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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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 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

15

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

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 �̂�𝑡2 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=1

𝑇 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

�̂�𝑊𝑀𝐿,𝑡2 = 21 ∑

𝑟𝑊𝑀𝐿,𝑑𝑡−1−𝑗2

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

�̂�𝑡𝑟𝑊𝑀𝐿,𝑡

17

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 �̂�𝑡 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/

19

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/

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 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,

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 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

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 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

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 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

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 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.

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.

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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.

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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.

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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

47

Appendix B