Momentum strategies on
the Swedish market
Master’s Thesis 30 credits
Department of Business Studies Uppsala University
Spring Semester of 2019
Date of Submission: 2019-05-29
Simon Bergsten
Supervisor: Alexander Rad
ACKNOWLEDGEMENTS
I would like to thank my supervisor Alexander Rad who has supported and guided me throughout my journey with valuable feedback and advice. Further, I would like to thank friends and family for their support. Lastly, I would like to thank peer students for their constructive feedback.
Abstract
Comparing the performance of a pure momentum strategy with a strategy based on intermediate past returns on OMXS 1999-2018, this study shows that a pure momentum strategy significantly outperforms a strategy based on intermediate past returns. The pure momentum strategy delivers significant returns, primarily for portfolios based on shorter formation and holding periods. Furthermore, this study show that these significant returns are not due to loading on common systematic risk factors. Moreover, this study shows that by implementing a scaling component to the pure momentum strategy, investors can mitigate the crash risk in momentum strategies to some extent.
Keywords: Financial markets, Sweden, Investment decisions, Momentum Strategy, Intermediate Past Returns, Risk, Volatility
TABLE OF CONTENTS
1 Introduction ____________________________________________________________________ 1 2 Previous Literature _______________________________________________________________ 4 2.1 Momentum strategy ___________________________________________________________ 4 2.2 Pure Momentum strategy ______________________________________________________ 6 2.3 Pure Momentum in Sweden ____________________________________________________ 8 2.4 Intermediate past returns _______________________________________________________ 9 2.5 Risk-adjusted momentum _____________________________________________________ 10 3 Method _______________________________________________________________________ 12 3.1 Pure momentum ____________________________________________________________ 12 3.2 Intermediate time past returns __________________________________________________ 14 3.3 Risk-Adjusted Momentum ____________________________________________________ 15 3.4 Risk-Factors Construction _____________________________________________________ 17 3.6 Critical analysis of the methodology _____________________________________________ 18 4 Data _________________________________________________________________________ 19 4.2 Data sources _______________________________________________________________ 19 4.3 Sample Design and Treatment__________________________________________________ 20 4.4 Critical overview of the data selection process _____________________________________ 21 5 Empirical Results & Analysis _____________________________________________________ 22 5.1 Pure Momentum Returns ______________________________________________________ 22 4.2 Intermediate past Returns _____________________________________________________ 28 5.3 Risk-Adjusted momentum _____________________________________________________ 31 5.4 Robustness check ___________________________________________________________ 36 6 Discussion ____________________________________________________________________ 37 7 Conclusion & Suggestions for further research ________________________________________ 38 7.1 Conclusion _________________________________________________________________ 38 7.2 Further Research ____________________________________________________________ 39 References ______________________________________________________________________ 41 Appendix A _____________________________________________________________________ 43 Appendix B _____________________________________________________________________ 47
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1 Introduction
Momentum, the tendency of an object in motion to stay in motion, is a pervasive anomaly in asset prices (Barroso & Santa-Clara, 2015). The consistency of momentum returns has put some serious challenges on leading financial markets theories and become a focal point in the discussion regarding market efficiency. The strategy, consisting of buying assets which have outperformed in the short or intermediate past (one to twelve months) while simultaneously selling underperforming assets during the same period have evidently shown to generate excess returns across multiple markets and throughout different periods in time (e.g.
Jegadeesh & Titman, 1993; Rouwenhorst, 1998; Fama & French, 2012; Asness, et al., 2013).
Given the consistency and magnitude of the momentum returns, the pursuit of viable explanations for the market anomaly have yielded in multiple competing theories. Most researchers agree though that the returns can be explained by either behavioral or risk elements.
Research regarding momentum strategy boosted after De Bondt & Thaler (1985, 1987) contention that investor can earn abnormal returns by advocating a strategy referred to as contrarian. According to De Bondt & Thaler (1985), a contrarian strategy exploit investors overreaction to information in the long-term (3 to 5 years), and thus buy past losers while simultaneously sell past winners since investors drive stock prices too far into one direction which consequently lead to a reversion in the future. In their study, De Bondt & Thaler (1985) show that this strategy yielded abnormal returns since past winners was outperformed by past losers because both assets had overreacted to information. In the aftermath of the findings attributable to a contrarian strategy, studies such as Jegadeesh (1990) and Lehmann (1990) focused on the short-term effects and found evidence that investors can earn abnormal returns in the short-term by following the recent trend of the assets. This provided a hypothesis that in the short run, up to twelve months in Jegadeesh & Titman (1993), investors underreact to information and consequently, investors can earn abnormal returns by following the trend of the stocks, more commonly referred to as a momentum strategy.
Momentum returns are a phenomenon which have drawn significant attention in the financial research due to its consistency, magnitude and disobedience of widespread financial market theories such as the efficient market hypothesis. In their pioneer study regarding momentum returns, Jegadeesh & Titman (1993) found that stocks which have performed relatively well in
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the past 12 months outperform stocks that have performed relatively poor in the same period with as much as 1.49 percent on average per month over the following three months. More specifically, Jegadeesh & Titman (1993) rank stocks in ascending order based on their relative performance in the past 3,6,9 or 12 months, referred to as the formation period. Then, the stocks with the best relative performance over the formation period are bought while the worst performing stocks are sold and then held over what is called the holding period, which constitutes of the upcoming 3, 6, 9 or 12 months following the formation period. The
portfolios constructed by buying past winners and simultaneously sell past losers are referred to as the winners-minus-losers (WML) portfolios. Over the years, multiple researcher has adopted the methodology for portfolio construction as described in Jegadeesh & Titman, (1993) and this particular strategy will be referred to as the pure momentum strategy.
Today, there is a plethora of studies regarding momentum returns in the financial research.
While many reserchers have focused on pure momentum strategies as suggested by Jegadeesh
& Titman (1993), others have developed new models. Two of the more recent models have been proposed by Novy-Marx (2012) and Barroso & Santa-Clara (2015). Novy-Marx (2012) argues that momentum returns can be improved if investors use intermediate past returns, meaning returns from 12 to seven months prior to formation of the portfolios rather than having formation and holding period connected. This strategy is referred to as the
intermediate past return strategy. On the other hand, Barosso & Santa-Clara (2015) argue that while momentum strategies have provided large abnormal returns historically, the strategy suffers significant losses from time to time, which are due to the specific strategy and not the market. Thus, Barosso & Santa-Clara (2015) suggest that returns can be boosted if investors account for risk by scaling the amount invested in the momentum strategy by a factor which depends on the realized variance from previous six months. This strategy is referred to as a risk-adjusted momentum strategy.
In this study, the primary purpose is to examine whether momentum returns exist on the Swedish market using the two distinct methodologies proposed by Jegadeesh & Titman (1993) and Novy-Marx (2012), respectively. Furthermore, this study aims to study whether a pure momentum strategy can be improved after accounting for risk as suggested by Barosso
& Santa-Clara (2015). Hence, the methodologies proposed by Jegadeesh & Titman (1993)
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and Novy-Marx (2012) will first be compared regarding their predictive power of momentum returns. Then, this study will further investigate whether a risk-adjusted momentum strategy as suggested by Barosso & Santa-Clara (2015) can further improve a momentum strategy. In this study, I will focus on the pure momentum as the baseline for the risk-adjusted strategy.
Moreover, this study is conducted on the Swedish market, which is an interesting market to study given the inconclusive results from previous studies. Chui et al. (2010) found that abnormal momentum returns are prevalent in Sweden and link these findings to signs of overconfidence and self-attribution bias among investors. Moreover, studies such as Fama &
French (2012); Leippold & Lohre (2011); Gong et al. (2015); Asness et al. (2013) all find excess momentum returns on the Swedish market. On the other hand, Griffin et al. (2003) and Rouwenhorst (1998) are unable to find any significant momentum returns on the Swedish market.
For the outline of this paper, previous literature is reviewed and discussed in chapter two. The previous literature section starts with some more theoretical studies regarding momentum which are then followed by a review of previous findings from multiple research papers.
Following the previous literature, section three will describe the methodology used in this study. Here, the focus will be on following the approaches taken in previous well-cited papers by Jegadeesh & Titman (1993) for the construction of the pure momentum strategy, Novy- Marx (2012) for the intermediate past return momentum and Barroso & Santa-Clara (2015) for the risk-adjusted momentum. Section four presents the data selected and the data treatment process. Section five presents the results and analysis of the study. Section six presents a discussion regarding the results found and their implications for investors. Lastly, section seven presents the conclusion and suggestions for further research.
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2 Previous Literature
This section reviews some of the extensive research that has been made regarding momentum strategies. First, more theoretical papers will be reviewed which seeks to explain why
abnormal momentum returns exist. Moving on, previous literature regarding pure momentum will be scrutinized. While most of the research has been conducted on the U.S market,
primarily the earliest studies, there are still multiple studies on the European and Swedish market which will be reviewed in greater detail given that Sweden is the market of choice in this study. Furthermore, considering that this study aims to investigate more recent
developments such as the intermediate past returns strategy and a risk-adjusted momentum strategy, research papers with these two methodologies have been further reviewed.
2.1 Momentum strategy
While most researchers such as Bird & Casavecchia (2007) are unable to find a plausible explanation to why stocks underreact in the shorter-term (up to twelve months) in accordance with the momentum effect and then overreact and thus experience a long-term reversal in the longer-term (contrarian), most researchers agree that momentum returns exist due to either behavioral biases among investors, or more rational explanations such as higher risk.
Researcher advocating the behavioral explanation claim that it is the investment decision relying on behavioral biases that leads to higher returns. Hence, investors are considered irrational as they are unable to evaluate all information. Multiple evidence support the hypothesis that investors are not fully rational. Kahneman & Tversky (1974) showed that people tend to hold heuristics and biases when they make decisions under uncertainty.
Furthermore, as suggested by Barberis et al. (1998), people respond slowly to new
information. Consequently, it has been argued that in the short and medium term horizon (one to twelve months), people underreact to new information and thus prices adjust slowly which lead them to exhibit positive autocorrelation (e.g. Frazzini, 2006; Shiller, 1981). However, over longer time horizons, it is argued that people overreact to information and thus, prices drifts too far into the same direction, making a contrarian strategy plausible as suggested by De Bondt & Thaler (1985, 1987).
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In line with the behavioral explanation, Hong & Stein (1999) concluded that both short-run continuation (underreaction) and long-run reversal (overreaction) occurred more significantly in smaller stocks, in which information diffuses more slowly and thus, the drift is more apparent, which is in line with the behavioral explanation. Moreover, Daniel et al. (1998) argue that investors that suffer from overconfidence will overestimate their ability to generate information, or to identify the significance of existing data that others neglect and thus
underestimate his or her forecast errors. Hence, Daniel et al. (1998) argue that overconfident investors will put to much weight on their beliefs which causes stocks prices to overreact.
Furthermore, building upon the behavioural explanation, Chui et al. (2010) accounts for cultural differences between countries when examining whether individualism affect momentum profits. Chui et al. (2010) adopt the definition of individualism from Hofstede (2001), who defines individualism as the degree to which people focus on their internal attributes, such as their own abilities, to differentiate themselves from either. By applying the individualism index created by Hofstede (2001), Chui et al. (2010) examined whether there are any differences in momentum profits across countries based on the individualism index.
The results from Chui et al. (2010) suggest that in countries with higher individualism,
momentum profits are more significant. Consequently, Chui, et al. (2010) argue that investors behavioral attributes such as overconfidence and self-attribution bias seem to have an impact on momentum returns.
As discussed, multiple researchers have attributed momentum returns to behavioral attributes among investors. However, a second group of researchers have argued that momentum returns have a more rational explanation. These researchers argue that momentum returns exist since the strategy is riskier and thus, the returns are simply a result of higher risk premiums. For example, Johnson (2002) provide a more rational explanation for the
momentum returns. According to Johnson (2002), a model of firm cash-flows discounted by and ordinary pricing kernel can deliver a strong positive correlation between past realized returns and current expected returns. Hence, Johnson (2002) argues that a direct, plausible and rational mechanism can explain the momentum effects puzzle. Furthermore, Johnson (2002) states that firms that recently have had large positive (negative) price moves are more likely to have had positive (negative) growth rate shocks than other firms. As a result, momentum strategies will tend to sort firms based on recent growth rate changes. Overall, Johnson (2002) argues that the model has validity since stock prices depend on growth rates in a highly sensitive, nonlinear way. Hence, recent performance is correlated with levels of expected
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growth rate, which is monotonically related to risk. Conclusively, Johnson (2002) states that the momentum effects are economic rationale: conditioning on a large stock return (the event) is like conditioning on a persistent shock to dividend growth, which should alter expected returns in the same direction. The results presented by Johnson (2002) raises the possibility that the same basic mechanism could play a role in all the anomalies that fall under the category of underreaction. Other studies such as Sagi & Seasholes (2007) also identifies several observable firm-specific attributes that can drive momentum. According to Sagi &
Seasholes (2007), momentum strategies that use firms with relatively high revenue growth volatility, low costs, or valuable growth options generates improved momentum returns compared to a pure momentum. Furthermore, Chordia & Shivakumar (2002) argue that abormal returns generated from momentum strategies can be linked to informational assymetries in financial markets. According to Chordia & Shivakumar (2002), momentum returns does not per se represent a market risk in itself but potentially correlates to an
unobserved source of risk and therefore serves as a proxy of this particular risk. Conclusively, Chordia & Shivakumar (2002) state that several macroeconomic variables are related to momentum returns and consequently, abnormal momentum returns can be explained by an increased level of risk.
2.2 Pure Momentum strategy
In their pioneer paper, Jegadeesh & Titman (1993) established a positive relationship between past returns and future returns. In other words, stocks have positive autocorrelation and do not simply follow a random walk. Consequently, Jegadeesh & Titman (1993) claim that investors can earn abnormal returns in the short and medium term (one to 12 months) by buying stocks with the highest relative returns in the past while simultaneously selling stocks with the lowest relative returns. More specifically, Jegadeesh & Titman (1993) found that portfolios containing stocks with the highest relative returns in the past 12 months outperform portfolios with the lowest relative performance in the same period with as much as 1.49 percent on average per month when these portfolios are held in three months. However, Jegadeesh &
Titman (1993) found that the abnormal returns evaporate over longer time periods. In fact, the excess returns from a momentum strategy evaporates in the years following the holding period of maximum twelve months. Stocks included in the Jegadeesh & Titman (1993)
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portfolios experience negative abnormal returns starting at around 12 months after the portfolio formation date and the negative returns continues up to thirty-one months after the formation. Jegadeesh & Titman (1993) link the results of excessive returns in the short to intermediate time horizon and then negative abnormal return in the longer periods to delayed price reaction for firm-specific information. However, as a concluding remark, Jegadeesh &
Titman (1993) argue that any existing theories for explaining the compelling evidence of inefficiencies in the market are too simplistic to explain the results. The initial hypothesis that reversals in returns following the holding period is due to overreaction is not strong enough and thus, a more sophisticated model is needed to explain the results. Since the pioneer study regarding momentum by Jegadeesh & Titman (1993), multiple researchers have found similar results. Chan et al. (1996) examines whether the predictability of future returns from past returns is due to market’s underreaction to information, particularly to past earnings news.
The results show that past returns and past earnings surprise both predict large drifts in future returns after controlling for other variables. Chan et al. (1996) tries to trace the sources of predictability of future stock returns based on past returns and conclude that one possibility is that the profitability of momentum strategies is entirely due to a component of medium horizon returns that is related to certain earnings-related news. A second possibility suggested is that profitability of momentum strategies originates from overreaction induced by positive feedback trading strategies. This explanation would then suggest that investors that try to chase trends reinforce movements in the stock price even in absence of fundamental information and hence, the returns for past winners and losers are temporary at nature to a degree. Chan et al. (1996) state that ones the market gets surprised by good or bad news regarding earnings, the market continues to be surprised in the same direction in the subsequent announcements. Overall, Chan et al. (1996) conclude that the market shows syndrome of initial underreaction. Moreover, Barberis et al. (1998) present a model that tries to explain investors sentiment, accounting for how investors form expectations of future earnings. Barberis et al. (1998) conclusion is that when making forecasts, people pay too much attention to the strength of the evidence they are presented with and too little attention to its statistical weight. Consequently, this leads to underreaction in stock prices for events such as earning announcements.
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Furthermore, while most of the earliest studies examined the U.S market, momentum returns have been further studies on international markets. Fama & French (2012); Asness et al.
(2013) both found evidence of momentum returns across multiple international markets. Also, momentum returns do not seem to be a strategy that has lost its significance over time. Using more recent data, Hou et al. (2011) found that momentum returns are still present in markets today.
2.3 Pure Momentum in Sweden
Chui et al. (2010) hypothesized that excess momentum profits are more likely to be persistent in countries with higher individualism scoring, based on the index developed by (Hofstede, 2001). The results supported their initial hypothesis, and consequently, Sweden, being one of the top countries regarding individualism were one of the markets in which momentum profits were most significant. The significant returns associated with momentum strategies in
Sweden are further confirmed in studies such as Gong et al. (2015), whom concluded that momentum returns generated on average 1.32 percent per month in a sample stretching from 1982 to 2012. Furthermore, Parmler & González (2007), also found significant momentum returns on the Swedish market using portfolios created in line with the methodology presented by (Jegadeesh & Titman, 1993). However, studies on the Swedish market have not presented unanimous results. In contrast, several studies have found insignificant results on the Swedish market. Rouwenhorst (1998) studied 12 international markets and reached the conclusion that momentum returns were present in almost all markets except for Sweden. For example, other Nordic countries such as Denmark and Norway both showed signs of significant momentum returns while Sweden stood out as an outlier. Rouwenhorst (1998) used data for the years 1978 to 1995 and the sample consisted of 134 stocks on the Swedish market. In line with Rouwenhorst (1998), studies such Griffin et al. (2003); Barber et al. (2013); Goyal & Wahal (2015) have all found insignificant results on the Swedish market.
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While most researchers regarding momentum strategies have focused on how long the past return period should be, no studies have focused on whether portfolio formation could be improved by forming portfolios based on returns which are not the most recent. Novy-Marx (2012) questioned the underlying assumption of the pure momentum strategy in which the formation and holding period are closely connected. Novy-Marx (2012) founds evidence of stocks that have risen the most over the six past months but performed poorly during the first half of the preceding year significantly underperform those stocks that have fallen the most over the past six months but performed strongly over the first half of the preceding year.
Consequently, Novy-Marx (2012) argues that intermediate horizon past returns has better predictive power for future performance than the most recent returns. Consequently, Novy- Marx (2012) suggests that instead of using a pure momentum strategy, investors should create portfolios based on intermediate past returns in order to increase the overall returns.
Moreover, Novy-Marx (2012) argue that pure momentum strategies were successful in the past, but they have lost a significant portion of its predictive power in later years. However, no viable explanation for this is presented in the study. On the other hand, strategies based on intermediate past returns has, if anything, become even better over time. The results from the intermediate past returns are impressive, risk-adjusted returns measured with the Sharpe ratio are twice as high compared to pure momentum. However, according to Novy-Marx (2012), these results cannot be explained by any of the traditional explanations of momentum such as Barberis et al. (1998); Hong & Stein (1999) or any of the more rational explanations such as Johnson (2002); Sagi & Seasholes (2007). Novy-Marx (2012) thus show that the assumptions made about the power of past returns to predict future returns decays monotonically over time is false. Furthermore, the results presented by Novy-Marx (2012) are in contrast to previous studies such as Hong et al. (2000) contention that the profitability of momentum strategies are driven by the losers continuous underperformance. Instead, Novy-Marx (2012) argue that both winners and losers contribute about the same to the overall performance.
10 2.5 Risk-adjusted momentum
The impressive performance of momentum strategies found in multiple studies may make it look like a free lunch for investors. However, there are significant risks associated with the strategy which could make the strategy unattractive for many investors. Grundy & Martin (2001); Daniel & Moskowitz (2014) show that momentum strategies involve time-varying factor exposures in accordance with performance of common risk factors during the formation period which could lead significant losses for the investors. Grundy & Martin (2001) argue that the momentum strategy’s abnormal returns reflect momentum in the stock-specific component of returns. Thus, if the market outperforms the risk-free interest rate, winners tend to be stock with betas above one. Consequently, a momentum strategy tends to place a
positive beta bet on the market in bull markets, meaning that the strategy is long in stocks with betas greater than one while being short in stocks with betas less than one.
Correspondingly, when the market has fallen, the momentum strategy has reversed so that it has a negative beta bet on the market, implying that the strategy is long in stocks with betas less than one while being short in stocks with betas greater than one. Thus, when the market reverse from a bear market to a bull market, momentum strategies hold the wrong stocks in the long and short portfolio respectively. The consequences of having a wrong beta bet on the market can be catastrophic. Barroso & Santa-Clara (2015) studied how a momentum strategy performed in the aftermath of the 1932 market crash and concluded that the strategy would have provided a negative return of −91.5% in just two months after the crash. According to Barroso & Santa-Clara (2015), an investor investing one dollar using the momentum strategy in July 1932 would not have recovered from the losses until April 1963, 31 years later. In the market crash in 2009, the returns were −73.42% in the three months following the market crash. To mitigate the crash risk of the momentum strategy, Grundy & Martin (2001) suggest that by hedging against the strategy’s dynamic exposure to size and market factors, monthly return variance drop with as much as 78.6 percent.
However, Daniel & Moskowitz (2014) state that the portfolios constructed by Grundy &
Martin (2001) are not feasible in real time since they are using forward-looking betas, which cannot be implemented. Daniel & Moskowitz (2014) show that the results presented by Grundy & Martin (2001) possess a strong bias in estimated returns and that a hedging strategy based on ex ante betas does not exhibit performance improvements as reported by Grundy &
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Martin (2001). Daniel & Moskowitz (2014) suggest a different approach to mitigate the crash risk in momentum strategies. Daniel & Moskowitz (2014) state that crashes in momentum strategies occur when the market rebound from a bear market and argue that these momentum crashes that occur when the market rebounds are predictable to a certain degree. According to Daniel & Moskowitz (2014), market crashes tend to occur in terms of market stress, when the market has fallen, and ex ante measures of volatility is high, coupled with an abrupt rise in contemporaneous market returns. Hence, Daniel & Moskowitz (2014) suggest that investors should construct a momentum strategy in which the winner-minus-losers (WML) portfolio is levered up or down over time so that the Sharpe ratio of the portfolio is maximized.
Although Daniel & Moskowitz (2014) show how the risk-adjusted returns can be improved by accounting for time-varying betas, Barosso & Santa-Clara (2015) take a different approach to reduce the magnitude of negative performance following market crashes than both Daniel
& Moskowitz (2014) and Martin & Grundy (2001). To mitigate the crash risk in momentum strategies, Barosso & Santa-Clara (2015) scale the amount invested in the momentum strategy using a target level of volatility and realized variance from daily returns from the past six months. According to Barosso & Santa-Clara (2015), this procedure is superior to using the method presented by Daniel & Moskowitz (2014); Grundy & Martin (2001) due to two reasons. First, most of the risks with momentum strategies is attributable to the strategy itself and not the market. In fact, Barosso & Santa-Clara (2015) found that the market component only constitutes of 23 percent of the overall volatility in momentum strategies. Thus, 77 percent of the volatility is specific to the strategy. Secondly, Barosso & Santa-Clara (2015) claim that the volatility of the strategy is more predictable than any market factors. In their study, Barosso & Santa-Clara (2015) found that the risk-adjustment returns almost doubled compared to pure momentum when the risk-adjusted strategy was implemented.
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3 Method
The purpose of this study is to examine whether momentum returns can be found on the Swedish market for the pure momentum strategy and intermediate past returns strategy.
Hence, I will compare these models on the Swedish market. Moreover, the study investigates if there are any benefits with adopting a risk-adjusted momentum strategy. The pure
momentum strategy is the strategy that has been most extensively researched and, in this study, I will follow the popular approach taken by Jegadeesh & Titman (1993) for the construction of pure momentum portfolios. Furthermore, for the intermediate past returns’
strategy, I will mimic the approach taken by Novy-Marx (2012). Finally, as Barosso & Santa- Clara (2015) suggested, momentum strategies have significant crash risks, which can be controlled by scaling the amount invested in the momentum strategy using realized variance.
Thus, I will follow the approach taken by Barosso & Santa-Clara (2015) for the risk-adjusted approach to examine whether a risk-adjusted momentum strategy is fruitful on the Swedish market. Furthermore, to control for risk-factors, the pure momentum and intermediate past returns will be evaluated after accounting for Fama & French (1992, 1993) three factor model.
The construction of Fama & French 3-factor model will be described.
3.1 Pure momentum
For the construction of the pure momentum strategy, I will follow the methodology suggested by (Jegadeesh & Titman, 1993). In their study, stocks are selected based on their performance in the past J = 3,6,9 or 12 months, which is referred to as the formation period. The portfolios then have a holding period, starting from the first day in the next month after the formation period. Similar to the formation periods, holding periods are K = 3,6,9 or 12 months as well.
Consequently, sixteen portfolios with no gap between formation and holding period are constructed and studied. For example, there are four portfolios based on a formation period J = 3, since each formation period can be held in either K = 3,6, 9 or 12 months. Moreover, in accordance with Gong et al. (2015), a second set of portfolios are constructed in the exact same manner with the only difference being a one-month gap between formation and holding period. The purpose of having a gap between formation and holding period is to reduce the
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potential impact of bid-ask spread, price pressure and lagged reaction effects which have been documented (e.g. Jegadeesh, 1990; Lehmann, 1990). In total, 32 portfolios are studied for the pure momentum strategy.
For the pure momentum strategy, overlapping portfolios are adopted to increase the power of the tests. Overlapping portfolios work as follow: for instance, the portfolio returns for June with a three-month holding period (K=3) is the equally weighted return from the first month return of the portfolio formed in May, the second month return of the portfolio formed in April and the third month return from the portfolio formed in March. For the overlapping portfolios, simple t-statistics are reported to examine whether the monthly returns generated from the momentum strategy is significantly different from zero. According to Byun et al.
(2016), simple t-statistics are enough when evaluating overlapping portfolios since the overlapping portfolios reduce autocorrelation. The procedure of creating overlapping
portfolios is the most widely used in previous studies. See Figure 1 for a visual representation of how returns are calculated for a strategy with a holding period of three months (K=3).
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For the construction of the portfolios, stocks are ranked in ascending order based on their performance during the formation period (J months). Stocks with the lowest returns during the formation period are selected into portfolio 1, the group with the second lowest returns are selected in portfolio 2 and so on. Hence, the stocks with the highest returns during the
formation period are selected in portfolio 10. Thus, stocks are always ranked in decile groups where the best performing stocks goes into portfolio 10 while the lowest performing stocks goes into portfolio 1. Portfolio 10 is referred to as the winner’s portfolio while portfolio 1 is referred to as the loser’s portfolio. Previous studies on the Swedish market such as Bird &
Casavecchia (2007) used quantile portfolios rather than decile portfolios due to the relatively low number of stocks on the Swedish market. However, in my sample, 30 stocks are on average selected into each decile portfolio and consequently, a long-short portfolio consist of 60 stocks on average which is quite a large sample from a practitioner’s point of view and thus sufficient in my opinion.
3.2 Intermediate time past returns
Research regarding momentum has focused on what the optimal length of the test period over which past performance is evaluated when constructing momentum portfolios. For example, Jegadeesh & Titman (1993) evaluated portfolios based on J = 3,6,9 and 12 months. However, almost no attention has been devoted to how long the optimal gap should be between
formation period (J) and holding period (K). Novy-Marx (2012) argues that this lack of research may reflect the presumption that the returns to buying winners and losers was due to momentum, short-run autocorrelation in stock returns, and that the power of past returns to predict future returns, therefore decays monotonically over time. Given the arguments proposed by Novy-Marx (2012), I will examine portfolios constructed in the way suggested by Novy-Marx (2012) and thereby compare the approach against pure momentum. The construction of the portfolios occurs in a similar way as the construction for the pure momentum strategy, stocks are ranked based on their past performance and sorted into ten portfolios in ascending order. Thus, there is no difference yet between the two approaches.
However, Novy-Marx (2012) suggested that instead of not having any gap between formation and holding period, a gap of six months produce more significant returns. Thus, a strategy referred to a n-m is implemented which implies that stocks are held based on their cumulative
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returns in month n to m months prior to portfolio formation. The n-m strategy and its returns series are both denoted 𝑀𝑂𝑀𝑛,𝑚. More specifically, Novy-Marx (2012) argues that the strategy referred to as 𝑀𝑂𝑀12,7 with a holding period (K) equal to one month is the strategy that performs best, and thus, this is the strategy that I perform statistical tests to. See figure 2 for a graphical overview of the intermediate past returns’ strategy.
While Novy-Marx (2012) evaluates both equally weighted and value weighted portfolio returns, I will only focus on the equally weighted portfolios in order to compare apples to apples when the strategy is compared to the pure momentum strategies.
3.3 Risk-Adjusted Momentum
For the risk-adjusted strategy, I will mimic the method suggested by (Barosso & Santa-Clara, 2015). Instead of using time-varying betas in accordance with Grundy & Martin (2001);
Daniel & Moskowitz (2014), Barosso & Santa-Clara (2015) choose a target level of volatility and then scale their investment in the momentum portfolio each month so that the volatility level is kept constant at the desired level at all time. Barosso & Santa-Clara (2015) set the target level of volatility to be 12 percent per year. In greater detail, the strategy goes as follow: An investor puts one dollar in a risk-free asset initially. Simultaneously, the investor invests a certain percentage of that dollar invested in the risk-free rate into the winner-minus- losers (WML) momentum strategy. The percentage invested in the WML depends upon the two parameters historical volatility and the target level for volatility. These two parameters determine how much of the capital is invested in either the risk-free asset or the momentum
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portfolio. Each month, the strategy reinvests the accumulated wealth in the risk-free rate and again spends a certain percentage of this investment into the WML portfolio.
Furthermore, the scaling procedure work as follows: estimated momentum risk is calculated in order to scale the exposure to the strategy to achieve a constant level of volatility
throughout time. The variance forecast is computed using daily returns from the past six months. Since the WML strategy is a zero-investment strategy, in other words, self-financed, it can be scaled without any constraints. Hence, compared to the pure momentum strategy, which would have a scaling factor of one at all time, the risk-adjusted approach allows the amount invested in the momentum strategy to go above and below one dependent on the daily volatility from the past six months and the target level of volatility. This strategy depends only on ex ante information which makes it feasible in real time.
I will use an estimate of momentum volatility to scale the exposure to the strategy to have constant risk over time. For each month, I compute the variance forecast 𝜎̂𝑡2 from daily returns in the previous six months. Let {𝑟𝑊𝑀𝐿,𝑡}
𝑡=1
𝑇 be the monthly returns of momentum and {𝑟𝑊𝑀𝐿,𝑑}
𝑑=1
𝐷 , {𝑑𝑡}𝑡=1𝑇 be the daily returns and the time series of the dates of the last trading sessions of each months. On average, the number of trading days per month is 21. Therefore, for the estimated volatility each month, the daily volatility from the past six months (21 ∙ 6 = 126) are multiplied with 21 to yield the monthly variance forecast. The variance forecast thus becomes
𝜎̂𝑊𝑀𝐿,𝑡2 = 21 ∑𝑟𝑊𝑀𝐿,𝑑2 𝑡−1−𝑗
126 .
125
𝑗=0
Then, I use the forecasted variance to scale the investment in the scaled momentum strategy.
The returns from the risk-managed version each month becomes 𝑟𝑊𝑀𝐿∗,𝑡 =𝜎𝑡𝑎𝑟𝑔𝑒𝑡
𝜎̂𝑡 𝑟𝑊𝑀𝐿,𝑡
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where 𝑟𝑊𝑀𝐿,𝑡 is the pure momentum returns, 𝑟𝑊𝑀𝐿∗,𝑡 is the scaled or risk-adjusted momentum returns, 𝜎𝑡𝑎𝑟𝑔𝑒𝑡 is a constant corresponding to the target level of volatility and 𝜎̂𝑡 is the volatility forecast.
3.4 Risk-Factors Construction
Nothing would be puzzling about momentum’s returns if they simply correspond to a high level of risk. To control for risk factors, the Fama & French (1992, 1993) three factor model will be utilized. These factors will work as control variables so that the portfolio returns are not simply due to fundamental risk factor loading. The factors included in Fama & French (1993) are Market (MRKT), Small-Minus-Big (SMB) and High-Minus-Low (HML). The market risk factor is constructed in line with CAPM
𝑀𝑅𝐾𝑇𝑡 = 𝑅𝑚,𝑡 − 𝑅𝑓,𝑡
where 𝑅𝑚,𝑡 is the monthly general index return from January 1999 to December 2018
collected form Swedish Investment Fund Association, the risk-free return 𝑅𝑓,𝑡 is the Swedish 1-month T-bill rate collected from the Swedish Riksbank. The Small Minus Big (SMB) factor and High Minus Low (HML) are constructed by splitting the entire sample in two sets based on market capitalization, using the median as the cutoff point. The entire sample is also divided into three sets based on their book-to-market and the cutoff points are at 30 and 70 percent. Hence, six portfolios are constructed based on the cutoff points for the factors SMB and HML (SmallValue, SmallNeutral, SmallGrowth, BigValue, BigNeutral, BigGrowth). In order to follow the procedure taken by Fama & French (1992), book-to-market value are calculated in June for every year 𝑡, book values are calculated as book value of equity plus deferred taxes for the firm’s latest fiscal year, ending in the prior calendar year. For the market capitalization, the number used comes from December in year 𝑡 − 1. The stocks are sorted into portfolios each June, and monthly value-weighted returns for the six portfolios are calculated from July in year t until June year 𝑡 + 1. Each portfolio is rebalanced at the end of June in 𝑡 + 1. The SMB and HML factors are the equal weighted averages of the portfolios as follows:
18 𝑆𝑀𝐵 =1
3(𝑆𝑚𝑎𝑙𝑙𝑉𝑎𝑙𝑢𝑒 + 𝑆𝑚𝑎𝑙𝑙𝑁𝑒𝑢𝑡𝑟𝑎𝑙 + 𝑆𝑚𝑎𝑙𝑙𝐺𝑟𝑜𝑤𝑡ℎ) −1
3(𝐵𝑖𝑔𝑉𝑎𝑙𝑢𝑒 + 𝐵𝑖𝑔𝑁𝑒𝑢𝑡𝑟𝑎𝑙 + 𝐵𝑖𝑔𝐺𝑟𝑜𝑤𝑡ℎ) 𝐻𝑀𝐿 =1
2 (𝑆𝑚𝑎𝑙𝑙𝑉𝑎𝑙𝑢𝑒 + 𝐵𝑖𝑔𝑉𝑎𝑙𝑢𝑒) −1
2(𝑆𝑚𝑎𝑙𝑙𝐺𝑟𝑜𝑤𝑡ℎ + 𝐵𝑖𝑔𝐺𝑟𝑜𝑤𝑡ℎ).
3.6 Critical analysis of the methodology
The study is conducted with the programming languages Python and R. These programming languages are open-source and therefore, anyone can write packages for these languages.
However, in this study, I rely on packages such as Numpy, Scipy, Scikit-learn & Pandas in Python and PerformanceAnalytics in R. These packages are widely used for statistical analysis and they are considered to be accurate and reliable. Consequently, I find these packages to be a valid choice for this study. Furthermore, for the construction of the pure momentum strategy, I follow the code provided by Wharton Business School1. The purpose of the code was to mimic the results presented in Jegadeesh & Titman (1993) and thus, the code replicates the methodology suggested by Jegadeesh & Titman (1993). In this study, I use the same code with some modifications in order for the code to be applicable for the data collected on the Swedish stock market. Furthermore, this code work as the baseline for the intermediate past returns and risk-adjusted returns since it only need a few modifications.
1 See https://wrds-www.wharton.upenn.edu/pages/support/applications/portfolio-construction-and-market- anomalies/replicating-momentum-strategies-jegadeesh-and-titman-jf-1993-python/
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4 Data
The aim with the following section is to establish transparency behind the data gathering process, reasoning behind why the chosen data have been selected and motives for the treatments which has been made to the original data. The data consists of three sorts. First, daily price data for the stocks included in the study has been collected. This data is needed for the creation of the momentum strategies since portfolios are created based on stocks previous returns. Secondly, fundamental data for all stocks included in the study is collected. The fundamental data will be incorporated in the risk-controlling factors which will examine the momentum strategies after accounting for common risk factors. Thirdly, market data such as the returns for the general index and the risk-free interest rate is collected.
4.2 Data sources
For the construction of the momentum portfolios, data is collected for all stocks listed on the Swedish stock market for the period January 1999 to December 20182. The data has been collected from Thomson Reuters Datastream. In order to minimize survivorship bias, stocks that have been delisted during the period are included as well. Furthermore, for stocks that have multiple type of shares (A, B, C, etc.), only one return series is included in the dataset.
Furthermore, the construction of Fama & French (1993) risk factors requires fundamental data as well as market data. Market capitalization, book value per share, number of shares outstanding and deferred taxes are all collected from Thomson Reuters Datastream in order to construct the risk-factors SMB and HML. For the third risk factor, the market factor, data is collected from the Swedish Investment Fund Association3 and the risk-free return is collected from the Swedish Riksbank4. Moreover, one criterion for stocks to be included in the sample
2 All firms traded on Stockholm Stock Exchange’s Small-, Mid-, and Large Cap
3 Returns for Six Return Index (SIXRX) is collected from
https://www.fondbolagen.se/fakta_index/marknadsindex/six-index/sixrx/
4 1-month Treasury Bills are collected from http://www.riksbank.se/en/Interest-and-exchange-rates/
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is that fundamental data must exist for the stock. Conclusively, the sample consist of 576 stocks which translates into 1 5591 308 observations before any further treatment. The observations span over 240 months, or 5217 days.
4.3 Sample Design and Treatment
Several treatment steps have been conducted to the original dataset. The treatment steps are conducted to remove certain outliers which may distort the study. First, stocks must have at least 24 months of data. This is because I want stocks that are included in the dataset to have the possibility to be included in a strategy which consist of a formation period (J) equal to 12 months and a holding period (K) equal to 12 months. Furthermore, following the approach taken by Jegadeesh & Titman (1993), stocks that show negative book-to-market values throughout the sample are omitted. Additionally, observations outside of the 5th and 95th percentile in book-to-market are omitted. The treatment steps are conducted as I wish not to trade in extreme book-value measures. After the treatment, the data sample still consists of 515 number of stocks. Table 1 presents an overview of the untreated and treated data for the stocks. All stocks included in the raw and treated dataset are listed in Appendix A.
21 4.4 Critical overview of the data selection process
The data have been processed in open source programming languages such as Python & R.
Thus, it relies on packages with could be written by anyone. However, the data processing has been conducted using the Python package Pandas which is widely used. Furthermore,
secondary source data have been collected from Thomson Reuters Datastream, which is a well-recognized source of financial information and provided by the University. Moreover, for this particular study, the number of stocks is significantly less than previous studies such as Jegadeesh & Titman (1993), which are conducted on the world’s largest financial market, the U.S market. As the sample size increases, the certainty of the results increases as well, which is unfavorable for the results in this study. However, the number of constituents is significantly greater than previous studies such as Rouwenhorst (1998) on the Swedish market. Furthermore, the large number of observations in total make it possible that the data is not treated sufficiently which could impose biases.
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5 Empirical Results & Analysis
In this section, the results from the study will be presented and analyzed. First, the results from the pure momentum strategy as suggested by Jegadeesh & Titman (1993) will be evaluated. Furthermore, the results will be evaluated after accounting for Fama & French three factor model. Thereafter, the results from the intermediate past returns as suggested by Novy-Marx (2012) will be presented and analyze. Lastly, the results from the implementation of a risk-adjusted momentum strategy as suggested by Barosso & Santa-Clara (2015) will be examined. The results from the pure momentum and intermediate past returns strategy will be compared to evaluate whether momentum strategies, either by using pure momentum or intermediate past return have any significant results on the Swedish market.
5.1 Pure Momentum Returns
First, this study investigates whether momentum returns exist on the Swedish market for the years 1999-2018. As mentioned, previous studies have provided with inconclusive results on the Swedish market. Table 2 presents the average monthly returns for the overlapping
portfolios from the different buy and sell portfolios as well as the zero-cost Winners-Minus- Losers (WML) portfolio. In panel A, formation period and holding period are interrelated, meaning that there is no gap between them. Panel B on the other hand, have a one-month gap between formation and holding period to overcome potential bid-ask spread, price pressure and lagged reaction effects which have documented (e.g. Jegadeesh, 1990; Lehmann, 1990).
In total, 32 portfolios have been created and tested. The main conclusion from Table 2 is that pure momentum returns exist on the Swedish market for the years 1999-2018. Overall, all portfolios have positive mean returns in the sample. However, the test results differ
significantly between winners and losers. For the winner portfolios, all the results in Panel A as well as in Panel B are statistically significant at a 95 percent confidence level. In general,
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the winner portfolios generate large mean returns which are significant. The largest mean returns are generated by a winner portfolio based on a formation period (J) = 6 and a holding period of (K) = 3 with an average monthly return of 2.1 percent. On average, the mean return for the winner portfolios are 1.7 percent per month for the portfolios in Panel A and 1.6 percent for portfolios in Panel B. While the past winners continuous to perform well in the future, the loser portfolios do not follow the same pattern, which is good news for the WML portfolios. Although the signs of the loser’s portfolios are positive, they are not statistically significant, not even on a 90 percent confidence level. Furthermore, the largest mean returns are 0.61 percent for the losers in Panel A and 0.68 for the portfolios in Panel B.
For the WML portfolios, 87.5 percent of the portfolios are statistically significant at a 95 percent significant level. The only two portfolios which are not statistically significant are the portfolios J/K = 12/9 and 12/12 respectively. The exact same pattern is present for the
portfolios in Panel B. Consequently, this suggest that momentum portfolios based on longer formation and holding period are inferior to portfolios based on shorter formation and holding periods. In fact, the WML portfolio with the highest monthly average returns is the portfolio based on J/K = 6/3 in Panel A as well as in Panel B with an average monthly return of 1.83 and 2.03 percent respectively. These results differ from Jegadeesh & Titman (1993)
contention that the most successful WML is based on a 12-month formation and three-month holding period.
Conclusively, Table 2 show that the momentum strategies generate significant returns on the Swedish market. The strong statistics overall make it unlikely that the statistics are simply by chance. The returns for the momentum returns are impressive and they are of even greater magnitude than the results presented in Gong et al. (2015), whom found that a momentum strategy yielded 1.32 percent per month on average on the Swedish market in a sample stretching from 1982 to 2012. These results are in contrast to studies such as Rouwenhorst (1998) conclusion that Sweden is one of the few markets in Europe where momentum returns are not feasible. However, Rouwenhorst (1998) used a significantly smaller sample, and an entirely different time period. Furthermore, the results are not in line with Hong et al. (2000) claim that momentum returns are primarily driven by the continuous underperformance of the loser stocks. The results suggest that winners are contributing to the overall returns
significantly. The large returns for the WML portfolios become of such a great magnitude due
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to the large dispersion between winners and losers. While the losers continue to perform poorly in line with Hong et al. (2000), they are financing the long portfolio which generate high returns continuously.
Considering the many portfolios examined in Table 2, it becomes unpractical to analyze all portfolios in greater detail. Thus, for the remainder of the analysis, the focus will be on the momentum strategy J/K = 6/6, in line with previous studies such as (Jegadeesh & Titman,
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1993, 2001). This specific strategy is according to Jegadeesh & Titman (1993) representative for all momentum strategies.
Table 3 shows summary statistics for the WML portfolio with J/K = 6/6. The table shows that the portfolio consisting of losers does not only have the lowest mean returns but it is also the portfolio with the highest standard deviation. While the mean standard deviation for all ten portfolios are 6.23 percent, the monthly standard deviation for the loser portfolio is as high as 10.65 percent. In contrast, the winner portfolio has only slightly higher standard deviation than the average portfolio and still, almost twice as high monthly mean returns than the average of 0.96 percent for all portfolios with its 1.96 percent per month.
The pattern for the standard deviation forms a u-shape, implying a higher standard deviation for the stocks in the most extreme portfolios. See figure 3 for a visual representation. These results are in line with Rouwenhorst (1998) contention that stocks with higher standard
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deviation are more prone to show unusual performance and past unusual performance is cross-sectionally correlated with volatility.
However, nothing would be puzzling about the impressive returns if they simply
corresponded to a higher level of risk and thus, no improvement in risk-adjusted returns.
Given this, an ordinary least squares (OLS) regression on the returns of the WML strategy including Fama & French (1992) three factors is conducted (t-statistics in parenthesis). The regression yields the following outcome:
Equation 1 show that after controlling for the Fama & French risk factors, the momentum strategy returns are increased to monthly returns of 1.955 percent. The momentum returns are increased due to the strategy’s negative relationship with the Fama & French (1992) risk- factors. All the coefficients are statistically significant at a 95 percent confidence level.
Overall, the negative loading on the risk factors suggest that the momentum strategy is a
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diversified strategy according to (Barosso & Santa-Clara, 2015). Moreover, the results are in line with Rouwenhorst (1998) contention that WML is negatively related to the SMB factor, which suggest that losers behave more like small stocks than winners irrespective of size. The main conclusion from the regression is that a risk-adjustment for market and size makes the momentum effect appear more at odds with the joint hypotheses of market efficiency and the Fama & French three-factor model.
In table 4, I further consider the possibility that momentum portfolios select riskier stocks in general and thus, benefits from the increased risk. Table 4 presents estimates for betas and average market capitalization for the ten 6-month/6-month portfolios. According to Jegadeesh
& Titman (1993), these estimates are the two most common indicators of systematic risk.
Table 4 demonstrates that the betas for the best performing stocks and worst performing stocks are on average higher than the average beta for the full sample of 1.05. However, the beta for the extreme past losers are higher than the beta for the extreme past winners.
Consequently, the beta of the WML portfolio is negative. These results reinforce the results from the regression. The WML portfolios have a negative relation with the market returns.
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Furthermore, the market capitalization for the winners as well as losers show that in general, the winners and losers portfolios consist of stocks with lower market capitalization than average. However, loser stocks have significantly lower market capitalization than winner stocks on average. Thus, the loser portfolios do not only behave more like small stocks as suggested by Rouwenhorst (1998), the results show that loser stocks in fact are smaller stocks.
These results are in line with Hong & Stein (1999) claim that underreaction occurs more significantly in smaller stocks, in which information diffuses more slowly which can be attributed to behavioral attributes among investors.
4.2 Intermediate past Returns
Having established evidence of momentum returns on the Swedish market, I proceed to investigate whether pure momentum returns are superior or inferior to portfolios based on intermediate past return. Suggested by Novy-Marx (2012), by using intermediate past returns investors can achieve higher returns than returns from pure momentum. Hence, Novy-Marx (2012) questioned the underlying assumptions that momentum strategies where the holding and formation period is closely connected. Thus, in this section, the results from using intermediate past returns as suggested by Novy-Marx (2012) instead of pure momentum strategies are presented.
Table 5 presents the results from the 𝑀𝑂𝑀12,7 strategy. In line with Novy-Marx (2012), the holding period is one month. Although the results have the same sign as the pure momentum, the results are not as strong as the results for the pure momentum. In fact, the results for the WML portfolio is insignificant. Table 5 show that, in similarity with pure momentum, winners continues to provide significant positive returns in the following period. However, the mean returns from the winners are considerably lower for the intermediate past returns compared to pure momentum. While the pure momentum yielded 1.97 percent for the winners in portfolios based on J/K = 6/6 with no gap between formation and holding, the winner portfolio based on intermediate past returns yielded only 1.22 percent per month on average.
The insignificant results are in line with the results found by Gong et al. (2015), whom evaluated the intermediate past returns suggested by (Novy-Marx, 2012). According to Gong et al. (2015), the results found by Novy-Marx (2012) depends on an estimation bias in the model specification. Gong et al. (2015) state that due to annual seasonality, the intermediate
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past momentum effect is overestimated when the same calendar month one year ago is
included in the intermediate past horizon. In contrast, Gong et al. (2015) argue that recent past month effect is underestimated when prior month 2 is included in the recent past horizon. This is due to the short-term return reversal from two months prior.
Conclusively, the results from this study show that the returns for the intermediate past
returns strategy on the Swedish market does not follow the similar pattern as the returns found by Novy-Marx (2012) on the U.S market. Instead, the results suggest that momentum
strategies based on more recent performance generate higher returns in the future. This reinforces the results from the pure momentum where it was found that the best momentum strategy was based on a six-month formation period and a three-month holding period.
To further investigate the performance of momentum returns based on past performance, Figure 4 presents the performance of the strategies formed on the basis of performance in a single month. The strategies are thus formed using just a single month’s returns from one month up to fifteen months prior to the portfolio formation. The bars represent the monthly average returns for the equal-weighted portfolios.
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Figure 4 reinforces the previous results suggesting that more recent performance have more predictive power than intermediate past performance as suggested by Novy-Marx (2012).
From the figure, we can clearly see that the first six months have a positive relationship with the upcoming months returns for the stocks. This is in sharp contrast to Novy-Marx (2012) contention that the bars are sloping upward until 12 months prior to the formation and then falls drastic. In this study, the pattern is clear that the six months closest to the formation have positive contribution to the momentum portfolio. Moreover, only the results for month
2,3,4,5,6 and twelve are significant at a 95 percent significant level. See Appendix B for the statistical results. Interestingly, a momentum strategy based solely based on the most recent month have no statistical significance. This could be due to the short-term effects considered in (Lehmann, 1990; Jegadeesh, 1990). Overall, the rejection of intermediate past returns being superior to pure momentum strategies based on more recent past performance are in line with Gong et al. (2015) conclusion that the majority of momentum profits comes from recent months. Furthermore, Gong et al. (2015) argue that the significant results found by Novy- Marx (2012) are primarily driven by the returns 12 months ago, which can be considered to carry a seasonal effect.
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Running a regression with the Fama & French (1993) three-factor model yields the following results:
Equation 2 show the results from the regression which accounts for Fama & French (1993) risk-factors. In similarity with the pure momentum strategy, the intercept increases after accounting for the risk-factors and the intercept is statistically significant. However, equation 2 show that the intermediate past returns have a positive but insignificant relationship with the market factor. Furthermore, the SMB factor is also insignificant in equation 2. Instead, the intermediate past returns load heavily on the HML risk factor.
5.3 Risk-Adjusted momentum
Having established that significant momentum returns exist on the Swedish market and further, that short-term past return yields significantly better returns than portfolios based on intermediate term returns as suggested, this study continues to examine whether there are any benefits with applying a risk-adjusted momentum strategy as proposed by Barosso & Santa- Clara (2015). As previously described, Barosso & Santa-Clara (2015) scale the amount invested in the momentum strategy based on the realized variance in the past six months.
Barosso & Santa-Clara (2015) argued that the scaling method works since most of the risk associated with the strategy is associated with the strategy itself and moreover, the volatility is predictable to a high degree.
Table 6 presents a comparison for the unadjusted pure momentum WML based on J/K = 6/6 and the risk-adjusted momentum portfolios WML*. Table 6 present a couple of notable takeaways. First, the table illustrates a significant drop in kurtosis that occur when switching from a pure momentum strategy to the risk-managed approach. The kurtosis of a distribution
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is a measure of how much mass is in its tails, and therefore, is a measure of how much of the variance that arises from extreme values (Stock & Watson, 2011). A higher kurtosis implies fatter tails, which suggest that more variance comes from extreme values. Thus, a reduction in kurtosis make outliers less common and consequently, the volatility in returns are lower, implying reduced risk. Moreover, the skewness is reduced as well. Skewness refers to how symmetric the distribution of returns is (Stock & Watson, 2011). A negative skewness suggest that the returns distribution has a left tail (negative returns) which is not fully offset by the positive returns. Hence, by reducing the skewness, the returns become more symmetric distributed. In other words, large negative outliers are reduced which make the distribution more symmetric.
Furthermore, Table 6 suggest that extreme outliers are reduced, especially on the downside, where the most dramatic downfall over one month is -19.86 percent for the risk-adjusted approach compared to -43.94 percent for the unscaled pure momentum approach. In
summary, kurtosis and skewness drop dramatically for the risk-managed approach, indicating that the crash risk is severely reduced when applying a risk-adjusted approach on the Swedish market.
Furthermore, the volatility for the pure momentum returns are 7.84 percent per month which is in similarity to Barosso & Santa-Clara (2015) higher than the average volatility of the market (OMXSPI5) at 5.31 percent. The risk-adjusted approach has the desirable attribute of
5I use OMXSPI for the comparison between the risk-adjusted strategy and the market since I use monthly volatility calculated from daily returns in the past six months. Data for OMXSPI is collected from http://www.nasdaqomxnordic.com/index/historiska_kurser/?Instrument=SE0000744195
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reducing the monthly volatility to 5.12 percent per month. Thus, the results suggest that while the mean returns are slightly reduced for the risk-adjusted returns, the reduction in standard deviation is large enough to offset this reduction and consequently, risk-adjusted returns are increased.
Suggested by Barosso & Santa-Clara (2015), the large benefits with the volatility scaled momentum strategy approach comes from the reduction in crash risk. Table 7 present a comparison between the pure momentum and risk-managed momentum when it comes to drawdowns. Drawdowns refers to how much an investment is down from the peak before it recovers back to the peak. Table 7 suggest that the drawdowns are significantly reduced when the risk-managed approach is followed compared to the pure momentum strategy. Here, one can see the large benefits with the risk-managed version. To start, the average drawdown at 9.8 percent is significantly lower than the average drawdown of 16.06 percent for the pure momentum strategy. Moreover, while the maximum drawdown for the pure momentum strategy is 45.52 percent, the maximum drawdown for the risk-managed version is only 24.59 percent which is a significant reduction. Consequently, it takes the risk-managed version significantly less time to recover from drawdown periods. The results in table 7 thus suggest that the scaling approach suggested by Barosso & Santa-Clara (2015) have merits on the Swedish market. The results suggest that the risk-managed approach significantly reduce the risk of large drawdown periods due to its scaling component. The major benefits with the risk-managed strategy comes from the fact that the strategy does not experience the same magnitude in crashes. But still, the risk-adjusted approach is still able to generate significant returns in bull markets such as in 2006-2007. In bull markets, the volatility is often relatively low, which increase the amount invested in the momentum strategy and thus, the strategy is able to generate returns when the market is in a strong positive trend.
