” levels would exist.

 

Limitation 4 – Signal line accuracy

When directional strength is low, the MACD will be near the equilibrium line and/or close to the signal line. As such, signal line crossovers will be frequent, giving many (false) signals. This phenomenon is one of the “Achille’s heels” of trend-following system behavior in low momentum environments in general.

The MACD is no exception.

In chart 5, this is easily observed during the May to August 2016 period, where 6 loss producing crossovers signals occurred in a range bound, low momentum environment. As a consequence of limitation 3 (lack of momentum level scaling), these cannot be avoided by way of -say- rejecting the signals that occur within an objectively and quantitatively defined low momentum environment.

 

Chart 2  MACD behavior in low momentum – FTSE 100 (February – August 2014)

 

Limitation 5 – Signal line timing

When momentum is high, MACD signal accuracy is (one) of its main strengths.

However, when the market is pushing higher (lower) with too much force – to the point where the MACD line has built significant distance from the signal line- but then changes its trend to the downside (upside) abruptly, it takes some time before the lagging MA’s catchup to the new data (raw price), which translates into a directionally correct (accurate), but late (from a timing point of view) signal.

This phenomenon is more often observed in fast bearish trends, which then proceed to form a V-shaped bottom (when a counter-trend bounce occurs). Given the trend-following nature of the MACD, it is guaranteed that it will signal the turn, but it will produce a signal line cross over that maybe some distance away from the actual price bottom itself.

For example, the S&P 500 bottomed at 2532.69 on the 9th of February 2018, but the MACD signaled the turn at 2747.30 on the 23rd of February, which means it was “late” by 8.47%.

 

Chart 3 MACD in high momentum trend reversal- S&P 500 (Feb 2018)

Again, as a direct consequence of limitation 3 (and the lagging nature of the signal line), it is impossible to improve signal timing by first identifying a high momentum environment.

 

PPO: An improvement, but not a solution

Construction

A solution to deal with Limitations 1 & 2, is to normalize the readings of the MACD, so as to become comparable across time & securities.

A well-known suggestion is to place the raw MA spread as a function of the absolute price of the underlying security, so that momentum (MACD) is placed in context. This is then multiplied by 100, to obtain the output on a percent (%) basis.

Thus the formula for the MACD Line now becomes:

This resulting indicator is commonly known as the PPO (percent price oscillator).

Let’s see what the effect of the PPO on the MACD limitations is.

 

Chart 4 MACD & PPO – FTSE 100 (February to October 2016)

 

Limitation 1 – The PPO across time

Since the PPO readings are expressed on a percent basis, that means that they should be comparable across time for the same security on a “apples to apples” basis. Let’s confirm this by revisiting the S&P 500.

 

Chart 5 S&P 500 & PPO (1970 – 2021)

Although specific stationarity tests could be employed to prove the point, we can easily observe that the range of fluctuation (variable’s dispersion around zero) is more stable, as the MA spread is normalized on a percentage basis. In fact, if we set lower and upper boundaries in such a way that it contains 95% of the observations, since the 3rd of Feb 1975, the PPO has oscillated within 2% and -2%.

 

Table 2 PPO Ranges (S&P 500)

PPO Ranges > 2% 2% to -2% < – 2%
% of time 2.2% 94.3% 3.5%

 

The PPO retains all of the advantages that the MACD has, but also adds reading uniformity across time for the same security. It would appear that Limitation 1 is solved.

Limitation 2 – The PPO across markets

One would be tempted to assume that since the PPO is expressed on a percent (%) basis and it is comparable across time, then cross market comparisons would be also be feasible. However, upon closer inspection, it would appear that the PPO fails the test. Let’s see this via an example:

 

Chart 6 German Bund and PPO (1991 – 2021)

Using the aforementioned upper/lower boundaries used for the S&P 500, it would appear that the Bund has never traded above the upper level of 2% and never below the lower -2% level, in its entire history. It is evident that there is considerable variation in the data and in order to see where 95% of the PPO values for the Bund reside we would need to establish different levels.

 

Table 3 PPO Ranges (German Bund futures)

PPO Ranges > 0.7% 0.7% to -0.7% < – 0.7%
% of time 3.5% 93.6% 2.9%

 

Thus a PPO reading higher than 0.5% for the Bund would constitute a strongly trending environment. The same reading for the S&P would be indicative of an almost range bound market. What constitutes “high momentum” in one market, may very well be classified as “low momentum” in another.

 

Chart 7 Natural Gas futures and PPO (1990 – 2021)

The aforementioned differences become more pronounced as we examine a very volatile market such as Natural Gas futures.  Chart 7 depicts the PPO ranging most of the time (94.2%) from +7% to -7%.

 

Table 4 PPO Ranges (across markets)

NG – PPO Ranges > 7% 7% to -7% < – 7%
% of time 1.4% 94.2% 4.4%
SP 500 – PPO Ranges > 2% 2% to -2% < – 2%
% of time 2.2% 94.3% 3.5%
BUND – PPO Ranges > 0.7% 0.7% to -0.7% < – 0.7%
% of time 3.5% 93.6% 2.9%

 

Thus, it appears that the PPO is not a truly normalized momentum comparison tool for cross market purposes, as it fails to provide uniform benchmarks levels due to fact that markets may have significantly different volatility structures.

Limitation 3 – PPO Momentum Framework

Since the PPO cannot be standardized both across time AND securities, it is then not possible to deal with momentum level definition in a uniform framework.

It would be perhaps feasible on a – per individual market basis – to create levels where historically each market in question is deemed as “overstretched” or with adequate levels of trend strength, but this would not be practical as it would require massive amounts of optimization for an almost limitless universe of securities and the findings for each market would not be transferable to another.

 

Limitations 4, 5 – PPO Signal Line accuracy & Timing

Consequently, the lack of a uniform “high/low” momentum definitions, renders Limitations 4 & 5 unsolved under the PPO as well, as cross over signal filtering is not feasible

 

MACD-V: Volatility Normalized Momentum

Construction

Since “normalization by price” results in cross market momentum valuation discrepancies due to differences in volatility, then it would be preferable to normalize by volatility itself.

As the tool for the measurement of volatility, we will be using Welles Wilder’s Average True Range (ATR)

Thus the MACD line formula now becomes:

In order to distinguish the new indicator from the classic MACD, I will name it by adding a “V” at the end of the original name (“MACD-V”) and refrain from creating a completely new name altogether, so as to honour the original inventor.

Let’s examine now, how MACD-V measures against the five shortcomings of the classic MACD.

 

The MACD-V across time

We will be firstly checking how MACD-V behaves across time for the S&P 500.

 

Chart 8 S&P 500 and the MACD-V (1975 – 2021)

It is easily observable that MACD-V fluctuates within a finite range of a values around its equilibrium line (similar to the PPO’s behaviour). Any indicator reading discrepancies across time have been eliminated, – again – due to normalization.

If we try to find the range where 95% of the data fluctuate, and define the rest as “extremes”, then since February 1975, for the S&P 500 the MACDv oscillates between 150 and -150.

 

Table 5 MACD-V Ranges (S&P 500)

MACDv Ranges > 150 150 to -150 < – 150
% of time 4.4% 95% 0.6%

 

The MACD-V across markets

Will the MACD-V succeed where the PPO failed?

Does the range of 150 to -150, also hold 95% of the MACD-V values for other markets?
Below we feature the charts of the German Bund and Natural Gas futures and the levels.

The range of fluctuations for the two MACD-V’s is considerably more uniform than when comparing the equivalent ones for the two PPO’s. They essentially oscillate the same amount around the equilibrium line, as differences in volatility have been eliminated.
Slight & sporadic extremes are strictly attributable to strong momentum (prolonged moves in a particular direction), since the MACD -at its core- is a boundless indicator.

 

Chart 9 German Bund and the MACD-V (1990 – 2021)

 

Chart 10 Natural gas and the MACD-V (1990 – 2021)

 

Table 6 MACD-V Extreme Ranges (S&P 500, 1975 – 2021)

 

Table 7 MACD-V Extreme Ranges (Bund, 1991 – 2021)

 

Table 8: MACD-V Extreme Ranges (Natural Gas, 1990 – 2021)

All 3 markets share similar exhaustion levels (when momentum is 1.5 times its volatility), despite the fact that they have completely different absolute volatilities in general. In addition the Min and Max values differ for each market since the MACD-V is a boundless indicator, and not constrained by a, say, 0 to 100 scale.

 

MACD-V Ranges

Since MACD-V readings are comparable across time and markets, that means that we can create a Momentum Lifecycle RoadMap, that will rank both momentum’s direction (“bullish” or “bearish”), and strength as well (“low” vs “high” momentum, and “overbought” vs “oversold”). However the MACD-V since is an unbounded indicator it will have the added advantage that it will not be limited by the scaling boundaries (0-100) of conventional oscillators, and thus will avoid the problem of “pegging” at high levels.

OBOS (extreme) Momentum: When the market has advanced too far, too fast, the EMA spread will have reached a point where historically it becomes unstainable to progress any further in the short to intermediate term. This should be around 5% of the data, and is located when momentum is 1.5 or -1.5 times its volatility.

Strong (High) Momentum: When the market begins to gain some directional strength, then distance between the 2 EMA’s (12 & 26) begins to increase, as the shorter EMA is being driven away from the longer one, and thus the MACD-V would move significantly away from the equilibrium line. This should be around 35%-40% of the data, and is located when momentum is over +0.5 or -0.5 times its volatility.

Weak (Low) Momentum Range: When there is little directional conviction (low momentum), the MA’s (12 & 26) should be relatively close, and thus their spread (MACD-V) should be close to zero, the equilibrium line. This should be around 45% – 50% of the data, and is when momentum is between 0.5 or -0.5 times its volatility.

Based on this framework, we can test the objective momentum levels that would hold across securities, using the MACD-V.

 

Table 9 MACD-V Ranges (S& 500, 1975 – 2021)

Using data since 1975 (11,817 days) for the S&P 500, we observe that the index has been above the overbought benchmark (>150) around 4% of the time and below the oversold level (-150) around -1% of the time, reflecting the “upward drift” (bullish bias) of the market.  The time spent between the “neutral zone” that is close to the equilibrium line (50 to -50) is around 45% of the time. Finally, time spent on the strong momentum zone (50<x<150 & -150<x<-50) is respectively 36% and 14%, reflecting the bullish bias for the S&P 500.

Table 10 MACD-V Ranges (Bund, 1991 – 2021)

Using data on the German Bund (a fixed income market with different volatility characteristics) we observe that the data that fall into the aforementioned brackets are roughly the same with the S&P 500.

 

Table 11 MACD-V Ranges (Natural gas, 1991 – 2021)

Table 11 reflects the data for Natural gas. A market with completely different trend and volatility DNA. However the data support that again we have achieved a unified definition of “fast vs slow vs overbought/oversold” without having presented boundaries to the values that the indicators can have (eg. RSI, etc).

The extreme levels (>150 &  <-150) capture roughly 5% of the data in the market again, while the “fast” range (50-150 & -50 to -150) is around 50% of the data.

Based on this framework, we can test the objective momentum levels under different Trend Regimes and across markets.

 

MACD-V Ranges and Trend Regime Filter v.1

 

Table 12 MACD-V Ranges and Trend Regime Filter v.1 (S&P 500, 1975 – 2021)

If we were to dissect the MACD-V data by a basic trend rule (above or below a 200 EMA), we would see that the S&P 500 stands above the EMA 76% of the time, (i.e having an “upward drift”, bullish bias) and 24% below. Let’s examine how the MACD-V behaves in each of these conditions. A similar concept (observation) has been suggested by Andrew Cardwell (RSI range rules). Thus I will keep the same term (range rules) to study the behavior of the MACD-V.

All of the occurrences (100%) of the MACD-V reaching the overbought range have been recorded in the Bullish Stage, and it has never reached the oversold level while over the 200 EMA. While in the Bullish Stage, 99.4% of market action is contained with readings of the MACD-V > -100. If we observe the data more closely, 5% of the data on the downside are captured within the -50 to -150 range, thus becoming the “new” oversold level while the market stands above the 200 EMA. As long as the market stays above the 200 EMA, we would not expect it to fall below the – 100 range of the MACD-V.

Analogous behavior is observed on the Bearish Stage (< 200 EMA) as there are zero occurrences of the indicator reaching the overbought range (>150), and 100% readings of the oversold range. While in the Bearish Stage, 99.8% of market action is contained with readings of the MACD-V < 100, which is a quite similar number to the Bulls (99.4%).

Thus while the market is bearish (< 200 EMA) we would expect a maximum stretch, until the MACD-V reaches the 100 level (Bear Market Rally)

 

Table 13 MACD-V Ranges and Trend Regime Filter v.1 (Bund, 1991 – 2021)

Table 13 displays the data for the Bund. A market with different trend characteristics (i.e. > 200 EMA 67% of the time vs 76% of the time for the S&P 500) and certainly different volatility DNA. However the same observations (range rules) can be made.

While the market is in the Bullish Stage (> 200 EMA) it has 100% of the occurrences of overbought readings (>150), 0% of the oversold readings (<-150), and 98.9% of the data are captured by the >-100 level. Thus –similarly to the S&P 500 – any Bull Market decline can be expected to stop at the -100 MACD-V level (if the market is to stay above the 200 EMA).

Symmetrically for the Bearish Stage, it has 100% of the occurrences of oversold readings (<-150), 0% of the overbought readings (>150), and 99.8% of the data are captured by the <100 level. Thus –similarly to the S&P 500 – any Bear Market rally can be reasonably expected to stop at the 100 MACD-V level (if the market is to stay below the 200 EMA).

 

Chart 11 Bund and extreme MACD-V readings (1994 – 2021)

 

Table 14 MACD-V Ranges and Trend Regime Filter v.1 (Natural Gas, 1991 – 2021

The data for NG are even more compelling, as this market has completely different trend characteristics (spends an equal amount of time in Bullish/Bearish Stages, each one is 50% of the data) and is considerably more volatile than the aforementioned ones. However the exact same observations (range rules) can be made.

While the market is in the Bullish Stage (> 200 EMA) it has 100% of the occurrences of overbought readings (>150), 0% of the oversold readings (<-150), and 99.8% of the data are captured by the >-100 level. Thus –similarly to the S&P 500 – any Bull Market decline can be expected to stop at the -100 MACD-V level (if the market is to stay above the 200 EMA).

Symmetrically for the Bearish Stage, it has 100% of the occurrences of oversold readings (<-150), 0% of the overbought readings (>150), and 99.5% of the data are captured by the < 100 level. Thus, similarly to the S&P 500, any Bear Market Rally can be reasonably expected to stop at the 100 MACD-V level (if the market is to stay below the 200 EMA).

 

Chart 12 Natural gas and the Bear Market Rallies (2014 – 2016)

 

MACD-V Ranges and Trend Regime Filter v.1 & Swing Filters

Another way to help study the data even further would be to create a swing line, as an additional price filter and then observe where market tops & bottoms occur.

For the S&P 500, we will use a 3% swing line. Our personal preference for this type of filtering work is using swing based on ATR (not %’s), but for this study we will use percentage calculations, to keep things relatively simpler.

Table 15 records where these swing highs/lows are placed within the Trend Regime Filter v.1. Since 1975 the S&P 500 has made 651 swings that had a magnitude of 3% or more.  233 swing highs were recorded in the Bullish Stage and 93 in the Bearish Stage.

 

Table 15 3% Swing line Stats per Stage (S&P 500, 1975 – 2021)

We will provide more context to the total number of highs and lows per Stage, by relating them to the MACD-V

 

Table 16 3% Swing line Stats per MACD-V Ranges (S&P 500, 1975 – 2021)

Table 16 sheds more light. When the market is in the Bullish Stage, almost 60% of swing highs occur in the “Strong Momentum” Range (50 to 150) and almost all (99.1%) above the -100 range of the MACD-V. Similarly 72% of swing lows in the Bullish Stage occur in the weak momentum range (50 to -50), while almost all (99.7%) are above the -100 level for the MACD-V. This confirms the findings of tables 11 – 13, that should the market stay above the 200 EMA, then the “maximum” decline it can have should be around -100 of the MACD-V.

Table 17 3% Swing line Stats per MACD-V Ranges (S&P 500, 1975 – 2021)

Table 16 shows the data for the Bearish Stage, and they are analogous to the Bulls.

 

Table 18 Trend Regime Filter v.1, Swing line(1%) & MACD-V Stats (Bund, 1991 – 2021)

In order to study the Bund, we will use a 1% swing line, since the volatility for fixed income markets is considerably less than for their equity counterparts. However the results are very similar to the ones presented for the S&P 500. The range rules for one market are applicable across other markets as well.

 

Table 19 Trend Regime Filter v.1, Swing line(5%) & MACD-V Stats (NG, 1991 – 2021)

In order to complete our cross-market validation, we will present the same study for natural gas. The difference is with the swing line again. In this instance we employ a 5% swing filter, in order to deal with the elevated inherent volatility of this market.

The rest of the data lead to the same results, which we will leave to the reader to validate and explore further.

 

MACD-V Ranges and Trend Regime Filter v.2

The numbers in tables 11- 13, could be more insightful by using a more detailed Trend Regime Filter. The rules for Trend Regime Filter v.2 (Chart 13) were created –to our knowledge – by Chuck Dukas[3]. We will examine the Bullish Stages (1,2,3)

The swing line percentages will remain the same for each market.

 

Chart 13 MACD-V Ranges and Trend Regime Filter v.2

 

Table 20 MACD-V Ranges and Trend Regime Filter v.2, Stage 2 (S&P 500, 1975 – 2021)

These are the relevant numbers for the S&P 500, in Stage 2 (i.e. C >50>200). This time the maximum downside stretch of the MACD-V is -50, as the range 150 to -50 contains 99.8% of the data.

Thus if one thinks that on any pullback the market will not break the 50 EMA, then any dive that would cause the MACD-V > -50 would provide a definition of a Stage specific oversold level.


T
able 21 MACD-V Ranges, Trend Regime Filter v.2 (Stage 2) & 3% Swings (S&P 500, 1975 – 2021)

The table above shows that out of the 233 swing highs above the 200 EMA, 87.1% of these (203) have occurred in Stage 2 (C > 50 EMA > 200 EMA). The vast majority of these (59.6%) where in the 50-150 range of the MACD-V, while around 10% occurred while in the overbought range.  Almost all of the highs (99.5%) where over the -50 range of the MACD-V.

Turning our attention to swing lows in Stage 2, these are really rare events as we have seen 29 occurrences, in the past 46 years. 100% of these were over the -50 range of the MACD-V.

It would seem that if one expects a larger than 3% correction, that would not extend below the 200 EMA, then the odds greatly favour that the S&P 500 would breach the 50 EMA (Stage 3) and the MACD-V to be in the -50 to -50 range (or -50 to -100 in the case of stronger corrections).

 

Table 22 MACD-V Ranges and Trend Regime Filter v.2, Stage 3 (S&P 500, 1975 – 2021)

When the market has progressed into Stage 3, the vast majority of times (72.4%) the MACD-V is in the neutral range (50 to -50). In quite rare occurrences we may have a dip below the -100 level, but it would be an exception as 96.7% of the values in the Stage are above that.

 

Table 23 MACD-V Ranges, Trend Regime Filter v.2 (Stage 3) & 3% Swings (S&P 500, 1975 – 2021)

When the market has slided below the 50 EMA, in the vast majority of cases, the reversal swings associated in the Stage are lows (101) vs highs (11).  A notable statistic is that 82.2% of the swing lows that occur in this Stage are in the “neutral zone” of 50 to – 50 and a few extend to the -50 to -150 range. In total 97% of swing lows in Stage 3, occur over the -100 range of the MACD-V.

Thus pullbacks into this Stage could end in the aforementioned ranges, for a possible resumption of the trend.

 

Table 24 MACD-V Ranges and Trend Regime Filter v.2, Stage 1 (S&P 500, 1975 – 2021)

Stage 1 does not occur very often, or rather does not register for long. It is usually an explosive move to the upside coming off of a low. Hence it is the only stage (except 2) that manages to drive the market into the overbought zone (>150). In the vast majority of cases the market is in the “fast” range of the MACD-V (50 to 150), and in 100% of the cases the MACD-V stays above -50

 

Table 25 MACD-V Ranges, Trend Regime Filter v.2 (Stage 1) & 3% Swings (S&P 500, 1975 – 2021)

There aren’t many reversals (swings) occurring in this Stage and almost all are high (19) vs lows (2) in the 46 year history of the data. Notable stats are that these aforementioned highs occur in the 50 to 150 range of the MACD-V (73.7% of the occurrences).

The following pages will display the same studies for the Bund and Natural Gas markets. They exhibit similar behavior, thus we will leave it up to the readers to dive deeper into the data, without our commentary. Please note that we used a 1% swing line for the Bund and a 5% swing line for natural gas, to account for different volatility levels. Moreover in our private work, we use ATR-based swing lines and more sophisticated Trend Regime Filters.

 

Table 26 Trend Regime Filter v.2 – Key statistics (Bund, 1991 – 2021)

 

Table 27 Trend Regime Filter v.2 – Key statistics (Natural gas, 1991 – 2021)

 

MACD-V Momentum Lifecycle RoadMap

At this stage we can introduce the signal line (9 period EMA of the MACD line) as it is the tool that signals changes in momentum. The signal line is guaranteed to highlight momentum shifts, but its lagging nature does so at the expense of accuracy and timing sometimes  (please refer to parts 2.5 and 2.6). Thus we chose to replace it with another tool, that deals (to some extent) with the aforementioned issues. However, we made a conscious choice not to present the modifications we have made on the signal line, and just focus on the MACD line, as the length of this paper would increase significantly in length.  Therefore henceforth any mention of the signal line assumes that we would use the 9 period EMA.

Table 28 presents the Ranges and how the MACD-V line relates to the signal line.

There are in total 8 ranges that the MACD-V can take, which can of course can be easily programmed in any language of your choice (python, amibroker AFL, etc).

 

Table 28 MACD-V & Signal Line combinations

RANGE ABOVE SIGNAL LINE BELOW SIGNAL LINE
> 150 Risk
50 < x < 150 Rallying Retracing (in price or time)
-50 < x < 50 Ranging Ranging
-150 < x < -50 Rebounding Reversing
-150 < Risk

 

Chart 14 MACD-V Momentum Lifecycle RoadMap

This opens up new and unexplored opportunities to use the MACD. Up until today the MACD could be used either in 2 ways, either above/below the signal line, and/or above/below the 0-line.  The MACD-V now presents us with 8 different scenarios to explore, and of course these are multiplied in the case of cross asset comparisons.

 

MACD-VH: Volatility Normalized Histogram

Further to the MACD, Thomas Aspray in 1986 created the MACD Histogram, which is constructed as follows: MACD Histogram à Signal Line à MACD Line.

Since the MACD line has (now) been normalized, similar properties should also be shared by the 4th derivative of price, the MACD-V Histogram (MACD-VH). That means that it is possible to detect indicator levels which are associated with short term extreme price levels. This is a unique property of the MACD-VH, as thus far the applications of the MACD Histogram were confined to comparisons of the height of each bar of the histogram relative to the preceding ones (higher vs lower), and not relative to the absolute level that each bar has.

It appears that when the MACD-VH is above 40 (or below – 40), that would imply that the market is mildly stretched to the upside (downside).

 

Chart 15 MACD-VH Momentum Lifecycle RoadMap

 

Table 29 MACD-VH extreme levels for 3 markets

 

Chart 16 MACD-VH Mildly Overbought / oversold (>40, <-40)
(FTSE 100, 2014 – 2015)

 

Chart 17 MACD-VH Mildly Overbought / oversold (>40, <-40)
(FTSE 100, 2015 – 2016)

 

Epilogue

This paper is the definition of “standing on the shoulders of giants”, as it would not have been possible without the knowledge shared by esteemed technicians, past and present.

I sincerely hope that we have added a small brick on the huge wall of the Body of Knowledge of Technical Analysis.

 

References

Appel, Gerald. “Technical Analysis: Power Tools for Active Investors”, FT Press, Reprint Edition (2005).

Demark, Tom. “The New Science of Technical Analysis”, Wiley; 1st edition (2007).
Dukas ,Chuck. “The TrendAdvisor Guide to Breakthrough profits”, John Wiley & Sons, 1st edition (2006).

Raschke, Linda. “Trading Sardines”, Self-published (2018).

Elder, Alex. “Come Into My Trading Room”, Wiley; 1st edition (2002).

Investopedia. “Average True Range (ATR)”, https://www.investopedia.com/terms/a/atr.asp

[1] Gerald Appel – “Technical Analysis: Power  tools for active investors”, p. 165 – 200

2 Tom Demark – “The New Science of Technical Analysis”, p. 89

[3] “The TrendAdvisor Guide to Breakthrough profits”, Chuck Dukas

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