外匯市場動能效果分析 - 政大學術集成

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(1)國立政治大學金融學(系)研究所碩士學位論文. 外匯市場動能效果分析 THE ANALYSIS OF THE MOMENTUM EFFECT IN MONTHLY CURRENCY MARKET. 研究生：謝皓雯撰 (Hao-Wen Hsieh) 指導教授：林建秀博士 (Dr. Chien-Hsiu Lin). 中華民國一○四年六月.

(2) 中文摘要本文主要研究外匯市場在 1983 年 11 月到 2014 年 10 月期間是否存在動能效果(momentum effect)，並再更深入探討可能造成動能效果的原因。本文以美國投資者的角度，使用 62 個國家的貨幣，發現在使用較短期的遠期外匯及回顧較近期的歷史報酬作為判斷是否交易的依據，這樣的動能策略可以招致較高且較穩定成長的累積報酬；但是若使用較長天期遠期外匯及以較遠期的歷史報酬判斷，動能策略可能較不顯著，並且累積報酬也較不穩定，甚至在外幣國家發生突發性貨幣危機時，在外匯市場通常會發生反轉效果。另外也驗證出動能策略的超額報酬很大部分是受到交易成本和即期匯率波動的影響。我們發現國家風險和動能效果平均而言呈現正向關係，流動性風險相較於國家風險對於動能效果的影響性較低。. Abstract We investigate whether momentum effect exist or not in the foreign exchange market. We find, based on a sample of 62 market currencies and view U.S Dollar as based currency, the evidence of higher and more stable momentum excess returns as we apply the short formation and holding period in our momentum strategy portfolios. However, when we apply long formation and holding period in our momentum strategy portfolios, we find less momentum effect and unstable cumulative excess returns, and even in the crisis, we find reversal rather than momentum. Additionally, we provide the evidence that transaction cost and spot rate change is the dominant influence on momentum effect. The relationship between country risk and momentum effect is positive significance and liquidity risk provide less evidence on momentum effect.. Key words: momentum returns, foreign exchange market, currency crisis, country risk. I.

(3) 謝辭. 首先我要感謝我的指導教授林建秀博士，在我碩士一年級下學期的時候收我當論文指導學生，並在我撰寫論文的這一段期間內細心的領導我到正確的方向，並且在每次遇到問題時，也會耐心的和我討論，讓我可以更明確的瞭解到如何解決問題，使得我的論文得以順利且如期完成。也要感謝來參加論文口試的口試委員，廖四郎博士以及程智男博士，在百忙之中抽空來參與我的口試，而且在口試後也給我許多論文上極具建設性的建議、提出了許多我也沒有想到的疑問，讓我的論文得以修改得更加完整及嚴謹。也感謝政大金融所的教授們在課堂上的心細教導，啟發我對本論文內容更多的想法。另外，在寫作過程中也要感謝我的父母，在這段期間在旁邊默默地一直支持我並也為我打氣。也感謝林律志同學，在過程中指導我如何撰寫程式來做資料整理，讓我的資料整理時間更加縮短，想要再做其他相關延伸的研究也更加方便。還有何奕嘉同學，在我論文寫作過程中也給我很多統計上及資料整理上的建議。兩年碩士生活轉眼即逝，經歷了和大學時期很不一樣的生活，雖然辛苦忙碌，但卻充實豐富，不僅只是課程的加深加廣，業界實習、程式撰寫學習、考取證照、完成論文，這些事更是我在碩士期間完成的事。其實，一面撰寫論文，一面考取 CFA 證照，還要找工作的日子真的是蠟燭多頭燒，但因為有了以上這些教授親友的相助，讓我可以順利的同時完成這些事，真的是不慎感激。未來也期許自己可以成為有影響力的人，才不負導師們的苦心栽培以及親友的一路相挺。. 民國 104 年 6 月謝皓雯於台北. II.

(4) Table of Contents. 1. Introduction ............................................................................................................ 1 2. Literature review.................................................................................................... 4 3. Data 3.1.Data for FX momentum strategy ..................................................................... 7 3.2.Data for a measurement of country risk ....................................................... 11 4. Methodology 4.1.Currency excess return ................................................................................... 14 4.2.Portfolio construction ..................................................................................... 15 5. Result 5.1.Excess return of momentum strategy ............................................................ 16 5.2.UP and DOWN in foreign exchange market ................................................. 23 5.3.Momentum return and market stress ........................................................... 25 5.4.Momentum excess return in sub periods ..................................................... 28 5.5.The spot rate change ....................................................................................... 30 5.6.Transaction cost ............................................................................................... 32 5.7.The relationship between country risk and the momentum excess return 34 5.8.The result from time-series regression .......................................................... 36 6. Conclusion and Suggestions ................................................................................ 39 Reference .................................................................................................................... 42. III.

(5) List of tables. Table 1. Descriptive statistic: individual currencies ................................................. 9 Table 2. Descriptive statistic on CRISK ................................................................... 13 Table 3. Excess return of momentum strategy in the whole period ...................... 17 Table 4. The “reversal” position during the crisis .................................................. 22 Table 5. The net position in strong momentum period ........................................... 22 Table 6. Momentum returns in UP and DOWN FX market states ....................... 24 Table 7. Momentum return and market stress ........................................................ 27 Table 8. Momentum excess return in sub periods................................................... 29 Table 9. Return of the spot rate change in the whole period ................................. 31 Table 10. Excess return of momentum strategy with transaction cost.................. 33 Table 11. Momentum excess return sorting by country risk .................................. 34 Table 12. Liquidity risk and momentum excess return .......................................... 38. IV.

(6) List of figures. Figure 1. Number of available currencies .................................................................. 8 Figure 2. Average CRISK in each year .................................................................... 13 Figure 3. Cumulative excess returns of momentum strategies .............................. 19 Figure 4. The relationship between MOM(12,12) and the FX market situation.. 26. V.

(7) 1. Introduction Momentum effect already have significant evidence on stock market (Jegadeesh and Titman 1993). Stocks that do well relative to the market over the last three to twelve months tend to continue to do well for the next few months, and stocks that do poorly continue to do poorly. Momentum effect is left unexplained by the traditional pricing model, like CAPM, which we used to measure in the financial market, and have more evidence of unsystematic risk, such as credit risk(Avramov, Chordia, Jostova and Philipov 2007) and transaction cost(Korajczyk and Sadka 2004). In this paper, we are curious about whether the momentum effect exist in the foreign exchange market. With a view to knowing this, we first investigate whether the momentum strategy is profitable or not in the foreign exchange market, and try to interpret the existence of excess returns. Foreign exchange markets have very different market condition from stock market. Foreign exchange markets are more liquid and highly competitive, and have the largest size, so it’s hard to charge transaction cost. In addition, there are almost no short-selling constraint, so we can fully implement the momentum strategies. Some earlier researches have tried to explain the excess returns of momentum strategies. And if we attribute the change of stock price to the company’s condition, such as size or B/M ratio (Fama and French 1993) or credit risk(Avramov, Chordia, Jostova and Philipov 2007), maybe we can ascribe the change of the exchange rate to the country’s condition. Most recently, Menkhoff, Sarno et al. (2012) find some evidence from momentum strategies in one to twelve months in foreign exchange returns in 48 different currencies and provide a general research on momentum return. However, they don’t mention whether the momentum effect exist continuously or it just happen in some of periods, so we try to explain why some period have strong evidence of momentum, but some of not. 1.

(8) We start by forming the momentum portfolio. That is, we long the currencies with high lagged excess returns which we regard as winners and short the currencies with lower lagged excess returns which we regard as losers as our portfolio of momentum strategy. We rank the return of currencies every period on the basis of lagged excess return and form zero investment long-short portfolio from a momentum perspective. If the portfolio has positive (negative) return, this is the evidence of momentum (reversal). We act as a US investor’s point of view, apply up to 62 currencies to generalize our result, and consider formation and holding periods of 1, 3, 6, 9 and 12 month. As a consequence, we apply total of 25 strategies. Our sample period covers from November 1983 to October 2014. We find large and significant excess returns on momentum strategies of up to 10% per year, but not exist all the time, it strongly depend on period by period. To explain this, we examine whether the different currency market condition will affect the existence of momentum. We use UP or DOWN market, high volatility of the involved currencies, market stress and crisis to explain why some of period have strong momentum and some of they have strong reversal. To rationalize the high excess return of momentum strategies, we examine whether currency momentum is affected by (i) spot rate change, (ii) transaction cost, (iii) country risk, and (iv) liquidity risk. we apply the bid-ask price when we form the portfolio, since we thought the dealers usually adjust bid-ask spread while they expect that there may be a change in country’s condition. Unfortunately, we find the transaction cost seems fairly affect the momentum strategy and the large part of momentum excess return is wiped out as we take transaction cost into account. It indicate that when we practically apply momentum strategies in the foreign exchange market, dealer will charge amount of transaction cost. Through comparing the excess return with spot rate changes, we find that most of the 2.

(9) excess return of momentum strategies are dominated by the changing spot rate. It imply that the momentum excess returns are different from carry trade return, which have been studied in some empirical literature (Lustig, Roussanov and Verdelhan 2011) and believed that the returns are dominant by differential in interest rates across countries. We also observe the relationship between country risk and the momentum excess return and find that is exist. Excess returns of momentum portfolio on high country risk are larger and more significant than the excess returns on low country risk. In order to test whether illiquidity risks or country risk will have significant impact on momentum excess return or not. We run a time-series regression and find that there is little evidence that liquidity risk help explain the momentum excess returns. We also find the positive and significant relationship between the momentum excess returns and country risk, but it’s insignificant on liquidity risk. The results indicate that, comparing to the currency’s liquidity, the level of country risk have more impact on the momentum excess returns. We may say that momentum excess returns are affected more by country risk of the involved currencies, and the influence may include the illiquidity in the involved currencies, but it hardly result from the US Dollar illiquidity. In summary, we provide the evidence that, although momentum excess return have been proof exist in the earlier studies, it’s not continuous exist, especially when the exchange rate become volatile and continuous depreciation. Moreover, the momentum excess returns are subject to home market condition, which is condition of U.S. Dollar market here, and some idiosyncratic characteristic of involved currencies. The rest of this paper proceeds as follows. We discuss earlier literature in Section 2. Section 3 details our data. Section 4 describes our methodology, such as portfolio formation procedure. Section 5 illustrate our empirical result of various momentum strategies and the relationship between the excess returns of the momentum strategy and the country risk. We conclude in Section 6. 3.

(10) 2. Literature review Several recent papers have documented that, at medium-term horizon ranging from three to twelve months, stock returns exhibit momentum. That is, past winners continue to perform well, and past losers continue to perform poorly. This kind of study starts from Jegadeesh and Titman (1993) who use a U.S. sample stock over the period from 1965 to 1989, find that a strategy that buy six-month winners and short past six-month losers earn approximately one percent per month over the subsequent six month. Subsequent studies find some robust results. For example, Rouwenhorst (1998) obtain similar results in a sample of 12 European countries over the period 1980 to 1995. Earlier research find that the profitability of these strategies are not due to their systematic risk or to delayed stock price reactions to common factors (Jegadeesh and Titman 2001). After this, lots of researchers endeavor to investigate the reason which result in existence of the momentum effect. For example,Chui, Titman and Wei (2010) investigate how cultural differences influence the returns of momentum strategies and conclude that momentum profits are negatively related to firm size and volatility. In addition, previous work shows that average returns on common stocks are related to firm characteristics like short-term past return. And they are called anomalies, because these patterns in average returns apparently are not explained by the CAPM (Fama and French 2012). Some researchers find that the medium-term momentum in stock returns would be influenced by firm-specific information and gradually across the investing public. (Hong, Lim and Stein 2000) From these earlier academic works, we know that the explanations of momentum effect are very various. We can categorize these into three main group. (1) risk-based and characteristic-based explanations (2) explanations invoking behavioral biases (3) explanations based on the limits of arbitrage. Now we give some explanation to these previous findings, the first one is “risk4.

(11) based and characteristic-based explanations”. In early studies, Jegadeesh and Titman (1993) show that momentum is not driven by market risk and Fama and French (1996) show that their unconditional three-factor model cannot explain momentum either. However, there are more evidence of characteristic-based explanations. For example, Hong, Lim and Stein (2000) find that small firms have more momentum and Johnson (2002) find that momentum arises from a positive relation between expected returns and firm growth rates. The second is “explanations invoking behavioral biases”, which focus on imperfect formation and revision of investor expectations in response to new information. We can divide explanation of these theories into overreaction and underreaction. Overreaction is mainly observed by trading volume. Chan, Hameed and Tong (2000) indicates that momentum return continuation is stronger following an increase in trading volume. It’s consistent with the herding behavior theory, in which investors tend to follow the crowd in buying and selling securities. Contrary to the hypothesis of overreaction, some study find the evidence in explaining by underreaction. For example, Hong, Lim and Stein (2000) find that small firms with low analyst coverage have more momentum. Moskowitz and Grinblatt (1999) demonstrate that industry momentum is large, which Hou, Barberis and Chen (2001) argues is due to slow information dilution within industries. Some researchers conclude the results in both of overreaction and underreaction. Grinblatt and Moskowitz (2004) discover that momentum is more prevalent for small firms with few institutional owners, growth firms, and firms with high volume. The last one explanations based on the “limits of arbitrage”. Some studies are mainly test the influences when there are several market frictions, like transactions costs, margin accounts, short-selling buffers, and higher borrowing rates (Ali, Hwang and Trombley (2003); Hogan, Jarrow, Teo and Warachka (2004)). Some find the large 5.

(12) momentum excess returns link to funding liquidity risk and funding constraints. (Brunnermeier and Pedersen 2009) Apart from the momentum effect in stock market, past theories also find a lot of empirical evidence in the currency momentum. Okunev and White (2003) use moving average to form the momentum portfolio and report the profits of up to 7% per year in eight currencies. Chong and Ip (2009) claim that a momentum trading strategy generated approximately 20% per year in emerging currency markets over the 20 years from 1985 to 2004. Asness, Moskowitz and Pedersen (2013) apply 10 currencies and find the currency momentum profit of over 3% per year. The most recent and general study in monthly momentum effect is by Menkhoff, Sarno, Schmeling and Schrimpf (2012). They investigate whether currency momentum is significantly affected by (1) transaction costs, (2) business cycle risk and other traditional risk factors, and (3) different forms of limits of arbitrage. They conclude that the momentum returns are fairly sensitive to transaction cost and cannot be explained by systematic risk factors. However, the profitability of currency momentum strategies can induce arbitrage limitation, captured by idiosyncratic characteristic of the currencies involved, such as country risk and volatility of currency, for the major currency market participants. Recently, there are some studies investigate the momentum effect in short horizon (one to four week), instead of medium horizon. In the study of Raza, Marshall and Visaltanachoti (2014), they find, based on a sample of 63 currencies, evidence of momentum effect and excess returns are around 9% per year. Momentum excess returns increase with the increase in formation period and don’t relate to the FX carry trade returns. Further, the weekly momentum excess returns are larger in the expansionary phases of the U.S. business cycle and in periods following continuous depreciation of the involved currencies, but the large excess returns are not exist during the periods of 6.

(13) extreme stress, which is high volatility coupled with continuous depreciation in the currency market. In this paper, we apply monthly data of longer time period, which is from November 1983 to October 2014, and much larger cross-section of currencies, and include both developed and emerging countries. Consequently, we can analyze the general magnitude of both cross-section and time-series aspects. We mainly continue using the portfolio-constructed method in Menkhoff, Sarno, Schmeling and Schrimpf (2012) and focus on investigating the relationship between momentum excess return and country risk to give more detail.. 3. Data 3.1.Data for FX momentum strategy The data we use are spot rate and 1, 3, 6, 9, 12 month forward exchange rate on monthly frequency for 62 countries, and cover the sample period from November 1983 to October 2014. The data was obtained from Datastream. The spot rate and forward rate are all end-of-month data and quoted against the US dollar. Our sample is composite of the following numbers countries: UAE, Argentina, Australia, Austria, Belgium, Brazil, United Kingdom, Bulgaria, Canada, Chile, Colombia, Croatia, Cyprus, Czech Republic, Denmark, Germany, Egypt, Estonia, European zone, Finland, France, Greece, Hong Kong, Hungary, Iceland, India, Ireland, Israel, Italy, Japan, Kazakhstan, Kenya, Kuwait, Latvia, Lithuania, Malta, Mexico, Morocco, Netherlands, Romania, New Zealand, Norway, Pakistan, Philippines, Poland, Portugal, Qatar, Russia, Saudi Arabia, Singapore, Slovakia, Slovenia, South Africa, South Korea, Spain, Sweden, Switzerland, Taiwan, Thailand, Tunisia, Ukraine, China. Our effective sample size varies during the sample period, due to the availability 7.

(14) of some emerging countries’ currencies or adoption of Euro zone countries. To illustrate this point, we plot the number of available currencies with our monthly data in figure 1. At the beginning of the sample period, we just have 6 available currencies; we have 53 available currencies until 2004, which is our maximum sample size of the period. As a result, we have total sum of actual observation 11177, and individual start and end dates for each currency are shown in Table1.. 30 20 10. Number. 40. 50. Number of Available Currencies. 1985-01-01. 1990-01-01. 1995-01-01. 2000-01-01 time. 2005-01-01. 2010-01-01. 2015-01-01. Number of available currencies. Figure1. Number of available currencies. The vertical axis indicates the Number of available currencies. (i.e. available currencies with one month forward rate). 8.

(15) Table 1. Descriptive statistic: individual currencies This table shows excess return, forward discount and bid-ask spread for individual currency. Means and standard deviation are annualized and in percent. Bid-ask spread are in basis point. The sample period is from November 1983 to October 2014. Currency. Sample Period. Excess Return. Forward Discount. Bid-Ask Spread. Start. End. Mean. Std. Mean. Std. Mean. Std. UAE DIRHAM. 1996/12. 2014/10. 0.00%. 0.09%. 0.00%. 0.07%. 1.60. 1.67. ARGENTINE PESO. 2004/03. 2014/10. 0.70%. 2.70%. 0.52%. 2.30%. 38.66. 66.90. AUSTRALIAN. 1985/01. 2014/10. 0.29%. 3.46%. 0.25%. 0.24%. 10.33. 6.25. AUSTRIAN SCHIL.. 1997/01. 1998/12. -0.50%. 2.76%. -0.01%. 0.01%. 4.68. 1.25. BELGIAN FRANC. 1997/01. 1998/12. -0.51%. 2.74%. -0.01%. 0.02%. 9.38. 4.09. BRAZILIAN REAL. 2004/04. 2014/10. 0.88%. 4.26%. 0.25%. 0.29%. 8.95. 9.20. UK POUND. 1990/06. 2014/10. 0.07%. 2.68%. 0.06%. 0.29%. 4.36. 2.14. BULGARIAN LEV. 2004/04. 2014/10. 0.05%. 3.06%. 0.01%. 0.26%. 25.10. 111.45. CANADIAN DOLLAR. 1985/01. 2014/10. 0.11%. 2.05%. 0.07%. 0.14%. 6.44. 4.54. CHILEAN PESO. 2004/04. 2014/10. 0.23%. 3.61%. 0.06%. 0.37%. 13.59. 12.36. COLOMBIAN PESO. 2004/04. 2014/10. 0.45%. 3.67%. 0.08%. 0.25%. 10.82. 9.51. CROATIAN KUNA. 2004/04. 2014/10. 0.15%. 3.10%. 0.05%. 0.25%. 27.20. 26.76. CYPRUS. 2004/4/30. 2007/12. 0.40%. 2.02%. 0.00%. 0.17%. 25.37. 12.53. CZECH KORUNA. 1997/01. 2014/10. 0.15%. 3.69%. 0.03%. 0.40%. 12.48. 5.10. DANISH KRONE. 1985/01. 2014/10. 0.26%. 3.13%. 0.08%. 0.27%. 7.50. 5.18. GERMAN MARK. 1983/11. 1998/12. 0.17%. 3.38%. -0.04%. 0.28%. 6.85. 4.19. EGYPTIAN POUND. 2004/04. 2014/10. 0.85%. 1.19%. 0.32%. 0.88%. 32.61. 28.14. ESTONIAN KROON. 2004/04. 2010/12. 0.17%. 3.34%. 0.01%. 0.30%. 4.01. 4.21. EURO. 1999/01. 2014/10. 0.03%. 3.04%. 0.00%. 0.28%. 3.61. 2.09. 9.

(16) FINNISH MARKKA. 1997/01. 1998/12. -0.59%. 2.80%. -0.01%. 0.03%. 14.11. 4.89. FRENCH FRANC. 1983/11. 1998/12. 0.33%. 3.25%. 0.06%. 0.26%. 11.18. 6.63. GREEK DRACHMA. 1997/01. 2000/12. -0.39%. 2.90%. 0.05%. 0.69%. 1.67. 60.09. HONG KONG. 1989/10. 2014/10. 0.00%. 0.16%. 0.00%. 0.09%. 1.16. 0.85. HUNGARIAN FORINT. 1997/11. 2014/10. 0.39%. 4.13%. 0.27%. 0.28%. 12.59. 6.37. ICELANDIC KRONA. 2004/04. 2014/10. 0.10%. 4.59%. 0.17%. 0.30%. 27.77. 58.74. INDIAN RUPEE. 1997/11. 2014/10. 0.21%. 2.19%. 0.25%. 0.30%. 17.37. 23.12. IRISH PUNT. 1993/11. 1998/12. 0.13%. 2.23%. 0.01%. 0.09%. 19.87. 12.49. ISRAELI SHEKEL. 2004/04. 2014/10. 0.20%. 2.55%. 0.02%. 0.09%. 19.96. 22.36. ITALIAN LIRA. 1984/04. 1998/12. 0.32%. 3.26%. 0.15%. 0.28%. 14.82. 11.77. JAPANESE YEN. 1983/11. 2014/10. -0.02%. 3.24%. -0.21%. 0.26%. 7.07. 2.36. KAZAKHSTAN TENGE. 2004/04. 2014/10. 0.05%. 2.42%. 0.09%. 0.72%. 13.33. 29.68. KENYAN SHILLING. 2004/04. 2014/10. 0.07%. 2.52%. 0.06%. 0.37%. 39.30. 31.27. KUWAITI DINAR. 1990/06. 2014/10. 0.12%. 0.96%. 0.09%. 0.73%. 14.93. 16.02. LATVIAN LATS. 2004/04. 2013/12. 0.12%. 3.12%. 0.02%. 0.33%. 12.85. 7.15. LITHUANIAN LITAS. 2004/04. 2014/10. 0.02%. 3.05%. 0.00%. 0.27%. 8.47. 6.03. MALTESE LIRA. 2004/04. 2007/12. 0.42%. 1.99%. 0.01%. 0.10%. 40.71. 15.10. MEXICAN PESO. 1997/01. 2014/10. 0.38%. 2.97%. 0.36%. 0.64%. 14.00. 28.05. MOROCCAN DIRHAM. 2004/04. 2014/10. 0.27%. 2.49%. 0.09%. 0.21%. 32.12. 18.26. NETH. GUILDER. 1983/11. 1998/12. 0.19%. 3.38%. -0.03%. 0.27%. 8.09. 7.24. NEW ROMANIAN LEU. 2004/04. 2014/10. 0.41%. 3.90%. 0.15%. 0.47%. 28.95. 53.49. NEW ZEALAND. 1985/01. 2014/10. 0.50%. 3.58%. 0.34%. 0.38%. 16.67. 13.69. NORWEGIAN KRONE. 1985/01. 2014/10. 0.26%. 3.15%. 0.17%. 0.31%. 7.22. 4.28. PAKISTAN RUPEE. 2004/04. 2014/10. 0.06%. 1.37%. 0.51%. 0.34%. 36.35. 38.99. PHILIPPINE PESO. 1997/01. 2014/10. 0.13%. 2.65%. 0.21%. 0.34%. 54.39. 71.04. 10.

(17) POLISH ZLOTY. 1996/09. 2014/10. 0.41%. 3.91%. 0.29%. 0.46%. 20.09. 21.64. PORTUGUESE ESCUDO. 1997/01. 1998/12. -0.44%. 2.62%. 0.00%. 0.07%. 8.41. 4.43. QATARI RIAL. 2004/04. 2014/10. 0.00%. 0.09%. 0.00%. 0.08%. 4.28. 3.58. RUSSIAN ROUBLE. 2004/04. 2014/10. 0.12%. 3.15%. 0.15%. 0.74%. 12.19. 54.05. SAUDI RIYAL. 1990/06. 2014/10. 0.01%. 0.11%. 0.01%. 0.05%. 1.61. 2.69. SINGAPORE. 1985/01. 2014/10. 0.04%. 1.61%. -0.10%. 0.18%. 9.31. 8.87. SLOVAKIAN KORUNA. 2002/03. 2008/12. 1.11%. 3.33%. 0.03%. 0.34%. 16.98. 19.57. SLOVENIAN TOLAR. 2004/04. 2006/12. 0.22%. 2.17%. 0.00%. 0.15%. 27.76. 21.86. SOUTH AFRICA RAND. 1983/11. 2014/10. 0.48%. 5.02%. 1.05%. 2.16%. 43.13. 119.59. SOUTH KOREAN WON. 2002/03. 2014/10. 0.28%. 3.47%. 0.06%. 0.32%. 14.21. 20.01. SPAN.PTA. 1986/11. 1998/12. 0.38%. 3.17%. 0.15%. 0.33%. 22.92. 17.57. SWEDISH KRONA. 1985/01. 2014/10. 0.19%. 3.27%. 0.13%. 0.27%. 10.15. 4.29. SWISS FRANC. 1983/11. 2014/10. 0.07%. 3.39%. -0.14%. 0.22%. 7.51. 7.28. TAIWAN. 1992/02. 2014/10. -0.01%. 1.58%. 0.05%. 0.38%. 18.49. 21.95. THAI BAHT. 1995/04. 2014/10. 0.13%. 3.36%. 0.15%. 0.47%. 20.61. 27.61. TUNISIAN DINAR. 2004/04. 2014/10. -0.03%. 2.29%. 0.09%. 0.32%. 45.15. 40.72. UKRAINE HRYVNIA. 2004/04. 2014/10. -0.05%. 3.62%. 0.22%. 0.79%. 47.30. 95.14. CHINESE YUAN. 2002/03. 2014/10. 0.11%. 0.48%. -0.03%. 0.30%. 29.60. 457.40. 3.2.Data for a measurement of country risk Since we will investigate the relationship between the excess return of momentum strategy and country risk, we adopt the composite country risk rating of currency (CRISK) as our measurement of country risk. These data are based on the International Country Risk Guide (ICRG) database from the Political Risk Service (PRS) group. The CRISK which we adopted comprises 22 variables in three subcategories of risk, 11.

(18) including political, financial, and economic and is a quite common as a proxy for country risk. All of the countries we used are almost included in the CRISK, except for Euro zone. Therefore, we average the CRISK of each countries in Euro zone as the measurement for Euro zone’s CRISK. The countries in Euro zone includes Austria, Belgium, Cyprus, Germany, Estonia, Finland, France, Greece, Ireland, Italy, Latvia, Malta, Netherlands, Portugal, Slovakia, Slovenia and Spain. The table 2, shown in the left hand side, is descriptive statistic on CRISK for each year. We show the mean, US country risk, difference between US and other country and standard deviation of CRISK in each year. We average the CRISK of each sample countries in the same year, and calculate their standard deviation. The “diff” is calculated by subtracting average CRISK from US’s CRISK. It show us the historical average CRISK is between 63 and 78. In addition, the CRISK is gradually higher through time pass, since we just have CRISK of around 60 in the past, but now we have CRISK of more than 70. Further, the US’ historical CRISK are from 72 to 88. From diff, we can find there are almost negative, it mean the US’s CRISK are higher than other country’s average CRSIK except for 2003-2008, indicating that the country risk of US is lower than the average CRISK of other countries in the past time. However, the difference are much lower and gradually close to zero, so we can know that the country risk between US and other countries are more indifferent recently. In the last column, we also can find the standard deviation are getting smaller, suggesting that the country risk are more stable in the recent period. Figure 2 show the average CRISK of each sample country from 1984 to 2014 in descending order. According to the figure, the country which have lower country risk (higher CRISK) concentrate on developed countries, such as Japan, Netherlands and Switzerland. In the opposite, the country which have higher country risk (lower CRISK) concentrate on emerging countries, such as Pakistan, Kenya, Egypt and Colombia. 12.

(19) Table 2 Descriptive statistic on CRISK. CRISK for each country. The table shown descriptive statistic on CRISK for each year. We show the mean, US country risk, difference between US and other country and their standard deviation from 1984 to 2014. time. average. US. diff. std. 1984. 66.48. 88.19. -21.71. 16.01. 1985. 65.18. 84.28. -19.10. 14.91. 1986. 63.50. 81.42. -17.92. 14.74. 1987. 64.18. 79.71. -15.53. 14.08. 1988. 64.99. 76.45. -11.47. 13.56. 1989. 64.85. 77.90. -13.05. 13.37. 1990. 63.75. 77.86. -14.11. 13.54. 1991. 63.46. 73.11. -9.66. 12.73. 1992. 66.61. 71.63. -5.02. 10.10. 1993. 66.60. 72.50. -5.90. 8.22. 1994. 67.86. 75.29. -7.43. 7.04. 1995. 68.75. 75.02. -6.28. 7.05. 1996. 70.92. 76.02. -5.10. 7.26. 1997. 73.50. 80.66. -7.15. 8.30. 1998. 74.02. 81.21. -7.19. 13.65. 1999. 73.18. 82.58. -9.39. 12.93. 2000. 74.72. 82.14. -7.42. 8.82. 2001. 75.98. 82.94. -6.96. 8.24. 2002. 77.02. 80.38. -3.36. 8.23. 2003. 76.80. 76.54. 0.26. 8.46. 2004. 78.24. 77.52. 0.72. 6.68. 2005. 78.25. 76.00. 2.25. 6.62. 2006. 78.22. 74.77. 3.45. 6.48. 2007. 77.73. 73.79. 3.94. 6.82. 2008. 76.72. 75.96. 0.77. 7.27. 2009. 73.34. 74.08. -0.74. 7.22. 2010. 74.37. 77.15. -2.78. 6.92. 2011. 74.64. 76.08. -1.45. 7.19. 2012. 73.63. 76.26. -2.63. 7.20. 2013. 73.92. 75.87. -1.95. 7.35. 2014. 74.20. 76.18. -1.98. 7.58. 0.00. 20.00. 40.00. 60.00. 80.00. 100.00. Switzerland Norway Netherlands Japan Austria Finland Denmark Singapore Sweden Canada Germany Taiwan Ireland Belgium New Zealand United Kingdom United States Australia France EURO Malta Iceland South Korea Czech Republic Italy Cyprus Spain Portugal Slovenia Slovakia Kuwait Hong Kong UAE Chile Lithuania Estonia Hungary Saudi Arabia Kazakhstan Croatia China Qatar Latvia Thailand Mexico Poland South Africa Greece Ukraine Tunisia Morocco Russia Israel Bulgaria Brazil Argentina India Philippines Colombia Egypt Kenya Romania Pakistan. Figure 2. Average CRISK in each year. The figure show the average CRISK of each sample country from. 13. 1984 to 2014 in descending order..

(20) 4. Methodology 4.1.Currency excess return We calculate the monthly excess return to a U.S. investor holding foreign currency 𝑘. as following equation:. 𝑘 𝑘 𝑟𝑥𝑡+1 = 𝑖𝑡𝑘 − 𝑖𝑡 − ∆𝑠𝑡+1 ≈ 𝑓𝑡𝑘 − 𝑠𝑡+1. Where 𝑖 𝑘 denotes the interest rate in country 𝑘, 𝑖. (1). denotes the interest rate in. U.S. (assume U.S. is the investor’s home country), 𝑠 is the spot rate after logarithm and 𝑓 is the forward rate (foreign currency unit per USD) after logarithm, ∆𝑠 denotes the change of spot rate. Since the return of investing foreign currency comes from two components, one is the appreciation or depreciation (∆𝑠𝑡+1 ) and the other is the interest we earned from foreign country ( 𝑖𝑡𝑘 − 𝑖𝑡 ). In addition, if the covered interest rate parity (CIP) holds, the difference between two countries’ interest rates is equivalent to the forward discount( 𝑓𝑡𝑘 − 𝑠𝑡𝑘 ), and then it also imply that the excess return can approximately equate to the difference between the forward rate in this period and the spot rate in next period. Dealer usually adjust the bid and ask price to avoid the potential risk (ex. country risk, liquidity risk, etc.) during the transaction. Since we assume there may be some relationship between the excess return of momentum strategy and the country risk of the target currencies. We also calculate the bid-ask spread of the individual currencies by using ask price of currency’s spot rate minus bid price of currency’s spot rate and then dividing the midpoint of the spot rate as our bid-ask spread. We report the excess return, forward discount and bid-ask spread for individual currency in table1, where both of excess return and forward discount are calculated with one month forward rate, because it’s the most sufficient sample data among 1, 3, 6, 9 and 12 month forward rate data. 14.

(21) We also consider bid-ask spread as the transaction cost when we invest in foreign currency. Excess return for long and short position can be represented in the following equations, respectively:. 𝑙𝑜𝑛𝑔. 𝑎 𝑟𝑥𝑡+1 = 𝑓𝑡𝑏 − 𝑠𝑡+1. (2). 𝑠ℎ𝑜𝑟𝑡 𝑏 𝑟𝑥𝑡+1 = 𝑓𝑡𝑎 − 𝑠𝑡+1. (3). An 𝑎 superscript indicates the ask quote and a 𝑏 superscript indicates the bid quote.. 4.2.Portfolio construction We form these portfolios based on the lagged excess return over the previous f=1, 3, 6, 9, 12 month and treated it as formation periods of the portfolio. Furthermore, the holding period cover h=1, 3, 6, 9, 12 month. Since we assume that investor will hold to the maturity, we use 1, 3, 6, 9, 12 month forward rate as our investment target. With a view to using the momentum strategy, the one-sixth of currencies with the highest lagged return are classed in the winner currencies, and the one-sixth of currencies with the lowest lagged return are classed in the loser currencies. In addition, we long the winner currencies and short the loser currencies with equal-weighted average method. These portfolios are denote as 𝑀𝑂𝑀𝑓,ℎ , where 𝑓 and ℎ are formation and holding period, respectively. This method is provided by Menkhoff, Sarno, Schmeling and Schrimpf (2012). For example, if we want to construct the portfolio whose formation period is 3 month and the holding period is 6 month, we should use the 6 month forward rate and look back for previous return constructed with 3 month forward rate. As the first step, we look back the previous return constructed with 3 month forward rate (it was constructed three month ago, and now is time to maturity), and we select one-six 15.

(22) of currencies with the highest return as the winner and select one-six of currencies with the lowest return as the loser. Next, we use 6 month forward rate of these winner and loser currencies to calculate the excess return and form the portfolio 𝑀𝑂𝑀3,6 .. 5. Result 5.1.Excess return of momentum strategy Table 3 shows the average annualized excess returns of the portfolio of momentum strategy for the whole sample period, calculated by high minus low and use 1, 3, 6, 9, 12 month as formation and holding period. We find that almost all of the excess return are positive, except for 𝑀𝑂𝑀6,9 and 𝑀𝑂𝑀12,9 . Furthermore, the shorter holding period of the momentum strategy, the larger positive excess return is. The insignificant excess return start to show up when the holding period of the momentum strategy is above 9 month in our sample, such as 𝑀𝑂𝑀1,9 , 𝑀𝑂𝑀3,9 , 𝑀𝑂𝑀6,9 and 𝑀𝑂𝑀9,12 . However, many instances of momentum return with longer holding periods are still significant, so the momentum sometimes work when we hold for longer period. In addition, when we use longer formation period with the same holding period, the excess return are also smaller and less significant. For example, the excess return of 𝑀𝑂𝑀1,1 strategy is 8.85% (T-stat=3.77), but the excess return of 𝑀𝑂𝑀12,1 strategy is 4.57% (T-stat=1.93). However, this trend is more obvious when we use shorter holding period. Since we also record the average return of winner and loser currencies, we can find that the positive return of the momentum strategy is contribute more from the winner currencies. Take 𝑀𝑂𝑀1,3 as an example, the excess return is 5.77%, and 5.53% is from winner currency. We also calculate the Sharpe ratio of the portfolio by using the formula “the excess return divide the standard deviation”. We find the Sharpe ratio decrease when the formation and holding period of momentum strategy is longer, indicating that the momentum effect is more effective if we implement it in short period. 16.

(23) Table 3. Excess return of momentum strategy in the whole period. This table present the average return of the Winner-loser portfolio using 62 currencies against U.S. dollar for whole sample period (November 1983 to October 2014), calculated by winner minus loser and use 1, 3, 6, 9, 12 month as formation and holding period. The excess return is calculated 𝑘 𝑘 by 𝑟𝑥𝑡+1 = 𝑓𝑡𝑘 − 𝑠𝑡+1 . Means and standard deviation are annualized and in percent. T-stat are based on HAC standard error and the Sharpe ratio are. calculate by the formula “the excess return divide the standard deviation”. ***, ** and * are significant at 1%, 5% and 10%, respectively. Formation. win. lose. W-L(1). win. lose. W-L(3). win. lose. W-L(6). win. lose. W-L(9). win. lose. W-L(12. 1. Mean. 6.65. -2.20. 8.85***. 5.53. -0.24. 5.77***. 3.89. 0.87. 3.02**. 3.10. 2.39. 0.71. 4.02. 1.06. 2.95***. Std. 8.80. 9.76. 9.96. 10.31. 9.76. 10.17. 11.14. 10.17. 10.24. 9.88. 13.46. 14.17. 11.26. 10.09. 10.76. 3. 6. 9. 12. T-stat. 3.77. 3.93. 2.72. 0.62. 3.73. Sharpe. 0.89. 0.57. 0.29. 0.05. 0.27. Mean. 7.02. -1.64. 8.66***. 5.52. 0.43. 5.09***. 4.81. 1.84. 2.97**. 3.21. 2.76. 0.45. 4.69. 1.20. 3.49***. Std. 8.92. 9.49. 10.15. 10.00. 10.10. 9.96. 11.38. 10.05. 10.93. 10.09. 14.84. 15.70. 10.60. 10.59. 11.13. T-stat. 3.71. 3.45. 2.65. 0.37. 4.44. Sharpe. 0.85. 0.51. 0.27. 0.03. 0.31. Mean. 6.15. 0.96. 5.18**. 4.95. 1.54. 3.41**. 4.81. 1.52. 3.29***. 2.65. 3.33. -0.67. 4.41. 1.34. 3.08***. Std. 8.94. 9.44. 10.31. 10.10. 10.05. 10.60. 11.68. 9.75. 11.74. 10.64. 15.05. 17.03. 10.75. 10.09. 12.00. T-stat. 2.21. 2.29. 2.91. 0.54. 3.96. Sharpe. 0.50. 0.32. 0.28. -0.04. 0.26. Mean. 6.24. -0.68. 6.92**. 5.16. -0.37. 5.53***. 3.86. 1.06. 2.77**. 4.02. 0.99. 2.96**. 2.17. 1.19. 0.95. Std. 9.10. 8.92. 10.46. 10.88. 9.60. 11.77. 12.38. 9.37. 12.44. 15.29. 9.04. 14.00. 11.91. 9.07. 11.54. T-stat. 2.65. 3.21. 2.13. 2.45. 1.08. Sharpe. 0.66. 0.47. 0.22. 0.21. 0.08. Mean. 6.06. 1.48. 4.57*. 5.25. 2.03. 3.22**. 4.52. 2.41. 2.11*. 1.05. 4.44. -3.39**. 3.91. 2.35. 1.56**. Std. 8.97. 9.40. 10.91. 9.74. 10.45. 11.40. 10.94. 10.19. 12.12. 10.54. 16.44. 18.21. 11.37. 8.81. 11.78. T-stat. 1.93. 2.14. 1.88. 2.54. 2.03. Sharpe. 0.42. 0.28. 0.17. -0.19. 0.13. 17.

(24) We also plot the cumulative excess return for whose holding period and formation period are equal to 1, 6 and 12 month, respectively. The first figure shows cumulative return of momentum strategy for holding 1 month and the second and third one are for holding 6 and 12 month, respectively. Figure 3 shows that no matter holding period is 1, 6, or 12 month, the shorter formation period, the greater cumulative excess return the investor would earn. Moreover, when holding period is getting longer, the correlation of the cumulative excess return are becoming smaller among different formation period. In these figures, we can find that momentum strategies are more profitable during 2000 to 2004 and the profit is more uncertain in other period, and also learn that the shorter holding or formation periods, the more stable momentum excess returns you will get. Later we will have sub period analysis for more details. We find that the cumulative excess returns of momentum strategies are decreasing during the 1991 to 1993, 1998 to 2000 and 2008 to 2010, when we hold for 6 and 12 month, especially 𝑀𝑂𝑀12,12. The decreasing may be related to some crisis happen in these periods, such as Sterling Crisis and European Exchange Rate Mechanism crisis in 1992, Asian financial crisis in mid-1997, and European debt crisis in 2008. During crisis, the exchange rates may become very volatile or continuous depreciation. In table 4, we calculate the proportion of “reversal” position which have the negative returns in winners and positive returns in losers in the crisis period, when we apply 𝑀𝑂𝑀12,12 as our momentum portfolio. For example, during March 1991 to June 1993, we have 50% of investing Australian Dollar in winner position have negative return.. 18.

(25) 0. 1. return. 2. 3. Cumulative return for 1 month holding period. 1985-01-01. 1990-01-01. 1995-01-01. 2000-01-01 time. MOM(1,1). MOM(6,1). 2005-01-01. 2010-01-01. 2015-01-01. MOM(12,1). .6 0. .2. .4. return. .8. 1. Cumulative return for 6 month holding period. 1985-01-01. 1990-01-01. 1995-01-01. 2000-01-01 time. MOM(1.6). MOM(6,6). 2005-01-01. 2010-01-01. 2015-01-01. MOM(12,6). .4 .2 0. return. .6. .8. 1. Cumulative return for 12 month holding period. 1985-01-01. 1990-01-01. 1995-01-01. 2000-01-01 time. MOM(1.12). MOM(6,12). 2005-01-01. 2010-01-01. 2015-01-01. MOM(12,12). Figure 3. Cumulative excess returns of momentum strategies. These figures are cumulative excess returns for whose holding period and formation period are equal to 1, 6 and 12 month, respectively. The first picture shows cumulative return of momentum strategy for holding 1 month and. 19.

(26) the second and third one are for holding 6 and 12 month, respectively. We calculate the cumulative return by converting the momentum excess return into monthly return and adding up the previous monthly returns.. We can find that, during early 1990s, both short and long position are disadvantage to momentum strategies, and it mainly happen in Europe country, especially the countries which were going to adopt euro as their currency. Since the adoption of Euro zone countries need to implement their preceding policies, the countries which want to join the European Monetary Union should obey some rules of exchange rate. For example, if the exchange rate ever neared the boundary of its permitted range, the government would be obliged to intervene, even though the acts would be counter to the improving the country’s economic. This cause that some countries’ currency are overvalued and continuously have stress in depreciation. Some speculator observe this situation, short these currencies in a large position and then reinforce the depreciation stress. Once the currencies fell below the lower band of the ERM, it always accompany severe cash outflow and currency depreciation, and increase the volatility of exchange rate of these countries, the. As a result, the momentum effect are not significant in this period. We find, in table 4, there are many Europe currencies have reversal effect, such as Denmark, France, Germany, Italy, Netherlands, Spain, Sweden, Switzerland and UK. In addition, the decreasing during the 1998 to 2000 may have connection to the Asian Financial Crisis which start from around 1997. During the crisis, lots of Asian currencies are obvious depreciation, especially Thai Baht. In table 4 we find there are some Asian currencies have large proportion of reversal position in the period between August 1997 and December 1999. We tend to take a lot proportion of the positive excess returns in short position, which will contribute the negative return to our momentum 20.

(27) portfolio. It may because that although many Asian currencies depreciate during the Asian Financial Crisis, they reverse the trend after the mid-1998. But we have some invest lag, we still treat these currencies as losers and short them. So we have lots of negative excess return in short position. The third significant decreasing in the cumulative excess returns may due to European debt crisis, September 2008 to May 2010. In table 4, we find that the long position have more negative contributions to momentum portfolio, and there are almost the European country, such as Poland, Iceland, Czech Republic, Ukraine, United Kingdom, Hungary and Romania. At the time, lots of cash outflow to the U.S., the safer country, aggravating the depreciation situation in Europe country. Table 5, we calculate the position of individual currency in the strong momentum period, June 2003 to June 2005, realized that each currency have more stable position, and would not change over time. If the currency is the winner currency from the beginning of this period, it continue to be a winner in the rest of time. If the currency is the loser currency from the beginning of this period, it continue to be a loser in the rest of time. We think it may result from stable depreciation of U.S. dollar, the base currency, so that the winners are become relative strong. Consequently, the momentum effect are relatively strong in this period.. 21.

(28) Table 4 The “reversal” position during the crisis.. Table 5 The net position in strong. We use the portfolio of 𝑀𝑂𝑀12,12 as representation and report the each currencies. momentum period.. position. We calculate the number of positions which have the negative returns in. “win” is winner currencies in long. winners and positive returns in losers and divided them by total number of the currency. position and “lose” is loser. being winner or loser, respectively.. currencies in short position. “net”. 199103-199306. win. lose. 200809-201005. win. lose. is the difference between “win”. Australia. 0.5. 0. UK. 0. 0.6. and “lose” in which the currency. Canada. 1. 0.6. Russia. 0. 1. Denmark. 0.875. 1. South Korea. 0. 0.412. 200306-200506. win. lose. net. France. 1. 1. Sweden. 0. 0.75. New Zealand. 21. 0. 21. Germany. 0. 1. Ukraine. 0. 1. Slovakia. 14. 0. 14. Hong Kong. 0. 1. Australia. 1. 1. South Africa. 18. 4. 14. Italy. 0.667. 0. Brazil. 1. 0. Australia. 12. 0. 12. Japan. 0. 1. Canada. 1. 1. Hungary. 12. 0. 12. Netherlands. 0. 1. Chile. 1. 1. Norway. 8. 0. 8. New Zealand. 0. 0.625. Croatia. 1. 0. Czech Republic. 6. 0. 6. Singapore. 0.3. 1. Hong Kong. 1. 0.182. UK. 2. 0. 2. Spain. 0.8. 0. Iceland. 1. 0.333. Denmark. 1. 0. 1. Sweden. 1. 0. India. 1. 0. Sweden. 1. 0. 1. Switzerland. 1. 0.75. Romania. 1. 0. Switzerland. 1. 0. 1. UK. 0.5. 0. New Zealand. 1. 0.8. Poland. 0. 1. -1. 199708-199912. win. lose. Norway. 1. 1. Thailand. 0. 1. -1. Canada. 0. 1. Philippines. 1. 0. Canada. 0. 3. -3. Germany. 0. 0.667. Poland. 1. 0.8. Philippines. 0. 4. -4. Finland. 0. 1. Thailand. 1. 1. Singapore. 0. 4. -4. India. 0. 1. Czech Republic. 0.889. 0. Saudi Arabia. 0. 6. -6. Japan. 0. 0.1. Colombia. 0.857. 0. Taiwan. 0. 6. -6. Netherlands. 0. 0.364. Hungary. 0.857. 0. Japan. 0. 8. -8. Singapore. 0. 1. Latvia. 0.833. 0. China. 0. 9. -9. Taiwan. 0. 1. Israel. 0.75. 0. Mexico. 0. 15. -15. Australia. 1. 0.667. Slovakia. 0.667. 0. Hong Kong. 0. 17. -17. Greece. 1. 0. Saudi Arabia. 0.6. 0. UAE. 0. 18. -18. Italy. 1. 0. Kuwait. 0.5. 0. New Zealand. 1. 0.6. Switzerland. 0.5. 0. South Africa. 1. 1. Argentina. 0.4. 0. Sweden. 1. 0. Japan. 0.25. 1. Thailand. 1. 0.818. UAE. 0.2. 0. Czech Republic. 0.625. 0. Egypt. 0. 0. Mexico. 0.429. 1. Qatar. 0. 0. Philippines. 0. 1. China. 0. 1. 22. involved..

(29) We can conclude that reversal effect is exist during crisis. However, reversal effect does not significantly happen when we just hold for 1 month, since we have more flexibility to deal with this kind of emergency. We can realize that longer formation period have more serious change in cumulative excess returns.. 5.2.UP and DOWN in foreign exchange market To prove our assumption, we investigate the performance of momentum strategies in UP and DOWM currency markets. We use the RX currency slope factor of Lustig, Roussanov and Verdelhan (2011) as the currency benchmark. RX is the mean currency excess return to a U.S. investor who goes long all the foreign currencies available in the forward FX market. We define an UP currency market whereby the cumulative return of RX factor is positive over the past 36 months. Similarly, the currency market is in a DOWN state if the cumulative return of the RX factor is negative or zero over the immediately cumulative return of the 36 months.. 𝑀𝑂𝑀𝑓,ℎ,𝑡 = 𝛽𝑈𝑃 ∗ 𝐷𝑈𝑃 + 𝛽𝐷𝑂𝑊𝑀 ∗ 𝐷𝐷𝑂𝑊𝑀 + 𝜖𝑡. (4). In this equation, 𝑀𝑂𝑀𝑓,ℎ,𝑡 is excess return of momentum strategies, whose formation period is 𝑓 and holding period is ℎ . 𝐷𝑈𝑃 and 𝐷𝐷𝑂𝑊𝑀 are dummy variables in UP and DOWM state, respectively. We show our result in table 6. The momentum effect are more significant in the UP state, we find there is a positive relation between momentum and UP state. The t-statistics are significant at the 5% confidence level for 7 of 16 strategies. However, there is seldom momentum effect in DOWN state, and the reversal effect is more significant as we use long formation and holding period, such as 𝑀𝑂𝑀6,6 , 𝑀𝑂𝑀6,12 , 𝑀𝑂𝑀12,6, 𝑀𝑂𝑀12,12 . 23.

(30) Table 6 Momentum returns in UP and DOWN FX market states. MOM (f,h) refers to the f month formation period and h month holding period. UP is a dummy variable which is one when the cumulative excess return of the USD (RX) factor is positive over past 36 month. DOWN is a dummy variable which is one when the cumulative excess return of the USD (RX) factor is negative and zero over past 36 month. The t-statistic, which is in the bracket, are based on Newey-West standard errors. ***, ** and * are significant at 1%, 5% and 10%, respectively. Strategies. UP market. DOWN market. MOM(1,1). 0.007806***. -0.00032. [4.11]. [-0.11]. 0.015705***. -0.0009. [3.45]. [-0.12]. 0.033214***. -0.00825. [4.79]. [-0.8]. 0.00305**. 0.003201. [1.59]. [1.01]. 0.024557***. -0.02331**. [4.77]. [-2.68]. 0.035007***. -0.02538**. [4.46]. [-2.03]. 0.00183. 0.003776*. [0.92]. [1.15]. 0.014076**. -0.02027**. [2.64]. [-2.48]. 0.032917***. -0.05318***. [4.07]. [-4.53]. MOM(1,6). MOM(1,12). MOM(6,1). MOM(6,6). MOM(6,12). MOM(12,1). MOM(12,6). MOM(12,12). 24.

(31) The results also prove the previous findings. During the period of 2000 to 2004, U.S. Dollar continuous depreciate and other currencies are relatively appreciation, so the RX factor become positive. We treat this period as UP market and it have stronger momentum effect in currency market. However, those periods which have decreasing cumulative excess returns have some regional currency crisis occurred, such as 1991 to 1993 have European Exchange Rate Mechanism) and 1998 to 2000 have Asian financial crisis. The currencies suddenly severely depreciate and also influence the neighbor country’s currency. Since USD is relatively safe currency, the hot cash flow into the U.S., causing the USD relatively appreciate. If we construct the momentum portfolio in these periods, we might get the negative return. Consequently, we can conclude we have very weak momentum effect, and even reversal effect sometime exist in these periods.. 5.3.Momentum return and market stress Because we find the decreasing cumulative excess returns during crisis, we analyze the behavior of the momentum excess return in these periods. We define the crisis is the period of high currency volatility and continuous depreciation. We construct our exchange volatility proxy by employing our sample currencies using following equation:. 𝜎𝑣𝑜𝑙,𝑡 =. ∑ |𝑟𝑡𝑘 | 𝐾𝑡. (5). 2 Where 𝜎𝑣𝑜𝑙,𝑡 is the FX volatility in month t. 𝑘 is the number of the available. currencies in month t and |𝑟𝑡𝑘 | is the absolute return of currency k in month t. Further, 25.

(32) we also estimate FX volatility innovations (∆𝜎 2 𝑣𝑜𝑙,𝑡 ) by calculating the first difference of FX volatility, which is similar to the suggestion by Menkhoff et al. (2012) except we use the monthly data.. 𝑀𝑂𝑀𝑓,ℎ,𝑡 = 𝛼 + 𝛽𝐷𝑂𝑊𝑀 ∗ 𝐷𝐷𝑂𝑊𝑀 + 𝛽𝑣𝑜𝑙 ∗ 𝜎 2 𝑣𝑜𝑙,𝑡 + 𝛽𝑖𝑛𝑡 ∗ 𝐷𝐷𝑂𝑊𝑀 ∗ ∆𝜎 2 𝑣𝑜𝑙,𝑡 + 𝜖𝑡. (6) 𝑀𝑂𝑀𝑓,ℎ is the excess return of momentum strategies. 𝐷𝐷𝑂𝑊𝑀 is dummy variable. in DOWM state. 𝜎 2 𝑣𝑜𝑙,𝑡 is FX volatility. The interaction term 𝐷𝐷𝑂𝑊𝑀 ∗ ∆𝜎 2 𝑣𝑜𝑙,𝑡 represent the market stress factor in currency market. We show our result in table 7. In the table 7, we can find there are negative relationship between momentum excess return and market stress, which is included the DOWN state, high volatility and extreme market stress. In figure 4, we also can find when the currency become more volatile or the market is in DOWN state, the momentum effect would be weak. The results indicate that reversal effect exist when the exchange is continuous depreciation or become more volatile. It prove our explanation of the decreasing cumulative return during crisis.. .02. .04. volatility. .4 .2. 0. 0. return. .6. .06. .8. .08. 1. The relationship between MOM(12,12) and the FX market situation. 1985-01-01. 1990-01-01. 1995-01-01 DOWN. 2000-01-01 time. 2005-01-01. MOM(12,12). 2010-01-01. 2015-01-01. volatility. Figure 4. The relationship between MOM(12,12) and the FX market situation. We use MOM(12,12) as our representation, since the volatility of MOM(12,12)are most obvious. The gray area are DOWN state in foreign exchange market. The dot line is the cumulative excess return of MOM(12,12) without overlapping. The dark bar are volatility of the excess 26 return of investing 12 month forward..

(33) Table 7. Momentum return and market stress. MOM (f,h) refers to the f month formation period and h month holding period. DOWN is a dummy variable which is one when the cumulative excess return of the USD (RX) factor is negative and zero over past 36 month. Volatility refers to FX volatility, which we calculate by 𝜎𝑣𝑜𝑙,𝑡 =. ∑ |𝑟𝑡𝑘 | 𝐾𝑡. . DOWN*vol is the interaction term. represent the extreme market stress. The t-statistic, which is in the bracket, are based on Newey-West standard errors. ***, ** and * are significant at 1%, 5% and 10%, respectively. Strategies MOM(1,1). MOM(1,6). MOM(1,12). MOM(6,1). MOM(6,6). MOM(6,12). MOM(12,1). MOM(12,6). MOM(12,12). alpha. DOWN. volatility. DOWN*vol. beta. 0.01. 0.00. 8.22. 12.65. [t-stat]. [2.02]. [-0.45]. [0.94]. [1.27]. beta. 0.02. 0.00. -0.72. -15.70***. [t-stat]. [3.54]. [-0.14]. [-0.54]. [-6.11]. beta. 0.02. -0.01. 2.79**. -6.04. [t-stat]. [1.83]. [-0.60]. [2.50]. [-1.40]. beta. 0.01. 0.00. -6.28. -3.43. [t-stat]. [2.29]. [1.20]. [-1.05]. [-0.40]. beta. 0.05. -0.02**. -8.67***. 2.42. [t-stat]. [8.70]. [-2.69]. [-5.06]. [0.68]. beta. 0.04. -0.03**. -0.04. -4.25*. [t-stat]. [3.86]. [-2.09]. [-0.03]. [-1.68]. beta. 0.00. 0.00. -2.10. -9.04. [t-stat]. [1.05]. [1.28]. [-0.28]. [-0.98]. beta. 0.02. -0.02**. -3.48. 0.33. [t-stat]. [3.35]. [-2.42]. [-1.17]. [0.11]. beta. 0.01. -0.05***. 3.13**. -5.30. [t-stat]. [1.35]. [-4.36]. [2.14]. [-1.74]. 27.

(34) 5.4.Momentum excess return in Sub periods We separate the whole sample into four sub periods, which is 199208-1995031, 199705-1998062, 200704-2011063 and 200912-2010054. These periods are all suffer from regional currency crisis which we have mentioned in session 5.1. The result are shown not only the excess return of the winner-minus-loser portfolio, but also the excess return of winner and loser currencies in Table 8. We compare the momentum excess return among different sub periods, finding that momentum effect are not significant in these periods. Additionally, we have very low returns in both winner and loser currencies in the period of 199208-199503, 199705-199806 and 200912-201005, because serious depreciation. Even if we have greater momentum in loser currencies, the reversal of winner currencies still dominant the momentum portfolio. That is, although we have positive return in momentum portfolio, the momentum effect is not significant at all. In the period of 200704 to 201106, we have very small return in both winner and loser currencies. It may because the period cover the subprime mortgage crisis, which is very serious and spread out to become global crisis, not just influence regionally. As a result, the momentum excess returns are actually relatively small in this period. 1. This period is start from Sterling Crisis in August 1992, and end in the last depreciation of Spain and. Portugal’s currencies. 2. This period cover the Asian financial crisis, which start from May 1997 to June 1998. The boundary. are set from the previous essay. http://nccur.lib.nccu.edu.tw/bitstream/140.119/37815/1/110.pdf 3. The period cover the subprime mortgage crisis. It start from New Century Financial Corporation, the. second-biggest subprime mortgage lender in the United States, filed for Chapter 11 bankruptcy. And the crisis end in the implementation of quantitative easing 2 4. European debt crisis happen in this period. It start from September 2009, when all of three ratings. agencies, Moody's, Standard & Poor's and Fitch, downgraded the Greece from A- to BBB+ and consider Greece will become negative growth prospects. And end in May 2010, when the Greek government requested an initial loan from the EU and International Monetary Fund (IMF). 28.

(35) Table 8 Momentum excess return in sub periods. This table present the average return of the Winner-loser portfolio using 62 currencies against U.S. dollar for sub-sample periods, calculated by winner minus loser and 𝑘 𝑘 use 1, 3, 6, 9, 12 month as formation period and 1 month holding period. The excess return is calculated by 𝑟𝑥𝑡+1 = 𝑓𝑡𝑘 − 𝑠𝑡+1 . Means and standard deviation are. annualized and in percent. T-stat are based on HAC standard error and the Sharpe ratio are calculate by the formula “the excess return divide the standard deviation”.. ***, ** and * are significant at 1%, 5% and 10%, respectively. formation. win. lose. W-L(1). win. lose. W-L(3). win. lose. W-L(6). win. lose. W-L(9). win. lose. W-L(12). 199208-199503 Mean. 8.94. -7.24. 16.18**. 1.93. -2.76. 4.69. 3.74. 0.28. 3.46. 7.97. -4.78. 12.76. 5.05. -2.32. 7.37. std. 8.72. 8.32. 8.96. 9.82. 8.16. 9.82. 8.83. 8.46. 11.01. 11.77. 9.84. 13.54. 9.13. 8.61. 10.07. T-stat. 2.29. 0.61. 0.47. 1.40. 0.98. Sharpe. 1.81. 0.48. 0.31. 0.94. 0.73. 199705-199806 Mean. -4.30. -13.23. 8.94. -7.86. -15.59. 7.73. -6.29. -9.38. 3.09. 1.42. -4.03. 5.44. -6.85. -6.76. -0.09. std. 7.52. 9.57. 10.43. 6.35. 11.59. 9.78. 7.30. 12.73. 10.95. 4.77. 11.07. 10.17. 8.50. 13.84. 13.07. T-stat. 0.81. 0.64. 0.23. 0.49. 0.01. Sharpe. 0.86. 0.79. 0.28. 0.54. -0.01. 200704-201106 Mean. 5.62. 0.47. 5.16. 6.70. 0.10. 6.60. 4.37. 1.56. 2.81. 3.31. 1.64. 1.67. 3.63. 4.10. -0.47. std. 9.24. 11.89. 10.30. 9.42. 10.87. 10.23. 9.75. 11.04. 9.87. 9.20. 11.50. 9.69. 9.66. 11.64. 9.95. T-stat. 0.71. 0.95. 0.39. 0.23. 0.06. Sharpe. 0.50. 0.64. 0.28. 0.17. -0.05. 200912-201005 Mean. -14.08. -26.63. 12.55. -10.00. -18.62. 8.62. -8.29. -20.48. 12.19. -5.43. -16.37. 10.94. -4.14. -2.57. -1.57. std. 7.97. 10.31. 7.55. 8.16. 6.49. 6.12. 6.92. 9.74. 7.36. 5.05. 10.06. 7.32. 8.34. 3.50. 6.74. T-stat. 0.71. 0.60. 0.75. 0.71. 0.13. Sharpe. 1.66. 1.41. 1.66. 1.49. -0.23. 29.

(36) 5.5.The spot rate change Table 9 present the average return of the spot rate change, we find that most of the excess return of momentum strategies are dominated by the changing spot rate. The excess return of spot rate change are play important role when we apply longer formation and holding period, especially when we use 12 month as our formation period in momentum strategies, the excess momentum returns are almost the same as the excess returns on spot rate change. As a result, we can say that the returns are dominant by differential in interest rates across countries. This result is almost the consist with the findings of Menkhoff, Sarno, Schmeling and Schrimpf (2012) who show us the profitability of the momentum strategies is clearly visible in spot rate changes.. Taking one month formation period as an example, the excess return of 𝑀𝑂𝑀1,1 is 8.85% (reported in table 3) and the spot rate change has return of 5.64%, it indicate that almost one-third of the momentum excess return (𝑀𝑂𝑀1,1) is contributed from the forward discount. However, 𝑀𝑂𝑀12,1 have 4.57% of excess return, but 4.17% are attribute to the spot rate change. In this case, the forward discount isn’t important to the momentum return.. 30.

(37) Table 9. Return of the spot rate change in the whole period. This table present the average return of the spot rate change, and the Winner-loser portfolio using 62 currencies against U.S. dollar for whole sample period (November 1983 to October 2014), calculated by winner minus loser and use 1, 3, 6, 9, 12 month as formation and holding period. Means and standard deviation are annualized and in percent. T-stat are based on HAC standard error. ***, ** and * are significant at 1%, 5% and 10%, respectively. holding. formation. 1. 1. win. lose. W-L. win. lose. W-L. win. lose. W-L. win. lose. W-L. Mean. 4.05. -1.59. 5.64***. 2.68. -1.08. 3.76***. 1.46. 0.15. 1.31*. -0.81. -1.75. 0.93. 1.05. -0.76. 1.82***. Std. 9.99. 8.49. 9.94. 10.10. 9.28. 9.47. 10.66. 9.35. 9.39. 9.92. 10.26. 9.81. 10.63. 9.69. 10.78. 3.16. 3.78. 1.89. 1.54. 3.20. Mean. 4.53. -1.88. 6.42***. 2.12. -0.76. 2.88**. 0.86. -0.42. 1.28*. -0.23. -1.76. 1.53**. 1.14. -1.17. 2.31***. Std. 10.0. 8.53. 10.86. 10.47. 9.06. 10.22. 10.73. 9.83. 9.89. 9.61. 10.43. 10.22. 11.26. 9.91. 11.30. 3.28. 2.68. 1.75. 2.42. 3.87. Mean. 1.81. -0.95. 2.77. 1.58. -0.88. 2.46**. 1.62. -1.35. 2.97***. 0.11. -1.37. 1.48**. 1.30. -1.46. 2.75***. Std. 10.1. 8.86. 10.73. 10.58. 9.28. 10.14. 10.64. 10.25. 11.29. 9.33. 10.22. 10.35. 10.64. 9.83. 11.70. 1.42. 2.30. 3.53. 2.30. 4.44. Mean. 1.64. -2.53. 4.16**. 1.69. -1.98. 3.68***. 0.87. -1.31. 2.18***. 0.58. -0.98. 1.56**. 0.22. -0.73. 0.95*. Std. 9.39. 9.03. 10.76. 9.48. 9.59. 10.63. 8.87. 10.39. 9.95. 8.87. 11.05. 10.68. 8.80. 10.67. 10.29. T-stat. 12. 12. W-L. T-stat. 9. 9. lose. T-stat. 6. 6. win. T-stat. 3. 3. 2.09. 3.20. 2.87. 2.34. 1.69. Mean. 2.47. -1.70. 4.17**. 1.78. -1.42. 3.20**. 1.11. -1.48. 2.58***. -0.10. -1.22. 1.11*. 0.55. -1.29. 1.84**. Std. 9.63. 8.80. 11.00. 10.78. 9.26. 11.59. 10.27. 9.99. 11.89. 8.77. 10.25. 9.67. 9.00. 11.39. 12.28. T-stat. 2.07. 2.60. 2.90. 31. 1.84. 2.79.

(38) 5.6.Transaction cost Table 10 show excess return of momentum strategy with transaction cost. we apply the bid-ask price when we form the portfolio, since we thought the dealers usually adjust bid-ask spread while they expect that there may be a change in country’s condition. Unfortunately, we find the transaction cost seems fairly affect the momentum strategy and the large part of momentum excess return is wiped out as we take transaction cost into account. It indicate that when we practically apply momentum strategies in the foreign exchange market, dealer will charge amount of transaction cost. For instance, we have 4-9% return in momentum portfolio without transaction cost when we hold for 1 month, but we only have 0-4% return if we deduct the transaction cost from the momentum excess return.. 32.

(39) Table 10. Excess return of momentum strategy with transaction cost. This table present the momentum excess return with transaction cost, and the Winner-loser portfolio using 62 currencies against U.S. dollar for whole sample period (November 1983 to October 2014), calculated by winner minus loser and use 1, 3, 6, 9, 12 month as formation and 𝑘 𝑘 holding period. The excess return is calculated by 𝑟𝑥𝑡+1 = 𝑓𝑡𝑘 − 𝑠𝑡+1 . Means and standard deviation are annualized and in percent. T-stat are. based on HAC standard error. ***, ** and * are significant at 1%, 5% and 10%, respectively. holding. formation. 1. 1. win. lose. W-L. win. lose. Mean. 4.12. 0.19. 3.93**. 4.49. 0.55. Std. 8.81. 9.76. 10.03. 10.25. 9.60. T-stat. 3. 2.18. win. lose. W-L. win. lose. 3.94***. 3.24. 1.24. 2.00**. 2.67. 2.57. 10.14. 11.02. 10.15. 10.27. 9.80. 13.40. 3.73. 2.63. W-L. 12. win. lose. 0.11. 3.54. 1.30. 2.25***. 14.15. 11.25. 10.11. 10.9. 0.11. W-L. 3.91. 0.34. 3.84**. 4.35. 1.18. 3.17***. 4.03. 2.06. 1.98**. 2.65. 3.26. -0.61. 4.10. 1.45. 2.66***. Std. 8.94. 9.38. 10.08. 9.87. 10.09. 10.10. 11.28. 10.03. 10.96. 9.97. 15.29. 16.15. 10.50. 10.55. 11.11. 2.11. 3.01. 2.44. 0.55. 4.53. Mean. 3.77. 3.08. 0.69. 4.00. 2.34. 1.66. 4.18. 1.96. 2.22**. 2.24. 3.56. -1.32. 4.06. 1.64. 2.42***. Std. 8.99. 9.39. 10.33. 10.00. 10.03. 10.54. 11.48. 9.61. 11.54. 10.59. 15.13. 17.04. 10.59. 10.00. 11.9. 0.37. 1.50. 2.58. 1.13. 3.83. Mean. 3.88. 1.03. 2.85. 4.05. 0.26. 3.79**. 3.26. 1.39. 1.87*. 3.57. 1.19. 2.38**. 1.73. 1.39. 0.33. Std. 9.12. 9.04. 10.48. 11.01. 9.76. 11.94. 12.30. 9.52. 12.59. 15.29. 9.05. 14.29. 11.84. 9.16. 11.8. T-stat. 12. 9. 4.19. T-stat. 9. W-L. 6. Mean. T-stat. 6. 3. 1.32. 2.66. 1.75. 2.40. 0.47. Mean. 3.50. 3.79. -0.29. 4.36. 3.02. 1.34. 4.07. 2.92. 1.14. 0.72. 4.68. -3.97***. 3.60. 2.67. 0.93. Std. 9.02. 9.76. 11.06. 9.61. 10.43. 11.15. 10.76. 10.30. 12.14. 10.42. 16.57. 18.29. 11.22. 8.89. 11.8. T-stat. 0.14. 1.14. 1.26. 33. 3.17. 1.47.

(40) 5.7.The relationship between country risk and the momentum excess return In order to investigate whether momentum returns are different between currencies with high or low country risk, so we double-sort the currencies into two portfolios. We first sort currencies into two group depending on whether the individual country risk is higher or lower than the U.S.’s country risk and then we form these two groups of currencies into three portfolios depending on their lagged excess return. That is, we treat the one-third of the currencies with the highest lagged return as the winner currencies, and the one-third of currencies with the lowest lagged return as the loser currencies. Here we also use formation period for 1, 3, 6, 9 and 12 month, but we only consider 1 month holding period.. Table 11. Momentum excess return sorting by country risk. This table present the average return of the Winner-loser portfolio using 64 currencies against U.S. dollar for whole sample periods, first classed with the CRISK, then calculated by winner minus loser and use 1, 3, 6, 9, 12 month as 𝑘 𝑘 formation period and one month holding period. The excess return is calculated by 𝑟𝑥𝑡+1 = 𝑓𝑡𝑘 − 𝑠𝑡+1 . Means and. standard deviation are annualized and in percent. T-stat are based on HAC standard error. ***, ** and * are significant at 1%, 5% and 10%, respectively.. M(L). M(M). M(H). ∆M. Mean. 0.39%. 2.82%. 3.82%. 3.44%**. T-stat. [0.23]. [1.82]. [2.51]. [2.42]. Mean. -5.32%. 2.44%. 10.89%. 16.23%***. T-stat. [-2.23]. [1.76]. [6.01]. [5.46]. Mean. -5.59%*. 0.34%. 7.20%**. 12.79%***. T-stat. [-1.97]. [0.16]. [3.00]. [5.12]. Formation period. 1. CRISK(L). CRISK(H). ∆CRISK. 34.

(41) 3. CRISK(L). CRISK(H). ∆CRISK. 6. CRISK(L). CRISK(H). ∆CRISK. 9. CRISK(L). CRISK(H). ∆CRISK. 12. CRISK(L). CRISK(H). ∆CRISK. Mean. 0.50%. 2.63%. 2.98%. 2.47%*. T-stat. [0.32]. [1.75]. [1.89]. [1.84]. Mean. -3.09%. 3.03%. 8.50%. 11.66%***. T-stat. [-1.46]. [2.25]. [4.28]. [4.02]. Mean. -3.59%. 1.52%. 5.59%**. 9.18%***. T-stat. [-1.37]. [0.14]. [2.18]. [3.74]. Mean. 2.68%. 2.51%. 1.31%. -1.35%. T-stat. [1.66]. [1.54]. [0.81]. [-0.99]. Mean. 1.81%. 2.64%. 6.09%. 4.33%. T-stat. [0.90]. [1.87]. [2.97]. [1.49]. Mean. -0.79%. 0.45%. 4.89%*. 5.68%**. T-stat. [-0.34]. [0.12]. [1.83]. [2.36]. Mean. 1.84%. 1.08%. 3.01%. 1.15%. T-stat. [1.16]. [0.63]. [1.83]. [0.88]. Mean. 1.52%. 1.80%. 8.20%. 6.53%**. T-stat. [0.85]. [1.23]. [4.20]. [2.54]. Mean. -0.11%. 0.52%. 5.28%**. 5.38%**. T-stat. [-0.14]. [0.38]. [2.04]. [2.44]. Mean. 2.81%. 2.37%. 1.97%. -0.81%. T-stat. [1.81]. [1.39]. [1.21]. [-0.61]. Mean. 4.85%. 2.75%. 5.01%. 0.27%. T-stat. [3.22]. [1.74]. [2.48]. [0.06]. Mean. 2.06%. -0.16%. 3.14%. 1.08%. T-stat. [0.95]. [-0.20]. [1.17]. [0.53]. 35.

(42) We divide the whole sample currencies into two group, high CRISK and low CRISK, and make the momentum portfolios in each group. In the table 11, we show the result of the momentum excess return sorting by country risk. ∆M is the return of momentum strategy portfolio (that is M(H)’s return minus M(L)’s return) and ∆CRISK is CRISK(H)’s return minus CRISK(L)’s return. In the group of low country risk, we find that differences between winner and loser are smaller, and the momentum excess returns are not significant at 10% confidence level. However, in the group of high country risk, the momentum excess returns are larger and positively significant. Furthermore, the return of ∆CRISK have significant difference from zero as well. These results indicate that the returns are significant difference between the group of low and high country risk and excess returns of momentum portfolio on high country risk are larger and more significant than the excess returns on low country risk.. 5.8.The result from time-series regression In this part, we want to test whether illiquidity risks or country risk will have significant impact on momentum excess return by running a time-series regression. Our proxy variable for illiquidity risks are TED and term spread for time period of November 1863 to October 2014. The time-series regressions are as follows:. 𝑀𝑂𝑀1,1 = 𝛼𝑡 + 𝛽𝑇𝐸𝐷,𝑡 𝑇𝐸𝐷𝑡−1 + 𝛽𝑡𝑒𝑟𝑚,𝑡 𝑇𝑒𝑟𝑚𝑡−1 + 𝛽𝐶𝑅𝐼𝑆𝐾,𝑡 𝑟𝑒𝑡(𝐶𝑅𝐼𝑆𝐾)𝑡−1 ( 7 ). Where 𝑇𝐸𝐷𝑡−1 is lagged TED spread, 𝑇𝑒𝑟𝑚𝑡−1 is lagged term spread and ret(𝐶𝑅𝐼𝑆𝐾)𝑡−1 is lagged conditional return which is calculated by lagged return on high CRISK minus lagged return on low CRISK. TED Spread is the difference between the LIBOR (London Interbank Offered Rate) and the 3 Month Treasury bill. The LIBOR is Europe's equivalent to the United States 36.

(43) Federal Funds Rate. A high TED Spread indicates higher perceived risk in lending, as interbank rates rise against risk-free treasury rates, and it is also an evidence that liquidity is being withdrawn from the financial markets. The term spread is the difference between yields on 10 year Treasury bill and 3 month Treasury bill. The higher the yield spread, the greater liquidity premium is, implying there is illiquidity risk. If we have positive 𝛽𝑇𝐸𝐷,𝑡 or 𝛽𝑡𝑒𝑟𝑚,𝑡 , it means the larger spread (less liquidity on currency market) would cause larger momentum excess return. We double-sort the currencies into two portfolios. We first sort currencies into two group depending on whether the individual country risk is higher or lower than the U.S.’s country risk and then we form these two groups of currencies into three portfolios depending on their lagged excess return. That is, we treat the one-third of the currencies with the highest lagged return as the winner currencies, and the one-third of currencies with the lowest lagged return as the loser currencies. Then, we construct the highminus-low momentum portfolio. From this variable, we can easily realize that if we have positive 𝛽𝐶𝑅𝐼𝑆𝐾,𝑡 , it means the larger difference between lagged return on high CRISK and lagged return on low CRISK would cause higher momentum excess return. Table 12 shows results from time series regression of momentum returns on liquidity and country risk variables. We include the ted and term spread as our liquidity risk variables, and CRISK as country risk variable. The first three rows are coefficients from univariate regression and others are coefficients from multivariate regression. Numbers In the brackets are t-statistic based on Newey and West (1987) standard errors. The column of right is shown F-statistic for testing whole regression.. 37.

(44) Table 12. Liquidity risk and momentum excess return. This table shows results from time series regression of momentum returns on liquidity and country risk variables. Ted and term spread are represented liquidity risk variables. retCRISK is country risk variable, calculated by lagged return on high CRISK minus lagged return on low CRISK. Numbers In the brackets are t-statistic based on Newey-West (1987) standard errors. ***, ** and * are significant at 1%, 5% and 10%, respectively. constant. ted. 0.02. -0.01. [4.70]. [-1.65]. termspread. retCRISK. F-test. [2.74]. 0.01. 0.00. [3.08]. [1.52]. [2.32]. 0.01. 0.41***. [6.05]. [3.21]. 0.02. -0.01. 0.00. [2.70]. [-1.40]. [1.06]. 0.01. 0.00. 0.44***. [-0.59]. [-0.59]. [3.29]. [10.29]. [2.76]. 0.01. 0.00. 0.41***. [2.75]. [0.44]. [3.17]. 0.01. 0.00. 0.00. 0.44***. [1.92]. [-0.50]. [0.23]. [3.26]. [5.86]. [7.37]. [4.13]. In the univariate regression, coefficients of country risk variables are significant at 5% confidence level and coefficients of liquidity risk variables are just significant at 10% confidence level. In the multivariate regression, we find that ted and term spread are not significant anymore, indicating that there is little evidence that liquidity risk 38.

(45) help to explain the momentum excess returns. However, the retCRISK are all positively significant, implied that the larger difference between the high and low CRISK return, the higher momentum excess return we will earn in next period. That is, we will more possibility to earn larger momentum excess return if country risk is higher in last period.. 6. Conclusion We investigate whether the momentum effect exist in the monthly foreign exchange market using a broad basket of 62 market currencies. By forming currency portfolios on basis of past returns and employing various horizon formation and holding period, we find there are strong evidence of momentum effect. Annualized excess return of momentum strategies reach up to 9% per year. Annualized momentum excess returns decrease as the increase in formation and holding period. However, when we examine the sub period of the momentum effect, we find the momentum effect doesn’t exist continuously, especially the period which have happened some currency crisis. We find that reversal effect exist in Sterling Crisis and European Exchange Rate Mechanism crisis around 1992, Asian financial crisis in mid-1997 and European debt crisis which starting around mid-2008. During crisis, the exchange rates may become very volatile or continuous depreciation, and some speculators take this opportunity inducing the worsen currencies situation. As a result, we have lots of negative returns in long position and positive returns in short position in our data. Furthermore, because when the currencies become illiquid or risky, the currency dealer tend to apply wider bid-ask spread. We are wondering whether the momentum excess returns just reflect the transaction cost, so we also take the transaction cost as our consideration, finding that momentum excess returns still exist, but most of the excess returns are fairly wiped out. We conclude that the transaction cost is the important component of excess momentum returns, but not really effect the change of 39.