Editor’s note: in recent years, technical analysis has been a popular research topic. In this paper, the authors found that technical analysis can be used to generate profits in the markets. Among the papers published recently is A New Anomaly: The Cross-Sectional Profitability of Technical Analysis by Yufeng Han, Ke Yang and Goufu Zhou. The full paper is available at SSRN or by clicking here.
Abstract: In this paper, we document that an application of a moving average timing strategy of technical analysis to portfolios sorted by volatility generates investment timing portfolios that often outperform the buy-and-hold strategy substantially. For high volatility portfolios, the abnormal returns, relative to the CAPM and the Fama-French three-factor models, are of great economic significance, and are greater than those from the well known momentum strategy. Although both the moving average timing and momentum strategies are trend-following strategies, their performances are surprisingly uncorrelated and behave differently over the business cycles. In addition, the abnormal returns cannot be explained by market timing ability, investor sentiment, default and liquidity risks.
Introduction
Technical analysis uses past prices and perhaps other past data to predict future market movements. In practice, all major brokerage firms publish technical commentary on the market and many of their advisory services are based on technical analysis. Many top traders and investors use it partially or exclusively (see, e.g., Schwager, 1993, 1995; Covel, 2005; Lo and Hasanhodzic, 2009). Whether technical analysis is profitable or not is an issue discussed in empirical studies going as far back as Cowles (1933) who found inconclusive evidence. Recent studies, such as Brock, Lakonishok, and LeBaron (1992) and Lo, Mamaysky, and Wang (2000), however, find strong evidence of profitability when using technical analysis, primarily of using a moving average scheme, to forecast the market. More recently, Neely, Rapach, Tu and Zhou (2011) find that the stock market forecasting power of technical analysis is as good as using economic fundamentals. From a theoretical point of view, Zhu and Zhou (2009) demonstrate that technical analysis can be a valuable learning tool under uncertainty about market dynamics.
Our paper provides the first study on the cross-sectional profitability of technical analysis. Unlike existing studies that apply technical analysis to either market indices or individual stocks, we apply it to volatility decile portfolios, i.e., those portfolios of stocks that are sorted by their standard deviation of daily returns. There are three factors that motivate our examination of the volatility decile portfolios. First, we view technical analysis as one of the signals investors use to make trading decisions. When stocks are volatile, other signals, such as earnings and economic outlook, are likely to be imprecise, and hence investors tend to rely more heavily on technical signals. Therefore, if technical signals are truly profitable, this is likely to show up for high volatility stocks rather than for low volatility stocks. Second, theoretical models, such as Brown and Jennings (1989), show that rational investors can gain from forming expectations based on historical prices and this gain is an increasing function of the volatility of the asset. Third, our use of technical analysis focuses on applying the popular technical tool, the moving averages, to time investments. This is a trend-following strategy, and hence the profitability of the strategy relies on whether there are detectable trends in the cross-section of the stock market. Zhang (2006) argues that stock price continuation is due to under-reaction to public information by investors, and investors will under-react even more in case of greater information uncertainty which is well
approximated by asset volatility. Therefore, to understand the cross-sectional profitability of technical analysis, it is a sensible starting point to examine the volatility decile portfolios.
We apply the moving average (MA) strategy to 10 volatility decile portfolios formed from stocks traded on the NYSE/Amex by computing the 10-day average prices of the decile portfolios.[2] For a given portfolio, the MA investment timing strategy is to buy or continue to hold the portfolio today when yesterday’s price is above its 10-day MA price, and to invest the money into the risk-free asset (the 30-day Treasury bill) otherwise. Similar to the existing studies on the market, we compare the returns of the 10 MA timing portfolios with the returns on the corresponding decile portfolios under the buy-and-hold strategy. We define the differences in the two returns as returns on the MA portfolios (MAPs), which measure the performance of the MA timing strategy relative to the buy-and-hold strategy. We find that the 10 MAP returns are positive and are increasing with the volatility deciles (except one case), ranging from 8.42% per annum to 18.70% per annum. Moreover, the CAPM risk-adjusted returns, or the abnormal returns, are also increasing with the volatility deciles (except one case), ranging from 9.34% per annum to 21.95% per annum. Similarly, the Fama-French risk-adjusted returns also vary monotonically (except one case) from 9.83% per annum to 23.72% per annum.[3] In addition, the betas are either negative or negligibly small, indicating that the MAPs have little (positive) factor risk exposures.
How robust are the results? We address this question in four ways. First, we consider alternative lag lengths, of L = 20, 50, 100 and 200 days, for the moving averages. We find that the abnormal returns appear more short-term with decreasing magnitude over the lag lengths, but they are still highly economically significant with the long lag lengths. For example, the abnormal returns range from 7.93% to 20.78% per annum across the deciles when L = 20, and remain mostly over 5% per annum when L = 200. Second, we also apply the same MA timing strategy to the commonly used value-weighted size decile portfolios from NYSE/Amex/Nasdaq, which are a proxy of the volatility deciles. Excluding the largest size decile or the decile portfolio that is the least volatile, we obtain similar results that, when L = 10, the average returns of the MAPs range from 9.82% to 20.11% per annum, and the abnormal returns relative to the Fama-French model range from 13.70% to 21.87% per annum. Third, we examine the trading behavior and break-even transaction costs. It turns out that the MA timing strategy does not trade very often and the break-even transaction costs are reasonably large. Finally, we assess the performance over subperiods and find that the major conclusions are unaltered.
The abnormal returns on the MAPs constitute a new anomaly. In his extensive analysis of many anomalies published by various studies, Schwert (2003) finds that the momentum anomaly appears to be the only one that is persistent and has survived since its publication. The momentum anomaly, published originally in the academic literature by Jegadeesh and Titman (1993), is about the empirical evidence that stocks which perform the best (worst) over a three- to 12-month period tend to continue to perform well (poorly) over the subsequent three to 12 months. Comparing the momentum with the MAPs, the momentum anomaly earns roughly about 12% annually, substantially smaller than the abnormal returns earned by the MA timing strategy on the highest volatility decile portfolio. Furthermore, interestingly, even though both the momentum and MAP anomalies are results of trend following, they capture different aspects of the market because their return correlation is low, ranging from -0.01 to 0.07 from the lowest decile MAP to the highest decile MAP. Moreover, the MAPs generate economically and statistically significant abnormal returns (alphas) in both expansion and recession periods, and generate much higher abnormal returns in recessions. In contrast, the momentum strategy fails to generate any risk-adjusted abnormal returns during recessionary periods. In short, despite the trendfollowing nature of both strategies, the MAP and momentum are two distinct anomalies.[4]
To understand further the abnormal returns on the MAPs, we address two more questions. First, we analyze whether the strategy has any ability in timing the market, and whether there is still abnormal returns after controlling for this ability. We find that there is certain timing ability, but the abnormal returns remain after controlling for it. Second, we examine whether the abnormal returns can be explained by a conditional version of the Fama-French model (see, e.g., Ferson and Schadt (1996)). We find that returns on the MAPs are not sensitive to changes in investor sentiment and P´astor and Stambaugh (2003) liquidity factor, but have lower market betas in recessions and higher betas during periods with higher default risk. Nevertheless, the abnormal returns are robust, and remain statistically and economically significant.
The rest of the paper is organized as follows. Section II discusses the investment timing strategy using the MA as the timing signal. Section III provides evidence for the profitability of the MA timing strategy. Section IV examines the robustness of the profitability in a number of dimensions. Section V compares the momentum strategy and the MA timing strategy over the business cycles and examines the sensitivity of the abnormal returns to economic variables. Section VI provides concluding remarks.
The Moving Average Timing Strategies
We use one set of 10 volatility decile portfolios and one set of 10 size decile portfolios in this paper. All of the data are readily available from the Center for Research in Security Prices (CRSP). More specifically, the first set is constructed based on the NYSE/Amex stocks sorted into ten groups (deciles) by their annual standard deviations estimated using the daily returns within the year.[5] Once stocks are assigned to portfolios, portfolio index levels (prices) and daily returns are calculated via equal-weighting.[6] The portfolios are rebalanced each year at the end of the previous year. The second set is the 10 value-weighted size decile portfolios sorted by firm size with stocks traded on the NYSE/Amex/Nasdaq. Similar to the volatility deciles, the size deciles are ranked using the firm size at the end of the previous year and rebalanced each year. The sample period for both the volatility decile portfolios and the size decile portfolios is from July 1, 1963 to December 31, 2009 to coincide with the Fama-French factors.
Denote by Rjt (j = 1, . . . , 10) the returns on either of the two sets of decile portfolios, and by Pjt (j = 1, . . . , 10) the corresponding portfolio prices (index levels). The moving average (MA) at time t of lag L is defines as
which is the average price of the past L days. Following, for example, Brock, Lakonishok, and LeBaron (1992), we consider 10-, 20-, 50-, 100- and 200-day moving averages in this paper. The MA indicator is the most popular strategy of using technical analysis and is the focus of study in the literature. On each trading day t, if the last closing price Pjt−1 is above the MA price A jt−1,L, we will invest in the decile portfolio j for the trading day t, otherwise we will invest in the 30-day Treasury bill. So the MA provides an investment timing signal with a lag of one day. The idea of the MA is that an investor should hold an asset when the asset price is on an uninterrupted up trend, which may be due to a host of known and unknown factors to the investor. However, when the trend is broke, new factors may come into play and the investor should then sell the asset. Its theoretical reasons and empirical evidence will be examined in the next section.
Mathematically, the returns on the MA timing strategy are
where Rjt is the return on the j-th volatility decile portfolio on day t, and rft is the return on the risk-free asset, the 30-day Treasury bill. Similar to existing studies on the performance of the market timing strategy relative to the buy-and-hold strategy of the market portfolio, we focus on the cross-sectional profitability of the MA timing strategy relative to the buy-and-hold strategy of the volatility decile portfolios. In other words, we focus on how Ṝ jt,L outperforms Rjt; that is, we will be interested in the difference Ṝ jt,L – Rjt. Because the performance of this difference depends on the usefulness of the MA signal, we call the difference the return on the MA portfolio (MAP). With the 10 decile portfolios, we thus obtain 10 MAPs,
A MAP can also be interpreted as a zero-cost arbitrage portfolio that takes a long position in the MA timing portfolio and a short position in the underlying volatility decile portfolio. The abnormal performance of the MAPs indicate the profitability of the MA investment timing strategy.
Profitability of the Moving Average Portfolios
In this section, we provide first the summary statistics of the volatility decile portfolios, the 10-day MA timing portfolios, and the corresponding MAPs, and then the alphas (abnormal returns) of the MAPs, which reveal strong evidence of the cross-sectional profitability of the MA timing strategy. Finally, we explore some explanations for the profitability.
Summary Statistics
Table I reports the basic characteristics of the returns on the decile portfolios, Rjt, the returns on the 10-day MA timing portfolios, Ṝ jt,L,10, and the returns on the corresponding MAPs, MAPjt,10.
Panel A provides the average return, the standard deviation, the skewness, and the Sharpe ratio of the buy-and-hold strategy across the ten volatility deciles. The returns are an increasing function of the deciles, ranging from 10.81% per annum for the lowest decile to 44.78% per annum for the highest decile.[7] The last row in the table provides the difference between the highest and the lowest deciles. Similarly, the MA timing portfolios, reported in Panel B, also have returns varying positively with the deciles, ranging from 19.22% to 60.51% per annum.[8] In addition, the returns on the MA timing portfolios not only are larger than those on the decile portfolios, but also enjoy substantially smaller standard deviations. For example, the standard deviation is 4.16% versus 6.82% for the lowest decile, and 14.41% versus 20.29% for the highest decile. In general, the MA timing strategy yields only about 65% volatility of the decile portfolios. As a result, the Sharpe ratios are much higher for the MA timing portfolios than for the volatility decile portfolios, about four times higher in general. Furthermore, while the volatility decile portfolios display negative skewness (except for the highest volatility decile), the MA timing strategy yields either much smaller negative skewness or positive skewness across the volatility deciles. Panel C reports the results for the MAPs. The returns increase monotonically from 8.42% to 18.70% per annum across the deciles (except for the highest volatility decile). While the standard deviations are much smaller than those of Rjt in the corresponding deciles, they are not much different from those of Ṝ jt,L. However, the skewness of the MAPs across all deciles is positive and large. In the last column of Panel C, we report the success rate of the MA timing strategy, which is defined as the fraction of trading days when the MA timing strategy is on the ”right” side of the market, i.e., it is out of the market when the decile returns are lower than the risk-free rate; it is in the market when the decile returns are higher than the risk-free rate. The success rate is about 60% across the deciles, indicating good timing performance of the MA timing strategy.
The simple summary statistics clearly show that the MA timing strategy performs well. The MA timing portfolios outperform decile portfolios with higher Sharpe ratios by having higher average returns and lower standard deviations. Furthermore, the MA timing portfolios have either less negative or positive skewness, and in particular the MAPs all have large positive skewness and above 50% success rates, which suggests that more often than not the MA timing strategy generates large positive returns. However, it is unclear whether the extra returns can be explained by a riskbased model. This motivates our next topic of examining their portfolio return differences, the MAPs, in the context of factor models.
Editor’s note: additional tests and statistics are found in the paper. They support the conclusion are omitted for brevity.
Concluding Remarks
In this paper, we document that a standard moving average of technical analysis, when applied to portfolios sorted by volatility, can generate investment timing portfolios that outperform the buy-and-hold strategy greatly, with returns that have negative or little risk exposures on the market factor and the Fama-French SMB and HML factors. Especially for the high volatility portfolios, the abnormal returns, relative to the CAPM and the Fama and French (1993) threefactor models, are high, and higher than those from the momentum strategy. While the moving average strategy is a trend-following one similar to the momentum strategy, its performance has little correlation with the momentum strategy, and behaves differently over business cycles. Furthermore, the abnormal returns are not sensitive to changes in investor sentiment, default and liquidity risks.
Our study provides new a research avenue in several areas. First, our study suggests that it will be likely fruitful to examine the profitability of technical analysis in various markets and asset classes by investigating the cross-sectional performance, especially focusing on the role of volatility. Given the vast literature on technical analysis, potentially many open questions may be explored and answered along this direction. Second, our study presents an exciting new anomaly in the finance literature. Given the size of the abnormal returns and the wide use of technical analysis, explaining the moving average anomaly with new asset pricing models will be important and desirable. Thirdly, because of its trendfollowing nature, various investment issues that have been investigated around the momentum strategy can also be investigated with the moving average strategy. All of these are interesting topics for future research.
References are available in the original document which is available at SSRN or by clicking here.
[2] We obtain similar results with volatility deciles formed from stocks traded on the Nasdaq or NYSE, respectively.
[3] These major results are replicated by a conference discussant, PhD students from top universities and practitioners around the world.
[4] Han and Zhou (2011) explore how technical analysis can help to enhance the popular momentum strategy.
[5] In CRSP, portfolio (decile) one contains the stocks with the highest standard deviation. We follow the convention of published studies on sorted portfolios by reversing the order, so our portfolio (decile) one contains the stocks with the lowest standard deviation.
[6] CRSP does not have value-weighted volatility decile portfolios while the value-weighting is an interesting alternative, which is the reason we also analyze the value-weighted size decile portfolios below.
[7] Ang, Hodrick, Xing, and Zhang (2006) document a negative relation between lagged idiosyncratic volatility and future returns, while Han and Lesmond (2011) argue that the negative relation is due to liquidity bias in the estimation of idiosyncratic volatility, and Huang, Liu, Rhee, and Zhang (2009) argue that the negative relation is due to return reversal. However, positive contemporaneous relation between stock returns and volatilities (on both the aggregate market and individual stock level) has been supported by both theory (e.g. Merton, 1973, 1987; Malkiel and Xu, 2004) and empirical evidence (e.g. Lehmann, 1990; Malkiel and Xu, 2004; Spiegel and Wang, 2005; Ghysels, Santa-Clara, and Valkanov, 2005; Fu, 2009).
[8] To put the performance of the volatility decile portfolios and MA timing portfolios in perspective, the equal-weighted NYSE/Amex index has an average return of 17.45% per annum, and a standard deviation of 13.53% per annum in the same period. Therefore, even the lowest decile of the MA timing portfolios earns higher returns than the equal-weighted index, while the returns of the lowest four volatility deciles are lower than those of the index. The standard deviation of all the MA timing portfolios is also smaller than that of the index except for the highest decile.
