momentum strategies on the swedish market
TRANSCRIPT
Momentum strategies on
the Swedish market
Masterβs 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 marketβs 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 & GonzΓ‘lez (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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2.4 Intermediate past returns
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.
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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 strategyβs 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 β91.5% 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 β73.42% 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 strategyβs 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 returnsβ
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 winnerβs portfolio while portfolio 1 is
referred to as the loserβs 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 practitionerβs 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
15
returns in month n to m months prior to portfolio formation. The n-m strategy and its returns
series are both denoted ππππ,π. More specifically, Novy-Marx (2012) argues that the
strategy referred to as πππ12,7 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 returnsβ 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
16
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 οΏ½ΜοΏ½π‘2 from daily returns
in the previous six months. Let {ππππΏ,π‘}π‘=1
π be the monthly returns of momentum and
{ππππΏ,π}π=1
π·, {ππ‘}π‘=1
π 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 β 6 =
126) are multiplied with 21 to yield the monthly variance forecast. The variance forecast thus
becomes
οΏ½ΜοΏ½πππΏ,π‘2 = 21 β
ππππΏ,ππ‘β1βπ2
126.
125
π=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
ππππΏβ,π‘ =ππ‘πππππ‘
οΏ½ΜοΏ½π‘ππππΏ,π‘
17
where ππππΏ,π‘ is the pure momentum returns, ππππΏβ,π‘ is the scaled or risk-adjusted momentum
returns, ππ‘πππππ‘ is a constant corresponding to the target level of volatility and οΏ½ΜοΏ½π‘ is the
volatility forecast.
3.4 Risk-Factors Construction
Nothing would be puzzling about momentumβs 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
ππ πΎππ‘ = π π,π‘ β π π,π‘
where π π,π‘ is the monthly general index return from January 1999 to December 2018
collected form Swedish Investment Fund Association, the risk-free return π π,π‘ 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 π‘, book values are calculated as book value of equity plus
deferred taxes for the firmβs latest fiscal year, ending in the prior calendar year. For the
market capitalization, the number used comes from December in year π‘ β 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 π‘ + 1. Each portfolio is rebalanced at the end of
June in π‘ + 1. The SMB and HML factors are the equal weighted averages of the portfolios as
follows:
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πππ΅ =1
3(πππππππππ’π + ππππππππ’π‘πππ + ππππππΊπππ€π‘β) β
1
3(π΅ππππππ’π + π΅πππππ’π‘πππ + π΅πππΊπππ€π‘β)
π»ππΏ =1
2 (πππππππππ’π + π΅ππππππ’π) β
1
2(ππππππΊπππ€π‘β + π΅πππΊπππ€π‘β).
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 Exchangeβs 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/
20
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 worldβs 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.
22
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,
23
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 loserβs 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
24
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,
25
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
26
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 strategyβs 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
27
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.
28
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 πππ12,7 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
29
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 monthβs 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.
30
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.
31
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
32
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
5 I 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
33
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.
34
Panel A in Figure 5 show the scaling factor over the period January 2000 to December 2018
for the risk-adjusted approach. The scaling factor was set to a fixed volatility target of 12
percent per year, in line with (Barroso & Santa-Clara, 2015). The scaling factor ranges from
0.145 in November 2001 to its maximum value of 2.62 in January. On average, the scaling
factor is at 0.795, implying that the risk-adjusted strategy has a lower amount invested in the
momentum portfolios on average than the pure momentum strategy which would have a
scaling factor of one. Considering that the risk-adjusted momentum strategy is self-financed
(zero-cost), the strategy can be scaled without constraints. Panel B in Figure 5 shows the
rolling six months volatility on the OMXSPI index between January 2000 and December
2018. While the average rolling six-month volatility is 5.31 percent, there are periods such as
in the beginning of 2015 and 2017 where the volatility is significantly lower. During these
periods, the risk-adjusted approach scales up the amount invested in the risk-adjusted
approach as seen in Panel A. Thus, the peaks of the scaling factor coincide with the periods
when the market is at its lowest level of volatility. Hence, the risk-adjusted strategy has little
amount invested in the momentum strategy in times after the market has crashed. As a result,
the risk-adjusted strategy does not suffer as much as the pure momentum strategy when the
market rebound as described in Grundy & Martin (2001); Daniel & Moskowitz (2014) since
the amount invested is significantly lower.
35
Figure 6 show the cumulative returns for the pure momentum strategy and the risk-managed
momentum strategy. Figure 6 show that the risk-managed version outperforms the pure
momentum strategy over the period from January 1999 to December 2018. While the risk-
managed version does not suffer from the same magnitude in losses in periods such as 2008-
2009, it still manages to perform well in bull markets since these periods are in general less
volatile as seen in Panel B Figure 5, which leads to a higher amount invested in the
momentum strategy. On the other hand, during periods of a market crashes such as in 2008,
2015 and late 2018, the preceding months are in general more volatile than average as seen in
Panel B Figure 5 and hence, the risk-managed approach quickly scales down the investment
in the momentum strategy, leading to lower losses.
36
5.4 Robustness check
As a robustness check, the data sample was split into two evenly divided subsamples, the first
spanning from January 1999 to December 2008 and the second spanning from January 2009
to December 2018. Overall, the results suggest that the pure momentum strategy provides
significant returns in both subsamples. For the 6/6 pure momentum strategy, the winners
provide positive significant returns of 1.85 percent per month while the losers provide
insignificant positive mean returns. The WML portfolio generates 1.81 percent in monthly
returns and these returns are statistically significant. In the later subperiod, starting from
January 2009, the momentum strategy generates even higher returns. The winner portfolio
generates mean returns of 1.99 percent per month and the WML portfolio generates 1.94
percent per month. The results for the second subsample produce even greater t-statistics than
the results for the first subsample. These results are in direct contrast to Novy-Marx (2012)
contention that the pure momentum strategy has lost its strength over time. Instead, these
results suggest the opposite, since the significance of momentum returns has increased over
time. These results are in line with more recent studies such as Hou et al. (2011) claim that
momentum returns are still an anomaly in markets today.
37
6 Discussion
In this study, the results show that the momentum effect is present on the Swedish market.
Both the pure momentum strategy and the risk-adjusted strategy generate strong returns over
the sample period. However, some potential issues exist with momentum strategies which
could make the strategy less plausible. In this study, transaction costs have been disregarded
when calculating the returns for the respective strategies. This is not realistic. Instead
momentum strategies are trading intensive which implies that transaction costs could be
relatively high. Lesmond et al. (2004) found that momentum profits are not feasible when
investors encounters for the transaction costs. They found that pure momentum strategies
require frequent trading in disproportionally high cost securities which distort the abnormal
returns from the strategy. Hence, the stocks that contribute the most to the overall returns are
the same stocks with the highest trading costs. Moreover, while Chan et al. (1996) found
evidence of momentum returns in their study, they concluded their paper with two final
remarks. First, they argued that transaction costs must be considered sine the strategy is
trading intensive. Secondly, they argued that investors may have constraints such as being
unable to short-sell stocks. Hence, investors may be unable to establish optimal momentum
portfolios. In this study, both winners and losers are stocks which are on average smaller in
market capitalization than the average stock on the market. Thus, the trading costs could be
relatively high in this type of stocks and it may not be possible to go short in some stocks,
which could reduce the potential returns of the strategy. Furthermore, Pettengill et al. (2006)
argue that while both individuals and professionals use momentum strategies in their
investment decisions, only the professionals are able to generate abnormal returns. The
individuals are on the other hand outperformed by the market. Given this, Pettengill et al.
(2006) suggest that individuals should not engage in momentum strategies. According to
Pettengill et al. (2006), one of the reasons behind this underperformance by individuals could
be due to lack of expertise or the information to successfully mimic the momentum strategies
and therefore, individuals instead pursue momentum strategies that relies more exclusively on
price increases. This type of behavior could potentially lead to security selection that is based
on longer-term positive momentum which may suggest that the stocks selected are closer to
reversal. Furthermore, the results from this study suggest that a risk-adjusted strategy could
increase the overall returns compared to a pure momentum strategy. However, the risk
adjusted strategy is even more trading intensive than the pure momentum which consequently
38
leads to higher transaction costs. According to Barosso & Santa-Clara (2015), this should not
discourage investors from applying the risk-adjusted strategy. Barosso & Santa-Clara (2015)
found that for the pure momentum strategy to be superior compared to the risk-adjusted
strategy, transaction costs would have to be 38 percent higher for the risk-adjusted approach.
7 Conclusion & Suggestions for further research
7.1 Conclusion
The purpose of this thesis was to explore if momentum profits can be obtained on the Swedish
stock market with different methodologies between the years 1999 and 2018. The
methodologies evaluated was primarily the pure momentum strategy developed by Jegadeesh
& Titman (1993) and the intermediate past returns strategy developed by Novy-Marx (2012).
Furthermore, this study investigated whether a pure momentum strategy can be enhanced by
applying a risk-adjusted approach as suggested by Barosso & Santa-Clara (2015). The results
from this study presents three key points.
First, the evidence show that pure momentum returns exist on the Swedish market which is in
line with previous studies such as (Chui et al. 2010; Leippold & Lohre, 2011; Gong et al.
2015). By constructing portfolios in accordance with Jegadeesh & Titman (1993, 2001), a
pure momentum strategy generates as much as 1.83 percent per month on average for winner-
minus-losers portfolios when the formation period is six month and the holding period is three
months. Furthermore, these results cannot be explained by loading on common risk factors. In
this study, the momentum returns were evaluated when accounting for Fama & French (1992,
1993) risk-factors (Market, Small-Minus-Big & High-Minus-Low) and the results suggest
that the momentum returns increases when accounting for the risk-factors due to the negative
relation with the Fama & French risk-factors. Hence, these results are in contrast with studies
such as Sagi & Seasholes (2007); Johnson (2002), which both suggest that momentum returns
are due to increased risk. Instead, in line with studies such as Hong & Stein (1999), the
momentum effect is larger in smaller stocks where the information diffuses more slowly,
making the underreaction more apparent since the drift is present for longer time. This is in
line with the behavioral explanation to the momentum return which suggest that investors
39
underreact to new information. These results are further in line with studies such as Barberis
et al. (1998) and Chan et al. (1996) which both suggest that investors underreact to new
information.
Secondly, this study evaluates whether portfolios based on intermediate past returns are
superior to momentum strategies based on recent performance. The results show that
momentum based on more recent performance have stronger predictive power than
intermediate past returns. The intermediate past returns do not produce any significant results
in this study. Thus, the results are in contrast with the claim proposed by (Novy-Marx, 2012).
Instead, the results are in line with previous studies such as Gong et al. (2015), whom argued
that momentum returns are most significant in the short-term and that the strong predictive
performance from intermediate past returns are mostly driven by the performance from 12
months ago, which is most likely due to a seasonal effect.
Thirdly, momentum returns can be enhanced on the Swedish market by applying a risk-
adjusted strategy suggested by (Barosso & Santa-Clara, 2015). By scaling the amount
invested in the momentum strategy, investors can reduce the crash risk in momentum
portfolios which have been documented to be severe in previous studies such as (Daniel &
Moskowitz, 2014; Grundy & Martin, 2001). This study finds that scaling the amount invested
in the momentum strategy leads to higher returns compared to a pure momentum strategy.
The risk-adjusted strategy is still able to capture the strong returns in a bull market but also
keep the amount invested in the momentum strategy low in periods of high volatility, when
crashes are most likely to occur.
7.2 Further Research
In this study, I have concluded that momentum strategies can earn excess returns on the
Swedish market. For further research, I have three suggestions. First, it would be interesting
to further investigate whether investors can find a more optimal past returns horizon. For
example, the evidence from this study suggest that month 2,3,4,5,6 and 12 prior to formation
have significant predictive power for a momentum strategy, while the other months does not
show any evidence of any predictive power on a statistically significant level. Thus, it could
be interestingly to investigate whether investors could combine months with the most
significant results. Secondly, in this study, I have kept the volatility at a fixed target of 12
40
percent per year for the risk-adjusted strategy. This is in line with previous studies but still,
given that the risk-adjusted approach experience relatively large drawdowns after periods of
very low volatility when the scaling factor has become very large, it could be interesting to
investigate whether one can mitigate the crash risk better by allowing the volatility to increase
(decrease) dependent on whether the market experience high (low) volatility. Thirdly, while I
forecast the variance from the realized variance in the last six months, it could be interesting
to investigate whether it could be beneficial to allow forecast the variance with longer or
shorter periods of realized variance.
41
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Appendix A
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46
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Appendix B