Behavior of Momentum in the Foreign Exchange Market: Evidence

from Portfolio Approach

Hasib Ahmed

Phuvadon Wuthisatian

Atsuyuki Naka

Introduction

• Momentum Strategy

• the trend of the market that is winner stocks will continue to rise while loser stocks tend to keep falling (Jegadeesh and Titman, 1993).

• Momentum in other asset classes:

• Equity, currency, bond, international assets.

• Foreign Exchange (FX) market

• Most highly traded market in the world

• Average trading of $5.1 trillion per day (BIS, 2016).

Existence of Momentum

• Jegadeesh and Titman (1993) observe the trading strategy according to the past performance, buying well-performed stocks and selling poorly-performed stocks, they find that this strategy generates positive returns from holding period of 3 to 12 months approximately 12% per annum.

• Moskowitz, Ooi, and Pedersen (2012), which they test for 58 instruments and find that a strong significance of stock return predictability based on the past performance for all the instruments. They also document that the excess returns of these instruments reverse over longer horizon suggesting that momentum strategies disappear after certain period of time.

• Menkhoff, Sarno, Schmeling, and Schrimpf (2012b) use cross section of currencies and report spread in excess return of up to 10% per annum using winner minus losers (WML) strategy for foreign currencies.

• Okunev and White (2003) use the cross-sectional analysis of eight major currencies. Using month to month performance, they find momentum strategy creates approximately 6% per annum.

Motivation

• Currency momentum is particularly interesting, because it provides high returns unrelated to carry trade returns.

• It does not make much sense theoretically that such huge abnormal return for momentum strategy in the currency market exists and arbitrageurs are not exploiting it enough to make the strategy (closer to) obsolete.

• One explanation could be the possibility of problem of large crashes in the FX momentum.

• So, our objective for this study is to look for the problem of large crashes in the FX momentum.

• If crashes contributes to the returns of the strategy, then we should be able to observe the source of returns whether from winner or loser portfolio.

Momentum Crashes

• Daniel and Moskowitz (2016) provide an empirical evidence of momentum crashes and implement the dynamic momentum strategy based on forecast of momentum’s mean and variance to improve the momentum strategies. Their result suggest that the dynamic momentum strategy can help double the alpha and Shape ratio. Their finding also extends to other asset classes such as foreign exchange (FX) market.

• Note that their study is based on 10 developed currencies – potential selection bias.

• We follow their approach to investigate whether the crashes contribute to the abnormal returns in currency momentum by extending up to 66 currencies.

Risk-Managed Momentum

• Barroso and Santa-Clara (2015) explain that risk-managed momentum should provide higher mean return, less volatility, less skewness, and higher Sharpe ratio than the plain momentum strategy.

• We believe that using risk-managed momentum of winner-minus-loser (WML) portfolio would benefit investors to hedge themselves against the financial crises.

Contributions

• (i) unlike stock market, out sample does not behave as it is predicted by Daniel and Moskowitz (2016) result,

• (ii) the loser portfolio, however, acts the same way as it does in stock market, and

• (iii) the source of returns from WML is mainly from loser portfolio rather winner portfolio.

Data

• Source: Barclays Bank International, Reuters (Datastream).

• Years: December, 1984 through December, 2015.

• The currencies are required to have at least five years of spot and forward rate data.

• Final sample: 66 currencies.

Methodology

• Monthly excess returns for holding foreign currency k as,

• Given that covered interest parity (CIP) holds even at very short horizons (Akram, Rime, and Sarno (2008)), equals .

• The last date observations are used as observation for the month.

• The end of month net return

• long position:

• short position:

• If a currency stays in the portfolio at the end of month:

• long position:

• short position:

Portfolio Construction

• We then construct the net excess returns into portfolios based on the lagged returns under previous formation period, months, and these portfolios are held in holding period, months.

• The winner minus loser (WML) portfolios are formed by taking long position in the winner portfolio and short position in the loser portfolio.

• The portfolios, in our analysis, are dividing into five deciles ranging from lowest 20% of excess return up to top 20% excess return.

Sources of Momentum Return

• We follow Daniel and Moskowitz (2016) to estimate the time-varying betas of winner and loser portfolios using 126-day rolling market model regression with daily data. The estimation of betas is calculated based on the ten daily lags of market return as follows:

•• where is the daily market return.

• Then, we sum the estimation coefficients to determine the betas for winner and loser portfolios.

Option-like behavior

• We use four-time series regressions on a set of independent variables.• Excess monthly market return index in month t

• A bear market indicator is characterized by . We assign the value equal to one if the past 12-month return is negative and zero otherwise.

• Up-market indicator is defined as The value is equal to one if the excess return of currency portfolio is greater than risk-free in month t.

• Up-Down market indicator is defined as . The variable is assigned to extent to capture the trend of up-down market.

•••

Momentum Optimality

• We analyze further for optimality of momentum portfolio. We run a regression by assigning the variable to indicate either bear or bull market. The regression is described as:

••

Risk-managed momentum• I estimate the realized variance in month as

• ,

• An AR(1) regression of realized variances will produce the realized volatility of momentum and market.

• I’ll also get the persistence measure of risk ( coefficient).

• Using the monthly return of momentum as and daily return as , the variance forecast will be

• As WML is a zero-investment and self-financed strategy, it can be scaled without constraints.

• So, the returns are scaled as

•

• where is the unscaled momentum and is scaled momentum. is a constant target level of volatility.

• Then, I compare the performances of and .

Table 2: Mean returns of plain momentum strategy of winner minus loser (WML) of 67 currencies from December 1984 to December 2015. Portfolios are formed based on the formation and holding period of 1, 3, 6, 9, and 12-month period. The winner portfolios represent return from long position and loser portfolios represent return from short position. The WML portfolios report the net return. The t-statistics are estimated following Newey and West (1987) and are reported in parentheses.

Mean Returns

Formation Period Holding Period 1 3 6 9 12

1 0.122596 0.115238 0.056708 0.097358 0.082632

(5.71) (5.56) (4.50) (4.46) (4.06) 3 0.127805 0.109885 0.059415 0.097033 0.078171

(5.58) (5.14) (4.67) (4.96) (4.32) 6 0.111386 0.103434 0.059357 0.088905 0.069703

(3.38) (3.64) (3.89) (4.09) (3.53) 9 0.109598 0.105932 0.060197 0.083963 0.065070

(4.48) (4.37) (4.08) (3.85) (3.52) 12 0.091400 0.084980 0.051265 0.076964 0.064756

(4.97) (4.64) (4.15) (3.73) (3.73)

Table 5: Momentum Portfolio Characteristics from December 1984 to December 2016. The portfolios are grouped up based on the excess returns. Portfolio 1 is the lowest 20% excess return. Portfolio 5 is top 20% excess return. 5 -1 (WML) represents the winner minus loser strategy based on the top 20% excess turn and lowest 20% excess return. The last row provides the market excess returns as the benchmark.

Portfolio Mean Std. Dev. Min Max Sharpe Ratio Skewness

1 -0.321 0.322 -1.837 0.181 -0.996 -1.729 2 -0.112 0.253 -1.273 0.443 -0.443 -1.439 3 0.014 0.264 -1.102 0.819 0.053 -0.501 4 0.133 0.231 -0.526 1.014 0.575 0.857 5 0.360 0.262 -0.181 1.644 1.376 1.294

5-1 (WML) 0.681 0.299 0.136 2.319 2.282 1.610 Market 0.011 0.264 -1.149 0.773 0.041 -0.401

Figure 4: Cumulative Monthly Return from December 1984 to December 2015. The figure represents the return of (i) risk-free rate return, (ii) market return, (iii) spot excess return, (iv) winner portfolio return, and (v) loser portfolio return. The left hand side represents the $1 investment at the beginning period and the right hand side is the end of the period return on investment.

02

46

1985m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1Date

Risk-free MarketSpot WinnersLosers

Figure 5: Beta Estimation. The figure reports the betas for winner and loser portfolios from December 1984 to December 2015. The solid line represents the winner portfolio betas while the dot line represents the loser portfolio betas. The beta estimation is based on equation (2): 𝑟ҧ𝑖,𝑡𝑒 = 𝛽0𝑟ҧ𝑚,𝑡𝑒 + 𝛽1𝑟ҧ𝑚,𝑡−1𝑒 + ⋯+ 𝛽10𝑟ҧ𝑚,𝑡−10𝑒 + 𝜀ҧ𝑖,𝑡. The estimated betas are the sum of individual coefficients 𝛽መ0 + 𝛽መ1 + ⋯+ 𝛽መ10.

-15

-10

-50

5Jan 01, 1985 Jan 01, 1990 Jan 01, 1995 Jan 01, 2000 Jan 01, 2005 Jan 01, 2010 Jan 01, 2015

Date

Winner Loser

Coefficient Variable WML Winner Loser 1 2 3 4 1 2 3 4 1 2 3 4α0 Constant (Alpha) 0.0034 -0.0008 -0.0008 0.0016 0.0031 0.0016 0.0016 0.0024 0.0003 -0.0024 -0.0024 -0.0008

(2.22)** (-0.43) (-0.44) (1.01) (1.01) (1.58) (1.60) (2.79)** (0.30) (-1.89)* (-1.91)* (-0.76)αB Alpha in Bear Market 0.0014 0.0091 -0.0010 0.0031 0.0024 0.0061

(0.50) (2.54)** (-0.62) (1.54) (1.23) (2.43)**β0 Market Excess Return 0.0147 0.5868 0.5868 0.5530 0.8303 1.1214 1.1214 1.1100 -0.8156 -0.5346 -0.5346 -0.5570

(0.21) (6.82)** (6.92)** (6.55)** (21.67)** (23.56)** (23.87)** (23.88)** (-17.97)** (-9.02)** (-9.08)** (-9.51)**ΒB Bear Market indicator -1.2803 -0.8607 -1.0543 -0.0010 -0.4539 -0.5191 -0.6064 -0.4068 -0.5352

(-9.89)** (-4.85)** (-6.53)** (-0.62) (-4.62)** (-5.84)** (-6.81)** (-3.30)** (-4.78)**Β U, B Up-Down Market -0.9792 -0.5190 -0.5135 -0.3586 -0.4657 -0.1604

(-3.41)** (-2.31)** (-3.22)** (-2.89)** (-2.33)** (-1.03)R-square 0.0001 0.2159 0.2407 0.2269 0.5675 0.6542 0.6640 0.6618 0.4741 0.5361 0.5431 0.5355

Table 6: Market Timing Regression. The table represents the estimated coefficients from regressions of monthly excess return of WML, winner, and loser portfolio. The regression models are: model (1) - equation (3): unconditional market model, model 2 - equation (4): conditional bear market indicator, and model (3) and (4) - equation (5): the up-market indicator. α0 represents the intercept of the regression model, αB is the bear market indicator, β0 is the market excess return, βB is the up-market indicator, and βU, B is the up-down market indicator. The t-test is reported as Newey-West t-statistic test. The t-tests are reported in parentheses. *, ** shows the significance of 5%, and 10%.

Table 7: Momentum portfolio optimality. Table 7 represents the estimated coefficients from regressions of monthly excess return of bear and bull market. Panel A reports the bear market result while Panel B represents bull market. The bear market regression described as equation (6): 𝑟ǁ𝑖,𝑡 = (𝛼0 + 𝛼𝐵𝐼𝐵,𝑡−1)+(𝛽0 + 𝐼𝐵,𝑡−1(𝛽𝐵 + 𝐼𝑈,𝑡𝛽𝐵,𝑢 )𝑅෨𝑚,𝑡𝑒 + 𝜀ǁ𝑡 and the bull market is described as equation (7): 𝑟ǁ𝑖,𝑡 = (𝛼0 + 𝛼𝐿𝐼𝐿,𝑡−1)+(𝛽0 + 𝐼𝐿,𝑡−1(𝛽𝐿+ 𝐼𝑈,𝑡𝛽𝐿,𝑈 )𝑅෨𝑚,𝑡𝑒 + 𝜀ǁ𝑡. α0 represents the intercept of the regression model, αB is the bear market indicator, β0 is the market excess return, ββ is the up-market indicator, and Β U, β is the up-down market indicator. Portfolio 1 indicates the lowest 20% of excess return portfolio while portfolio 5 represents the top 20% of excess return portfolio. WML is the winner minus loser based on the difference between portfolio 5 and 1. WML* is the our momentum strategy based on 11-month period. The t-test is reported as Newey-West t-statistic test. The t-tests are reported in parentheses. *, ** shows the significance of 5%, and 10%.

Panel A: Bear Market

1 2 3 4 5 WML WML* α0 -0.2225 -0.0430 0.0823 0.1866 0.4030 0.6255 -0.0008

(-10.27)** (-2.40)** (4.30)** (10.88)** (21.00)** (29.02)** (-0.44) αB -0.2129 -0.1273 -0.1253 -0.1082 -0.1229 0.0900 0.0091

(-4.97)** (-3.59)** (-3.31)** (-3.19)** (-3.24)** (2.11)** (2.54)** β0 -0.4834 -0.4065 -0.4056 -0.3581 0.2842 0.7676 0.5868

(-0.50) (-0.50) (-0.47) (-0.47) (0.33) (0.79) (6.92)** ΒB 1.9167 1.7960 1.8100 0.2851 -1.4681 -3.3848 -0.8607

(0.91) (1.03) (0.97) (0.17) (-0.79) (-1.61) (-4.85)** β B, u -0.8905 -0.9605 -0.7624 1.0832 3.7235 4.6140 -0.9792

(-0.26) (-0.34) (-0.25) (0.40) (1.22) (1.34) (-3.41)** R-square 0.1183 0.0712 0.0610 0.0415 0.0359 0.0467 0.2407 Panel B: Bull Market

1 2 3 4 5 WML WML* α0 -0.4424 -0.1778 -0.0489 0.0869 0.3094 0.7518 0.0006

(-17.68)** (-8.58)** (-2.21)** (4.39)** (13.92)** (30.12)** (0.29) αL 0.2393 0.1404 0.1394 0.1100 0.0948 -0.1444 0.0042

(5.90)** (4.18)** (3.89)** (3.43)** (2.63)** (-3.57)** (1.22) β0 1.0517 0.9779 1.0777 0.3912 0.4118 -0.6399 -0.6935

(0.92) (1.03) (1.07) (0.43) (0.41) (-0.56) (-7.24)** βL -0.2506 -1.0184 -0.9443 -0.0610 -0.0496 0.2011 1.6561

(-0.12) (-0.57) (-0.5) (-0.04) (-0.03) (0.09) (8.93)** β L, U -2.3694 -0.6751 -0.9944 -1.2696 -0.1440 2.2254 -0.7024

(-0.83) (-0.28) (-0.39) (-0.56) (-0.06) (0.78) (-2.81)** R-square 0.1198 0.0711 0.0612 0.0420 0.0320 0.0436 0.2329

Table 8: momentum return and market variance. The table represents the estimated coefficient of a time series regression based on the equation (8): 𝑟ǁ𝑖,𝑡 = 𝛾0 + 𝛾𝐵,𝑡−1𝐼𝐵,𝑡−1 + 𝛾𝜎𝑚2 𝜎ො��𝑚,𝑡−12 + 𝛾𝑖𝑛𝑡𝐼𝐵𝜎ො��𝑚,𝑡−12 + 𝜀ǁ𝑡to forecast the future WML return. 𝐼𝐵is the bear market indicator, and 𝜎ො��𝑚,𝑡−12 is the variance of daily returns of the market over the 126-day. Model 1 and 2 use one variable at a time. Model 3 uses both variables simultaneously. Model 4 uses only the interaction term between bear market indicator and market variance. Model 5 uses all variables at the same time. The t-test is reported as Newey-West t-statistic test. The t-tests are reported in parentheses. *, ** shows the significance of 5%, and 10%

WML Model 1 2 3 4 5

0.0031 0.0056 0.0051 0.0043 0.0041

(-1.53) (2.83)** (2.21)** (2.63)** (-1.25)

0.0008 0.0013 0.0027 (-0.25) (-0.42) (-0.63)

-0.0116 -0.0119

-0.0057

(-1.73)* (-1.76)* (-0.39) -0.0097 -0.0078 (-1.45) (-0.47) Winner

Model 1 2 3 4 5

0.0091 0.0051 0.0092 0.0055 0.0106

(5.55)** (3.08)** (4.85)** (4.02)** (3.99)**

-0.0105

-0.0105

-0.0123

(-4.20)** (-4.16)** (-3.50)**

-0.0028 -0.0007

-0.0087

(-0.50) (-0.12) (-0.72)

-0.0097 0.0101

(-1.74)* (-0.75) Loser

Model 1 2 3 4 5

-0.006 0.0005 -0.0041 -0.0012 -0.0065

(-3.41)** (-0.29) (-2.00)** (-0.79) (-2.30)**

0.0113 0.0118

0.015

(4.20)** (4.37)** (3.99)**

-0.0088 -0.0112

0.003

(-1.46) (-1.90)* (-0.23)

0.000 -0.0179

(0.00) (-1.24)

Figure7: Portfolio weight. The weight is estimated by dividing a constant (one-half of mean realized variance) by

six-month variance forecast as it is calculated by equation (12): 𝑟𝑥𝑊𝑀𝐿∗,𝑡+1 = 𝜎𝑡𝑎𝑟𝑔𝑒𝑡𝜎ො�� 𝑡+1 𝑟𝑥𝑊𝑀𝐿 ,𝑡+1. The dash line

represents winner weight, dot line represents loser weight, and WML is represented by the solid line.

01

23

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1985m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1Date

WML WinnerLoser

Table 10: Portfolio Returns. The returns of WML portfolio based on 11-month formation period and 1 month holding period. The table provides a comparison among market, WML, winner, and loser returns. The estimation is based on the weights assigned from figure 7.

Variable Observation Mean Std. Dev. Skew Sharpe Market 360 0.0410 0.3462 -0.4825 0.1184 WML 354 0.0249 0.4102 -0.3878 0.0606

Winner 354 0.0158 0.4465 -1.4377 0.0354 Loser 354 0.0697 0.4314 0.4358 0.1615

Conclusion

• We analyze the momentum strategy based on winner minus loser portfolio. • We also explore the possible sources of the returns of momentum strategy

using Daniel and Moskowitz (2016) approach. • Our result, however, contradicts to what they find. • We find that the momentum strategy is mainly from the loser portfolio, which

indicates the return during the financial stress attributed to the return in the momentum strategy.

• We also test for the risk-managed momentum; however, our result does not indicate much improvement of implementing such strategy.