The Profitability of the Momentum
Strategy in the US Equity Market after
the Credit Crisis
Master Thesis by Hanjun Chen
Supervised by Dr. Chris Florackis
Master in International Finance
University of Amsterdam, Amsterdam Business School
August 2014
Abstract
The momentum strategy investigated in this paper is a common practice adopted by investors to construct a zero-cost portfolio that buys the past performance “winners” and sells the “losers”. This paper aims to compare the profitability of the momentum strategy before and after the financial crisis in 2007. Finally, the results document an average monthly abnormal return of 15 basis points, and prove the disappearance of abnormal return in the post-crisis period. The “Buy” portfolio is found performing better than the “Sell” portfolio. The source of return to “Buy” portfolios is small-sized firms and growth stocks. In contrast to previous literatures, the significant negative return in January is not observed.
Table of Content
Abstract ... 1
Chapter 1 Introduction ... 1
Chapter 2 Literature review ... 4
2.1 Background ... 4
2.2 Academic theories ... 5
2.3 Empirical evidence ... 8
Chapter 3 Data ... 10
3.1 Sample selection and data overview ... 10
3.2 Variables and Data Description ... 12
Chapter 4 Methodology ... 13
4.1 Portfolio Construction ... 13
4.2 Risk-adjustment Models ... 15
Chapter 5 Results and Analysis ... 18
5.1 Return of Momentum Strategy ... 18
5.2 Subperiod Analysis ... 20
5.3 Risk-adjusted Abnormal Return ... 23
5.4 Return of 5 investment strategies ... 25
Chapter 6 Conclusion ... 27 Reference ... 28 Appendix ... 1 Table I ... 1 Table II ... 2 Table III ... 3 Table IV ... 4 Table V ... 5 Table VI ... 6 Figure I ... 7
Chapter 1 Introduction
One of the key objectives of either individual or institutional investors is to construct portfolios that outperform the market. Many tactical or strategic stock-picking strategies have been developed to achieve this goal. For example, investors buy small-size stocks while selling large cap firms, or they purchase value stocks that are underpriced based on fundamental analysis and sell growth stocks that are overpriced. However, the high return generated through these strategies can be explained by taking extra risks as it is shown in Fama and French model. In other words, the outperformance is purely the compensation for investors to bear high risks. In 1993, Jegadeesh and Titman observed one of the most puzzling anomalies, called momentum phenomenon. Academically, they proved that momentum strategy achieves abnormal returns that are not captured by the traditional risk-return models.
The momentum strategy that has been widely adopted by investors is to construct a zero-cost portfolio that buys the past performance “winners” and sells the “losers”. Among all the strategies that try to take advantage of the market inefficiency, momentum is the most straightforward one and is easy to implement. By filtering the past performance of all stocks in a certain market, both best and worst performed stocks are selected to construct a portfolio, in which the “winners” in the top return decile are held, while the “losers” in the
bottom return decile are going short. The portfolio will then be held for a short period ranging from 3 to 12 months before they are rebalanced. Going back to 1993, Jegadeesh and Titman documented abnormal return of 1% per month in US stock market during the period of 1965 to 1989. Their followed-up study in 2001 extends the test period to 1998, a decade after the first research and documents a persistent existence of the momentum anomaly. More recently, the chief of the asset management firm, Gerstein Fisher, said in 2014 "Momentum is
persistent, pervasive, and well documented in virtually every investment and in every country."
However, some practitioners argue that momentum anomaly has disappeared after the dot-com bubble burst in the beginning of 2000s. “Momentum investing,
the notion that you ride rising stocks, got discredited after the dot-com blow-up.”
said Matthew Tuttle, the head of Tuttle Wealth Management.
After the dot-com bubble, global financial markets experienced another big recession due to the credit crisis In the middle of 2007. An important research question is whether the crisis has influence on the existence of momentum abnormal return? It is interesting to further examine the validity and the magnitude of the momentum strategy before and after the credit crisis. The research question is as follow.
Research question: Does the profitability of the Momentum strategy persist in
Since US stock market is representative and is the biggest market in which not only US companies but also international firms are listed, this paper will focus on the US stock market. Another reason to study the US market is that it is where the momentum anomaly was first observed. Also, the Credit Crisis was originated in US. As a result, its financial market took the biggest impact. Therefore, the comparison of how well the momentum strategy performed between pre- and post- crisis period is worth of investigating.
The remainder of this paper consists of five chapters. In Chapter 2, a literature review is given to recap the background, definition and explanation of momentum strategy academically and empirically. Chapter 3 and 4 describe the data and methodology applied in this paper respectively. Chapter 5 presents the results of the paper, including the return of all the portfolios constructed, the interaction of seasonality and momentum, the existence of momentum strategy in post-crisis period, and the influence of crisis on the abnormal return of the strategy. Finally, a conclusion is provided in chapter 6.
Chapter 2 Literature review
2.1 Background
Early in 1985, DeBondt and Thaler identified the long run reversal of stock prices, which suggests that investors should short past “winners” and buy past “losers” due to the overreaction of stock prices to the newly released information. At the time, researchers had a fierce debate on this long-term phenomenon. However, Jagadeesh and Titman(1993) have their eyes on the portfolio performance in the short to medium period. They focus on the momentum strategies, which investigates the relationship between stock historical performance and future return.
Momentum is an anomaly that shows a positive autocorrelation in stock returns over short term. In other words, the stock price movement is implicitly predictable, given its past performance. In the long run, the stock returns are found to reverse in 13-60 months, which is the same as what predicted by DeBondt and Thaler (1993, Jegadeesh and Titman). This observation in 1990s further proves the violation of the most basic assumption of almost all traditional financial models - Efficiency Market Hypothesis(EMH).
Jegadeesh and Titman are not the first who observe the anomaly. Back to 1967, Levy already used relative strength trading rules to test EMH. The relative strength trading rule, which buy “winners” and sell “ losers” is same to the
momentum strategy. But further research that against Levy, argues that the abnormal return reported is due to heavy data mining and bias stock selection, since the high return disappeared when the testing period is extended.
2.2 Academic theories
To resolve the puzzle, many researchers have investigated the cause of abnormal returns yield by momentum strategy. Traditional finance theories, however, fail to explain this anomaly. Almost all traditional finance models assume that the underlying market is efficient and investors are rational. Market efficient hypothesis consists of three forms. The weak form market efficient hypothesis(EMH) states that current asset price already reflects all the past available information, which is rejected by the presence of momentum, as historical return is positively correlated to future price movement. Thus, future price incorporates the information of past performance.
Moreover, Fama and French (1996) propose the price momentum phenomenon as one of the major flaws of their model to which further robustness tests on other recent data sets would be appropriate. Grundy & Martin(2001) also showed that two- and three-factor model could not explain the abnormal returns, even taking into account the dynamics in the factor betas of a momentum
strategy. They suggest that the profitability is a reward for taking firm-specific risks, which is contrary to CAPM and three-factor model.
Some others who support EMH suggest that the presence of momentum anomaly is either due to data mining or simply the failure of risk-adjustment. Among them, a paper of Conrad and Kaul(1998) is notable. They do not believe the predictability of time-series momentum strategy, but insist that the variation of cross-sectional expected returns leads to the high alpha.
As an alternative, behavioral finance theory provides the explanation of momentum anomaly. Past studies mainly highlighted three reasons, including underreaction, overreaction and the combination of both. Originally, researchers simply believed momentum was the result of delayed response to firm-specific factors, like earning surprises. To assess the validity of underreaction, Jegadeesh and Titman(1993) test the return of the momentum portfolio when there is a one-week lag between ranking period and formation period. The portfolio return with one-week lag is slightly higher than the return of the portfolio formed immediately after ranking period. The finding confirms the effect of underreaction.
While De long, Sheleifer, Summers and Waldmann(1990), who support for investors overreaction, argue that the stock return is intensified due to positive-feedback trading, though the fundamental analysis is not solid. Later, Lee
and Swaminathan(2000) argued that both underreaction and overreaction are part of the process that incorporates stock prices. The second paper of Jegadeesh and Titman(2001) on momentum strategy focused on explaining the source of momentum abnormal return. They document the persistence of momentum abnormal return and a reversal pattern in the postholding period. The pattern is consistent to the behavioral explanation.
The behavioral finance predicts that the abnormal return in crisis period is different from it is before crisis. According to behavioral theories, the reaction of irrational investors is related to the market status. The higher the loss and the profit, the more risk-averse investors are. Therefore, during financial crisis period, when the overall market performance was unsatisfied, the reaction of investors is more conservative. It is more likely that investors would underreact to the market. Combining with Jegadeesh and Titman’s finding(1993), underreaction would lead to a higher momentum portfolio return.
In addition to the traditional risk-return theory and investor’s rationality, some other factors are believed to play a role in explaining the momentum. Moskowitz and Grinblatt(1999) show that certain industries have significantly higher profitability on momentum than others in the US market. After controlling for momentum across industries, no momentum is found in individual stock return. Chordia and Shivakumar (2002) state that profits to momentum strategies is resulted from a set of lagged macroeconomic variables and payoffs. Lee and
Swaminathan (2000) proved that past trading volume has an explanatory power on the magnitude of the future price momentum. They interpret the trading volume as a proxy for investors’ interests in a stock, and in turn, related to the speed of transferring information into prices.
2.3 Empirical evidence
The abnormal returns on momentum strategy is not US-market specific, but are globally observed. A large body of research confirms the prevalence of the momentum anomaly in both developed markets and emerging markets over time. Chan et al. (2000) examine the momentum effect based on individual stock market indices in 23 countries all over the world, with the test period of 15 years from 1980 to 1995. They demonstrate that the alpha (abnormal return) is significant and the magnitude is especially large for the four-week holding period. So did Rouwenhourst (1998), who observed the momentum phenomena in 12 European countries. In the Netherlands, Van der Sar & De Haas (2000) documented more than 1% monthly abnormal return in the AEX Stock Exchange of the period from 1973 to 1998. Though the momentum strategy was not observed in Japanese market, Cliffored (2011) argues that it does generate abnormal return after incorporating the value strategy. Therefore, the failure of momentum in Japan cannot be interpreted as the evidence of data mining that reject the findings in prior academic papers.
Prior literature also demonstrates the disappearance of momentum during the market downturn. Cooper, Gutierrez and Hameed(2004) report a mean monthly momentum profit of -0.37% following negative market returns and conclude that momentum profit is positively correlated to market state. More recently, Lee(2012) tests the momentum strategy after Credit Crisis and suggest that liquidity risks partly explain the weak performance of momentum strategy after the crisis.
Chapter 3 Data
The data for this paper comes from DataStream. A list of sample firms selected based on the criteria illustrated in the previous section and the corresponding characteristics of those stocks, including listed exchange, market capitalizations, adjusted closing price and book-to-market ratio, are retrieved from DataStream. Factors related to risk adjustment, such as market premium, firm size factor, and value/growth factor, are obtained through Fama-French data center.
3.1 Sample selection and data overview
The data used to test for the research question are collected from Thomson DataStream. Since the start point of the Credit Crisis is July 2007, the testing period will be in total 12 years from April 2002 to May 2014(including the formation period), which represents 5 years before the crisis and 7 years after. The data consist of all the stocks listed on NYSE and NASDAQ. Since the paper investigates the stocks of all industries, sample data includes all the firms registered under the Standard Industrial Codes (SIC). However, American Depositary Receipts (ADRs), Real Estate Investment Trusts (REITs), closed-end funds, and foreign stocks are excluded, according to the conventions of previous literatures that study the momentum anomaly. Those going public or delisted during the testing period are excluded for the reason that each stock should have a completed set of stock returns in the whole testing period. The monthly return
of each stock will be calculated through the monthly adjusted-closing price, which takes into account the dividend payments and new issues.
To get continuous monthly return in the whole sample period from April 2002 to May 2014, sample stocks includes only those listed before April 2002, and was not delisted during the sample period. Low priced stocks, which are stocks priced below $1, are excluded from samples to make sure that the results are not driven primarily by small and illiquid stocks or by bid-ask bounce indicated by Conrad and Kaul(1993). Small-size firms, measured by market capitalization are also discarded for the same reason pointed out by Conrad and Kaul(1993). After excluding those that are delisted, priced below $1 and small-sized firms, in total 2223 sample stocks are selected. However, due to the incompleteness of the database, finally, 1949 samples are adopted effectively. The effective rate is around 88%.
The monthly price data of these 1949 stocks is the adjusted closing price at the end of each month starting from April 30th 2002 to August 31st 2012. The adjusted price is defined as the closing price, which has been historically adjusted for dividends and rights issues. The data also contains the monthly market value and the monthly book-to-market 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. The book-to-market value is defined as the book value per share divided by the market value per share.
3.2 Variables and Data Description
The key characteristics and their descriptive statistics of 1949 sample stocks are provided in table I. All variables are described in terms of minimum, maximum, mean and standard deviation.
Market capitalizations of 1949 samples range from $27.5 million to $370768 million, with a mean of around $4783 million. It is also used as an indicator of firm size by doing natural log of the market capitalization. The variable shows a pattern of positive skewness.
Monthly average book-to-market value is 0.531, which means, on average, the market value of the sample firms are twice of their book value. The standard deviation of the reported firms is 1.512. This variable is negatively skewed.
Chapter 4 Methodology
4.1 Portfolio Construction
This paper follows the methodology introduced by Jegadeesh and Titman(1993). In particular, each stock will have two stages, one formation period, also called ranking period, and one holding period. The study focuses on the momentum strategy with 3-month ranking period, starting from July 31st 2002 and it will roll
over. To be specific, the first ranking period starts from July 31st 2002 to October
31st. To roll over, the second ranking period begins at August 31st 2002 and ends
up at November 30th 2002.
All sample stocks will be ranked according to their continuous compound return of the past 3 months(ranking period) in an ascending order. Based on this rank, 1949 sample stocks are divided equally into 10 portfolios 1-10, so that Portfolio 1 contains the past “losers” and Portfolio 10 is composed of the past “winners”. In each portfolio, the stocks are equally weighted.1 To more precisely test the
strength of the strategy, those 10 portfolios of each ranking period will then be held for 3 month, 6 months, 9 months and 12 months respectively. This means, four momentum strategies, in terms of different length of holding period will be examined to see the influence of time on the portfolio return. To easily identify the strategy, J presents the length of formation period, and K stands for the length of holding period. Therefore, J*K means to hold a momentum portfolio,
which is ranked by previous J month return, for K month.
For robustness purposes, a second set of 4 momentum strategies that have one month lag between formation period and holding period is constructed to get rid of the effect of bid-ask spread, lagged reaction and price pressure observed by Jagedeesh and Lehmann(1990). In other words, a 3*3 momentum portfolio, which is ranked by past 3-month compounded return of May to July, will be held from September to November. In this case, August is skipped.
This study adopts the overlapping holding period, which means in any given month, the portfolio includes a set of stocks selected in this month and K-1 month before. For example, a 3*3 momentum portfolio constructed in August contains 1/3 of stocks selected in August, 1/3 of stocks selected in July, and 1/3 of stocks selected in June.
The return of above-mentioned strategy will be applied to all buy and sell portfolios. According Jegadeesh and Titman(1993), the buy-and-hold return will be slightly higher than the return of the portfolios that are rebalanced at the end of each month. However, the difference is not significant. Therefore, this paper takes into account only buy-and-hold return.
4.2 Risk-adjustment Models
To examine how well the momentum strategy outperforms the market, and whether the superior performance comes from bearing extra systematic risks, the study applies two risk-adjustment models, Capital Asset Pricing Model(CAPM) and Fama-French Three-Factor Model.
One-Factor CAPM model
𝐸(𝑅𝑖) = 𝑅𝑓+ 𝛽 ∗ �𝐸(𝑅𝑚) − 𝑅𝑓� + 𝜀 （1）
Where
𝐸(𝑅𝑖) is the expected asset or portfolio return,
𝑅𝑓 is the expected return of a risk free asset,
𝐸(𝑅𝑚) is the expected return of the market,
𝛽 measures the sensitivity of an asset or a portfolio to the undiversified market risk.
𝜀 reflects the firm-specific risks
CAPM, Equiation (1), is the financial model aiming to properly price a security or a portfolio, in this case, the momentum portfolio. The momentum portfolio is a portfolio that buys the stocks whose past performance is in the top decile and sells the stocks whose past performance is in the bottom decile. Since the theory states that investors are not reward for bearing firm-specific risk, the expected return only compensates for taking the systematic risks that cannot be
diversified.
𝐸(𝑅𝑖) = 𝑅𝑖 − 𝛼 = 𝑅𝑓+ 𝛽 ∗ �𝐸(𝑅𝑚) − 𝑅𝑓� (2)
Where
𝑅𝑖 is the buy-and-hold return of the portfolio,
𝛼 is the abnormal rate of return.
As Equation(2) shows, 𝛼 is the excess return over the expected return estimated by CAPM. A positive 𝛼 indicates that the momentum strategy outperform the market, so that investors will profit from adopting the strategy. A negative 𝛼 suggests that holding the market portfolio is more profitable. Theoretically, CAPM should perfectly estimate the return of the portfolio under the condition that all assumptions are met, which means 𝛼 should be zero.
Fama-French three-factor Model
Similar to the CAPM model, Fama-French three-factor Model(FF) is extended to three variables based on the traditional CAPM model. In addition to the market premium, FF includes size premium and the premium of value stocks on growth stocks.
𝐸(𝑅𝑖) = 𝑅𝑓+ 𝛽𝑚∗ �𝐸(𝑅𝑚) − 𝑅𝑓� + 𝛽𝑠 ∗ 𝑆𝑀𝐿 + 𝛽𝑣 ∗ 𝐻𝑀𝐿 + 𝜀 (3)
Where
SML stands for small (market capitalization) minus large, HML means high (book-to-market ratio) minus low,
𝛽𝑠 is the sensitivity of the portfolio to the size factor,
𝛽𝑣 is the sensitivity of the portfolio to the value stocks premium.
Equation(3) decomposes the FF model into three sources. Since small-size stocks and value stocks outperform the market as a whole, the adding two variables explain part of the systematic risks that are not captured by the traditional CAPM model. Empirically, FF model explains on average 20% more portfolio returns that are well diversified than CAPM model does. Therefore, it is expected that the abnormal return measured by FF model would be lower.
𝐸(𝑅𝑖) = 𝑅𝑖 − 𝛼 = 𝑅𝑓+ 𝛽𝑚∗ �𝐸(𝑅𝑚) − 𝑅𝑓� + 𝛽𝑠∗ 𝑆𝑀𝐿 + 𝛽𝑣 ∗ 𝐻𝑀𝐿 + 𝜀 (4)
Equation(4) expresses the risk adjustment process of FF model. The abnormal rate of return, alpha, is the difference between the real rate of return of the momentum portfolio, represented by 𝑅𝑖, and the expected return measured by
FF model. Still, a positive alpha signals the existence of momentum anomaly. This paper compares the alpha, calculated under CAPM and FF model, in both pre- and post- crisis period to see the trend and profitability of momentum strategy.
Chapter 5 Results and Analysis
5.1 Return of Momentum Strategy
Table II presents the return of each of the 8 momentum strategies. The samples include 1949 firms selected in accordance to the criteria described in the previous chapter. The momentum portfolios are constructed based on the past 3 months performance and held for K months respectively. The strategy is defined as 3*K in the following of this paper. “Sell” portfolios are past losers in the bottom decile. “Buy” portfolios are best past performers in the top decile. The “Buy-Sell” portfolios are the so-called momentum portfolios that are built to test the anomaly.
Panel A reports 4 momentum strategies that are held immediately after the ranking period. As the 1st row shows, holding P1 portfolio for 3 months generates
the lowest return, more than 1% loss per month. The return of P1 goes up with the increase in holding period. For instance, comparing to 3-month investment period, holding the loser portfolio for 12 months earns a positive monthly return of 2.2%, which is 3% higher than the return of the 3*3 strategy. Thus, past losers is expected to reverse the performance in longer period, which confirms the findings in the prior literatures. Looking at the t-statistics, the return of holding past losers for either 2 quarters or a year is not significantly different from zero. The monthly returns of all other portfolios are significant in a 5% confidence
level.
The similar reversal trend is observed on P10 portfolio, which includes the top past winners. With a holding period of 3 months, the portfolio return is around 1.6%. While, the return drops to 1.28% as holding period is extended to 12 months. Taking the effect of both P1 and P10 into account, the combined 3-month relative strength portfolio achieves the highest return of about 2.7% per month among 4 momentum strategies. The result indicates that the monthly returns of the momentum portfolios gradually declines and becomes negative, as the return of the strategy with 12-month holding period is only negative 0.96%. This observation suggests that the profitable momentum strategy works for short term, but the profitability disappears in the long run.
In Panel B, the holding period of the portfolios starts one month after the end of the ranking period. The monthly return of a 3*3 strategy is 2.16%, 0.5% lower than the return of the 3*3 strategy documented in Panel A. Since some liquidity effects are avoided, the portfolios with one-month lag generate relatively lower returns than they do without the lag. This is contrary to the findings of Jegadeesh and Titman(1993) who state lagged portfolios have higher return. Furthermore, the reversal effect is not as strong as it is on the momentum portfolios without the lag. Comparing to the -0.96% monthly return of 3*12 momentum strategy reported in Panel A, a loss of 0.74% per month is observed for the lagged 3*12 momentum portfolio. Again, holding a “sell” portfolio that contains the past
losers for 2 quarters and a year does not earn a return that is significantly different from zero.
In summary, holding the momentum portfolio for 1 quarter to 3 quarters generates a maximum positive monthly return of 2.7%. However, the return of the momentum portfolio decrease as the holding period increases. The source of portability comes from “buy” portfolios that perform better than “sell” portfolios. With a month lag, the momentum portfolios are found less profitable than those without the lag.
5.2 Subperiod Analysis
Seasonal Patterns
This subsection investigates for the possible seasonal patterns presented in the momentum strategies. Previous papers suggest that timing has impact on the performance of the momentum portfolios formed between 1969 and 1989. Due to the burst of Dot-com Bubble in 2002 and the breakout of the Financial Crisis in 2007, it is suspected that the January phenomena will not be observed in the sample period of 2002 to 2014. Table III documents the returns of 4 momentum portfolios with different holding periods by calendar months. To avoid liquidity influence, these are lagged momentum portfolios, meaning that there is one-month time between the formation period and the investing period.
positive return in each of other months. However, they did not give the explanation of why momentum strategy does not work well in January. This study does not observe a negative performance in January, except for the 3*12 strategy whose January return is -1.02%. This is understandable, as the 3*12 strategy overall are not profitable (-0.74%) under the influence of the reversal effect.
As reported in the 3*3 strategy of Table III, an average return of 1.92% is realized in January of each sample year. Excluding January, the average return of the rest 11 months is 2.18%. Although the January return is lower than the average, it deviates from the evidence documented by previous literature, because other month in the year reports lower return. Moreover, the length of holding period does not affect the seasonal pattern. In other words, the same patterns are observed on the other three strategies. The disappearance of the significant low returns in January is in contrast to the findings of Jegadeesh and Titman in 1993. Although January does not show a specific pattern, the findings in Table III still suggest some other seasonal patterns. In all 4 strategies, the monthly return in May is relatively lower than each of the other months. For example, the return of May in the 3*9 strategy is 0.53%, comparing to the average monthly return of 0.67% in the other months. Meanwhile, October generally has the highest return among all calendar months. Still taking 3*9 strategy as an example, 0.86% monthly return in October is reported, which is 0.3% higher than the average
monthly return.
F-statistics test the joint significance of all monthly returns. The results show that if the momentum portfolios are held for less than 4 quarters, the returns of each calendar month are not significantly different from each other. The finding is persistent no matter January is included or not. This confirms the disappearance of underperformance in January observed in this paper. In the 3*12 strategy, a high F-statistics and P-value indicate that the returns of each calendar month are not jointly significant. Also, the return of January is significantly different from the returns of the rest months in the 3*12 strategy.
The Impact of the Credit Crisis
Using the same set of samples as it is in the previous tests, this subsection compares the momentum performance before and after the Financial Crisis breakout in summer 2007. The sample period narrows to 10 years from July 2002 to August 2012, which is 5 years before and after the Crisis respectively. Again, 4 momentum portfolios of different holding period are constructed with one-month lag to get rid of the interference of liquidity effect and short-run reversal.
Table IV documents the returns of 4 momentum portfolios in the pre- and post- crisis time. All 4 strategies show the same trend that the monthly return in the pre-crisis period is more than 0.5% higher than in the post-crisis period. For example, comparing to the pre-crisis return of 2.31%, the post-crisis monthly
return drops to 1.85% in the 3*3 strategy. Also, the hypothesis that the returns before and after the crisis are equal is rejected. In other words, p-value that compares the performance indicates that the returns before and after the crisis are significantly different.
It is interesting to find that the negative return of the 3*12 strategy is mainly due to the underperformance of the momentum strategy after the crisis. The strategy of the whole sample period loses 0.74% per month, while it earns a monthly return of 0.13% before the crisis. This means the 3*12 momentum strategy suffers from the financial crisis, as suggested by the post-crisis return of -0.81% per month.
5.3 Risk-adjusted Abnormal Return
Risk-adjusted Alpha
To investigate the existence of the momentum anomaly, this study calculates the abnormal return of the momentum strategy before and after the financial crisis. The test focuses on the 3*6 momentum strategy with one-month lag. Table V reports the alphas in both CAPM and Fama-French three-factor model, which are the intercepts of the regressions.
As reported by Table V, the 3*6 momentum portfolio has a positive return of 0.05% per month adjusted by CAPM, and a slightly lower return of 0.04% adjusted by FF model. The abnormal return measured by FF model is lower, since two more
factors, firm size and book-to-market ratio, explain part of the return as a reward for bearing risks.
Now compare the alphas before and after the crisis. This paper documents a positive abnormal return of 0.16% and 0.15% respectively by two risk-adjustment models in the pre-crisis time. While, the momentum portfolio is not profitable after the crisis, as it underperforms the market by 0.04% and 0.03% respectively. This finding confirms the disappearance of the momentum anomaly in the post-crisis period.
Factor Sensitivities
This section investigates the source of the abnormal return by looking into the factor sensitivities of the momentum portfolio. Table VI reports the CAPM and Fama-French factor sensitivities of each of the 10 portfolios and the “buy-sell” portfolio in the 3*6 momentum strategy with a month lag. The model sensitivities are the coefficients of the factors in the time-series regressions. According to Table VI, two portfolios of worst past performers and two portfolios of best past performers has a CAPM beta of more than 1. CAPM beta shows a unique pattern that the factor sensitivities of P1 and P10 are higher than that of the rest 8 portfolios, and it display a U-shape. This finding is consistent to the results of Jegadeesh and Titman(2001), who also find a U-shape of CAPM beta. The “buy-sell” portfolio, also called momentum portfolio, has a negative beta close to -0.1. The FF beta is relatively lower than the CAPM beta, and it does not
present the U-shape pattern. Different from a negative momentum portfolio beta of -0.1 in the CAPM model, the FF beta is positive(0.005).
SMB factor sensitivity has the same U-shape patter as CAPM beta. Also, Jegadeesh and Titman(2001) report that the “sell” portfolio is more sensitive to the firm size factor. However, this table VI suggests that P10, the “buy” portfolio, has the highest firm size sensitivity of 0.97.
Regarding to the value stock premium(HML), it is found that past losers are more sensitive to this factor. The sensitivity declines as the ranking of the portfolios goes up, which means P10 is least sensitive to the factor. T-statistics also indicate that the coefficients of P6 to P10 are not significantly different from zero. The momentum portfolio is found highly sensitive to the HML factor(-0.6).
5.4 Return of 5 investment strategies
This section compares the returns of 5 investment strategies, including holding “losers” portfolio, buying “winners” portfolio, holding momentum portfolio, buying risk free asset and investing in market index. Among all 5 strategies, the three related to momentum anomaly are based on the 3*6 strategy with one-month lag. The simulation assumes that 1 euro is invested from the beginning of the sample period, July 2002, to May 2014.
Figure 1 demonstrates how profitable momentum is comparing to other investment strategies. Within expectation, the “sell” portfolio performs the worst
among all 5 strategies, since only 0.12 euro left at the end of the investment period. Market index overall depicts a growing trend. While, the performance of the risk free asset is flat.
Compared with other 4 investment strategies, momentum portfolio is the most successful strategy, as 1 euro worth around 9 euros at the end of the sample period. Only in the period from July 2003 to July 2006, buying “winners” generates higher return than the momentum portfolio. After 2011, the return of momentum portfolio decreases gradually. This suggests that the momentum anomaly does not disappear immediately after the breakout of the financial crisis, but gradually disappearing after 2011.
Chapter 6 Conclusion
In conclusion, this paper proves that the momentum anomaly is less pronounced after the credit crisis in 2007. The results suggest, except for 3*12 momentum strategy, the rest 3 strategies are profitable with an average monthly return of 1.9% before the crisis, and significantly lower after the financial crisis. In particular, a negative abnormal return of 0.04% shows that momentum anomaly disappears in the post-crisis period. On average, the “buy” portfolio performs better than the “sell” portfolio, which deviates from the findings of Jegadeesh and Titman(2001), who show that “buy” portfolio returns and “sell” portfolio returns are not significantly different from each other.
Further investigation focuses on the subperiod analysis, which indicates that, the negative January return documented by prior literature is not found in our sample period. Among all calendar months, the momentum performance in May is the lowest, while October is the best month in terms of the momentum portfolio returns.
Risk-adjustment models suggest, the winner portfolio that achieves the highest return has higher market beta and SMB coefficient, as estimated by Fama-French model, but lower HML coefficient. This indicates that past winners consists of small size firms and growth stocks, which is opposite to the findings of Jegadeesh and Titman who find past winners are mostly small size firms and value stocks.
Reference
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Appendix
Table I
Table I
Descriptive Statistics
This Table reports the descriptive statistics of 1949 sample stocks. Mean, minimum, maximum and standard deviation of average monthly market capitalization and average monthly book-to-market value in the sample period are provided. The unit of market capitalization is in millions. The sample selection criteria are illustrated in Chapter 3.
Mean Median Minimum Maximum Std. Deviation
Market Capitalization 4782.795 796.773 27.500 370767.900 21479.841
Table II
Table II
Returns of Momentum Portfolios
The momentum portfolios are constructed based on the past 3 months performance and are held for K months. The 3-month lagged returns of the stocks are ranked in ascending order. The “sell” portfolio is an equally weighted portfolio that includes the stocks in the lowest return decile. The “buy” portfolio is an equally weighted portfolio that includes the stocks in the highest return decile. This table reports the returns of “sell”, “buy” and “buy-sell” portfolios. T-statistics is reported in the parentheses. The sample period is from August 2002 to May 2014.
Panel A J K= 3 6 9 12 3 Sell -0.0105 -0.0067 0.0064 0.0224 t-statistics (-3.31) (-1.73)* (0.52) (1.75)* 3 Buy 0.0163 0.0149 0.0150 0.0128 t-statistics (15.50) (11.16) (8.79) (7.86) 3 Buy-sell 0.0269 0.0216 0.0086 -0.0096 t-statistics (33.55) (32.04) (24.68) (-17.83) Panel B J K= 3 6 9 12 3 Sell -0.0084 -0.0053 0.0051 0.0175 t-statistics (-2.69) (-1.40)* (0.42) (1.39)* 3 Buy 0.0132 0.0119 0.0117 0.0101 t-statistics (11.40) (9.07) (15.03) (9.67) 3 Buy-sell 0.0216 0.0172 0.0067 -0.0074 t-statistics (24.85) (23.39) (17.76) (19.82)
Table III
Table III
Returns of Momentum Portfolios by Calendar Months
The momentum portfolios are constructed based on the past 3 months performance and are held for K months. The “sell” portfolio is an equally weighted portfolio that includes the stocks in the lowest return decile. The “buy” portfolio is an equally weighted portfolio that includes the stocks in the highest return decile. There are 12 January portfolios in 12 samples years, so do other calendar month portfolios. The January portfolio is constructed before January. This table reports the average monthly returns of the zero-cost “buy-sell” portfolios by calendar month. T-statistics is reported in the parentheses. The sample period is August 2002 to May 2014.
K= 3 6 9 12 Jan 0.0192 0.0134 0.0056 -0.0102 t-statistics (17.33) (8.71) (7.02) (7.59) Feb 0.0204 0.0185 0.0055 -0.0074 t-statistics (8.56) (4.87) (5.85) (3.81) Mar 0.0214 0.0185 0.0067 -0.0083 t-statistics (20.72) (12.97) (7.62) (9.13) Apr 0.0214 0.0157 0.0059 -0.0086 t-statistics (18.17) (15.29) (8.43) (8.87) May 0.0192 0.0155 0.0053 -0.0127 t-statistics (13.93) (7.48) (3.16) (1.46) Jun 0.0238 0.0186 0.0065 -0.0057 t-statistics (8.61) (11.02) (7.65) (4.94) Jul 0.0215 0.0191 0.0081 -0.0087 t-statistics (10.57) (11.16) (12.06) (12.15) Aug 0.0188 0.0176 0.0071 -0.0086 t-statistics (20.04) (16.32) (14.31) (11.77) Sep 0.0217 0.0181 0.0069 -0.0066 t-statistics (13.99) (9.59) (11.92) (5.26) Oct 0.0246 0.0170 0.0086 0.0038 t-statistics (4.17) (9.27) (6.54) (9.11) Nov 0.0228 0.0171 0.0068 -0.0089 t-statistics (13.55) (8.42) (8.32) (9.09) Dec 0.0242 0.0175 0.0069 -0.0074 t-statistics (15.05) (6.99) (4.57) (3.93) F-statistics1 4.12 3.28 1.72 6.33 P-value (0.00) (0.00) (0.43) (0.00) F-statistics2 3.98 3.19 1.66 5.74 P-value (0.00) (0.00) (0.41) (0.00)
1The F-statistics are measured under the hypothesis that the returns of the momentum portfolios are jointly equal in all calendar months. 2The F-statistics tests the hypothesis that the returns of the momentum portfolios are jointly equal in calendar month from Feb to Dec.
Table IV
Table IV
Comparison of Momentum Portfolios: Impact of Crisis
The momentum portfolios are constructed based on the past 3 months performance and are held for K months. The 3-month lagged returns of the stocks are ranked in ascending order. The “sell” portfolio is an equally weighted portfolio that includes the stocks in the lowest return decile. The “buy” portfolio is an equally weighted portfolio that includes the stocks in the highest return decile. This table compares the average returns of the zero-cost “buy-sell” portfolios before and after the crisis. The crisis breakouts since July 2007. The sample period is from August 2002 to July 2012, which is 5 years before and after the Crisis respectively. Associated t-statistics is reported in the parentheses. K= 3 6 9 12 Total 0.0216 0.0172 0.0067 -0.0074 t-statistics (24.85) (23.39) (17.76) (19.82) Pre crisis 0.0231 0.0194 0.0076 0.0013 Post crisis 0.0185 0.0128 0.0011 -0.0081 t-statistics (0.88) (2.01) (2.08) (3.48) P-value (0.00) (0.00) (0.00) (0.00)
Table V
Table V
CAPM and Fama-French Alphas
The momentum portfolios are constructed based on the past 3 months performance and are held for 6 months. The “sell” portfolio is an equally weighted portfolio that includes the stocks in the lowest return decile. The “buy” portfolio is an equally weighted portfolio that includes the stocks in the highest return decile. This table reports the risk-adjusted returns of the 3*6 momentum portfolio, which are the intercepts from the CAPM and Fama-French regressions. Associated t-statistics is reported in the parentheses. The sample period is August 2002 to July 2012.
Alpha CAPM FF Total 0.0005 0.0004 t-statistics (31.44) (31.23) Pre crisis 0.0016 0.0015 t-statistics (26.39) (24.83) Post crisis -0.0004 -0.0003 t-statistics (16.16) (15.91)
Table VI
Table VI
CAPM and Fama-French Factor Sensitivities
This table reports the CAPM and Fama-French factor sensitivities of each of the portfolio in the 3*6 momentum strategy with a month lag. The model sensitivities are the coefficients in the time-series regression. SMB stands for "small minus big", which is the firm size factor. HML represents " high minus low", which is the value stock premium. T-statistics are reported in the parenthesis. CAPM FF Factors Market Market SMB HML P1 1.1434 0.0000 0.9925 0.8262 0.6181 t-statistics (14.13) (0.00) (11.97) (4.35) (3.70) P2 1.0748 0.0000 0.9329 0.7766 0.5810 t-statistics (13.28) (0.00) (11.26) (4.09) (3.47) P3 0.9302 0.0000 0.8466 0.7772 0.2581 t-statistics (16.09) (0.00) (25.19) (10.09) (3.80) P4 0.9180 0.0000 0.8699 0.7323 0.1452 t-statistics (17.70) (0.00) (43.83) (16.11) (3.62) P5 0.8660 0.0000 0.8207 0.6908 0.1370 t-statistics (16.70) (0.00) (41.35) (15.20) (3.42) P6 0.8565 0.0000 0.8362 0.6767 0.0338 t-statistics (15.88) (0.00) (32.16) (11.35) (0.64) P7 0.8922 0.0000 0.8711 0.7049 0.0352 t-statistics (16.27) (0.00) (32.96) (11.63) (0.65) P8 0.9636 0.0000 0.9407 0.7613 0.0381 t-statistics (17.57) (0.00) (35.59) (12.56) (0.71) P9 1.0312 0.0000 0.9848 0.8872 0.0151 t-statistics (15.57) (0.00) (21.26) (8.36) (0.17) P10 1.1343 0.0000 1.0833 0.9759 0.0166 t-statistics (17.12) (0.00) (23.39) (9.19) (0.18) P10-P1 -0.0987 0.0000 0.0050 0.0715 -0.5951 t-statistics (-1.33) (0.00) (0.05) (0.32) (-2.97)
Figure I
This figure compares the returns of 5 investment strategies, including holding “losers” portfolio, buying “winners” portfolio, holding momentum portfolio, buying risk free asset and investing in market index. Among all 5 strategies, the three related to momentum anomaly are based on the 3*6 strategy with one-month lag. The simulation assumes that 1 euro is invested from the beginning of the sample period, July 2002, to May 2014.
0 2 4 6 8 10 12 14 7- 1-02 1-03 7- 1-03 1-04 7- 1-04 1-05 7- 1-05 1-06 7- 1-06 1-07 7- 1-07 1-08 7- 1-08 1-09 7- 1-09 1-10 7- 1-10 1-11 7- 1-11 1-12 7- 1-12 1-13 7- 1-13 1-14
Figure I, Five Investment Strategies
P1 P10 Risk free Market index Buy-sell
