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Does the Active Country Momentum Portfolio Beat the Passive Market Portfolio? : an empirical study on exchange-traded funds

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Does the Active Country Momentum Portfolio

Beat the Passive Market Portfolio?

- an empirical study on exchange-traded funds

Authors: Anton Ericsson (960607) and Anton Erickson (970831)

Autumn 2020

Master Thesis in Finance, Advanced Level 30 Credits Örebro University School of Business

Supervisor: Kamil Kladivko

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Abstract

The thesis examines the strategy of country momentum and is evaluated with 30 different country exchange-traded funds (ETFs) for the period 1996-2018. The empirical evaluation is designed to apply different formation- and holding periods with overlapping portfolios. The results show positive momentum returns in various periods and a few portfolios present a higher average return than the market. However, none of the portfolios is presenting any significant positive returns or alphas, meaning that the three hypotheses cannot be rejected. On the other hand, some portfolios have higher Sharpe ratios and Morningstar value than the market. Thus, meaning that the individual investor could prefer the momentum portfolio over the market despite the insignificant returns.

Keywords: Momentum strategy, Exchange-traded funds, Efficient markets,

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Table of contents

1. Introduction ... 1 1.1 Outline ... 2 2. Thesis settings ... 3 2.1 Momentum strategy ... 3 2.1.1 Momentum profits ... 3 2.2 Behavioral Bias ... 4 3. Previous literature ... 6 3.1 Investment strategies ... 6 3.2 Momentum literature ... 6

3.2.1 Global and European momentum performance ... 7

4. Theoretical framework ... 9

4.1 Modern portfolio theory ... 9

4.2 Capital Asset Pricing Model ... 9

4.3 Portfolio measurement ... 10

4.3.1 Returns ... 10

4.3.2 Variance and Volatility ... 11

4.3.3 Skewness and Kurtosis ... 11

4.3.4 Sharpe Ratio ... 12

4.3.5 Jensen’s alpha ... 12

4.3.6 Morningstar risk-adjusted return ... 12

4.4 Robustness check of the returns ... 13

5. Method and Data ... 14

5.1 Overlapping portfolios ... 15 5.2 Self-financing portfolio ... 16 5.3 Benchmarking portfolios ... 16 5.4 Data ... 17 5.4.1 Returns ... 18 5.4.2 Risk-free rate ... 18 6. Results ... 20 6.1 Momentum returns ... 20

6.1.1 Graphical overview of winners and losers ... 21

6.2 Momentum returns (without time lag)... 23

6.2.1 Graphical overview of momentum returns (without time lag) ... 23

6.3 Momentum returns (with one month time lag) ... 25

6.3.1 Graphical overview of momentum returns (with one month time lag) ... 25

6.4 Risk-adjusted momentum returns ... 27

6.4.1 Characteristics of the momentum portfolios (without time lag) ... 27

6.4.2 Characteristics of the momentum portfolios (with one month time lag) ... 28

7. Discussion ... 29

8. Conclusion ... 31

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1. Introduction

Investing in trends is an ancient strategy that has been around since the first day financial assets were traded. An early indication of this is the words of the economist David Ricardo to “cut short your losses” and “let your profit run on” (see Grant 1838). Since then, there have been various empirical tests on trading strategies, where all strategies follow the simple goal to “beat the market” (Conrad & Kaul 1998). A frequently used strategy both by individual investors and fund managers is the momentum strategy. The strategy is explained by its simplicity, it buys the winners and sells the losers based on previous returns. Jegadeesh and Titman (1993) proved that in the period 1965-1989, a momentum strategy with formation- and holding period of three to twelve months generated abnormal returns. After 1993, many papers have presented how the momentum strategy performs against the market. One of the frequently evaluated assets is stocks traded on the US market (Chan, Jegadeesh & Lakonishok 1996; Jegadeesh & Titman 2001). Even though stocks are common when testing a momentum strategy, other assets have been tested and shown abnormal returns, for instance, currencies (Menkhoff, Sarno, Schmeling & Schrimpf 2012), commodities (Miffre & Rallis 2007) and equity indices (Bhojraj & Swaminathan 2006). However, when summarizing all the momentum studies, there is one financial instrument that is not researched to the same extent as the others, exchange-traded funds (ETF) or more specific country ETFs. Therefore, the thesis will focus to examine if there are any momentum profits from using country ETFs.

The construction of an ETF is similar to a mutual fund but is traded directly on the stock market. With an ETF, the investor is provided with several equities included in one asset. This means that the investor will get a diversified portfolio in merely one trade, thus following the mutual fund strategy. The instrument is rapidly increasing in popularity and in 2018 one third of all trading in the US markets contained ETFs (Sullivan & Xiong 2018). One explanation of this upsurge is the instrument's high liquidity. With high liquidity, it provides the opportunity for the investor to enter the trade on any occasion (Berk & DeMarzo 2019).

Furthermore, if the investor would search for an even wider market than one specific country, the approach would presumably move towards a global perspective. This was studied by Rouwenhorst (1998) who included twelve international equity markets and this thesis continues on a similar path to include 30 country ETFs. As of today, there are not any ETFs that are

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2 replicating a global market and those who exist exclude some emerging and frontier markets. Therefore, the investor would need to search for ETFs representing each country. The concept of getting exposure to a global market and thus including emerging markets together with a momentum approach would coincide in a country momentum strategy. To measure the performance of the strategy, different risk-adjusted measurement is applied to validate the performance of each portfolio. In addition, it contributes to other aspects that the individual investors could value in their decision making.

The objective of the thesis is to examine if there are any abnormal returns in a country momentum strategy between 1996 and 2018. The thesis contributes with further knowledge on how the momentum strategy performs in a global market and especially for country ETFs. To examine this, an empirical evaluation is constructed to measure the performance of the country momentum strategy returns through three various hypotheses (see Section 4.4). Results with significant signs of abnormal returns would indicate that the Efficient Market Hypothesis does not hold and that it is possible to outperform the market with an active investment strategy. On the contrary, if there are no significant abnormal returns, this would prove that the market works efficiently. The results of these evaluations show no significance for either returns or alphas. Still, even though the portfolios are insignificant, some of the evaluated portfolios present higher Sharpe ratio and Morningstar values.

1.1 Outline

The thesis will be followed as: Chapter two presents how momentum strategy is constructed and continues by presenting information on behavioral bias and its effect on market returns.

Chapter three covers papers in active investing and in Chapter four the theoretical framework

is presented together with the measurements and hypotheses. The method and data are further explained in Chapter five. Chapter six covers the results and starts by presenting the winners versus the losers, followed by a presentation of the momentum portfolios and their characteristics. Following the results, Chapter seven covers a discussion about the results with regard to the theory. Finally, the conclusion and suggestions for further research are covered in

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2. Thesis settings

This chapter begins by describing momentum and momentum profits. It is followed by a summary of behavioral bias.

2.1 Momentum strategy

For trend strategies to be an attractive investment, it would have to beat the market, thus breaking the assumption that the market is efficient1. An active strategy that exploits this is the momentum strategy of Jegadeesh and Titman (1993), who were among the first to publish a study on the momentum strategy where the investor would buy the previous winners and sell the previous losers to generate abnormal returns.

This thesis has followed the methodology of Jegadeesh and Titman’s (1993) study. To create momentum profits, momentum portfolios would need to follow the trends of historical data. Furthermore, the ordinary momentum strategies are different regarding the time lag, formation- and holding period. The strategy in this thesis is based on historical returns, where each equity is ranked in percentiles according to the past returns during the predetermined formation periods2. After the formation period ends, the investment is made at time t based on which equities that should be bought (winners) and sold (losers). At this time, it is possible to adjust for time lag, where t+1 state that the investment would be made one month after the formation period ends. These equities are thereafter held for a number of holding periods3. After the holding period ends the portfolio is sold and this procedure is repeated throughout the intended evaluation period.

2.1.1 Momentum profits

One explanation on how momentum returns arise is due to the behavioral bias, which creates trend opportunities or as Johnson (2002) describes, a higher risk taking. Trend opportunities could arise because investors are biased to make decisions under uncertainty (Kahneman & Tversky 1979) together with people’s slow reaction to new and non-profitable information

1 The Efficient Market Hypothesis states that securities markets are well function markets with prices that incorporate new information without delay (Fama 1965; 1970).

2 The formation period is a predetermined number of months the investment decision is made on.

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4 (Barberis, Shleifer & Vishny 1998; Hong, Lim & Stein 2000). This would imply that prices do not react to information immediately and consequently creating trend investing opportunities.

However, as the momentum strategy captures trends, it is simultaneously exposed to the downsides (Daniel & Moskowitz 2016). The authors state that momentum portfolios generally have negative skewness and large values of kurtosis, indicating a larger risk of rapid losses. Further, the momentum strategy (winners-minus-losers) comes with large downsides (Barroso & Santa-Clara 2015). In 1932, the strategy delivered a -91.59 percent return in only two months in the US and a return of -73.42 percent in three months during 2009. These crashes occurred after previous declines in the global markets, which is explained by Barroso and Santa-Clara (2015) as the momentum strategies time varying systematic risk.

2.2 Behavioral Bias

Behavioral finance is a field within psychological research that has been applied to decision-making regarding investment selection (Shiller 2003). The researchers had seen anomalies in the market, which could not be explained by the existing theoretical models. One explanation of the irrationality in decision-making can be that the available information on the market is interpreted wrong. De Bondt and Thaler (1985) stated that investors have a representativeness bias, which means that the investor gets too optimistic about past winners and too pessimistic about past losers. The authors state that when the investor is influenced by representativeness bias, the movement of the stock price would not represent the actual change in price regarding the available information. The investor will benefit from the consistent tendency of over- or underreaction in these price movements. Overreaction indicates that the investors could profit from selling after the news and underreaction mean the investor could profit from buying after (Wouassom 2016). Hong and Stein (1999) argue that momentum investors could profit from these correction periods. The concept of making a profit from over- and underreaction will neither follow the Efficient Market Hypothesis nor does it follow the law of one price (Fama 1970).

Two models in behavioral finance could explain how different biases in decision-making can create over- and underreaction; BSV developed by Barberis, Shleifer and Vishny (1998) and DHS developed by Daniel, Hirshleifer and Subrahmanyam (1998). Two common behavioral biases that are explained within BSV is representativeness and conservatism. The

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representativeness is clarifying that the investor is overvaluing recent events, thus the investor

does not get the complete cause of what the price movement is depending on. Conservatism describes the model’s delay to get new information and reacting to it (Fama 1998).

BSV-model is capturing two judgment biases that occur because of investors’ belief of capturing patterns in the price movement, although the earnings are a random walk (Fama 1998). Regime A states that the prices are mean reverting, implying that stock prices underreact to the increased earnings since the investors think this is temporary effect. When the stock price is still increasing and is not following the expectation, there is a delayed effect on the stock price from the previous earnings (Fama 1970). On the other hand, Regime B states that the investor perceives price patterns in the time series and concludes that the stock is showing signals of a trend. The author explains that the investor therefore will incorrectly extrapolate this perception, resulting in an overreaction to the stock price. Since the earnings assumes to follow a random walk, the overreaction will expose the future income and therefore a reversal of the long-term returns. Fama (1998) points out that Regime A follows Jegadeesh and Titman’s (1993) philosophy about short-term momentum and Regime B follows De Bondt and Thaler’s (1985) contrarian strategy with long-term return reversal.

The DHS-model differs from the BSV-model, where it divides the investors into two groups: informed and uninformed (Fama 1998). The uninformed investors does not have any trading bias, meaning that the price is determined by informed investors. These investors are suffering from two biases: overconfidence and biased self-attribution. Overconfidence means that the investor is exaggerating their signaling of the right price for a stock. While biased

self-attribution implies that the investor is downgrading public signaling about the value of the

stocks, especially signals that are contrary to their own. The investors’ overreaction to private signals and underreaction to public signals gives a short-term continuous return. However, in the long-term, there will be a price reversal due to the overwhelming effect of the public signals (Fama 1998).

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3. Previous literature

This chapter will begin with a background of active investment strategy, followed by the momentum literature covering US, European and global studies.

3.1 Investment strategies

Strategies on how to beat the market have changed over time. In 1936, Keynes summarized that investors’ decision making is based on the result of animal spirits4. Studies that followed in 1936 showed that time-series patterns in returns were depending on market inefficiencies, which mean that there are possibilities to make abnormal profits (Conrad & Kaul 1998). This assumption suggests that the markets would be inefficient since the Efficient Market Hypothesis states that speculative assets, like ETFs, are non-forecastable (Timmerman & Granger 2004), thus making it impossible for investors today to know what the prices would be tomorrow. The return from the financial assets is therefore random, more precisely follow a random walk in the short-term given that the Efficient Market Hypothesis is true. This means that there would be no profit in finding strategies to beat the market. Nonetheless, trading strategies have remained popular in research and for individual investors, where the most common area of strategies is return based. The profits of these trading strategies are based on previous performance and contain a cross-sectional component that would maintain even if returns were completely random (Conrad & Gaul 1998).

3.2 Momentum literature

Based on earlier research, De Bondt and Thaler (1985) presented the contrarian strategy, a strategy that is the opposite of momentum, suggesting that you sell the stocks that have performed well in the past and buy the stocks that performed poorly. The authors presented a result where they achieved abnormal returns for portfolios with a formation- and holding period of three to five years. However, these results could be explained by the systematic risk and the effect of size (Jegadeesh & Titman 1993; Chan 1988; Ball & Kothari 1989). Therefore, a new strategy, based on the original contrarian strategy, arose called the momentum strategy. This strategy was presented by Jegadeesh and Titman (1993) who published significant returns with

4 Animal spirits meaning that human emotion can affect financial decision making in uncertain environments

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7 a formation- and holding period of three to twelve months. Jegadeesh and Titman (1993) found that the profitability of this strategy is not a result of the systematic risk or the delayed stock price reactions to common factors. In 2001, Jegadeesh and Titman presented a paper that proved the same results as in 1993 but changed the data set to the period 1990-1998.

This evidence would however not be the first relative strength strategy that would provide abnormal returns. An earlier example is Grinblatt and Titman (1989) who proved that most of the mutual funds showed a pattern of buying stocks that had an increase in price over the last quarter, hence suggesting that the relative strength portfolio may generate abnormal returns. After 1993 others presented similar results; Chan, Jegadeesh and Lakonishok (1996) proved that all primary stock listed only gradually reacted to new information, suggesting that there were momentum opportunities which were not explained by market risk, size or book-to-market factors. Studies have found momentum profit by using momentum strategies on both the stock-level characteristics and the past returns to select winners and losers (Bandarchuk & Hilscher 2013). However, the authors showed that the only effect which has an impact on momentum profits is the stocks with extreme past return and their characteristics5 will almost disappear. On the other hand, Daniel and Moskowitz (2016) found evidence that momentum investing shows a tendency of unexpected negative returns. According to the authors, this is due to volatile markets and stressed states and is observed under multiple periods with different asset classes.

3.2.1 Global and European momentum performance

In Europe, Rouwenhorst (1998) presented that the winners outperformed the losers in an empirical test using twelve European equity markets. Furthermore, Moskowitz and Grinblatt (1999) present positive results regarding industry momentum, which would beat an ordinary momentum strategy. Chui, Wei and Titman (2000) performed the empirical evaluation on several markets in Europe and Asia and presented a large economic profit. Continuing, Griffin, Ji and Martin (2003) explained that these profits reversed over a one to five year period. Similarly, Moskowitz, Ooi and Pedersen (2012) presented that different types of equities provided persistence in returns for one to twelve months that gradually would be reversed over longer horizons. More recently, Fuertes, Miffre and Fernandez-Perez (2015) show that

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minus-short portfolios capture risk premiums of commodity futures, but present that the

explanation of the cross-section returns is still a subject to debate.

Furthermore, there are studies where researchers have examined how the momentum strategy performed on country indices. Bhojraj and Swaminathan (2006) noted a profit of three to twelve months when they analyzed 38 country indices and showed a reversal effect on the price after 24 months. The authors claimed that the adjustment occurred due to overreaction. Chan, Hammed and Tong (2000) got similar results when they investigated 23 country indices and retrieved positive returns for periods shorter than 4 weeks, compared to Bhojraj and Swaminathans (2006) that get positive returns for three to twelve months.

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4. Theoretical framework

The chapter begins with modern portfolio theory and continues with evaluation measurements. Lastly, three statistical tests are presented to examine the robustness of the results.

4.1 Modern portfolio theory

The foundation of the portfolio theory that exists today has most of its heritage from Harry Markowitz (1952) who first published the importance of having a diversified portfolio (see Elton & Gruber 1997). Markowitz’s paper contains theories that would change the perspective of investments. The author showed how a diversified portfolio is less volatile than the equities would be separate, thus implying that assets cannot merely be chosen by their unique characteristics value. This resulted in the fundamental mean-variance portfolio, which is a portfolio with constant variance and maximized expected return while keeping the volatility as low as possible, also known as the efficient frontier (Markowitz 1952). Continuing, the mean-variance portfolio is central in the study of portfolio theory which depends on two factors according to Elton and Gruber (1997). First, the mean-variance theory process requires large data sets for the investors and there is no further evidence that adding additional moments, skewness and kurtosis, would improve the viability of the selected portfolio. The second reason is the widely developed implication of mean-variance; correlations between different assets are important for professionals to acknowledge before adding a new asset to a portfolio.

4.2 Capital Asset Pricing Model

In line with the optimization process from Markowitz, another model that was developed is the Capital Asset Pricing Model (CAPM). Sharpe (1964) presented the model which represents the expected return including different risk factors while including the risk-free rate. CAPM calculates the expected return of any financial assets compared to a given market.

𝐸𝐸[𝑅𝑅𝐸𝐸] = 𝑅𝑅𝑓𝑓+ 𝛽𝛽𝐸𝐸( 𝐸𝐸[𝑅𝑅𝑀𝑀] − 𝑅𝑅𝑓𝑓) (1)

where 𝐸𝐸[𝑅𝑅𝐸𝐸] is the expected return of the equity; 𝑅𝑅𝑓𝑓 is the risk-free rate; 𝛽𝛽𝐸𝐸 is the volatility for the stock in relation to the overall market; 𝐸𝐸[𝑅𝑅𝑀𝑀] is the expected return for the market index. The model includes the following assumptions (Berk & DeMarzo 2019):

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10 1) All investors are rational and aware of risk

2) All information is available for the investors 3) The investors’ portfolios are widely diversified

4) Anyone can lend and borrow money unlimited at a risk-free rate 5) All investors aim to maximize economic utility

Composed with the efficient frontier, it is possible to create a Capital market line that the investor could adapt to (see Figure 1). The efficient frontier is always the most efficient on the market. Otherwise, it would change immediately to become efficient again. Where the efficient frontier and Capital market line align, there is an opportunity to find the tangency portfolio which provides the highest return-to-volatility ratio, more known as the Sharpe ratio.

Figure 1. Tangency portfolio and Capital market line.

Source: Parker (2017).

4.3 Portfolio measurement

To measure portfolios against each other, it is preferable to use various measurements than average return since the portfolios have different characteristics that make them unique. Besides, the portfolio is affected by risk and therefore it requires adjustments for the uncertainty in the returns.

4.3.1 Returns

The simple return is used to calculate the return of the benchmark and to sum cross-sectional returns.

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𝑅𝑅𝑝𝑝 = 𝑃𝑃𝑡𝑡𝑃𝑃−𝑃𝑃𝑡𝑡−1𝑡𝑡−1 (2)

where 𝑅𝑅𝑝𝑝 is the return of the portfolio at time t, 𝑃𝑃𝑡𝑡 is the equity price at time t and 𝑃𝑃𝑡𝑡−1 is the equity price at time t-1.In addition to the simple return, the thesis uses the logarithmic return, which could be called a continuously compounding rate. The benefit of using log returns is that they are normally distributed and include the effect of compounding (Berk & DeMarzo 2019).

𝑟𝑟𝑝𝑝 = 𝑙𝑙𝑙𝑙 (𝑃𝑃𝑃𝑃𝑡𝑡

𝑡𝑡−1) = 𝑙𝑙𝑙𝑙 (𝑃𝑃𝑡𝑡) − 𝑙𝑙𝑙𝑙 (𝑃𝑃𝑡𝑡−1) (3)

Where 𝑟𝑟𝑝𝑝 is the logarithmic return of the portfolio. Another benefit of logarithmic returns is that they are additive in time, meaning that the returns are possible to sum.

4.3.2 Variance and Volatility

The variance and volatility are used for different hypotheses and risk measurements. These estimates are calculated by averaging squared deviations from the average return.

𝜎𝜎2 = 1

𝑇𝑇−1∑ (𝑟𝑟𝑇𝑇𝑝𝑝=1 𝑝𝑝𝑝𝑝−𝑟𝑟̅𝑝𝑝) (4)

and the standard deviation (volatility) follows as:

𝜎𝜎 = √𝜎𝜎2 (5)

where 𝜎𝜎2 is the variance for the portfolio; 𝜎𝜎 is the volatility for the portfolio; T is the number of observations; 𝑟𝑟𝑝𝑝𝑖𝑖 is the portfolio return at time i; 𝑟𝑟̅𝑝𝑝 is the average return for the portfolio.

4.3.3 Skewness and Kurtosis

Assuming that the returns are i.i.d6, it is possible to calculate the measurements of skewness and kurtosis. These measurements can have robust outliers in the data which could be solved by either manually removing outliers after visualizing the data or deciding which observations to include in the data set (Barroso & Santa-Clara 2015). However, the fat tails are explaining the extreme distribution of the returns in the portfolio with a positive fat tail indicating large positive returns. The skewness explains the distribution of the weights in the returns, where a positive skewness indicates that the fat tail is larger to the right (Berk & DeMarzo 2019). 6 Independent and identically distributed

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4.3.4 Sharpe Ratio

The Sharpe ratio is a risk-adjusted measurement (Sharpe 1966) and can be expressed as followed:

Sharpe Ratio

=

𝐸𝐸�𝑟𝑟𝑝𝑝�−𝑅𝑅𝑓𝑓

𝜎𝜎𝑃𝑃 (6)

The numerator is the difference between the equity return 𝐸𝐸�𝑟𝑟𝑝𝑝� and the risk-free rate 𝑅𝑅𝑓𝑓 while the denominator adjusts for the volatility of the evaluated equity (𝜎𝜎𝑃𝑃). This results in an intuitive measurement that adjusts for the portfolio’s total risk.

4.3.5 Jensen’s alpha

Jensen's alpha is defined as a comparison between the expected return from CAPM and the portfolio return with adjustments to the risk factor beta (Jensen 1968). If the assets have a positive alpha value, the portfolio performs a higher return than the market equilibrium.

𝛼𝛼𝑝𝑝 = 𝐸𝐸[𝑟𝑟𝑝𝑝] − �𝑅𝑅𝑓𝑓+ 𝛽𝛽𝑝𝑝�𝐸𝐸[𝑅𝑅𝑀𝑀] − 𝑅𝑅𝑓𝑓�� (7) Where 𝛼𝛼𝑝𝑝 is the alpha for the portfolio; 𝛽𝛽𝑝𝑝 measure the co-movement between the portfolio and the market. The alpha value is seen by investors as a sign of skill of the portfolio manager. Sorensen, Miller and Samak (1998) present that these signs of outperforming the market create societal views that the portfolio manager is successful.

4.3.6 Morningstar risk-adjusted return

The previously mentioned measurement Sharpe ratio does not account for investments in the risk-free rate (Bodie, Kane & Marcus 2018). Further explained, the Sharpe ratio is invariant to the investor's risk aversion in the sense of how much the investor invests in the risk-free rate compared to the risky portfolio. Further, the Sharpe ratio can be manipulated by increasing the measurement interval; the annualized volatility results are in general lower when calculating monthly returns compared to daily returns. This raises the question if there is a measurement that adjusts for the investor's risk aversion and if the investment decision would change. According to Bodie, Kane and Marcus (2018), the only measurement that is impossible to

manipulate is the Morningstar risk-adjusted return (MRAR). MRAR (y) = �1𝑇𝑇∑ �1+𝑟𝑟𝑝𝑝𝑖𝑖 1+𝑟𝑟𝑓𝑓𝑖𝑖� −𝑦𝑦 𝑇𝑇 𝑝𝑝=1 � −12𝑦𝑦 − 1 (8)

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13 where y is the risk aversion and since the formula assume that the investor is risk neutral, the risk aversion is predetermined as two7; T is the number of observations; 𝑟𝑟

𝑝𝑝𝑝𝑝 is the return for the portfolio at the time i; 𝑟𝑟𝑓𝑓𝑝𝑝 is the risk-free rate at the time i. The MRAR follows the theory of expected utility, where a poor outcome is more concerning than an unexpectedly good outcome is gratifying (Blake & Morey 2000). Meaning that the MRAR is the certain equivalent of the expected utility of risky portfolio (Bodie, Kane & Marcus 2018). An investor is willing to accept a lower return in exchange for a larger certainty of actual return, meaning that the MRAR adjusts the calculated value regarding how much risk the investor is willing to take. Thereafter all portfolios are ranked after their risk-adjusted returns (Bodie, Kane & Marcus 2018). The thesis uses this return to rank all the momentum portfolios, with and without time lag and together these are included with the MRARs of the market index8.

4.4 Robustness check of the returns

With the mentioned measurements, theory and thesis settings, it boils down to three different statistical t-tests. The result from these tests is then used as a foundation for the possible explanation of the existence of abnormal returns.

Test statistic: Winners portfolio – Losers portfolio > 0 (Test 1)

𝐻𝐻0: Expected excess return is not larger than zero

𝐻𝐻1: Expected excess return is positively separated from zero

Test statistic: Momentum portfolio – Market index ≠ 0 (Test 2)

𝐻𝐻0: Expected excess return is equal to zero 𝐻𝐻1: Expected excess return is not equal to zero

Test statistic: Jensen’s Alpha ≠ 0 (Test 3)

𝐻𝐻0: Expected value is equal to zero 𝐻𝐻1: Expected value is not equal to zero

7 MRAR with risk aversion of four is presented in Appendix 4.

8 The top ten percent with the highest risk-adjusted return received five stars; the next 22,5 percent receive four stars; the 35 percent in the middle receive three stars; two stars are retrieved by 22,5 percent; the ten percent in the bottom receive one star (Morningstar 2015).

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5. Method and Data

This section provides information on how the empirical test is constructed. It begins by explaining the portfolio construction and continues with a summary of the data set. In the final part of the section, the benchmarks and zero-cost portfolios are covered.

The investor’s first decision is to choose between cross-sectional or a time-series momentum approach. The cross-sectional approach is the most common where the relative performance is compared to the other assets, while in time-series the absolute performance, based on its historical return is the scale (Bird, Gao & Yeung 2017). Thereafter the length of holding- and formation period needs to be decided and if there should be any time lag for the investment. When the investor has determined the construction rules for the portfolio, there needs to be a decision about which market and types of equities to include. Jegadeesh and Titman (1993) constructed overlapping portfolios with F months in the formations period and H months of holding period and in each month at time t investments were made. A similar approach is the starting point for this thesis.

The empirical evaluation in this thesis is based on cross-sectional historical data and will examine formation- and holding periods of one, three, six, nine, twelve and 24 months. The test is computed with logarithmic returns of various country ETFs representing all continents. Furthermore, the test will be performed with an overlapping portfolio, with and without time lag. With these rules, an investment is made each month throughout the evaluation period, where the top 20 percent is bought and the bottom 20 percent is sold. These percentiles are based on the rankings in the predetermined formation period.

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5.1 Overlapping portfolios

To catch all the information and to increase the power of the empirical test, the thesis follows Jegadeesh and Titman's (1993) idea of using overlapping portfolios. Meaning that at any given period t, there is a new different holding period H based on formation period F returns. Thus, providing a test for the momentum strategy for every t in the data set (see Figure 3).

After the investment is made, the portfolios follow the buy&hold strategy, meaning that no adjustments are made to the portfolio during the holding period. At the end of the holding period

t+H the position is closed and the gain is reinvested. Hence, the portfolio is invested 1/H in

every portfolio that is available, an example from the figures below is that the return at time five is the average return from the portfolios that start investing at time three, four and five. Meaning that the return for every period is calculated by taking the average returns of the portfolio that is closed together with the portfolios that still are in period t+H.

To calculate with a time lag, the formation and holding period are separated by a determined number of lags (l), thus meaning that the holding period starts at t+l. The idea of adjusting with a time lag is to remove the short-term return reversal effect that the data can suffer from (Jegadeesh 1990). The thesis will focus on one month time lag, meaning that the holding period starts at t+1, visually explained in Figure 4.

Figure 3. Illustration of overlapping portfolios without time lag.

Figure 4. Illustration of overlapping portfolios with one month time lag.

t 1 2 3 4 5 t 1 2 3 4 5 1 F 1 F 2 F 2 F 3 F 3 F 4 H F 4 Time lag F 5 H F 5 H Time lag F 6 H 6 H Time lag 7 H 7 H Time lag 8 H 8 H Time lag 9 9 H 10 10 11 11

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5.2 Self-financing portfolio

The concept of a zero-cost momentum portfolio means that the investors buy and sell equities for the same amount, making the portfolio self-financed. This means that there should be no addition or withdrawal of money in the measurement period, where the investment needs to be based on activities in the portfolio (Bergman 1981). This concept has an impact on the portfolio beta, which make the measurement move towards zero. As the strategy is mostly theoretical, it helps the evaluation to calculate returns without determining any starting investment capital.

However, where the self-financing portfolio is possible in theory, there are obstacles for individual investors to use the strategy in practice. The problem starts when the investor tries to sell a specific asset to buy another. First, the investor needs to create a margin account at his or her broker. Second, there is the possibility that not all equities are available for short sell (Berk & DeMarzo 2019). Third, even if all equities are available, the equities still need to be on the market for borrowing and if there are no other investors in this agreement, the investment cannot happen. Making the practical construction complicated, but still possible.

5.3 Benchmarking portfolios

The results of the portfolios are compared to a benchmark that works as a reflection of the market where the equities in the empirical test are included. Since there are numerous stocks in the 30 ETFs, a market index must capture all included stocks. One representation of the global market is the MSCI ACWI who covers 23 developed and 26 emerging markets, which in total includes 3000 stocks (MSCI 2020). This type of index would in theory capture the movements of the global market, consequently making it suitable to use as a benchmark against a global active investment strategy. The global market index MSCI ACWI will be used in all tables, figures and evaluations. One of the reasons for this is due to the simplicity for the investor to evaluate the strategy to either choose the momentum strategy or to invest in an index that reflects an actual market.

The thesis has compared the results with other benchmarks to examine if the result would change. The results are however similar and are therefore not presented in the results. One alternative that was tested is a self-constructed index which was done by Jegadeesh and Titman (1993); De Bondt and Thaler (1985). The authors constructed an equally weighted portfolio

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17 including all stocks in their data set. Another alternative that was examined is the zero-cost buy&hold portfolio. Since the momentum strategy is self-financing, a buy&hold benchmark would need to follow the same structure where each investment must be financed by a loan at the cost of the risk-free rate.

5.4 Data

The data set is historical returns from various ETFs, where each ETF is replicating indices in a specific country. The ETFs prices are collected for the period from March 1996 to December 20189. A list of all countries, descriptive statistics and tickers for each ETF is presented in

Appendix 1. To include a large data set, the data collection starts three years after the first ETF

was launched (Deville 2007). In 1996 there were seventeen available refined countries ETFs that still are available today compared to 1993 when there was only one. These ETFs are from different continents, different sizes and have different market caps. The correlation between the markets is shown in Appendix 5. Solnik and McLeavey (2008) argue that the correlation between the international markets is increasing during bear markets and that this effect is widely known for the investor and within the financial press. Nevertheless, the thesis assumes by covering all the continents in the data set, it is possible to become closer to a global sample parable for the empirical evaluation to measure against.

Table 1. Descriptive data.

Full period 1996-2006 2007-2018

Minimum number of ETFs 17 17 22

Maximum number of ETFs 30 22 30

Number of observations 273 130 143

Maximum monthly return (in %) 1.13 1.13 0.37

Minimum monthly return (in %) -0.38 -0.38 -0.36

The ETFs are constructed to follow either a large country index or a selected number of the largest companies in each country. The ETFs are constructed similarly and the fees for owning the equity are close for every ETF. And since they both are represented in the momentum

9 The data was collected through the Bloomberg terminal, by using the function last price from the historical data

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18 portfolio and in one benchmark index, the thesis needs to assume how to measure this transaction fee of owning the equity.

A1. The cost of owning an ETF is constantly changing which creates a need to assume that the transaction cost of owning the equity is ignored.

However, the transaction cost of trading is still debatable. Jegadeesh (1990) used a transaction cost of 50 basis points, while Rouwenhorst (1998) suggested a transaction cost of 100 basis points, while some studies have not considered the transaction costs at all. The idea of not using transaction cost is to observe if the strategy can outperform the market without boundaries. Based on this, the thesis will calculate with a transaction cost of 25 basis points and without a transaction cost.

5.4.1 Returns

The return in this thesis is calculated from the monthly prices on ETFs retrieved from Bloomberg and is adjusted for dividends and splits (Bloomberg n.d.). The prices of the ETFs are all traded in dollars and the thesis ignores the currency effect. The thesis is unaware of how the ETFs adjust for currency risk and therefore it is simplified to be viewed from an American investor approach. One of the reasons that monthly data is used instead of daily data is because of nonsynchronous trading. Meaning that some of the trades that are done in one day can have an impact the following day in another country with a different time zone. A method that was used by Bhojraj and Swaminathan (2006) when they analyzed country indices.

5.4.2 Risk-free rate

In most of the established western countries, the risk-free rate in the last few years has been approximately close to zero. However, in the emerging markets in the world, the rates still are larger than zero. This creates the need for an assumption of how the risk-free rate should be calculated in this thesis and as all the included ETFs are traded in dollars the assumptions follow as:

A2. The risk-free rate is determined from the US three month Treasury bill and calculated as a simple average through the whole time-series.

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19 Assuming that the risk-free rate will be constant through time, a simplification made to use the same rate for all calculations; Sharpe ratio, Jensen’s alpha, CAPM and zero cost market index will therefore always follow the same risk-free rate.

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20

6. Results

This section covers the empirical data. The data is presented in figures and tables starting with the winners and losers followed by the momentum portfolios with and without time lag. It ends with evaluation measurements.

6.1 Momentum returns

The winners and losers portfolios in the momentum strategy are presented in Table 2. The table presents all evaluated portfolios, including all possible combinations of the determined evaluation months. The returns of the different portfolios present monthly returns in the interval from -0.03 to 0.41 percent for the momentum portfolios, 0.24 to 0.50 percent for winners and 0.03 to 0.36 percent for the losers. Overall, the highest monthly returns are generated with a formation period of six months and the lowest monthly returns are observed in the portfolios that are generated from the previous 24 months.

Some returns provide signs of being significantly different from zero, but only at a ten percent significance level (see Table 2). These are the momentum portfolios F6/H24 with and without time lag; F9/H24 without time lag; F12/H24 without time lag. However, neither of the winners nor losers portfolio show similar signs. The returns from all the portfolios are rarely separated from zero and the winners returns contribute positively to the momentum return, while the losers portfolio merely weakens the overall returns.

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Table 2. Winners and losers portfolios in the momentum strategy.

The returns are presented in percent and are rounded to two decimal points. The winners and losers generate the portfolio WML (winners-minus-losers portfolio). The WML is representing the momentum strategies’ average return. The small capped values in the table represent each returns t-test (see Test 1).

6.1.1 Graphical overview of winners and losers

Figures 5-10 show the cumulative return of buying the winners and losers without time lag.

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Figure 5. F1/H1, 0 Time lag Figure 6. F3/H3, 0 Time lag

Figure 7. F6/H6, 0 Time lag Figure 8. F9/H9, 0 Time lag

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6.2 Momentum returns (without time lag)

From the empirical tests, the results show how the portfolios perform during the full period, sample periods 1996-2006 and 2007-2018 (see Table 3). The portfolio returns are generally larger than zero, but none of the returns or alpha values show significant results that would be positively different from zero.

Table 3. Monthly returns and alpha value.

Momentum portfolios return and alpha, without transaction cost and time lag. All numbers are presented in percent and are rounded to two decimal points. The p-values apply to Test 1 in average return and Test 3 for alpha (see Section 4.4) and are reported in small capped values below the return. Rule: ‘*’ if significant on ten percent

Even though the test provides positive alpha values for the portfolios, the values are insignificant. This is consistent for all portfolios, which is further presented in Appendix 2. Thus, meaning that the portfolios that were significantly different from zero (see Table 2) does not have positive significant alpha values.

6.2.1 Graphical overview of momentum returns (without time lag)

Figures 11-16 show six different momentum portfolios compared against the global market

index. A trend in the data for all portfolios is a quick rise at the beginning of the period which is followed by a decreasing effect throughout the period. Some of the momentum portfolios are beating the market but towards the end of the period, the margin is decreasing. Eventually, there is only one portfolio that is beating the market, F6/H6. However, when calculating with a transaction cost, the F6/H6 loses its positive return towards the market (see Appendix 7).

Average monthly returns Alpha values

H F 1996-2018 1996-2006 2007-2018 1996-2018 1996-2006 2007-2018 1 1 -0.03 0.15 -0.20 -0.18 0.02 -0.37 0.90 0.76 0.51 0.52 0.97 0.20 3 3 0.13 0.30 -0.06 -0.01 0.22 -0.24 0.59 0.48 0.80 0.97 0.58 0.35 6 6 0.37 0.80 0.03 0.22 0.69 -0.14 0.16 0.10 0.90 0.40 0.15 0.61 9 9 0.28 0.60 -0.03 0.14 0.52 -0.21 0.29 0.23 0.92 0.60 0.29 0.42 12 12 0.27 0.43 0.14 0.13 0.34 -0.05 0.33 0.43 0.61 0.56 0.96 0.12 24 24 0.19 -0.07 0.36 0.04 -0.13 0.29 0.51 0.91 0.26 0.89 0.81 0.34 W-L

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Figure 11. F1/H1, 0 Time lag Figure 12. F3/H3, 0 Time lag

Figure 13. F6/H6, 0 Time lag Figure 14. F9/H9, 0 Time lag

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6.3 Momentum returns (with one month time lag)

The average portfolio returns are generally positive and two portfolios, F1/H1 and F6/H6 in the period 1996-2006 are significant on a ten percent significance level (see Table 4). However, these portfolios, like all portfolios, show little to no signs of having significant positive alpha values. Moreover, portfolios with shorter formation and holding periods present higher returns (see Table 4) while Table 3 presents larger returns on portfolios with longer formation and holding periods.

Table 4. Monthly returns and alpha value.

Momentum portfolios return and alpha without transaction cost. All numbers are presented in percent and are rounded to two decimal points. The p-values apply to Test 1 in average return and Test 3 for alpha (see Section 4.4) and are reported in small capped values below the return. Rule: ‘*’ if significant on ten percent.

6.3.1 Graphical overview of momentum returns (with one month time lag)

Figures 17-22 show six different momentum portfolios. A trend in the data is that all portfolios

have an uptrend at the beginning of the period. The momentum portfolios are beating the market in the early stage but throughout the period the margin is decreasing and the market index beats the momentum strategy except in the two portfolios: F6/H6 and F1/H110. These portfolios that in the period 1996-2006 provided significant results are when calculating for transaction cost disappearing and the market index is beating the portfolios (see Appendix 8).

10 Observe that the y-axis in figure 17 is between 0 and 4.5 compared to the others which are between 0 and 3.5. Average monthly returns Alpha values

H F 1996-2018 1996-2006 2007-2018 1996-2018 1996-2006 2007-2018 1 1 0.32 0.97 -0.26 0.19 0.93 -0.42 0.29 0.08 * 0.39 0.52 0.52 0.52 3 3 0.15 0.37 -0.07 0.00 0.27 -0.25 0.57 0.45 0.77 0.99 0.58 0.32 6 6 0.39 0.83 0.03 0.24 0.73 -0.15 0.13 0.08 * 0.92 0.34 0.11 0.60 9 9 0.24 0.56 -0.07 0.10 0.48 -0.26 0.37 0.28 0.78 0.72 0.34 0.32 12 12 0.25 0.41 0.13 0.10 0.32 -0.04 0.37 0.45 0.62 0.51 0.89 0.26 24 24 0.14 -0.19 0.32 -0.02 -0.25 0.26 0.64 0.74 0.33 0.95 0.64 0.41

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Figure 17. F1/H1, one month time lag10 Figure 18. F3/H3, one month time lag

Figure 19. F6/H6, one month time lag Figure 20. F9/H9, one month time lag

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6.4 Risk-adjusted momentum returns

In this subsection, different types of risk measurements are presented: skewness, kurtosis, Sharpe ratio and Morningstar risk-adjusted return.

6.4.1 Characteristics of the momentum portfolios (without time lag)

The measurements that are used to evaluate the performance are presented in Table 5. The portfolios show scattered values, but one portfolio separates from the others: F6/H6 has a positive insignificant alpha and a Sharpe ratio that is higher than the market index.

Table 5. Momentum measurements.

1/1 3/3 6/6 9/9 12/12 24/24 Market index Mean return -0.03 0.13 0.37 0.28 0.27 0.19 0.32-0.34 Volatility 4.63 3.94 4.31 4.28 4.51 4.62 5.32-5.40 Beta -0.17*** -0.18*** -0.12** -0.17*** -0.17*** -0.10* - Alpha -0.18 -0.01 0.22 0.14 0.13 0.00 - Skewness 0.21 0.22 0.21 -0.90 -2.13 -2.38 -1.08 Kurtosis 5.86 4.01 6.05 11.6 19.9 21.7 6.23-6.43 Sharpe ratio -0.044 -0.010 0.047 0.026 0.023 0.005 0.027-0.031 Morningstar ☆ ☆☆ ☆☆☆☆ ☆☆☆☆ ☆☆☆ ☆☆ ☆☆☆

A selection of all portfolios compared to the market index. Returns, volatility and alpha are presented in percent. Rule: “***” if significant on one percent, “**” if significant on five percent, “*” if significant on ten percent.

In addition, portfolios with shorter formation and holding periods (one to six months) show positive skewness and small values of kurtosis, indicating that the distribution of returns has a larger fat tail to the right. However, with a longer formation and holding period (nine to 24 months), the kurtosis gets bigger and the skewness shifts towards negative. Barroso and Santa-Clara (2015) imply that the portfolios have a higher risk of downside if a crash would happen, due to the combination leading to a larger negative fat tail.

Concerning the Morningstar risk-adjusted return, the numbers are similar to the Sharpe ratio. The results show that the highest performing portfolio, measured in Sharpe ratio, is awarded with four stars. This follows the results of the Sharpe ratio and puts F6/H6 as one of the attractive investment opportunities (see Table 5). Another portfolio with four stars is F9/H9.

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28 Despite this, the portfolio presents a lower Sharpe ratio than F6/H6 and the market index. The worst performing portfolio regarding MRAR and Sharpe ratio is F1/H1.

6.4.2 Characteristics of the momentum portfolios (with one month time lag)

The results presented are insignificant for portfolios measured for the full period neither does it gain significant alphas against the market with a time lag (see Table 6). Overall, the results with time lag are similar to the results without time lag. Especially where the formation and holding period is longer than six months. Still, in portfolio F1/H1 the result improves significantly with a shift from negative to positive returns, a insignificant positive alpha value and a Sharpe ratio that is higher than the market.

Table 6. Momentum measurements.

1/1 3/3 6/6 9/9 12/12 24/24 Market index Mean return 0.32 0.15 0.39 0.24 0.25 0.14 0.32-0.35 Volatility 4.95 4.33 4.17 4.37 4.51 4.57 5.33-5.41 Beta -0.23*** -0.12** -0.12** -0.17*** -0.16*** -0.10* - Alpha 0.19 0.00 0.24 0.10 0.10 -0.01 - Skewness 0.11 0.85 0.15 -1.60 -2.33 -2.56 -1.09 Kurtosis 7.67 9.36 6.53 16.7 21.7 22.96 6.20-6.41 Sharpe ratio 0.031 -0.005 0.054 0.016 0.018 -0.007 0.028-0.034 Morningstar ☆☆☆ ☆☆ ☆☆☆☆☆ ☆☆☆☆ ☆☆☆ ☆☆ ☆☆

A selection of all portfolios compared to the market index. Returns, volatility and alpha are presented in percent. Rule: “***” if significant on one percent, “**” if significant on five percent, “*” if significant on ten percent.

The skewness and kurtosis are similar to the portfolios without time lag. The portfolios with a formation and holding period shorter than nine months present a positive skewness and low kurtosis, a combination that would suggest that the distribution of returns has a larger fat tail to the right. However, as the formation and holding period becomes longer (nine to 24 months), the kurtosis gets bigger and the skewness shifts towards negative values.

Morningstar ratings for the portfolios with one month time lag are similar in the sense that the six and nine months portfolios are assigned with more stars than the other portfolios (see Tables

5 and 6). F6/H6 has five stars and is therefore ranked as one of the top ten percent of all

evaluated portfolios. Notable is that the Morningstar for F1/H1 portfolio has changed from one star without time lag to three stars with one month time lag.

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7. Discussion

In line with previous research, the results show higher average returns than the market. On the other hand, the momentum strategy is insignificant for the hypotheses regarding returns and alpha. Meaning that it is not possible for the thesis to state that a momentum portfolio generates abnormal returns against the market. Even though the results are insignificant, the positive returns against the market index are still in favor for the individual investor. The winners portfolio generally outperforms the losers portfolio (see Table 2). Moreover, it becomes clear that the returns of the losers are in general negative regarding the effect on the total momentum return. The winners in the data set follow the trend that creates momentum profits, meaning the past winners continue to outperform the market, which is in line with Jegadeesh and Titman's (1993) findings. Furthermore, it follows Regime A in the BSV-model, where the investor believes this price increase is merely a temporary effect, where the delayed price movement creates profits for the investors. However, the losers could be recognized to follow De Bondt and Thaler's (1985) evidence of overreaction, thus adjusting for the abnormality in the market. This follows representativeness bias and Regime B in the BSV-model where the investors think trends will continue and invest to capture them, leading to a reversal effect.

The positive portfolio returns and alpha value show no significant evidence on a five percent level in either period (see Tables 3 and 4). Nonetheless, there are some portfolios where the momentum strategy beats the market regarding the average monthly return, especially the best performing portfolio F6/H6. The alpha values, in Tables 3 and 4, are generally positive and higher in the period 1996-2006. The values are insignificant, indicating that the momentum portfolios are not superior to the market return, which is in line with the Efficient Market Hypothesis and the assumptions of CAPM. Furthermore, when calculating with the time lag effect, F1/H1 shows a clear difference in return (see Tables 3 and 4). An effect which follows Jegadeesh (1990) theory of short-term reversal effect, where the equity is supposed to adjust back from over- or underreaction. These effects are visually shown in Figures 13 and 17. However, this effect does not appear in the other portfolios with a holding period of one month (see Table 2), making the impact disputable.

The insignificant result can depend on many different factors and is not the primary goal for this thesis to solve. However, an explanation could be that previous studies evaluated a different period and the outcome can differ from this thesis evaluation period. Another explanation of

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30 the insignificant result could be due to the correlation between the countries. Solnik and McLeavey (2008) discussed that the correlation between the international countries is high, especially in downtrend markets, which diminishes the positive effect of diversification between the countries. As observed, the average correlation is higher than 0.6 between the country ETFs (see Appendix 5), thus suggesting that the co-movement between the countries is similar. This effect could have an impact on the momentum strategy since it depends on reversal movements between winners and losers portfolio.

Continuing, the momentum portfolio outperforms the market index at the beginning of the period (see for example Figures 13, 17 and 19). The effect could be explained from the strategy of selling losers where a few ETFs have a downward trend and show signs of underreaction to its market price. Further explained by the conservatism bias, where the investor does not react to the new information immediately and therefore miss the trend opportunity that occurs (Fama 1998). In addition, it follows the DHS-model, where the rational investor with biased

self-attribution will downgrade the public signals and with overconfidence bias value their private

signals, leading the investor to miss the movement. Hence, short-term continuous returns occur due to the delayed effect on the price. However, the trend is diminishing throughout the evaluation period. Another observation in the figures is that after the financial crisis the momentum portfolio is underperforming. These results are in line with Daniel and Moskowitz (2016) findings, which showed that the effect of the crisis has an impact on the country. And in the years that follow the momentum strategy have problems capturing the upward trend that arises after a crash.

Nonetheless, as the momentum portfolio is not generating any significant alpha value, there are still other risk measurements an investor evaluates when selecting a portfolio. As presented in

Tables 5 and 6, shorter formation- and holding periods have a positive skewness, which is in

line with the discussion that the momentum portfolio F6/H6 can be preferred even though it does not show significant results. In contrast, with longer formation- and holding periods, the portfolios deliver a different result, where the kurtosis is increasing and the skewness becomes negative. The Sharpe ratio shows that the F6/H6 portfolios have higher risk-adjusted returns compared to the market (see Tables 5 and 6). This indicates that these portfolios, according to Markowitz (1952), would be more optimal and closer to the tangency portfolio. This is a claim that could break the Efficient Market Hypothesis. In addition to the Sharpe ratio, the Morningstar ratio appears to follow the Sharpe ratios evaluation of the portfolios.

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8. Conclusion

The purpose of this study was to examine if the active country momentum strategy could beat the passive market portfolio. This paper has shown that a country momentum portfolio is unable to produce significant abnormal returns that would imply an inefficient market. A result that is conflicting with the early studies of momentum strategy. As the previous studies have primarily focused on stocks and futures markets, this thesis separates with country ETFs. In this study, some portfolios generate higher average returns which are in line with previous studies. However, the positive results from these portfolios are not significant on a five percent level, thus suggesting that the active investment strategy is not outperforming the passive.

In this thesis, the winners portfolio is generating value, hence following conservatism bias, while the losers follow the representativeness bias which has a negative effect on the returns in the momentum portfolio. This implies that the effect in the momentum strategy of buying and selling equities is canceled out and thus leading to lower momentum returns.

Following the conclusion of insignificant returns, the individual investor could still prefer the momentum portfolio when considering different risk measurements. With the assumption that an investor is risk averse and maximizes utility, the investor would prefer the portfolio with the highest Sharpe- and Morningstar ratio. Following this, an investor could preferably invest in the F6/H6 portfolio with one month time lag, which has the highest Sharpe ratio and is awarded with five stars from the MRAR, instead of investing in the market portfolio.

For further research, it would be interesting to examine which factors that affect the insignificant result for the ETFs. Possibly examined with different types of regressions using macroeconomic data, for example, risk-free rate, BNP, growth rate, book-to-market or VIX. This research could help to further explain why and how momentum profits arise in different periods.

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