Abstract

Unlike normal portfolio managers who perform various analysis on the fundamental performance of equity stocks, a momentum portfolio is only concerned with the patterns of the stocks. The portfolio will then take a long or short position on the stock in order to arbitrage from the continuation of its upward or downward movement, which is so called momentum. Inspired by Jegadeesh and Titman (2011), I focus the attention on the post-crisis performance of momentum trading strategy with the special focus on the negative return on the year 2009. A sample of 1294 firms from NYSE from July 2009 to June 2015 is investigated and the result from the regression shows that the return of the momentum strategy has been disappeared in the US. Based on the research, the adjusted returns, based on the Fama-French factor model, of all the winner and loser portfolios are not significantly different from zero. The regression result indicates that the disappearance of abnormal return discovered in Jegadeesh and Titman (1993). Therefore, this paper employs behavior model and attributes the return to the market over or under reaction to information. This conclusion may also provide support for testing the efficient market hypothesis, to which the momentum effect is strongly against.

Chapter 1 Introduction

Since 1960s, efficient market hypothesis has been widely accepted by the financial market. Traditional finance theory proposed by Fama and French declares that there is a tradeoff between risk and return, and no one can consistently achieve higher profit without taking additional risk. Later, the arbitrage pricing theory put out by Stephen Ross provided further explanation for the price movement under the efficient market situation. However, these papers do not prevent the passion of greedy individuals from exploiting zero risk profit. Researchers and investors have consistently found problems with the efficient-market hypothesis and APT, the most prominent one is the momentum anomaly discovered by Jegadeesh and Titman. The momentum strategy is based on the phenomenon that the best (worst) performed stocks during the past several months tend to continue to perform good (bad) over the following months. According to Jegadeesh and Titman (1993) this strategy could consistently generate an abnormal return of about 1% per month for the U.S. market over the period 1965-1989. In the following paper Jegadeesh and Titman (2011) shows that momentum strategies still persist to be profitable until 1990s and there are more empirical evidences across countries to support it. Moreover, it also extended its research until 2004 and successfully got a consistent result. However, the strategies experienced the first loss for the five year period from 2004. Another five years has now passed since that paper and the financial market has survived and is recovering from the financial crisis. It is interesting for the researcher to know how the momentum strategy performed after the financial crisis and what is the reason behind the dramatic change in the momentum profit.

So my research question is:

What is the performance of momentum portfolio after the global financial crisis?

In particular, this article will focus on the momentum strategy with a ranking period of six months and a holding period of also six months. Using the same lengths of ranking and holding periods as Jegadeesh and Titman (2001), we are in an attempt to compare with their result to see whether the successful performance of the momentum strategy still persists. In our follow-up study, the research will also be conducted on the performance of the momentum strategy with a ranking period of six months and a holding period of three months to see whether the result is consistent.

To illustrate our process in a nutshell, the sample consists of all the 1991 stocks listed on the NASDAQ exchange that have a continuous price record from June 30th 2009 to May 31st 2013. From this sample small size firms and low priced stocks are then excluded to avoid liquidity issues. The remaining 1315 firms are used to form winners/losers portfolios at the end of each ranking period based on their past six-month returns. These portfolios are then held for the next six months. Monthly roll over strategy is applied, which means, for every consecutive twelve months in our sample period starting from July 2009 to May 2013, there is a ranking and holding period formed. The winners/losers momentum return for a particular month is the average of returns of all the winners/losers portfolios held at that month. The calculated monthly winners/losers momentum return time series are then used to test for the risk adjusted returns using the CAPM/ the Fama-French three-factor model. Besides these, the average book to market value and the average market capitalization of firms under each momentum portfolio and the average monthly return of each momentum portfolio are also reported to assist in interpreting the result.

The remainder of this paper is constructed as follows: Chapter 2 provides a brief background of momentum studies. Chapter 3 details our data processing and methodology. Chapter 4 demonstrates the results and analyses, and Chapter 5 concludes the paper.

Chapter 2 Literature review and prior empirical evidence

2.1 What is momentum trading strategy

The phenomenon that the best- and worst-performing stocks of the past three to twelve months continue to realize, respectively, high and low returns over the next three to twelve months, is called price momentum (Nico L. van der Sar, Stock pricing and Corporate Events, 2nd edition 2011). The theoretically best trading strategy based on this phenomenon which basically takes a long position in the past winners while going short in the past losers is called the momentum trading strategy.

This strategy consists of two time periods. Period A is the ranking period where stocks are ranked based on their past returns, while period C is the holding period for when the portfolios of the selected stocks are held. Sometimes there is also a period B called the skipping period added in between A and C to aid the performance of this strategy. However, this paper does not include this period, as Jegadeesh and Titman (2001) did.

Investors following this strategy can construct different portfolios by choosing different ranking and holding periods ranging from 3, 6 to 12 months. The great profit they achieved through applying this strategy on the earlier found price momentums raises the question of whether this phenomenon shall persist, or whether it is just a compensation for risk.

[TBD]

2.2 Theories behind the momentum profit

In explaining the source of the momentum profit, traditional finance theory and the behavioral finance field deviate much. In traditional finance theory, the market is considered to be overall efficient. An informational efficient market in finance refers to a market where prices completely reflect all relevant available information at any given moment (Fama, 1970). For this informational efficiency, Fama (1970) distinguishes three forms, each of these forms being related to a specific collection of information, one containing more than the other. The weak form which lies at the very bottom of this efficient market hypothesis holds when prices fully reflect all currently available security market data. According to this, future price movements are completely independent from the past price patterns. Strategies like momentum trading are thus in vain. The risk adjusted abnormal returns achieved by Jegadeesh and Titman (1993) are therefore considered to be an anomaly which attempts to reject the EMH. However, due to the joint hypothesis problem, one can never reject the EMH since there is always a voice judging that the risk factor model may be not perfect. Conrad and Kaul (1998) thus argued that the momentum profits could be entirely explained due to the cross-sectional variation in mean returns rather than any predictable time-series variation in stock returns.

Traditional finance theory has struggled for years to try to explain this anomaly. Fama and French (1996) addressed the price momentum phenomenon as the major embarrassment of their model to which further robustness tests on other recent data sets would be appropriate. Grundy and Martin (2001) demonstrated that the high momentum profit could also not be explained by the Fama-French three-factor model even the dynamics of the factor betas were taken into account.

Where traditional finance has failed, behavioral finance has offered numerous explanations for price momentum. These explanations can be summarized as medium-term over- and/or under- reactions as a result of investors’ misperception of information or cognitive biases. Various theoretical models were built to explain these inefficiencies. Among them are the model built by Daniel, Hirshleifer and Subrahmanyam (1998) based on investor overconfidence and self-attribution, the model developed by Barberis, Shleifer and Vishny (1998) which has one security assumed to follow random walk and one investor who believes in either of two incorrect regimes, and the model developed by Hong and Stein (1999) which separates the population into two groups -‘the news watchers’ and ‘momentum traders’-and let information diffuse gradually among them.

2.3 Prior empirical evidence

Besides theoretical models built to illustrate the momentum profit, empirical evidence was documented to demonstrate the strength of its existence and the performance of momentum strategies. De long, Shleifer, Summers and Waldmann (1990) showed a strong evidence of positive feedback trading in the majority of 32 merging and mature stock index futures markets. Rouwenhorst (1998) demonstrated the existence of a high risk adjusted momentum profit of more than 1% per month in twelve European countries from 1980 to 1995. De Haas (1999) examined the price momentum effect for all stocks in the Netherlands from 1976 to 1998 and also achieved a significant abnormal return of over 1% per month. The results were also positive though low for emerging Asian markets documented by Chui, Titman and Wei (2000).

Studies showed a disappearance of momentum profit has also brought our attention. Muga and Santamaria (2007) in examining the momentum effect in the Spanish stock market during the 1990s showed that the evidence of momentum disappeared after the 1997 crisis. Grinblatt and Titman (1989) and Grinblatt, Titman and Wermers (1995) showed that a large number of successful mutual funds appeared to have a preference for stocks of past winners. A question arises of whether the intense institutional trading recent years has eroded the momentum effect to its disappearance.

Chapter 3 Data and Methodology

3.1 Data overview

The data used in this paper comes from the Datastream database[TBD]. It contains all the 1991 equity securities listed on the NASDAQ stock exchange from June 30th 2009 to May 31st 2013. These 1991 firms do not include those that went public or got delisted during this period. Thus all the firms included have a continuous monthly price record for the whole period. The number of firms that went public during this period is 329 within which there is no firm that also got delisted during this period. Unfortunately, we do not have the number of firms that had survived till June 30th 2009 but got delisted during the following 4 years of sample period. Further research will be conducted on this. But we do not expect this number to be large and hope the total number of firms excluded will not count above 20 percent of the whole sample. Also, firms tend to face a decline in their market value before delisted. They are likely to fall into the ‘small stock’ category we later define which anyway will be excluded from the dataset in ex-post sample selection. Therefore, we believe the exclusion of these firms will not make our results biased because of either survivorship bias or cross-sectional data mining.

The monthly price data we use for these 1991 firms is the adjusted closing price at the end of each month starting from June 30th 2009 to May 31st 2013. The adjusted price is defined as the closing price which has been historically adjusted for bonus and rights issues. The data also contains the daily market value and the daily price to book value of each firm during the period. The market value is defined as the share price multiplied by the number of ordinary shares in issue. We also have the daily ‘market value corporation’ data available for each firm which also takes into account the market values of other listed and unlisted equities. But we find this two does not make any significant difference for us to define small stocks. Thus only the market value is used. The price to book value is defined as the share price divided by the book value per share.

3.2 Sample selection and descriptive statistics

Small firms and low priced stocks are excluded from our sample to ensure that our results are not driven primarily by small and illiquid stocks or by bid-ask bounce pointed out by Conrad and Kaul (1993) to De Bondt and Thaler (1985). To achieve this, we define the market capitalization of each firm as the three-year average of their daily market value from January 1st 2010 to May 31st 2013. For the 1991 firms in total, we first rank them according to this average and exclude those that belong to the bottom decile. 200 firms are in this case excluded from the sample and the remaining 1791 firms have their market capitalization from $28.9 million to the highest $377 billion. We then count the number of times for each of the remaining firms to be priced below $5 per share at the ends of the total 36 ranking periods from December 31st 2009 to November 30th 2012. The length we use for a ranking period is six months. Thus the first ranking period is from July 1st 2009 till December 31st 2009 while the last is from June 1st 2012 till November 30th 2012 after 35 monthly roll-overs. Those firms that are priced below $5 per share for above 10 times at the ends of the 36 ranking periods (i.e. the holding periods’ beginnings) are excluded from the sample. These are what we define as low priced firms. 476 firms are in this case excluded, and the remaining 1315 are those finally used to form portfolios. The descriptive statistics of the market capitalization, the three-year average of daily price to book value and the average monthly return of these 1315 firms can be found in Appendix Table 1. Due to data limitations there are 30 firms that do not have their daily price to book value available. [TBD]

3.3 Methodology

By using the monthly adjusted closing prices, first the monthly returns for each firm from July 2009 to May 2013 are calculated. Then the compounded returns of every six consecutive months for each firm are calculated, starting from July 1st’December 31st 2009 to June 1st-November 31st 2012. These are the 36 ranking periods discussed in the previous section. Following Jegadeesh and Titman (1993), at the end of each ranking period we rank the 1315 stocks in our sample based on their past six-month compounded returns and then group them into 5 equally weighted portfolios based on these ranks. Each portfolio consists of 263 firms and is held for the next six months.

Ranking Period Holding Period

( Month -5 to Month 0 ) ( Month 1 to Month 6 )

TBD

Portfolio I always contains stocks ranked from 1-263 which are those stocks that perform worst in the ranking period. Portfolio II always contains stocks ranked from 264 to 789, and so on. It is the Portfolio V that holds the past winners. Each portfolio in our holding period is rebalanced monthly for simplicity. Since each portfolio is only held for six months every time, we believe our monthly returns for each portfolio will not deviate much from those if not rebalanced.

To increase the power of our tests, we also construct overlapping portfolios as Jegadeesh and Titman (1993) did: In this case, a momentum quintile portfolio in any particular month holds stocks ranked in that quintile in any of the previous six ranking months. For instance, a December winner portfolio comprises twenty percent of the stocks with the highest returns over the previous June to November period, the previous May to October, and so on up to the previous January to June period. Each monthly cohort is assigned an equal weight in this portfolio.

To put in another way, for every month (except the beginning five and the ending five months) we now have six Portfolio I s, six Portfolio II s and so on, and the return of the winner/loser portfolio (denoted as Portfolio 5/Portfolio1) in that month is the average of the returns of the six Portfolio Vs/Portfolio Is.TBD

Chapter 4 Results and Analyses

4.1 Average monthly returns

Appendix Table 2 presents the average monthly return from Jan 2010 to May 2013 for each of the five momentum portfolios. The sample is the 1315 stocks we selected. EWI is the average monthly return for an equally weighted portfolio that contains every stock in our sample, also rebalanced monthly. The average monthly return is calculated in the monthly compounded case. P1 is the equally weighted portfolio of 20 percent of the stocks with the lowest returns over the previous six months, while P2 is the equally weighted portfolio of 20 percent of the stocks with the next lowest past six-month returns, and so on. Compared with Jegadeesh and Titman (2001), the monotonic increasing pattern of returns over portfolio ranks observed in their result now disappears. Instead, our result reveals a symmetric U shape of returns over ranks. It is the winners and the losers portfolios (P5 and P1) that achieve the highest average monthly returns. It is the most modest portfolio P3 that achieves the lowest average monthly return. Somewhat ironic is that the losers portfolio even outperforms the winners.

However, these differences are all not statistically significant. The difference between the P5 and P1 portfolio returns is -0.037% and the t statistic is only -0.1068. This is in contrast to the 1.17% difference and 4.96 t statistic found in Jegadeesh and Titman (1993). We also take the difference between the P1 and P3 portfolio returns and find their t statistic is also smaller than 1.

[ Insert Appendix Table 2 ]

To see whether our result of the losers portfolio P1 outperforming the winners portfolio P5 on the average case is due to a potential outlier effect of one specific month, the monthly returns of the two portfolios from January 2010 to May 2013 are presented in Appendix Figure 1. Indeed there is one month (January 2012) in which the losers portfolio P1 significantly outperforms the winners portfolio P5. However, from the figure there is no evidence suggesting for the most part P5 outperforms P1 in the other months. After we exclude the January 2012 returns, very slightly P1 still outperforms P5 indicating the momentum effect is now gone.

[ Insert Appendix Figure 1 ]

4.2 Average price to book values and Average market capitalizations

Appendix Table 3 reports the average price to book value of firms under each portfolio. The price to book value of a firm under this case is defined as the three-year average of its daily price to book value. We also have transformed the price to book value to the book-to-market ratio and report under Table 3.

[ Insert Appendix Table 3 ]

There is a roughly increasing pattern of the book-to-market ratio from P5 to P1 indicating that the past winners portfolio P5 is to a large extent constructed by those glamour stocks named by Lakonishok, Shleifer and Vishny (1994), while the losers portfolio tends to contain the value stocks. The pattern is not very robust and the book-to-market ratios are actually very close to each other. This may be because that we have only divided the sample into five quintiles, and what most crucial is that we have used the three-year average (which does not vary with time) to define a firm’s book-to-market ratio under each holding period which varies with time and with the firm’s position changes within the five quintiles.

Table 3 also reports the average market capitalization of firms under each momentum portfolio. There is also an increasing pattern from P1 to P5 indicating that the past losers portfolio is to a large extent constructed by those stocks of small size firms while the past winners tends to contain big firms. Similar to the price to book value, here the market capitalization suffers from the problem of using the three year average of market value to define a firm’s market capitalization under each holding period.

The results above suggest that the highest average monthly return of P1 seems to be partly due to its smaller market capitalization and higher book-to-market ratio. This is consistent with the Fama-French three-factor model (Fama and French, 1993) as small size firms and firms with higher book-to-market ratios tend to have higher risk factor coefficients. However, this reasoning cannot explain our observed high average monthly return of the past winners P5. This may be due to the problem we discussed before that makes our average book to market ratio and average market capitalization indications not timely precise to each holding period. Also we have not considered the sensitivity of each portfolio to the market risk factor and its magnitude which explains the risk adjusted return in part as well. In order to look further on this, in the next section we test for the risk adjusted abnormal return using the three factor model and check the factor coefficients patterns among the five portfolios.

4.3 The risk adjusted abnormal returns

Though the winners portfolio P5 and the losers portfolio P1 on average outperform P2 P3 and P4, we have to check whether this outperformance is attributed to risk. Appendix Table 4 Panel A summarizes the factor sensitivities of each portfolio to the CAPM model and the Fama-French three-factor model with their t statistics reported in parentheses. The market sensitivity to the CAPM model is estimated by regressing the monthly return of each momentum portfolio less the risk-free rate (except for the zero investment P1-P3 and P5-P1 portfolios) on the monthly return of the NASDAQ composite index less the risk-free rate, while the factor sensitivities to the Fama-French three-factor model is estimated by regressing on the monthly returns of the three Fama-French factors.

CAPM: R-R_f=ï¿½ï¿½(R_m-R_f )+ï¿½ï¿½

FF: R-R_f=ï¿½ï¿½(R_m-R_f )+ b_s (SMB)+b_v (HML)+ï¿½ï¿½

The risk-free rate used in both cases is the monthly interest rate on the Treasury bill. This data is from the Wharton Research Data Services. And the data for the monthly returns of the three Fama-French factors is from the Kenneth R. French Data Library. Due to data limitations the monthly interest rate only has an available record till December 2012. However, as a result of the Federal Reserve quantitative easing policy, the monthly interest rates during the whole sample period are very close to zero with the highest only 0.01%. Thus even without minus these interest rates the results are the same. Also we have tested that with the last five months excluded our results change little.

[TBD]

Chapter 5 Conclusion

TBD

Are all results in accordance?

Do they really tell a story?

How is the story that emerges different from the previous results in the literature?

How would the results contribute or advance our current knowledge?

References

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Jegadeesh, N. and S. Titman (2001), Profitability of momentum strategies: An evaluation of alternative explanations, Journal of Finance 56, 699-720.

Conrad, J. and G. Kaul (1998), An anatomy of trading strategies, Review of Financial Studies 11, 489-519.

Barberis, N., A. Shleifer and R. Vishny (1998), A model of investor sentiment, Journal of Financial Economics 49, 307-343.

Hong, H., and J.C. Stein (1999), A unified theory of underreaction, momentum trading, and overreaction in asset markets, Journal of Finance 54, 2143-2184.

Daniel, K., D. Hirshleifer and A. Subrahmanyam (1998), Investor psychology and security market under- and overreactions, Journal of Finance 53, 1839-1885.

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De Long, J.B., A. Shleifer, L.H. Summers and R.J. Waldmann (1990), Positive feedback investment strategies and destabilizing rational speculation, Journal of Finance 45, 379-395.

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Lakonishok, J., A. Shleifer and R.W. Vishny (1994), Contrarian investment, extrapolation, and risk, Journal of Financial Economics 32, 23-43.

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Grinblatt, M., S. Titman and R. Wermers (1995), Momentum investment strategies, portfolio performance, and herding: A study of mutual fund behavior, American Economic Review 85, 1088-1105.

Fama, E.F. (1970), Efficient capital markets: A review of theory and empirical work, Journal of Finance 25, 383-417.

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Appendix

Figure 1

Monthly Returns of the Winners and the Losers Portfolios

This figure reports the monthly returns of the winners portfolio P5 and the losers portfolio P1 from January 2010 to May 2013. P1 is the equally weighted portfolio of 20 percent of the stocks with the lowest returns over the previous six months and P5 is the equally weighted portfolio of 20 percent of the stocks with the highest returns over the previous six months. The sample stocks used to form these portfolios is the 1315 firms selected from all the stocks listed on the NASDAQ exchange during the sample period of June 30th 2009 to May 31st 2013. The selection of the 1315 firms is based on the criteria illustrated in section 3.2 following which firms went public or got delisted during the sample period, firms with a market capitalization belong to the bottom decile and stocks priced below $5 for above 10 times at the 36 ends of ranking periods are excluded.

Table 1

Summary of Descriptive Statistics

This table reports the descriptive statistics of the average daily market value (market capitalization) and the average daily price to book value from January 1st 2010 to May 31st 2013 for the 1315 (except for the average PTBV where the data for 30 firms is missing) firms selected from all the stocks listed on the NASDAQ exchange during the sample period of June 30th 2009 to May 31st 2013. Also the descriptive statistic of the average monthly return from January 2010 to May 2013 of the 1315 firms is reported. This average monthly return is calculated in the monthly compounded case. The selection of the 1315 firms is based on the criteria illustrated in section 3.2 following which firms went public or got delisted during the sample period, firms with a market capitalization belong to the bottom decile and stocks priced below $5 for above 10 times at the 36 ends of ranking periods are excluded. The unit for MKT_CAP is in millions.

Table 2

Average Monthly Returns

This table presents the average monthly return for each of the five momentum portfolios formed based on past six-month returns and held for six months. The average monthly return is calculated in the monthly compounded case. P1 is the equally weighted portfolio of 20 percent of the stocks with the lowest returns over the previous six months, P2 is the equally weighted portfolio of 20 percent of the stocks with the next lowest returns, and so on. The sample NASDAQ Stocks is the 1315 firms selected from all the stocks listed on the NASDAQ exchange during the sample period of June 30th 2009 to May 31st 2013. The selection of the 1315 firms is based on the criteria illustrated in section 3.2 following which firms went public or got delisted during the sample period, firms with a market capitalization belong to the bottom decile and stocks priced below $5 for above 10 times at the 36 ends of ranking periods are excluded.

Table 3

Average Price to Book Values and Average Market Capitalizations

This table reports the average price to book value, the average book to market ratio and the average market capitalization of firms under each portfolio. The price to book value/market capitalization of a firm under this case is defined as its average daily price to book value/market value from January 1st 2010 to May 31st 2013. P1 is the equally weighted portfolio of 20 percent of the stocks with the lowest returns over the previous six months, P2 is the equally weighted portfolio of 20 percent of the stocks with the next lowest returns, and so on. The sample NASDAQ Stocks is the 1315 firms selected from all the stocks listed on the NASDAQ exchange during the sample period of June 30th 2009 to May 31st 2013. The selection of the 1315 firms is based on the criteria illustrated in section 3.2 following which firms went public or got delisted during the sample period, firms with a market capitalization belong to the bottom decile and stocks priced below $5 for above 10 times at the 36 ends of ranking periods are excluded. The unit for MKT_CAP is in millions.

Table 4

PANEL A CAPM and Fama-French Factor Sensitivities

This table presents the factor sensitivities of each momentum portfolio to the CAPM model and the Fama-French three-factor model. CAPM market sensitivities/FF factor sensitivities are the slope coefficients in the CAPM model/Fama-French three factor model time-series regressions. Their t statistics are reported in parentheses. The testing period is from January 2010 to December 2012. ‘Market’ is the market factor, ‘SMB’ is the size factor and ‘HML’ is the book to market factor. P1 is the equally weighted portfolio of 20 percent of the stocks with the lowest returns over the previous six months, P2 is the equally weighted portfolio of 20 percent of the stocks with the next lowest returns, and so on. The sample of firms used is the 1315 firms selected from all the stocks listed on the NASDAQ exchange during the sample period of June 30th 2009 to May 31st 2013. The selection of the 1315 firms is based on the criteria illustrated in section 3.2 following which firms went public or got delisted during the sample period, firms with a market capitalization belong to the bottom decile and stocks priced below $5 for above 10 times at the 36 ends of ranking periods are excluded.

PANEL B The Risk Adjusted Abnormal Returns

This table reports the risk adjusted returns of each momentum portfolio to the CAPM model and the Fama-French three-factor model. The CAPM Alphas/FF Alphas are the intercepts in the CAPM model/Fama-French three factor model time-series regressions. Their t statistics are reported in parentheses. The testing period is from January 2010 to December 2012. P1 is the equally weighted portfolio of 20 percent of the stocks with the lowest returns over the previous six months, P2 is the equally weighted portfolio of 20 percent of the stocks with the next lowest returns, and so on. The sample of firms used is the 1315 firms selected from all the stocks listed on the NASDAQ exchange during the sample period of June 30th 2009 to May 31st 2013. The selection of the 1315 firms is based on the criteria illustrated in section 3.2 following which firms went public or got delisted during the sample period, firms with a market capitalization belong to the bottom decile and stocks priced below $5 for above 10 times at the 36 ends of ranking periods are excluded.