In LiamMoorfieldYee/MoLo: Relative Strength Predicting Future Returns

knitr::opts_chunk$set(echo = FALSE)
library(MoLo)
library(ws.data)
library(lubridate)
library(dplyr)
library(ggplot2)
library(knitr)

Abstract

Using daily stock data, from 1998-2007, we investigate the theory of stock price momentum. Building on Robert Levy's paper, "Relative Strength As A Criterion For Investment Selection", we rank stocks based on their price performance over the past 26 weeks. By grouping stocks according to their relative historical ranks, we analyze the performance of these stocks over the next 4, 26, and 52-week time periods. We find evidence that past price performance, relative to the market, is a strong predictor of future returns. This trend is also present after accounting for stock volatility and market strength.

I. Introduction

Every year trillions of dollars flow into the stock market with the hope that excess returns, that is returns above and beyond general market performance, will be earned. Traders and portfolio managers employ many strategies to find stocks that will out perform in the coming days, weeks, months and years. They believe that they can beat the market providing outsized returns that even after their fees are taken out, will trump what’s expected from a simple index fund. However, in recent years this form of active management has come under fire from the idea of the Efficient Market Hypothesis.

The Efficient Market Hypothesis (EMH) is the belief that one cannot beat the market without taking on about average risk. Proponents claim that relevant information about a stock is immediately incorporated into the market, causing a stock's price reflects its true or intrinsic value at all times. There is a common stance that analyzing a stock’s past performance- prices, volatility, and patterns- is “no more useful in predicting future price movements than throwing a dart at the list of stocks in a daily newspaper” (Levy, 1967). They see all stock fluctuations simply as following a random walk, where any deviations from intrinsic value cannot be predicted, but are instead just random jumps before returning back to intrinsic value. It is clear that EMH backers would not believe in investment managers selling their services promising average returns to investors. Instead, the strategy of investing in passive index funds has gained popularity among EMH supporters. In recent years, extensive literature supporting the random walk theory has been published.

Yet, many have tried and successfully found quantitative algorithms to detect patterns within stock movements that predict future returns. Many of these strategies are rooted in the short-term momentum of a stock, and the belief that that momentum will carry into the future providing investors with above average returns. This paper will focus on the strategy laid out in “Relative Strength as a Criterion for Investment Selection” by Robert A. Levy. The paper was published in 1967 and uses data for the time period spanning October 24, 1960 to October 15, 1965. Levy found that his strategy for ranking and selecting stocks provided strong relative returns in the long-term. His strategy centered around forming a ratio consisting of the current weeks price divided by the 26-week trailing rolling average, and then ranking the stocks in order. He bases stocks on relative strength with peers, so that co-movement will not be a factor.

In this paper, we seek to replicate the results of Levy to find if the strategy holds up in our current time frame from 1998-2007. In Section II, we will delve deeper into Levy’s paper, including his methodology for ranking stocks and analyzing future returns. Next, Section III will provide a Literature Review regarding recent papers on the topic. Section IV goes into our Methodology, and the results of that Methodology are provided in Section V. Finally, our conclusion is described in Section VI.

II. Levy Paper

As mentioned above, Levy uses stocks during the time period of October 24, 1960 to October 24, 1965. His data set contains 200 stocks over the 260 week period, all of which are listed on the New York Stock Exchange. In order for a stock to make his selected list, they must make a preliminary list of stocks fulfilling three criteria. First, the stock must be listed on the New York Stock Exchange. It must also have been in the May 1965 edition of Moody’s Handbook of Widely Held Common Stocks. Finally, the stock had to be a component stock within the S&P Industry Stock Price Indexes in the 1964 Security Price Index Record. From the list compiled based on these requirements, the 200 stocks for his analysis were chosen first by dividing each stock into their respective industry grouping. He then chose stocks in order to have the same relative distribution of stocks within each industry that the S&P exhibited at the time.

Once he has all of his stocks compiled, he ranks them in order of their relative strength ratio. Before he does this he adjusts all prices for splits, dividends, and reinvestment of dividends and proceeds from sales. Every time that he uses the term current week’s price, he is referring to the Friday price of a stock for a given week. The first ratio he calculates is his historical ratio, which “is based upon data originating prior to and including C” with the “purpose of investment selection” (Levy, 1967). The ratio is designated by C/A26, which is defined as the current week’s price divided by the 26-week rolling average ending with the current week’s price. Through this ratio he is providing a value to quantify the strength at which a stock is performing compared to the past 6-months, with the highest ratio representing the current strongest stocks. He then ranked the stocks on a week-by-week basis in descending order based on this ratio.

The next two ratios he calculated were the future facing values, as “they are based upon data originating subsequent to and including C” and they are “used for purposes of measuring the results of investment selection” (Levy). The purpose of these ratios is to gauge how well each stock performs relative to current price and to other stocks in the short-term (4 weeks) and long-term (26 weeks). Both of the ratios are calculated in the same way but with a different numerator. The short-term ratio, denoted 4/C, is the current week’s price divided into the price of the asset 4 weeks into the future. The long-term ratio, 26/C, is the current week’s price divided into the price of the asset 26 weeks into the future. Each of the ratios will show, based on familiar time periods of one month and six months, how well a stock has performed when compared to itself. Also, by creating a ratio, we can also see how well stocks performed against their peers.

The first set of results that he produces are the simple ranks of each C/A26, from which he places into 10 groups. The 20 highest C/A26 ratios go into the top 10 percentile, followed by the next 20 highest historical ratios, until he has 10 groups of 20 stocks. From there, he reports the average 4/C and 26/C ratio for each group, as well as the average rank of the stocks, when each of the future ratios are ordered from largest to smallest. Therefore, we can see not only the average forward facing ratio, but also where each group stands in terms of ranking the average strength of these returns. When forming this table, he goes under the assumption that “Technical analysts contend that stocks which historically have been relatively strong tend to remain relatively strong for some significant period of time” (Levy). However, for the short-term, he finds no evidence that this is the case, with all of the 4/C averages being pretty much the exact same value, ranging from 1.008 to 1.01, and the average ranks all hovering very close and in no particular order. However, in the long-term, the numbers show the theme of continued relative strength. He finds that the average 26/C goes- for the most part- from highest to lowest with the strongest ratios corresponding to the highest historically ranked stocks. The numbers show that the top 10% average a return of 9.6% over the period, with the lowest 10% averaging 2.9% return. The average rank for the 26/C shows the same theme, with the highest ranks corresponding to the higher percentiles. Since he cannot find a discernable pattern in the short-term, for all subsequent results he omits the 4/C ratio.

The following two tables he creates by breaking down the weeks both by volatility and market strength. For the volatility ranks, he uses the coefficient of variation, which he found by taking the standard deviation of each of his 200 stocks, ending with the current weeks price and using the 27 latest weekly closing prices. He then divided that value by the arithmetic mean of the set. From there, the variation coefficients were ranked by stock, with the highest ratio being assigned a value of 1. Thus, the lowest ranked stocks were the most volatile and the highest ranked the least volatile. He also subclassifies stocks based on weekly historic market performance, in order to analyze the effect of market timing. To represent weekly market performance the sum of the C/A26 ratios for all 200 stocks, for all weeks, was computed. This measurement provides the strength of the market during that particular week and its performance over the preceding six months. Stocks were then ranked for all 234 weeks (260 weeks of data minus the 26 weeks he couldn’t use due to the inability to calculate 26- week rolling average) with the highest strength or sum with the highest rank.

For volatility, he makes three groups per week based on his coefficient of variation with his 25% most volatile stocks being in the first group, his 25% least volatile stocks in the third group, and the other 50% in the second group. Within each volatility group, he ranks the stocks based on the C/A26 ratio as was described above. The strongest results he finds are within the most volatile stocks, with the top 10% returning on average 10.4% over 26-weeks with an average rank of 85.7. As you move down the percentiles, the returns vary, but the average ranks move from lowest to highest. From looking at volatility ranks, he comes to the conclusion that “the selection of securities which historically had been both relatively strong and relatively volatile produced profits superior to those attainable from random selection” (Levy).

He divides up the market ranks table in a similar fashion, with the stocks in the strongest 25% weeks placed in the first group, the stocks in the 25% weakest weeks in the third group, and the remaining 50% in the second group. He finds that the first two groups (strongest market and medium strength) both supported the continuation of relative strength with the 10% strongest C/A26 ratios yielding average returns of 15% and average rank of 83.8 in strong markets, and 8.6% return and average rank of 88.6. However, in the weakest markets, there is no support for the relative strength continuation. In fact, out of every percentile, the strongest 10% in terms of C/A 26 had the third lowest returns over the next 26 weeks. He concludes that “the best results are attainable by buying stocks in a market which historically had been comparatively strong” (Levy).

III. Literature Review

This paper analyzes relative strength as a way to decide which stocks to choose as a predictor of future returns. The idea is to choose stocks on the basis of how they have performed relative to other stocks in their selected universe on the basis of current prices, volatility, and past returns. The Levy paper is from 1967 and shows that this strategy works to provide outsized returns in 1960’s. This takes place roughly 50 years ago, so the question is whether it still holds true. In 2010, Mebane Faber of Cambria Investments did a similar paper on relative strength titled “Relative Strength Strategies for Investing.” This paper attacks the relative strength methodology by presenting a different model, where instead of investing in individual securities, they rank sectors based on their strength and total returns. They then invested in the top X sectors for their criteria. They find that in their time periods, relative strength not only provides strong returns, but also that it outperforms a buy and hold method of investing in 70% of years.

Another similar study is “Time Series Momentum” by Moskowitz, Ooi, and Pederson. This paper is similar in that their analysis is done on the basis of analyzing how strong returns have been in the past as an indicator of future returns. While in the Levy paper, they see how strong prices are over the previous 26 weeks, the “Time Series Momentum” paper looks at the previous 52 weeks. They find that by analyzing the lagged 1-year returns is a strong indicator of how the next month will be for a stocks return. Comparatively, Levy shows that through the ratio of the current price and the previous 26-week period, one can rank stocks and through the formed portfolio, realize strong positive returns.

IV. Methodology

To start our analysis, we used a data set containing daily stock prices for every U.S. listed stock that was a top 1,500 corporation by market capitalization for at least one year. Our time frame was the ten-year span from 1998 to 2007. We had access to each stocks basic information- including its ID, symbol, name, sector, and industry-, yearly information- which added its market cap and if it was in the top 1,500 that year-, and daily information- which added each day’s price, volume, and return. For our analysis, we only needed intrinsic information of the stock to group them and its prices for each date. Thus, for our cleaned data set, we kept around each stock’s name, id, price, and date.

From there, we had to create variables to apply Levy’s approach, which first came in the form of our week variable. For every day in our set, we assigned it a number corresponding to what week of the year it was; so, the 3rd week of 2001 was assigned 3-2001. Next, we had to formulate our ratios, which as mentioned above were the C/A26, 4/C, and 26/C. For the C/A26, we first calculated the average of the prices over the previous 26 weeks. This was done by finding the rolling mean of the previous 130 days, assuming there are 5 trading days a week. We acknowledge that this may be an approximation because there may not be 5 trading days every week of the year, but this will give us a strong indication for the stock’s behavior over that period. The rolling mean was then divided into the current week’s price, which was simply the latest trading day available for a given week. We then grouped each individual week together and ranked them based on their C/A26 ratio, with the strongest ratios receiving the lowest ranking- so the best ratio has a rank of one. Next, we formed the two future facing ratios, the 4/C and 26/C ratios. First, the price for each stock, 4 and 26 weeks (approximately 20 and 130 days) in advance was found. This price was then divided by the current week’s price. To add onto Levy’s analysis we not only used these two ratios, but also formed a new one to represent a year in advance. He found that there was no sign that the C/A26 was an indicator of short-term performance, but in the longer term there was some predictive nature. We wanted to extend his results to see if for a full year the results were even stronger than for the six month period, as before time seemed to strengthen relative strength’s affect. Thus, we created the 52/C ratio, which was formed in the same manner as the 4/C and 26/C, but used the future price 260 days in advance. All four of these prices used were the latest price available for the given week. As done with the C/A26 ratio, we grouped by week and ranked each stock based on their ratio, with the highest ratios receiving the best (lowest) ranks.

Finally, we need to form the variables to describe volatility and market rank. For volatility, we performed the same steps as Levy by finding the standard deviation of each stock over the previous 26 weeks or 130 days and dividing it by the arithmetic mean of that stock over the same period. Each stock for every week was then ranked based on this value, with the highest volatility stocks getting the lowest rank. Next, we ranked each week based on its relative market strength. This was done by adding up every stocks C/A26 ratio for a given week. The weeks with the highest sum we considered to be the strongest relative strength markets, so we gave these weeks the lowest rank in terms of market strength.

V. Data Analysis

TABLE 1

4-Week And 26-Week Average Investment Performance By Stock Group
As Classified According To Historical Relative Strength Ranks

data(tbl1, package = "MoLo")
tb1 <- tbl1
kable(tb1, col.names = c("CA/26 Group Rank", "Average 4/C Ratios", "Average 4/C rank", 
                         "Average 26/C Ratios", "Average 26/C Rank"))

The results when every stock is considered are presented containing 2,886 stocks. As can be seen, the C/A26 is a strong predictor of both short-term and long-term stock performance, which differs from what Levy found, as he only saw this relationship for the long-term. For the average ratio columns, it is clear that the highest ranked stocks in terms of C/A26 perform the best. In the long-term 26-week period, the strongest relative strength stocks returned an average of 21%, which was by far the strongest of any group. The average rank of the stocks in terms of 26/C was 951, which was also the strongest among each group. For 4/C, the highest group returned an average of 3.67% over the following 4 weeks. This was the second highest ratio, with the last group actually having the best returns with 5.18%. However, this high return was caused by outliers where some stocks had very low C/A26 ratios due to very low prices, often a couple of cents. Thus, when they increased in price to a couple of dollars, the ratio was very high, causing a skew to the average ratio. We can say that the high ratio was caused by outliers as the average rank of the last group was by far the lowest at 1,097. This means that most of the last group had very low ratios, but a couple outliers cause the average to jump drastically.

TABLE 2 - A

4-Week Performance By Stock Group As Classified To Historical Relative
Strength Ranks And Subclassified According To Historical Volatility Ranks

Volatility Ranks

Top 25% Middle 50% Bottom 25%

data(tbl2, package = "MoLo")
tb2 <- tbl2 %>% select(ca26groupings, avg.C4.ratios.x, avg.C4.rank.x, avg.C4.ratios.y, avg.C4.rank.y, avg.C4.ratios, avg.C4.rank)

kable(tb2, col.names = c("CA/26 Group Rank", "Average 4/C Ratios", "Average 4/C rank", 
                         "Average 4/C Ratios", "Average 4/C rank",
                         "Average 4/C Ratios", "Average 4/C rank"))

TABLE 2 - B

26-Week Performance By Stock Group As Classified To Historical Relative
Strength Ranks And Subclassified According To Historical Volatility Ranks

Volatility Ranks

Top 25% Middle 50% Bottom 25%

data(tbl2, package = "MoLo")
tb2 <- tbl2 %>% select(ca26groupings, avg.c26.ratios.x, avg.c26.rank.x, avg.c26.ratios.y, avg.c26.rank.y, avg.c26.ratios, avg.c26.rank)

kable(tb2, col.names = c("CA/26 Group Rank", "Average 26/C Ratios", "Average 26/C rank", 
                         "Average 26/C Ratios", "Average 26/C rank",
                         "Average 26/C Ratios", "Average 26/C rank"))

In Tables 2A and 2B, we introduce the volatility ranks. We break the stocks into groups based on volatility: the highest 25%, lowest 25%, and middle 50%. Table 2A shows the results of each stock’s volatility group in the short-term 4/C ratio. In the short-term, the only real discernable difference comes in the most volatile 25% stocks. The stocks that have the strongest relative strength and are most volatile in the short-term return an average of 5.8% in the next 4 weeks and an average rank of 960, both values significantly stronger than the other groups. This is excluding the 10th group, which once again is skewed by outliers seen by an average return of 14% in 4 weeks, but by far the highest average rank of 1,152. The other two volatility groups do not seem to show a discernable or significant pattern over the 4 following weeks. For Table 2B, we see stronger results when volatility ranks are looked at over a longer-term 26-week period. For the most volatile stocks, we see an average return of 29.8% and an average rank of 933 for the greatest relative strength groups. These are the strongest values of all the groups. In terms of the middle volatile stocks, we start to see a pattern, where the greatest relative strength group return an average of 13.9% over the following 26 weeks for a 956 average rank. These are both the strongest values, and the values for the most part weaken as you move down ranking groups, displaying the trend seen in the most volatile groups in both the short and long-term of relative strength predicting future performance. In the least volatile 25% group, there is the strongest average ratio, returning 7.4% in the first group. However, the average rank is the highest among all groups, showing that within the lowest volatile groups, relative strength will not be a good indicator of future performance.

TABLE 3 - A

4-Week Performance By Stock Group As Classified To Historical Relative
Strength Ranks And Subclassified According To Historical Market Performance

Market Performance Ranks

Top 25% Middle 50% Bottom 25%

data(tbl3, package = "MoLo")
tb3 <- tbl3 %>% select(ca26groupings, avg.C4.ratios.x, avg.C4.rank.x, avg.C4.ratios.y, avg.C4.rank.y, avg.C4.ratios, avg.C4.rank)

kable(tb3, col.names = c("CA/26 Group Rank", "Average 4/C Ratios", "Average 4/C rank", 
                         "Average 4/C Ratios", "Average 4/C rank",
                         "Average 4/C Ratios", "Average 4/C rank"))

TABLE 3 - B

26-Week Performance By Stock Group As Classified To Historical Relative
Strength Ranks And Subclassified According To Historical Market Performance

Market Performance Ranks

Top 25% Middle 50% Bottom 25%

data(tbl3, package = "MoLo")
tb3 <- tbl3 %>% select(ca26groupings, avg.c26.ratios.x, avg.c26.rank.x, avg.c26.ratios.y, avg.c26.rank.y, avg.c26.ratios, avg.c26.rank)

kable(tb2, col.names = c("CA/26 Group Rank", "Average 26/C Ratios", "Average 26/C rank", 
                         "Average 26/C Ratios", "Average 26/C rank",
                         "Average 26/C Ratios", "Average 26/C rank"))

In Tables 3A and 3B, we bring in the variation for market strength, where we break down the stocks in the top 25% strongest markets, middle 50% market strength, and 25% weakest markets. For Table 3-A, we see the performance in the short-term, with the most discernable pattern coming from the strongest and middle market strength groups. For the first group, or greatest relative strength stocks, in the strongest markets, we see an average return of 6% and average rank of 964 and in the medium market, there’s an average return of 3.2% and rank of 971. These are the strongest values, excluding the outliers in Group 10, where we have an average return of 3.8%, but the highest average rank of 1,112. In the weakest markets, there does not seem to be a discernable difference or advantage given by relative strength in the short-term. In Table 3A, we have the performance in the long-term with the 26/C results in strong, medium, and weak markets. Here we find a pattern across all market strengths for the predictive power of relative strength. In the top grouping we find the strongest rank for 26/C ratios across all markets. Excluding the outlier in Group 10 of the weakest markets, the average ratio in Group 1 is the also the highest across all markets, returning 23.8%, 22%, and 19% across the strongest, medium, and weakest markets respectively. These results show that in any market in the long-term 26-week period relative strength is a strong indicator of future performance.

TABLE 4

52-Week Average Investment Performance By Stock Group
As Classified According To Historical Relative Strength Ranks

data(tbl4, package = "MoLo")
tb4 <- tbl4
kable(tb4, col.names = c("CA/26 Group Rank", "Average 52/C Ratios", "Average 52/C rank"))

As mentioned before, we also added in a third ratio for evaluating future performance, which is the 52/C. It looks at the price 1 year in the future for a longer-term analysis, to see if we can see a discernable pattern. Levy found that the results yielded a relationship between relative strength and future performance in a long-term six-month frame, so we wanted to see if the results were even stronger on a longer horizon. Table 4 gives the results for all of the 2,783 stocks in our universe for which we can look at the 52/C ratio. The groupings are arranged in the same fashion as before based on the C/A26 ratio. We find that the first group, as seen before, shows strong performance a year after, returning an average of 41.7% and an average rank of 955, both the strongest values in the analysis. Thus we continue to see that relative strength is a strong indicator of future returns.

TABLE 5

52-Week Performance By Stock Group As Classified To Historical Relative
Strength Ranks And Subclassified According To Historical Volatility Ranks

Volatility Ranks

Top 25% Middle 50% Bottom 25%

data(tbl5, package = "MoLo")
tb5 <- tbl5
kable(tb5, col.names = c("CA/26 Group Rank", "Average 52/C Ratios", "Average 52/C rank",
                         "Average 52/C Ratios", "Average 52/C rank",
                         "Average 52/C Ratios", "Average 52/C rank"))

In Table 5, we have the results for 52/C when variation is included. In this longer-term period, we find that the results are strong for the top grouping in the most volatile and medium volatility stocks. The top grouping in the most volatile stocks has the strongest average returns at 55% and second lowest average ranking with 954, second only to 952. Within the medium grouping, we see a very strong relationship with the average rank for the top grouping being 926, by far the lowest, and the average return being the highest at 27.8%. Within the lowest volatility stocks, as before, there doesn’t seem to be a strong pattern.

TABLE 6

26-Week Performance By Stock Group As Classified To Historical Relative
Strength Ranks And Subclassified According To Historical Market Performance

Market Performance Ranks

Top 25% Middle 50% Bottom 25%

data(tbl6, package = "MoLo")
tb6 <- tbl6
kable(tb6, col.names = c("CA/26 Group Rank", "Average 52/C Ratios", "Average 52/C rank",
                         "Average 52/C Ratios", "Average 52/C rank",
                         "Average 52/C Ratios", "Average 52/C rank"))

In Table 6, we introduced the market strengths for the 52/C ratio. Here we find an interesting result, where unlike before, the stocks in the strongest markets do not perform strong a year out with an average rank of 1,027, which is the third highest of the ten groups. However, the medium strength market produces very strong returns for the top grouping with the lowest rank of 913 and the highest return of 40% after a year. The top grouping also performed well in weak markets, with the lowest rank of all groupings with 967 and an average return of 43%.

VI. Conclusion

It is important to note when looking at these results that the period analyzed was 1998 to 2007, which was a period marked by extreme stock market price growth. This includes the dot COM bubble in the late nineties into the two thousands, as well as the leading up to the recession, without reflecting the drop in the economy in 2008. Keeping this is mind is important, as many stocks performed extremely well reaching prices that may not always have been justified, but contributed to the very high average returns over the periods seen in our various tables.

In his paper in 1967, Levy was able to find the result that in the long-term relative strength is a strong indicator of future profits. By ranking stocks based on past prices and performance, Levy provides evidence for continued relative strength, where stocks that are performing better than their their peers will continue to outperform in a 26-week time period. Our results support Levy’s findings that relative past performance is a good indicator of stocks’ relative future 26-week performance. Unlike Levy, we find strong evidence that relative strength is a good predictor of short and long-term returns. We found not only that relative strength was a strong indicator of future performance for the six-month time period, but also the one-month and one year time periods. When adding in volatility, we found that across all the time frames, the stocks that are performing better than peers as well as with above average volatility will continue to provide strong average returns across all time frames. Also, with the exception of our year-long ratio, the best time to buy stocks based on relative performance is in strong and moderate market environments.

Citations

Levy, Robert A. "Relative Strength as a Criterion for Investment Selection." The Journal of Finance 22.4 (1967): 595-610. JSTOR. Web.

Faber, Mebane T. "Relative Strength Strategies for Investing." SSRN Electronic Journal SSRN Journal (2010). Cambria Investment Management. Web.

Moskowitz, Tobias, Yao Hua Ooi, and Lasse Heje Pedersen. "Time Series Momentum." Journal of Financial Economics 104 (2012): 228-50. Web.

LiamMoorfieldYee/MoLo documentation built on May 8, 2019, 11:20 p.m.