Issue 74, Fall 2024

Abstract

The Bullish Percent Index (BPI), a market breadth indicator that has existed since the mid-1950s, is extolled for its value as a technical analysis tool in several books, magazine articles, and internet sources. Despite its history and the availability of resources on it, there is a lack of scholarly analysis on the merits of the BPI. This study applies statistical analysis to the BPI to determine its timeliness, accuracy, and profitability as a technical analysis tool. The findings indicate that the BPI is more effective at identifying market troughs than peaks. Specifically, the results show that the index can be used successfully as a long entry indicator when the BPI indicator is below 30. However, at the high end of the scale, the BPI fails to provide timely, accurate, or profitable exit signals.

Introduction

The Bullish Percent Index (BPI) has been lauded as the “greatest market indicator,”1 “the absolute best market indicator,”2 and “the most important indicator.”3 These are high praises of a single indicator that require evidence to support such claims. There are several means to measure the quality of any technical analysis indicator, but as a general statement, every useful indicator provides timely, accurate, and profitable trading and investing signals.

This paper uses statistical analysis to evaluate the BPI in light of these criteria. The timeliness of a technical indicator is related to how quickly an indicator provides a usable signal at an opportune time to get into or out of a trade. Accuracy is associated with how closely an indicator gives a signal to the actual start and/or end of a move. Accuracy is also measured by how often the indicator gives a false signal or fails to give a signal when it should. Profitability is determined by the consistency with which an indicator generates an economic alpha above some baseline or expected return. If the BPI is truly timely, accurate, and profitable, it may live up to its reputation as a great market indicator.

The rest of this paper is divided into six major sections. First, I provide some background on the BPI along with a short literature review of relevant books, articles, and media. Next, I describe the data used in this paper, followed by the methodology used to analyze the data. The results of the analysis are explained in the next section. In the last two sections, I summarize my findings and give my conclusions along with some suggestions for future research.

Background and Literature Review

Background and History

The history of the Bullish Percent Index begins in the mid-1940s with Earnest Staby’s search for “a soulless barometer.”4 Although Staby was unable to develop such an indicator, he laid the groundwork for Abe W. Cohen of ChartCraft to eventually create the Bullish Percent Index in 1955.5 Earl Blumenthal and Mike Burke continued to improve the BPI in the 1970’s and 80’s.6
As a market breadth indicator, the BPI is designed to gauge market risk levels on a scale of zero to one hundred. In general, when the BPI is low—below 30 is the traditional level—investors should take a long position because market risk is low, or oversold. In contrast, when the BPI is high—above 70—investors should look to exit long positions because the risk is high or overbought.7 While the actual employment of the BPI within a trading or investing system is more nuanced than what I describe here, this simplified explanation is sufficient for the purposes of this paper.

The BPI is derived from the Point and Figure (PnF) charts of all stocks in a particular index. While the BPI is based on the PnF charts of index components, the BPI itself can be plotted in either a PnF chart or a traditional time-based chart. Traditionally analysts have utilized the BPI PnF chart as part of their decision-making process, but more recently, practitioners have employed additional technical analysis indicators such as moving averages, oscillators, and candlestick patterns on time-based BPI charts. Both methods present advantages and disadvantages. Further details on how the BPI is generated can be found in Thomas Dorsey’s book, Point and Figure Charting: The Essential Application for Forecasting and Tracking Market Prices. Dorsey’s work represents the preeminent text on the background and uses of the BPI.

Books

In addition to Point and Figure Charting, Dorsey discusses the BPI in Tom Dorsey’s Trading Tips: A Playbook for Stock Market Success. An entire chapter is dedicated to bullish percent in Jeremy du Plessis’s book The Definitive Guide to Point and Figure. Du Plessis details how to use the BPI in both PnF form and in line chart form.8 He also covers bullish percent usage in 21st Century Point and Figure. Dorsey’s and du Plessis’s works compose the foundational resources of the BPI.

Du Plessis and Dorsey use different indexes as the basis for BPI in their books. Du Plessis focuses on European stocks such as the Financial Times Stock Exchange (FTSE) All Share Index (ASX) in the United Kingdom and the Deutscher Aktienindex (DAX) in Germany as examples of BPI in his books. While Dorsey’s aforementioned praise of the BPI arose in reference to the New York Stock Exchange (NYSE) Bullish Percent Index (the BPNYA), he also uses the over-the-counter (OTC) BPI as one of his primary market indicators. In addition, Dorsey discusses several secondary market indicators including the Bullish Percent Indexes of the S&P 500 (known as the BPSPX), the Nasdaq composite (the BPNDX), and sector and international indexes.

Dorsey spends several pages discussing how to use various sector BPIs to rotate investment dollars. This rotation involves reallocating assets from areas of high risk to areas of low risk to improve a portfolio’s return-to-risk ratio and outperform the market. The basic concept is relatively simple: Even though the overall market may be rising, and the BPI with it, the BPI of some sectors may rise faster than others; investors can potentially enhance their returns by moving money out of sectors that have crossed into a high-risk area (above 70) and into sectors with much lower risk.
Although Dorsey predominately relies on the BPNYA, this paper analyzes the BPSPX. Analysis of the BPSPX offers several advantages over the BPNYA: 1) the S&P 500 is the most followed index in the world10, and 2) while the BPNYA boasts a larger number of stocks, the BPSPX includes over 150 widely owned and heavily traded stocks that are not in the NYSE. The smaller number of stocks and the inclusion of non-NYSE stocks means that, in general, the BPSPX moves marginally faster than the BPNYA. Despite these differences, the application and outcome of the two BPIs are very similar.

Other Media

In addition to Dorsey and du Plessis’s books, a few magazines and newspapers have published pieces about the BPI. In their articles, Wayne Thorpe11 and Ron Walker12 build on Dorsey’s and du Plessis’s foundation and highlight additional ways to use the BPI. Additionally, articles published by Forbes and The Wall Street Journal have referenced various BPI indicators or included interviews with traders who use BPI to make trading decisions.

Numerous other websites and internet videos discuss bullish percent. Two of the best sites about BPI are ChartSchool from StockCharts14 and PnF University from Dorsey Wright and Associates.15 The series Market Misbehavior with David Keller, CMT 16 and the StockCharts TV videos on BPI represent some of the best video sources on the topic.

Motivation for Research

Despite the BPI’s lengthy history, there is a noticeable gap in academic research on the index’s merits. My survey of the available literature failed to identify any peer-reviewed papers on the BPI’s usefulness as a technical analysis tool. This study, therefore, aims to begin the process of filling this substantial knowledge gap via a simple statistical analysis of the BPI.

Data

The daily BPSPX levels for this study are drawn from StockCharts.com18. With this data, the BPSPX can be charted every trading day since January 11, 1996, except for September 27, 2023. The data may be charted as either a traditional timeline-based chart (line, bar, candlestick, etc.) or as a PnF chart. In this paper, I utilize all of the data available through October 31, 2023, for a total of 6,999 daily closing levels of the BPSPX.
The S&P 500 levels are from Yahoo! Finance.19 In order to calculate the annual, 6-month, 3- month, and 1-month returns from January 11, 1996, I collected the S&P 500 levels beginning on January 11, 1995. I also calculate daily returns (from previous close to current close) starting on January 11, 1996 to match the beginning of the BPSPX series. Table 1 provides summary statistics of both the daily S&P 500 returns and the BPSPX series.

Table 1: Summary Statistics of BPSPX and S&P 500 Daily Returns from January 1996 to October 2023

In Table 1, both the median and the mean of the BPSPX are above 60. This indicates that between January 1996 and October 2023 the market was bullish a majority of the time. Likewise, daily S&P 500 returns are slightly positive; the mean annualized daily return is around 9%. This does not include dividends.

The distribution of the daily BPSPX levels is displayed in Figure 1 using a bin size of 1. The mean and median from Table 1 are marked in the figure with vertical lines, as are the traditional risk levels of 30 and 70 and more extreme risk levels of 20 and 80.

Figure 1: Distribution of BPSPX Observations

The vast majority of observations (approximately 74%) are between 48 and 80. There is also a cluster of observations from 82 to 84 that form an additional small peak. The bin with the largest number of observations is the 74 to 75 bin with 239 observations.

The distribution in Figure 1 is distinctly left-skewed which results in some low statistical power issues due to limited observations on the lower end of the scale. Additionally, the fact that there are significantly fewer observations below 30 than there are above 70—this is also true for the extreme risk levels of 20 and 80—plays an important role in this study.

Methodology

This research paper uses statistical analysis to evaluate the BPSPX in terms of timeliness, accuracy, and profitability. I assess timeliness by examining how long the BPSPX spends above or below certain levels and how quickly the BPSPX gives a usable trading or investing signal at a trend change. For accuracy, I compare peaks and troughs in the BPSPX PnF to those in the S&P 500. To evaluate profitability, I analyze the probability of positive returns and the average level of returns in the S&P 500 around BPSPX levels.

Timeliness

             Consecutive Days within a Specified Range

Table 1 and Figure 1 both indicate that the BPSPX spends more time above 50 than below. 50 Neither the table or the figure, however, reveal the average length of time the BPSPX spends above or below certain levels. Using increments of 10, I measure the total number of consecutive days the BPSPX spends below 10, 20, 30, 40, and 50. I apply the same analysis for BPSPX levels above 50, 60, 70, 80, and 90.
After measuring consecutive days, I compare the results at low levels to the results at high levels. For example, I utilize the traditional levels of 30 as low (or oversold) and compare the average time to the average time above 70 as high (or overbought). I also compare 40 to 60 and 20 to 80. By these comparisons, I highlight the timeliness of BPSPX signals.

             Peak & Trough Timing

In the second test of timeliness, I evaluate the difference in the number of days between a usable investment signal from the BPSPX, either long or short, and the local peaks (troughs) in the S&P 500. Dorsey notes that the BPSPX is designed to indicate when investment risk is high or low, not necessarily to pinpoint peaks and troughs in the market.20 However, the ability of the BPSPX to allow an analyst to recognize local bottoms and tops in the market serves as a proxy for how well the BPSPX serves as an indicator of risk.

Local peaks (troughs) in the S&P 500 are identified after moves of at least 5, 10, 15, and 20 percent. After determining the S&P 500 peaks (troughs), I match them to the closest peaks (troughs) on the BPSPX PnF chart, with a peak being at the top of an X column and a trough being at the bottom of an O column. Due to the nature of the PnF chart, a peak (trough) is not evident until there is a 3-box reversal into the next column. I label the date that a 3-box reversal is realized as the Usable Date.

After all the peaks (troughs) are identified, I measure the absolute difference between the Usable Date and the S&P 500 peak (trough). Although an actual BPSPX peak (trough) day may closely match an actual peak (trough) of the S&P 500, the number of days to the Usable Date can vary greatly. I suspect this delay makes the Usable Date an ineffective market timing tool. Figure 2 provides a visual representation of how the peaks (troughs) and the 3-box reversal dates are identified.

Figure 2: Peaks and Troughs in the BPSPX and the S&P 500 during 2022

The BPSPX PnF chart for 2022 on the left side of this figure is labeled with the closest peak and trough dates corresponding to local peaks and troughs in the S&P 500 after moves of at least 5%. The line chart on the right side has the Usable Date labeled on the BPSPX dashed line. The crests and canyons of both the BPSPX and the S&P 500 are marked with small circles and diamonds, respectively. The vertical green dotted line marks the Usable Date so it can be seen clearly where the date falls on both the BPSPX and S&P 500.

Accuracy

To determine the accuracy of the BPSPX, I further exploit the peak/trough analysis. First, I repeat the procedure of measuring the absolute difference in days as I did for timeliness. However, instead of utilizing the BPSPX Usable Date, the statistic used to determine accuracy is calculated as the time between the actual PnF peak (trough) in the BPSPX and the actual S&P 500 peak (trough).

After examining the distance between peaks (troughs) in the BPSPX and peaks (troughs) in the S&P 500, I evaluate BPSPX’s failure to predict a peak (trough) in the S&P 500. This measurement is calculated by identifying the total number of instances where the S&P peaked (troughed) while the BPSPX failed to peak (trough). Finally, I quantify how frequently the BPSPX PnF incorrectly predicts a peak (trough) in the S&P 500. This calculation derives from the number of times the BPSPX PnF had a peak (trough) that did not correspond to an S&P peak (trough).

Profitability

For profitability, I calculate both the forward-looking and the trailing (backward-looking) 1-, 3-, 6-, and 12-month returns of the S&P 500 every day. I then find the average forward and trailing return of each timeframe for rolling BPSPX bin levels. For example, using a bin size of 10, I get the average return from 0 to less than 10. Then I calculate the average return from 1 to less than 11. This process is repeated through the last bin of 90 to less than 100. Within each bin, I also count the total number of observations and the number of observations with positive returns. Using these values, I calculate the percentage of up observations per bin. In addition to bins of size 10, I also use bin sizes of 5, 15, and 20. Table 2 shows the summary statistics for 1-, 3-, 6-, and 12-month trailing return starting January 11, 1996 and ending October 31, 2023. Forward return summary statistics are similar to the trailing return summary statistics with one exception: There are fewer overall observations in forward return summary statistics because the 12-month forward returns are not known after October 31, 2022, 6-month forward returns are unknown after April 28, 2023, 3-month returns after July 31, 2023, and 1-month after September 29, 2023. This table contains the baseline expectations for forward and trailing returns used to measure the profitability of the BPSPX.

Table 2: Summary Statistics of S&P 500 Trailing Returns from January 1996 to October 2023

For the BPSPX to give profitable signals, the average backward-looking returns are expected to be significantly negative (or at least well below the averages in Table 2) when the BPSPX is low (for example, below 30). Likewise, the percentage of positive returns (or percentage up) for backward- looking returns on low BPSPX days should be low (well below 50). The average forward-looking returns on days with low BPSPX levels should be significantly positive, and greater than the results in Table 2. Correspondingly, the percentage up of forward-looking returns are expected to be high (well above 50). In contrast, on days with high BPSPX levels (for example, above 70), the expectations for a profitable signal are reversed. In other words, the average backward-looking returns are expected to be significantly positive, and the backward-looking percentage up should be high. Likewise, the average forward-looking returns should be significantly negative, and the forward-looking percentage up is expected to be low.

The results of the profitability statistics are reported in both table and chart form. To conserve space, I only report the results of non-overlapping bins in the tables. For the charts, rolling bins are utilized for several reasons. First, the number of observations in the tails is limited, particularly at the low end; the larger bin size of the rolling bins means there are more observations per bin compared to using consecutive bins of size one, mitigating some of the limitation of low tail numbers. Second, like moving averages, rolling bins remove some of the noise associated with small-size, non-overlapping bins. The tails are notably noisy, but because the tails are of particular interest in this study, some smoothing helps identify trends in those crucial areas.

Results

Timeliness

          Consecutive Days within a Specified Range

The results of the first timeliness analysis are displayed in Table 3. The table shows the number of observations where the BPSPX spent any length of time within specified ranges. The table also displays the associated standard summary statistics for each range. It should be noted that at the extreme tails, the number of observations is below the acceptable threshold for statistical power. However, useful information can still be gleaned from the tails despite this drawback.

Table 3: Number of Days Within Specified Range Levels

While the number of observations above 50 and below 50 are nearly identical (96 and 97, respectively), the average number of consecutive days above 50 is more than triple the average number of consecutive days below 50. There are nearly twice the number of observations above 60 as there are below 40 (84 and 48, respectively), and the average consecutive days above 60 is more than triple below 40. This discrepancy also holds true when comparing above 80 to below 20. The results of comparing 70 to 30 are even stronger; the average number of consecutive days above 70 is over four times larger than that below 30.

Notice that when the BPSPX gets below 30, it only spends about eight consecutive trading days (around a week and a half) on average before rising back above 30. The longest consecutive time period it has spent below 30 is 23 trading days (about one month), which took place from the end of September 2008 to the end of October 2008, during the depths of the Financial Crisis. In contrast, the BPSPX spends over a month and a half (about 33 consecutive trading days) on average at or above 70; this includes seven observations where the BPSPX hit 70 exactly for one day. After five of those single-day observations, the BPSPX dropped back below 70 to between 67 and 69 for one day to one week before continuing back above 70 for a longer time span. Additionally, the far-right column of Table 3 shows that the BPSPX has spent more than 100 consecutive trading days over 70 on seven separate occasions. The longest of these occasions was eleven months (234 trading days) from the end of May 2003 to the end of April 2004 as the market recovered from the Dotcom bubble burst and subsequent bear market of 2001 and 2002.

Another finding from Table 3 comes from the standard deviation of the ranges. The standard deviation of 6.59 in the below-30 range means that 95% of the time the BPSPX spends from one day to one month (21 trading days) below 30 before rising back above 30. This is a relatively short period of time within which a local bottom in the stock market can be identified. Contrast that statistic with the standard deviation of 45.28 in above 70 range. Two standard deviations from the mean in this range indicate the BPSPX spends from one day to nearly six months (124 trading days) above 70 before falling back below 70. Six months is a long period of time to identify a local top. Even one standard deviation above the mean is 79 trading days, or nearly four months. Thus, simply comparing the standard summary statistics of low BPSPX levels to those of high BPSPX levels shows that low BPSPX levels are more timely in identifying local stock market troughs than high BPSPX levels are at identifying local market peaks.

Based on the information in Table 3, the BPSPX gives fairly timely signals below 30 for a long entry into the market, or to exit a short position. However, the timeliness as a long exit signal, or short entry signal, above 70 is questionable. When the BPSPX falls below 30, an analyst can have high confidence a market bottom will happen within a few weeks. Even if it is not the ultimate trough of a bear market, the market is likely to move higher before falling to a lower low; the analyst has an opportunity to take a long position for a short- term gain. On the other hand, when the BPSPX goes above 70, it could stay above 70 for a few months while the market continues to grind higher. Thus, using the BPSPX as a measure of timeliness to determine the end of a move up appears to be unreliable.

Peak & Trough Timing

The second measure of BPI timeliness comes from the difference in the time the S&P 500 peaks (troughs) and the time the BPSPX gives a usable investment signal. Table 4 presents the statistics for the absolute difference in the S&P 500 peak (trough) to the BPSPX peak (trough) and to the Usable Date of the peak (trough). The smallest observation may be negative if the BPSPX peaks (troughs) before the S&P 500, but only the absolute values of the negative numbers are used to calculate the statistical values.

Table 4: Absolute Difference in Days from Usable BPSPX to S&P 500 Peak (T rough)

The “Mean” column of Table 4 shows that it takes about a week and a half (a little over eight trading days) on average to identify a local trough as usable, once the BPSPX shifts over one column from O’s to X’s. Panel B shows that when the BPSPX is below 30, the usable date occurs even sooner, on average within one week (less than five trading days), making the BPSPX trough signal below 30 quite timely for medium to long-term traders and investors. The results in Table 4 confirm the timeliness results of Table 3 that the BPSPX is a timely indicator at the low end.

However, when the BPSPX is high, its timeliness is less certain. On average, the BPSPX peak signal is usable more than two weeks away (over ten trading days) from the S&P 500 peak. When the BPSPX is above 70, that time increases to almost 12 trading days. Because the range of Usable Peaks includes negative days nearly three months in advance, a 12 trading- day difference means the BPSPX gives a usable signal either 12 trading days early or 12 trading days late. For long-term investing, that signal may be timely enough, but it certainly is less timely than when the BPSPX is used to identify troughs .

Accuracy

The results in Table 3 and Table 4 not only speak to the timeliness of the BPSPX as an indicator, but also to its accuracy. The fact that the time the BPSPX spends below 30 is shorter and the standard deviation is smaller than when it is above 70 provides some evidence of the BPSPX being more accurate on the low end of the scale than on the high end. Furthermore, the comparison of the actual BPSPX peaks (troughs) to the S&P 500 peaks (troughs) provides even more documentation of accuracy at the low end versus the high end.

         Peak & Trough Timing

In Table 5, the BPSPX actual local trough is about two days from the S&P 500 local trough on average. That number falls to just over one day when looking only at observations where the BPSPX is below 30. Furthermore, over 90% of the BPSPX trough observations are within three days of the actual S&P 500 trough. That number increases to over 93% using only BPSPX observations below 30. In other words, the BPSPX and S&P 500 bottom at nearly the same time, regardless of whether or not the BPSPX is below 30. That means the BPSPX is highly accurate in identifying troughs.

Table 5: Absolute Difference in Days from Actual BPSPX to S&P 500 Peak (T rough)

On the other hand, the BPSPX actual peaks are on average about a week and a half (a little over eight trading days) from S&P 500 peaks. What is not shown in Table 5 is that over 30% of the observed BPSPX peaks occur before the S&P 500 peaks (compared to less than 10% of BPSPX troughs). About 25% of the BPSPX peaks happen five days or more before the S&P 500 peaks (compared to zero troughs). In other words, the BPSPX often peaks more than a week in advance of the S&P 500. While this may be advantageous to a trader wanting to use the BPSPX as a long exit signal, it highlights just how inaccurate the BPSPX is at identifying peaks.

Failed and Incorrect Peak & Trough Predictions

While the first measure of accuracy evaluated how close the BPSPX actual peaks (troughs) were to the S&P 500 peaks (troughs), the second and third measures of accuracy judge the number of failed and false predictions of peaks and troughs. The S&P 500 had 212 moves of at least five percent from 1996 to 2023, 106 upward moves and 106 downward moves. Those 212 moves include 13 moves of 20% or more (seven up and six down) another 16 of 15% or more (eight up and eight down), and 19 of 10% or more (nine up and ten down). The BPSPX had 174 peaks (troughs) that matched the S&P 500 peaks (troughs), but failed to provide a signal for 38 of the S&P 500 peaks (troughs). That means that 82% of the peaks (troughs) were correctly identified by the BPSPX. However, there were an additional 88 times when the BPSPX made a peak or trough, and there was no associated S&P 500 peak or trough. Thus, the BPSPX forecasted about 40% more peaks (troughs) from 1996 to 2023 than actually happened in the S&P 500.

Boiling it down to the 174 peaks (troughs) that match, Table 6 displays the count of S&P peaks (troughs) and BPSPX peaks (troughs) within each bin of size 20. When the BPSPX is below 20, it correctly indicates every S&P 500 peak (trough). But on the other end of the spectrum, the BPSPX forecasts 60% more peaks than what appeared in the S&P 500.

Despite the limited number of observations below 20, the evidence supports better accuracy at lower BPSPX levels than at higher levels

Table 6: Count of BPSPX and S&P 500 Peaks (T roughs) by BPSPX Bins of Size 20

Profitability

The final analysis looks at the profitability of the BPSPX at various levels. Table 7 shows the trailing returns and percentage of positive (% up) observations within each BPSPX bin of size 10 with the exception of the tails, where I use a bin size of 20. I use a larger bin size in the tails because there are so few observations in the extreme tails (below 10 and above 90). While I combine the bottom two bins and top two bins for Table 7, I do not combine them in the charts in Figure 3, which exhibit noticeable noise in the extreme tails. The Appendix contains tables and figures of using a bin size of 20, which smooths out the noise in the tails.

Table 7: Trailing S&P 500 Returns and Percentage Up using BPSPX Bin Size of 10

The first take-away from Table 7 is that the trailing returns when the BPSPX is low (below 40) are significantly negative for all time frames from one month to 12 months, as expected. These results are well below the mean and median returns found in Table 2. Furthermore, even in the 40 to 50 bin of Table 7, the trailing returns are significantly below the mean and median of Table 2. Additionally, a significant portion of the downward move appears to take place one to three months prior to the BPSPX reaching those lower levels. For example, below a BPSPX of 20, the average trailing return at 12 months is -22.77%, but over two- thirds of that move occurs in the last one-month period, and over 80% happens in the last three-month period.

Notice the values in the percentage of up observation columns when the BPSPX is low. These four far right columns of Table 7 show that when the BPSPX is below 20, all of the trailing returns are negative, except for the 12-month period. But even in the 12-month period, nearly 90% of the trailing returns are negative when the BPSPX is below 20. Similarly, below a BPSPX of 40, the percentage of up observations is low, as expected, except for at 12 months in the 30 to 40 bin, where the percentage of up observations is nearly 50%, although even that value is still well below the average in Table 2.

On the higher end of the BPSPX bins in Table 7, when the BPSPX is above 70, trailing returns are positive and significantly higher than the mean and median found in Table 2. Likewise, trailing percentage up is significantly higher than average when BPSPX is above 70. However, unlike in the lower tail where a majority of the move happens in the final three months, only a small portion of the upward movement happens in the last one- to three- month period.

There is also a noticeable imbalance when comparing the average S&P 500 returns at higher BPSPX levels to returns at lower BPSPX levels. The lower 50% of the BPSPX bins have significantly lower trailing returns than average while only the upper 30% provides significantly higher trailing returns than in Table 2. This is not surprising considering the distribution of BPSPX observations in Figure 1. However, what is somewhat unexpected is that the difference in the trailing returns for the upper 30% of the BPSPX bins compared to the average is not as great as the difference in the lower 40%.

Figure 3: Trailing S&P 500 Returns and Percentage Up using BPSPX Bin Size of 10

Figure 3 provides a visual depiction of Table 7. The trailing average return and the trailing percentage of up (positive return) observations for S&P 500 are plotted by rolling BPSPX bin levels with a bin size of 10. There are four graphs: (1) trailing 1-month return, (2) trailing 3-month return, (3) trailing 6-month return, and (4) trailing 12-month (1-year) return. The left- hand side of each chart is the scale for the average return in each bin. On the right-hand side is the scale for the percentage of positive return observations within each bin.

All the charts in Figure 3 show a negative return for BPSPX levels below about 40. There is a notable downward turn of both the average return curve and the percentage up curve above BPSPX levels of 90. This is most likely due to the limited number of observations of BPSPX above 89—there are only 15. Because of the limited number of observations, any observations with low returns have a substantial influence on the average in those bins. What is obvious from the charts is that in all time frames, the curves of both the average return and the percentage up start in the lower right and end in the upper left, which was expected.

While the trailing returns are as expected, the forward-looking returns are not quite what I hypothesized. Table 8 shows the forward-looking returns and percentage up using a bin size of 10. Again, in the table I combine the lowest two bins and highest two bins because of the lack of observations, but do not do so in the figure.

Table 8: Forward S&P 500 Returns and Percentage Up using BPSPX Bin Size of 10

The message communicated in Table 8 is different from that of Table 7. First, all the forward returns are positive, which is not what I expected. When the BPSPX is above 70, the forward returns and percentage ups of the S&P 500 for all time periods are not much different from the averages in Table 2. The one exception is the 12-month percentage up in the 80 to 100 bin. That value is significantly higher than the 12-month percentage up in Table 2, and is completely contrary to what I hypothesized.

However, when BPSPX is low (below 30), the S&P 500 forward returns and the percentage ups are much higher than the averages of Table 2. Here again the 12-month value is the exception, because it is similar to the Table 2 averages. Below 20, the results are particularly strong; the 1-month return is more than eight times bigger than the average, the 3-month return is four and a half times larger, the 6- month return is over three times bigger, and the 12-month return is almost three times as big.

The visual depiction of Table 8 is shown in Figure 4. The setup of Figure 4 is the same as in Figure 3, but it uses forward S&P 500 returns instead of trailing returns. The noise in the tails is readily obvious. With the exception of the noise in the tails due to low observation numbers, all of the average returns in the charts of Figure 4 start in the upper left and move to the lower right. However, the move downward happens quickly below a BPSPX level of about 40 and levels off above 40. In fact, there is even a move up in the average return around a BPSPX of 70 in some of the charts.

Figure 4: Forward S&P 500 Returns and Percentage Up using BPSPX Bin Size of 10

Another point to note from Figure 4 is the smile in the percentage up curve. This is most pronounced in the 12-month chart, but can be seen in the other charts, too. This may be related to momentum; as the overall market moves up, it continues to move up on the back of momentum. As the BPSPX moves higher above 50, the average forward return of the S&P 500 changes very little, but the number of positive return observations increases, creating the smile effect.

Application

The analysis of the BPSPX’s timeliness, accuracy, and profitability indicates that while it effectively identifies highly profitable long entry points at low levels, it is less reliable for making trading or investing decisions at high levels. When the BPSPX falls below 30, it provides timely, accurate, and profitable signals for technical analysts. However, at higher levels, the BPSPX proves neither timely nor accurate, and its signals are not profitable. In simpler terms, the BPSPX highlights a favorable risk/reward tradeoff at low levels— particularly below 20—but offers less clarity about the tradeoff at higher levels.

These findings seem to support Dorsey’s notion that when the Bullish Percent Index is low, investment risk in the market is low and investors should pile into the market. While the findings do not show strong evidence of being able to use the BPI as an exit indicator when it is high, they do not negate Dorsey’s claim that the risk of investing is high when the BPI is high.

In fact, this research gives every indication that Dorsey is correct. When the BPSPX is above 70, there is no abnormal positive return. Furthermore, there is ambiguity about whether the market will continue to rise or take a dramatic downturn. If the market does drop, there is uncertainty about whether that drop will happen in two days or two months. Since there is so much doubt about the future of the overall market as the BPI continues to rise higher, Dorsey’s sector rotation concept makes excellent sense; sector BPIs should be used to identify lower risk sectors to move investments into.

An additional application point from this research is that no single technical indicator should be used in isolation, and the BPI is no exception. There is a plethora of research on moving averages, candlestick patterns, and other technical analysis tools. These should be used in conjunction with the BPI, particularly when trying to isolate market peaks. But when the BPI gets really low (below 20), it often gives the investor an earlier entry point than could otherwise be found with other indicators.

Conclusion

While the Bullish Percent Index may still be a strong indicator, the research herein finds it is most useful at the bottom. When the BPI is low, it gives far more timely signals that are more accurate and profitable than when it is high. While I used simple statistical analysis tools, the findings overwhelmingly support the idea that investors should be bullish at the bottom— when the BPI is below

30. At that level, the BPI is timely, accurate, and profitable.

This paper starts to fill the void of academic research on the Bullish Percent Index. However, there is much research that remains to be conducted. Similar to other technical analysis indicators, the performance of the BPI within a trading or investing strategy can be improved by using chart patterns, bullish and bearish divergences, trendlines, and many other techniques. All of these ideas are areas for future research.

Furthermore, this paper only covered the BPSPX from 1996 to 2023. Opportunities exist to study the Bullish Percent Index using longer datasets, which may provide more robust results. Research into other BPIs such as the BPNYA, the BPNDX, various sector BPIs, and BPIs on foreign indexes could yield some significant findings that add to the body of literature on the BPI.

References

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Navin, John. “The Stock Market Is Topping. Here’s The Evidence.” Forbes, June 14, 2023. https://www.forbes.com/sites/johnnavin/2023/06/14/the-stock-market-is-topping-  heres-the-evidence.

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Appendix

This appendix contains additional profitability tables and figures using a bin size of 20.

Table A1: Trailing S&P 500 Returns and Percentage Up using BPSPX Bin Size of 20

Figure A1: Trailing S&P 500 Returns and Percentage Up using BPSPX Bin Size of 20

Table A2: Forward S&P 500 Returns and Percentage Up using BPSPX Bin Size of 20

Figure A2: Forward S&P 500 Returns and Percentage Up using BPSPX Bin Size of 20