MASTER THESIS MSc. Finance
MSc. International Financial Management (Double Degree)
International Momentum Strategies and the Currency Effect:
New Evidence of Foreign Exchange Momentum Profitability
By Thijmen M. Mellink
JEL classifications D84, E10, E44, F3, G10, G11, G15, G30
Keywords Efficient Markets, Momentum, Currency Exchange Rates Author Thijmen Michaël Mellink
Student number S1773798
Mail thijmenmellink@gmail.com
Phone +31 (0) 6 50 87 88 90 Place and date Groningen, 06-‐26-‐2014 Supervisor Dr. J.O. Mierau
International Momentum Strategies and the Currency Effect:
New Evidence of Foreign Exchange Momentum Profitability
Thijmen M. Mellink
ABSTRACT
This paper examines the profitability of momentum strategies implemented on international stock market indices regardless of currency movements. There is considerable evidence that indicates that multinational indices that perform the best (worst) over a specified time tend to continue to perform well (poorly) over the subsequent period of time. To isolate currency effects momentum strategies with one similar and one varying factor are constructed. I find no evidence of momentum returns in the five indices I examine just as the currency effects are negligible in all strategic momentum pairs I create. Significant momentum profits do appear in the short-‐term foreign exchange market momentum portfolios. Further I find that in the short run momentum movements for U.S. investors origin from time-‐series predictability in stock market indices, where in the long run composition derives from currency markets predictability. The results confirm the presence of momentum profits, albeit they move towards currency exchange markets.
I.
INTRODUCTION
“Sometimes thinking too much can destroy your momentum.”
-‐ Tom Watson
In this paper I study the influence of currency effects on international momentum strategies. Over the past three decades the field of stock market irregularities has caught the broad attention of both professionals and researchers. Momentum and contrarian effects have become one of the most thoroughly investigated phenomena in the field of modern Finance. Derived from the field of psychology, behaviourists argue that people systematically over-‐ or underreact to information and financial markets exhibit similar patterns. An initial overreaction leads to an over-‐proportional price movement that later returns itself. Based on these movements, momentum and reversal investment strategies have been developed to exploit these effects. Momentum investment strategies focus on profiting from continuation effects, whereas reversal strategies seek to capture contrarian effects. Focusing on behavioural strategies, De Bondt and Thaler (1985) find contrarian effects in U.S. stocks underperforming the market for a period of three to five years that later outperform in the subsequent similar enduring period. Following their research, Jegadeesh & Titman (1993) find that in U.S. markets the other behavioural strategy – momentum – is present over a shorter period of time. They find that in three to twelve month periods, outperforming stocks keep outperforming, whereas market underperformers keep underperforming in the successive period.One of the causes of the considerable interest in momentum and reversal effects is that efficient market theory cannot account for the excessive returns found. Fundamental for modern finance theory, efficient market theory by Fama (1965) assumes informational efficiency in stock market prices. Efficient markets will therefore not allow investors to systematically earn abnormal returns based on past performance alone. The enduring profitability of momentum strategies contradicts even the weak-‐form market efficiency, which states that historical price information is incorporated in current market prices so that no excessive returns can be earned purely from analysing past stock prices.
Hameed, and Tong add to the momentum research by finding abnormal returns on index level instead of individual stock level, which was the focus of research before.
In this paper I expand the analysis of momentum strategies in global equity markets, and contribute to the literature as follows. First, I implement the momentum strategies based on individual stock market indices. I supplement the research done by Chan et al. (2000) index level research with more recent data. As almost all international equity funds nowadays have access to foreign equity markets, portfolio managers continuously diversify and make decisions on international asset allocation to achieve the highest returns possible given certain levels of risk. By analysing momentum strategies based on stock market indices, I examine whether these strategies are useful for country and index selection.
Second, I examine how the profitability of international momentum strategies is affected by exchange rate movements. The previous mentioned portfolio managers encounter multiple currencies they need to take into account when allocating international assets. Profits from international momentum investment strategies depend on the interrelationship between the currency and exchange markets. An example: a Dutch investor invests €100 in a United Kingdom FTSE index tracker priced at £80 with an exchange rate of 0.80 (thus: €1.00 is worth £0.80; giving him exactly 1 tracker worth £80). The investor sells the tracker and exchanges its gains a month later in which the index tracker value grew 10% (£88). However, the value of the Pound Sterling depreciated with 10% (0.88 euro per Pound), returning him (88/0.88) €100. While his investment in the tracker is successful, the currency exchange rate dilutes his profits. The same accounts the other way around: if both the tracker and the exchange rate value grew 10%, the return for the Dutch investor would have been more than (88/0.72) €122. Isolating these currency effects is crucial in finding momentum effects.
Third, I examine if the foreign exchange market exhibits momentum effects. I already research on an international scale, which makes it a logical step to disregard index price movements and solely focus on foreign exchange rates. With foreign exchange momentum returns present, a portfolio manager can shift or expand its focus from index selection towards currency selection.
markets since they show what market is responsible for potential momentum returns over the four different holding periods.
First of all, no index momentum returns are found in the five indices included in my dataset. Second, I isolate the currency effect by comparing the means of two return portfolios that are constructed in a similar way but have varying return factors. I do not find a currency effect in the two paired return portfolios constructed using either local currency data or U.S. Dollar transposed data. Third I do, however, find momentum return in the currency exchanges associated with four of the five included markets. The Dollar market is excluded since its exchange will always be 1:1. The return momentum in the foreign exchange market yields a significant average 0,036% every four weeks. Finally, I decompose the U.S. Dollar denoted momentum portfolios and conclude that the majority of short-‐term momentum portfolios consist of index momentum, whereas the foreign exchange momentum contributes significantly in middle-‐term return predictability.
The paper is organised as follows. Section II provides the background literature of momentum strategies. Section III provides the framework of analysis of the momentum strategies in the asset markets as well as the foreign exchange market. If further outlines the methodology to isolate currency effects and provides the framework for decomposing U.S. momentum portfolios. Section IV provides the empirical results. Section V concludes the paper.
II.
LITERATURE
The following section provides an overview of the relevant literature for this paper. Subsection A provides a review of efficient market theory linked to behavioural momentum strategies. Here, I refer to several fundamental papers covering contrarian and momentum strategies. These studies are either pivotal to momentum literature or expand the literature into an broader and more international environment. Subsection B focuses on the international environment and introduces the importance to isolate currency effects when trading with international momentum strategies.
A.
Efficient Markets and Behavioural Momentum Strategies
As described by Fama in 1965, the stock market has the primary task to allocate ownership of the economy’s capital stock. When efficient, market prices provide the correct signals for resource allocation and investors will invest in stocks they judge as having the right reflection for the risk taken by the firms (Fama, 1965). Important here is the assumption that market prices always fully reflect all available information. In line with this information availability, the market efficiency theory further suggests that it is not possible to consistently earn higher-‐than-‐average returns based on past price information and performance. If a possibility occurs where an investor can earn a return that is normally linked to a higher risk level, this immediately will be arbitraged away, bringing the return back to its fundamental level (Fama, 1991).
An investor always invests in securities that constructs the portfolio which yields the most optimal level of profit and utility. Behavioural finance studies return anomalies due to phenomena efficient market theory fails to explain. It focuses on overreaction of investors to new information by failing to correctly incorporate price-‐sensitive news in prices, leading to both momentum and contrarian strategies (De Bondt and Thaler, 1985; Jegadeesh and Titman, 1993). Momentum theory states that outperforming stocks (winners) keep outperforming and underperforming stocks (losers) keep losing over a pre-‐ specified period. Contrarian strategies are based on regression to the mean: investors and – with them – stock prices overshoot to price sensitive information which later return to their appropriate level. Both momentum and contrarian strategies give possibilities to invest in these behavioural movements.
Jegadeesh and Titman (1993) follow up on this research and focus on another strategy: momentum. They state if reversal returns found by De Bondt and Thaler (1985) exist due to stock prices that overreact to specific information, profitable trading strategies using return persistence based on historical information will likely exist as well (Jegadeesh and Titman, 1993). To study whether these continuation effects are present, they analyse stocks during a so-‐called formation period. When this period is over, ‘winners’ and ‘losers’ are selected based on past return. The winners are the stocks that outperformed, while the losers consist of the underperforming stocks. Jegadeesh and Titman (1993) buy (go ‘long’) the winners, which they put in the winners portfolio W. Subsequently, they sell (go ‘short’) the worst performing stocks, which form the loser portfolio L. By holding these portfolios after the formation period expired, they find that winners keep winning, while losers keep losing over the following holding period, proving the presence of momentum effects. Where De Bondt and Thaler (1985) find that abnormal returns in the form of reversal strategies exist for a three to five year holding period, Jegadeesh and Titman (1993) extend this research by looking at momentum effects at a much shorter period: 3-‐ to 12-‐months. They find that especially the winner portfolios realize consistently higher returns in the 7 months following the portfolio formation period than do past losers (Jegadeesh and Titman, 1993).
Strategies based on return persistence or regression to mean are contradictory to the perspective of efficient markets as empirical studies show that the momentum effects cannot be explained using the asset-‐pricing models like the Capital Asset Pricing Model or the Fama and French three-‐factor models (Jegadeesh and Titman, 1993; Fong, Wong, and Lean, 2005). Fama and French (1996) try to rationalize a number of related empirical regularities, but fail to account for the profitability of the Jegadeesh and Titman (1993) strategies. In 1997, Carhart successfully captures the profitability by including an extension to the Fama and French three-‐factor model in the form of a momentum factor. Daniel, Hirschleifer and Subrahmanyam (1998) further elaborate on overconfidence in financial markets and find five drivers that influence overconfidence. In 2012, Fama and French conclude that the momentum effects are persistent and always present in modern financial markets.
B.
International Momentum and Foreign Exchange
With the introduction of internet-‐based trading, worldwide stocks markets are more accessible and monetary borders are easily crossed. Diversifying risk over several countries with multiple indices is nowadays straightforward and most necessary for portfolio managers to gain higher returns. In this international setting these managers are encountering different economic, political, cultural, and especially monetary environments. As explained in the introduction section any fluctuation in currency exchange rates will influence an investor’s profitability, making them essential to account for when studying international momentum strategies.
In 1998, Rouwenhorst broadens the field of momentum research by studying the international momentum movements. By converting worldwide stocks with different currencies to one common currency – the Deutsche Mark – he researches momentum on a large international scale. The portfolios he constructs yield on average a 1 percent return per month, an outperformance that he finds in all 12 markets from his sample. The momentum returns he finds, however, cannot be fully allocated to asset momentum returns, considering the currency exchange movements of the direct convertance of non-‐ Deutsche Mark stock returns to a Deutsche Mark denotation are not taken into account.
In 2000, Chan et al. expand research for momentum by analysing possible momentum returns on index price level. Where all previous studies focused on individual stock price momentum, they include 23 stock indices from an equal amount of countries. They find that especially for short holding periods (less than four weeks) momentum profits are statistically and economically significant. The study concludes with the notion that momentum profits can be increased by exploiting exchange rate information. They, however, find that in their dataset return continuation in stock prices is the main driver for the momentum returns (Chan et al, 2000).
strategies is hurdled due to professional – thus supposedly more rational – investors (Griffin, Ji, and Martin, 2005).
The previous studies on momentum effects leave room for further research in international markets and lead to three fields of study in this paper. First, it is mentioned by Chan et al. (2000) that currency exchange movements can influence the performance of markets. Regarding the modern international oriented stock markets, portfolio managers are at all times exposed to currency exchange movements. Next to the internationalisation, investors are increasingly trading higher level index trackers. Considering the fact an investor always strives to maximise profits with the lowest risk possible I research how international momentum strategies nowadays are affected by currency movements. Key here is to isolate currency movements from market movements. My second field of research is to study momentum returns in solely the foreign exchange markets. Already focusing on an international environment, the results can trigger investors to expand momentum strategies to foreign exchange markets. Third and last, to understand where U.S. momentum returns origin from it is crucial to decompose them. By doing so, I can see whether the underlying stock price movements or the currency exchange movements are the key contributors to these returns.
III. DATA AND METHODOLOGY
This section provides the data and methods I use in my research. First, I explain the data. Then, I elaborate on the framework I use for the analysis of momentum effects in equity markets. The section further outlines the methodology to isolate any currency effects. Similar to the model for finding momentum in asset markets, momentum in foreign exchange markets is researched. Finally this section provides the framework for decomposing U.S. momentum portfolios into their key components.
A.
Data
countries where all data is present. Next to that, these countries are considered politically and economically stable, minimizing the influence of as much external factors as possible. These are preferred indices an investor would consider investing in when following a momentum investment strategy. From each country the large cap index is chosen that is considered to be the leading index in the market, while also being a good reflection of all industries. Daily price returns of the selected indices are downloaded from Datastream. The daily U.S. Dollar exchange rates with the four corresponding different currencies (see table 1) are taken from in the Morgan Stanley Capital International (MSCI) database, giving the ability to transform each local currency price return in a U.S. Dollar price return.
Since the markets from my dataset are located in different time zones, their daily rates of return may reflect returns that are realized over different days. Therefore, following Chan et al. (2000), returns are analysed on a weekly basis, reducing potential estimation biases arising from this non-‐synchronous data. To further reduce the possibility for overlapping measurement periods, weekly formation and holding periods start and end on different days of the week. Formation periods start on Wednesdays and end on Wednesdays, whereas the holding periods commence on Thursdays and end on Thursdays. By doing so, it is not possible for any forming and holding period to overlap in the different time zones, creating non-‐ synchronous data. It further mitigates any microeconomic impacts.
Table 1: The Countries used in this paper, their corresponding Index’ names, the Index’ Symbol as well as the local Currency the indices are denoted in
Country Index name Symbol Currency
Germany DAX – XETRA GDAXI Euro (€)
Japan Nikkei 225 – Osaka N225 Yen (¥)
Switzerland SMI – VTX SSMI Swiss Franc (CHF)
United Kingdom FTSE 100 – FTSE FTSE Pound Sterling (£)
United States Dow Jones Industrial Average – DJI DJI US Dollar ($)
B.
Methodology
To find possible momentum returns, I follow the methodology of Chan et al. (2000). To begin, I calculate the daily returns1 of each individual index over a time period from 01-‐01-‐1999 to 04-‐14-‐2014. By adding-‐
up these daily performances, I calculate weekly, monthly, and yearly returns per index. Momentum investment strategies impose buying the stocks that show good performance and selling the ones that do not. Therefore, I monitor index returns during the so-‐called formation period, which lasts for a period of j weeks. After each formation period t-‐1, indices are ranked based on their return and the deviation from the market average Rm in the same period t-‐1. The market average is the average of the five indices
included in this dataset. The index with the highest positive value will become a ‘long’ position (be bought) in the momentum portfolio, whereas the lowest negative value will become a ‘short’ (be sold) position in the momentum portfolio.
The indices represented in the momentum portfolios of Chan et al. (2000) are proportionally distributed in the momentum portfolio based on their deviation from the market average. These momentum portfolios therefore always include all 23 indices of the dataset, but differ in weights and position (short or long). Since my dataset consists of five indices, I choose to follow a more discrete momentum strategy by buying only the absolute winner and selling the absolute loser. A holding period momentum portfolio therefore always exists of two indices. This creates an equally weighted and zero-‐sum investment momentum portfolio that can be monitored during the adjoining holding period. This holding period k always has the same duration as forming period j, so that if the forming period takes 12 weeks, the subsequent holding period also lasts 12 weeks. In the literature debate exists what holding periods are most appropriate in finding momentum returns. Since the arguments range from short-‐term to middle-‐long term forming and holding periods, I account for all these periods with forming and holding periods of 4, 12, 24, and 36 weeks. Considering that momentum effects are generally observed in the time period from 4 to 36 weeks most momentum effects are filtered from the dataset. The return of the momentum portfolio in the holding period t is calculated with formula 1:
(1) 𝜋!! 𝑘 = 𝑤!" 𝑘 ∗ 𝑅!" 𝑘 ! !!!
1
The logarithmic daily returns are obtained by 𝐿𝑁 !!
At the end of a formation period (i.e. formation period 1), the adjoining holding period 1 starts with monitoring the performance of the portfolio composed by the winner and the loser of formation period 1. At that same moment formation period 2 commences. When this period ends, holding period 2 and formation period 3 start. See figure 1 for clarification in a 4-‐week forming and holding period example.
Figure 1: Formation and Holding period process in a 4-‐week momentum strategy
Inasmuch as I go long in the winner index and short the loser index, the weight 𝑤!" (𝑘) to the long position is +100% whereas the weight in the short position is -‐100%, creating a portfolio in which the weights are summed to zero. The return of each individual index 𝑅!" (𝑘) is found by summing the natural logarithmic returns over the holding period used at that moment. The result from the long position will be positive if the outperforming index keeps outperforming in the holding period, whereas the short position will generate positive results if the underlying index will keep losing in the holding period.
I account for above-‐average return continuation of the created momentum portfolios by taking the average market movement into account. The market average of the holding period is therefore subtracted from the return provided by the momentum portfolio in the holding period (see formula 2). The results that follow from formula 2 provide data on the performance of the momentum portfolios. A positive result indicates the momentum portfolio outperformed the average market movement in the same period by holding on to the winner and shorting the loser in the preliminary formation period. A negative result implies the momentum portfolio underperformed the market average. This can either be because the winner index underperformed the market average and/or because the loser portfolio started to perform well. The results from this formula provide the Delta dataset: the differences between the momentum portfolio returns and the market average returns in each period. Each dataset has therefore two outcomes: 1) A momentum outcome where market averages are not taken into account and 2) A delta outcome, where these are taken into account.
(2)
𝜋!!"#$% 𝑘 = 𝑤!" 𝑘 ∗ 𝑅!" 𝑘 !
!!!
− 𝑅!" Where the average return of the market:
(3) 𝑅!" = 1 𝑁∗ 𝑅!" ! !!!
* The amount of indices is equal to N (in this case: N = 5)
Typically, I look for a positive value for 𝜋!!"#$% 𝑘 , since this would indicate that momentum strategy portfolios earn more than market average returns in the holding period.
To isolate the currency effect it is necessary to create momentum and delta portfolios in both the local currency as well as in one common currency, which in this paper is the U.S. Dollar. If no currency effects are observed, the local currency and Dollar denoted momentum portfolios would yield the exact same returns. In subsection III.C I will further examine the currency effect and how it can be isolated. To find the Dollar-‐denoted returns, 𝑅!"$(𝑘) is calculated as in formula 4:
(4) 𝑅!"$ = 𝐿𝑁 𝑅! 𝑅!!! + 𝐿𝑁 𝑋!"$ 𝑋!"!!$
𝑅! is the daily return in the market, denoted in the local currency. 𝑋!"$ is the U.S. Dollar exchange rate: the amount of U.S. Dollar per monetary unit of the local currency. This second factor is added to account for changes in return if corresponding exchange rate changes. It can be seen from this formula that if a local currency index has a positive return and the exchange value in terms of Dollars increases as well, an investor has a win-‐win return. The returns from formula 4 establish the hierarchy in the U.S. denoted dataset. To calculate Dollar denoted momentum returns in the holding period, formula 5 is applicable: (5)
𝜋!$! 𝑘 = 𝑤!"$ 𝑘 ∗ 𝑅!"$ 𝑘 !
!!!
Formula 6 is applicable in finding whether the created Dollar momentum portfolios have a positive return compared to the average market return in the same period:
(6) 𝜋!$!"#$% 𝑘 = 𝑤!"$ 𝑘 ∗ 𝑅!"$ 𝑘 ! !!! − 𝑅!"$
* The amount of indices is equal to N (in this case: N = 5)
Where the average return for the Dollar denoted market is: (7) 𝑅!"$ = 1 𝑁∗ 𝑅!"$ ! !!!
In this paper I assume no restrictions on short selling and no involvement of trading costs.
C.
Isolating the Currency Effect
To obtain well-‐grounded international momentum results in the dataset it is key to isolate the effects of currency exchange movements. The momentum portfolio formula consists of two factors: the long and short position of two indices and their corresponding returns. Both factors can originate from either the local currency market data or the U.S. Dollar converted data, giving a total of four variations. Portfolio composition derived from local currency [𝑤!" 𝑘 ] returns stem from pure local index return winners and losers. This composition corresponds to an investor investing in its home country with its domestic currency. The composition derived from U.S. Dollars however [𝑤!"$ 𝑘 ] find its origin in summing both the foreign index return and the varying currency exchange return (see formula 4). This corresponds to an investor that exchanges index returns from another country with a foreign currency into U.S. Dollars.
Formulas 7A, 7B, 7C, and 7D (A) 𝜋!! 𝑘 = 𝑤 !" 𝑘 ∗ 𝑅!" 𝑘 ! !!! (B) 𝜋! ! 𝑘 = 𝑤!"$ 𝑘 ∗ 𝑅!"$ 𝑘 ! !!! (C) 𝜋! ! 𝑘 = 𝑤!"$ 𝑘 ∗ 𝑅!" 𝑘 ! !!! (D) 𝜋! ! 𝑘 = 𝑤!" 𝑘 ∗ 𝑅!"$ 𝑘 ! !!!
* Components in formulas 7A, B, C, and D with a $ sign stem from the U.S. Dollar dataset. The ones without are from the local currency dataset.
In strategy 7A, I take both the winner and the loser that origin from the local currency dataset and multiply them with their corresponding local currency returns. Hence, I do not account for any external currency influences and measure the pure local market momentum returns. Strategy 7A is applicable when a global investor applies momentum investment strategies using the index returns denoted in the accompanying currencies. For example: If I buy a Japanese index tracker and sell a German, the returns are denoted in both Yen and Euro.
Formula 7C has the same criteria for determining the winners and losers [𝑤!"$ 𝑘 ] but a different return factor. The portfolio is composed using U.S. Dollar data while deriving the resulting momentum returns from the local currency dataset, excluding currency exchange effects in this second factor.
Strategy 7D adopts a strategy similar to 7C, only the other way around. The portfolio is computed using winners and losers from local currency data while returns stem from the U.S. dataset. U.S. investors that adopt momentum investment strategies in global equity markets and transform their obtained returns to the U.S. Dollar follow the 7D strategy.
The function of the four different momentum strategies is to isolate the currency effect. This is done by comparing the returns from the portfolios that are composed in similar ways. For strategies A, B, C, and D this means that the difference between strategy A and D as well as the difference between B and C is of important in finding possible currency effects. A and D have the same local currency composition [𝑤!" 𝑘 ] whereas in strategy B and C have the U.S. Dollar denoted returns determine the winner and loser indices [𝑤!"$ 𝑘 ]. Any significant deviation in momentum portfolio return between these two can be fully allocated to movements in the currency exchange rates.
D.
Momentum in the Foreign Exchange Market
I use daily return data for the different currencies to find possible momentum effects in the foreign exchange market. Corresponding to the momentum portfolios on index level, the momentum portfolios I create in the foreign exchange market differ in forming and holding periods. The returns in the foreign exchange market are calculated in an equivalent way as the returns from the indices, see formula 8 below. (8) 𝑋!"! = 𝐿𝑁 𝑋!" $ 𝑋!"!!$
(9) 𝜋!! 𝑘 = 𝑤!" 𝑘 ∗ 𝑋!"! ! !!!
Identical to the index method, the market average performance of the four currency exchanges is used to evaluate the performance of the momentum portfolios constructed.
(10) 2 𝜋!! 𝑘 = 𝑤!" 𝑘 ∗ 𝑋!"! 𝑘 ! !!! − 𝑋!"
E.
Decomposing the Momentum Portfolio
An international oriented U.S. investor following a momentum investment strategy can profit from momentum effects in this multi-‐country and multi-‐index setting. To see whether possible excess momentum returns origin from either stock market movements or currency effects, decomposition of U.S. momentum portfolios is essential. I break down the total momentum portfolio into two components: the local index momentum return component and the exchange rate momentum return component. Possible momentum found in the first component will be in line with momentum found in strategy 7A, considering I only look at local market index movements and exclude currency influences. Momentum found in the second component will overlap with momentum found from formula 9, thus only focussing on currency movements. By splitting the return components for a U.S. investor I am able to study if the returns of the two factors either amplify or weaken each other. If for example one of the two is continuously destroying the momentum return of the other, an investor can choose to stop investing with momentum strategies in the value-‐destroying market and focus on the value-‐adding market.
Calculating what momentum portfolios will return in all three markets independently, I can compare them and see how much they overlap. An example can be provided when I take an isolated and
2 𝑋!" = !
!∗ 𝑅!" !
separated view on the three markets. Imagine for example the United Kingdom’s FTSE showing a strong performance. It will be represented (as a winner) in the local currency momentum portfolio from a U.K. based momentum investor. If in the same period the Pound Sterling depreciates in value compared to the Dollar, it will be the loser of the currency exchange momentum portfolio of a currency momentum investor. For a U.S. based momentum investor, however, the increase of the FTSE and the depreciation of the Pound Sterling leads to an almost certain winning combination. It is then likely that the ‘winner’ of the U.S. investor’s momentum portfolio is composed by the United Kingdom’s movements (the markets + the currency). If one of these movements continuously counteracts the returns of the other, this will emerge by decomposing the returns.
Considering the individual data already of (1) local currency momentum portfolios, (2) foreign exchange currency momentum portfolios, and (3) the U.S. Dollar denoted momentum portfolios, I can study the independent influences using ordinary least squares (OLS). The U.S. momentum portfolio is the dependent variable whereas the local asset markets and the currency exchanges are the independent variables.
IV. EMPIRICAL RESULTS
This section reports the main results of the analyses. First, the statistical summary and correlation diagram are provided. Second, the results section provides outcomes of (1) the presence of actual momentum returns in the stock markets, (2) the isolation and presence of a currency effect, (3) momentum effects in the foreign exchange markets, and (4) the results of the OLS analyses. This section concludes with the precautionary measures taken to strengthen the results.
A.
Statistical Summary
-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ Insert tables A1a through A1e here -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐
-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ Insert table A2 here
-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐
B.
Results
Results in this section are obtained by constructing momentum portfolios using the dataset and framework described in the methodology section. To assess if currency influences exist, it is first necessary to analyse the momentum portfolios. Subsection 1 therefore contains and compares the market returns with the momentum portfolio returns, followed by assessing the currency effect in subsection 2. Subsection 3 exhibits the results of momentum strategies in the foreign exchange market. Subsection 4 shows the results of the Ordinary Least Squares tests.
1. International Momentum Returns
Assessing the profitability of momentum portfolios is done by comparing the returns of the momentum portfolios with the returns of the market average. Table A3 provides outcomes of comparing the means of the return momentum portfolios per category with the corresponding market average returns. None of the t-‐values is significant, indicating that none of the momentum portfolios are significantly different from the corresponding market returns. The absence of such returns shows that there are no signs of momentum premiums.
-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ Insert table A3 here -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐
weights and returns momentum strategy 𝜋!!shows a negative return of -‐0.0002% over the total timespan. The 𝜋!!strategy, which is computed using both U.S. Dollar weights and U.S. Dollar returns, shows a positive return of 0.0012%, being a little bit lower than the 𝜋!! strategy that yields 0.0013%. The C-‐portfolio is based on weights of the U.S. market, but is combined with the local currency returns. All are however insignificant, as well as momentum portfolio 𝜋!!. The result is that no momentum portfolio outperforms the average market movement over the complete timespan.
-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ Insert table A4 here -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐
2. Assessing the Currency Effect
To isolate the currency effect, I compare the means of the data samples using two-‐sample t-‐tests. The important comparisons are strategy 𝜋!!(𝑘) with 𝜋!!(𝑘) and strategy 𝜋!!(𝑘) with 𝜋!!(𝑘) since they are composed in similar ways. Any deviance in results can therefore be fully allocated to currency effects. Table 2 shows the t-‐statistics of the paired two-‐sample t-‐tests of all the 4-‐week momentum portfolio mix possibilities. The compare of means between the momentum portfolios and the Deltas portfolios are presented.
Table 2: Overview of the outcomes of the Compare of Mean T-‐Test for the 4-‐week holding period pairs K = 4 weeks 𝜋!!(𝑘) 𝜋 !!(𝑘) 𝜋!!(𝑘) 𝜋!!(𝑘) Momentum 𝜋!!(𝑘) 𝜋!!(𝑘) -‐0.275915 𝜋!!(𝑘) -‐0.296971 0.014370 𝜋!!(𝑘) -‐0.245177 -‐0.030005 -‐0.045134 K = 4 weeks 𝜋!!(𝑘) 𝜋!!(𝑘) 𝜋!!(𝑘) 𝜋!!(𝑘) Deltas 𝜋!!(𝑘) 𝜋!!(𝑘) -‐0.208747 𝜋!!(𝑘) -‐0.116305 -‐0.105089 𝜋!!(𝑘) -‐0.075668 -‐0.129660 -‐0.032229
The values are the t-‐values from the compare of means between the different strategies. Significance levels of 10%, 5%, and 1% are indicated with *,**,*** correspondingly. Bold figures are important comparisons.
The t-‐values of the momentum portfolio comparison between 𝜋!!(𝑘) and 𝜋!!(𝑘) show no significant result. Composed by the Dollar denoted winners and losers, the difference in returns result in a t-‐value of 0.014370, failing to reject the hypothesis that no currency effect is present. The outcome of the Delta portfolio comparison results the same conclusion: with a t-‐value of -‐0.105089 no currency effect is significantly present.
The mean comparisons of the two portfolios constructed using local currency winners and losers yield no significant values. The comparison shows an insignificant t-‐value of -‐0.245177, whereas this value is -‐ 0.075668 when the average market movements are taken into account. It can be seen from table 2 that no other pairs show significant t-‐values, albeit that these comparisons and results are less interesting for the currency effect. In appendix A, tables A5a through A5d show the results of the compare of means tests from the different forming and holding length-‐periods. Both the results of the momentum portfolios as well as the Delta portfolios are given.
-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ Insert tables A5a through A5d here -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐
3. Foreign Exchange Momentum
Focusing solely on the foreign exchange market, different results are seen. This dataset provides only four markets considering the U.S. Dollar to U.S. Dollar rate is per definition 1:1. Table 3 provides the mean of the momentum portfolios as well as the mean of the average market movement. I use compare of mean tests to analyse significant differences in return.
Table 3: Means from ForEx momentum portfolios and market portfolios
4-‐week 12-‐week 24-‐week 36-‐week
Mean Momentum 0.037054 0.007783 0.000330 0.033126
Mean Market 0.001024 0.003749 0.008602 0.010864
t-‐value -‐14.70800*** 0.475086 -‐0.492359 0.952323
Values given are the means of the corresponding dataset, differing in 4, 12, 24, and 36 weeks. The t-‐values are the result of a compare of means test between the momentum and the market portfolios in the foreign exchange market. Significance levels of 10%, 5%, and 1% are indicated with *,**,*** respectively.
In the 4-‐week forming and holding periods the mean of the momentum portfolio and the mean of the corresponding market portfolio are significantly different to each other. An international oriented momentum investor can therefore apply momentum strategies in the foreign exchange market using short-‐term forming and holding periods. This strategy returns 0.037%, compared to a diversified portfolio containing all four currencies that yields 0.001% per four weeks. A momentum portfolio consisting of one long position in a currency that yields positive results for a U.S. Dollar investor (i.e. the Dollar appreciates in value) combined with a short position in a currency that appreciates compared to the Dollar (i.e. the Dollar depreciates in value) leads to a consistent positive result over 4-‐week forming and holding periods. Graphs G1 through G4 show the returns of the two returns over all four forming and holding periods. Graph G1 provides an illustration of the positive currency momentum returns.
-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ Insert graphs G1 through G4 here -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐
