can we predict currency momentum crashes?strategies. in particular, when carry trade is recovering...

Can we predict currency momentum crashes?

Mario Cerrato and Zhekai Zhang∗

November 11, 2019

Abstract

We report robust empirical evidence that currency momentum crash is predictable. We

show that the payo� of a currency momentum strategy has a time-varying beta structure and

is linked to the carry trade factor (HML) proposed by Lustig et al. (2011). The currency

momentum beta to HML is conditioned on the previous and contemporaneous HML portfolio

returns. This risk pattern introduces a written call-option-like payo� in currency momentum

strategies. In particular, when carry trade is recovering from previous crashes, momentum

strategies lose money. We propose two currency momentum strategies to mitigate momentum

crash risk.

∗Adam Smith Business School, University of Glasgow. [email protected],[email protected]

1 Introduction

A momentum strategy consists of shorting assets that have recently yielded low returns and buying

those with high returns. The properties of this simple strategy have been extensively studied in

�nance literature. Jegadeesh & Titman (1993) were amongst the �rst to show the pro�tability of

a momentum strategy in the US equity market. Similar results have been reported for the equity

markets of di�erent regions as well as across di�erent asset classes.1 The momentum returns are

di�cult to explain by their unconditional risk exposure to standard risk factors (Jegadeesh &

Titman 1993, Grundy & Martin 2001, Fama & French 1996). To rationalize such a high excess

return, di�erent explanations have been suggested, but no consensus has yet been reached. For

example, Carhart (1997) suggests adding momentum as a fourth factor to the Fama French model.

Lesmond et al. (2004) emphasise the role of trading costs and argue that pro�ts that have been

balanced out as assets with high momentum returns are generally associated with high trading

costs. This result has been challenged in the subsequent literature. Korajczyk & Sadka (2004)

show that the excess return from an equal-weighted momentum strategy drops dramatically after

considering trading costs, but investors could easily amend equal weightings to lower the trading

cost and still earn a signi�cant excess return.

One explanation in the equity literature suggests that momentum strategies have time-varying risk

exposures to equity factors. This is intuitive as the momentum strategy is to buy past winners

that have positive (negative) loadings when past factor realization is positive (negative) and vice

versa for past losers (Kothari & Shanken 1992). Thus momentum's risk exposure is conditioned

on the realized value of the pricing factors, as shown by Cooper et al. (2004) and Stivers & Sun

(2010). A recent study by Daniel & Moskowitz (2016) �nds that the time-varying risk pattern

leads to momentum payo� which resembles that of a written-call option-like in the bear market.

That is, under bear market conditions, when the market falls, momentum strategy gains a little.

However, when the market recovers from previous drawdown, momentum strategy crashes. In the

fx literature, very little has been done on this important issue. The forex market is the largest

and most liquid �nancial market, with low transaction costs and no short-selling constraints. Cur-

rency momentum anomaly is a more di�cult challenge for asset pricing models to accommodate,

compared with the equity market cited above. This paper tries to �ll this gap. We show that in

1For momentum on international equity market see, for example, Rouwenhorst (1998) and Chan et al. (2000).For studies on di�erent asset classes, see for example the work of Shen et al. (2007) and Mi�re & Rallis (2007) forcommodity markets; Jostova et al. (2013) on �xed income markets; and Okunev & White (2003) and Menkho�et al. (2012b) on currency markets. A comprehensive study of momentum anomaly for di�erent asset classes isprovided by Asness et al. (2013).

1

a bear market, momentum and carry trade strategies are linked. We also show that momentum

strategy payo�, in a bear market, reseambes the one of a written call option and in so doing we

con�rm the main results reported for the equity market.

In addition, while the previous literature on the currency market has mainly focused on the time-

series approach and/or technical trading rules,2 two exceptions are Okunev & White (2003) and

Menkho� et al. (2012b) who focus on cross-sectional analysis, we also use a cross-sectional approach.

Okunev & White (2003) and Menkho� et al. (2012b) show signi�cant positive cross-sectional

momentum pro�ts from momentum currency strategies. In this paper, we follow this previous work

to design cross-sectional currency momentum strategies, but extend the sample to include the post-

�nancial crisis period. In line with Menkho� et al. (2012b), currency momentum strategies are still

highly pro�table, even allowing for the 2008 �nancial crisis. A $1 long/short momentum strategy

yields a signi�cant annualized return of 5.96% with Sharpe ratio of 0.87. However, we report

strong empirical evidence that currency momentum strategies are mostly negatively skewed, which

indicates momentum crashes on the currency market. We show that the dynamic risk model in

Daniel & Moskowitz (2016) is also appropriate for explaining currency momentum crash. Menkho�

et al. (2012b) suggest that momentum pro�ts are based on the risk characteristics of underlying

assets. To capture speci�c properties on the currency market, we link momentum risk exposure

to the carry trade high minus low factor (HML) proposed by Lustig et al. (2011). Burnside et al.

(2011) and Menkho� et al. (2012b) document that there is no unconditional correlation between

long/short momentum strategies with HML, and we con�rm this result but also show that the

existence of signi�cant time-variation for momentum risk exposure to HML depends on di�erent

market conditions. That is, when carry trade crashes, currency momentum returns are negatively

correlated with carry trade returns; when carry trade recovers from a previous crash, a signi�cant

positive risk exposure for momentum strategy is observed (i.e. momentum strategy crashes).

There is an asymmetric momentum beta change pattern to carry trade. From the time series

point of view, currency momentum crashes only when the carry trade is recovering from previous

drawdowns.

Our paper links currency momentum crash with carry trade crash. We argue that the asymmetric

risk exposure of momentum is closely related to the carry-trade-dominanted trading patterns in

the currency market.3 Brunnermeier et al. (2008) state that high interest rate currencies in carry

trades go up gradually but collapse due to the sudden unwind by speculators when they reach their

2A related literature review has been done by Menkho� & Taylor (2007).3Burnside (2011) suggests that a signi�cant part of trading activity is triggered by carry trade.

2

liquidity constraints, while the reverse holds for the low interest rate funding currencies. Once carry

trade crashes, momentum investors switch the long-short holdings rapidly by selling high interest

rate currencies and buying low interest rate currencies and as a consequence momentum does not

crash simultaneously with carry trade. However, when the carry trade gradually recovers from a

crash, momentum investors do not adjust their positions causing large losses. We argue that carry

trade is the decisive source for the asymmetric risk exposure in momentum strategy and show that

other currency factors such as the DOL factor do not contribute to explaining such a pattern. This

is also consistent with the empirical �ndings of Daniel & Moskowitz (2016) who show insigni�cant

time-varying betas of currency momentum to DOL.

Finally, we run a battery of robustness checks. We show that the risk pattern to HML is robust

after considering the DOL factor for the estimation of betas. We test the pro�tability of the time-

varying beta-adjusted portfolio as in Grundy & Martin (2001) and Daniel & Moskowitz (2016), to

show that the dynamic beta pattern is the primary driver of excess momentum returns.

Since our main results suggest that currency momentum crash is predictable, we design two cur-

rency momentum strategies. The �rst strategy simply closes the momentum position when the

previous cumulative HML return is negative. We show that this strategy can mitigate a possible

crash but can also open up to investment opportunities. The second strategy is an extension of the

dynamic weighting strategy of Daniel & Moskowitz (2016) for the equity market, which adjusts the

weightings by using the predictability of HML volatility. We �nd that both strategies outperform

the main momentum strategy in terms of Sharpe ratios. Most importantly, the negative skewness

is mostly mitigated.

The remainder of this paper is organized as follows: Section 2 describes our data and the currency

momentum anomaly. Section 3 documents the time-varying beta structure of currency momentum

strategies. Section 4 introduces the economic implication of the model by constructing optimal

currency momentum portfolios. Section 5 concludes.

2 Currency portfolios

This section describes the data, currency excess returns, currency portfolios and currency momen-

tum strategies based on di�erent formation and holding periods.

3

2.1 Data sample

The sample of exchange rates is obtained from WM/Reuters (via Datastream). It consists of end-

of-month spot exchange rates and 1-month forward rates for 31 currencies.4 The sample spans

from January 1997 to February 2017. All exchange rates are denoted as units of foreign currency

per US dollar (FCU/USD). Compared to the previous literature (Lustig et al. 2011, Menkho�

et al. 2012a), the maximum number of currencies available in this sample is smaller because we

do not include the euro-zone currencies before they joined the euro. Our sample starts late in the

1990s but includes recent periods when in�uential economic events happened: the US subprime

mortgage crisis in 2008 and the European sovereign debt crisis in 2013. The number of currencies

available varies over time in the beginning but reaches a maximum and remains stable for most of

our sample, as illustrated in �gure 1.

2.2 Currency excess return and portfolios

We follow the literature and compute currency excess return as the US dollar return of borrowing

US dollars at the risk free rate it and investing in foreign currency to earn the foreign currency

interest rate ikt . Combined with the covered interest parity, the currency excess return rxkt+1 for

currency k of period [t, t+ 1] is,

rxkt+1 = ikt − it − (skt+1 − skt ) ≈ fkt − skt+1

Where ikt , is the one-month interest rate for currency k, it is the US dollar interest rate. skt and

fkt denotes the logarithm spot and 1-month forward exchange rate for currency k in FCU/USD.

As in Lustig et al. (2011) we compute the DOL factor by taking the average returns across the

currencies in the sample:

DOLt+1 =1

Nt

∑k∈Nt

rxkt+1

Where Nt is the number of currencies available at time t.

4It includes G10 currencies: AUD, CAD, CHF, DKK, EUR, GBP, JPY, NOK, NZD, SEK; emerging marketcurrencies: CZK, HUF, ILS, ISK, PLN, RUB, TRY, ZAR; Asian currencies: HKD, KRW, MYR, PHP, SGD, THB;Latin American currencies: BRL, CLP, COP, MXN, PEN; and Middle Eastern currencies: JOD, KWD.

4

We form currency portfolios sorted on the previous interest rate and track the return of buying the

top decile high interest rate currencies and selling the bottom decile low interest rate currencies.

We denote this 'high minus low' HML carry trade portfolios.

To assess the contribution of spot exchange rates and interest rate di�erentials to currency mo-

mentum returns (Menkho� et al. 2012b), we also calculate the monthly logarithm changes of spot

rates.

∆skt+1 = skt+1 − skt (1)

Note that skt+1 is denoted as foreign currency unit per US dollar; a positive number of ∆skt+1

suggests appreciation of the US dollar and depreciation of foreign currencies during the period

[t, t+ 1].

2.3 Currency momentum returns

In each month t, we rank currencies according to their cumulative lagged excess returns from t−fto t − 1, for di�erent formation periods f = 1, 3, 6, 9, 12 months. All currencies are then grouped

into decile portfolios and these portfolios are held for h = 1, 3, 6, 9, 12 months. Assuming investors

liquidate their positions every month, we track the return di�erence between top decile winner

portfolio and bottom decile loser portfolio as the 'winner minus loser' momentum strategy and

denote it as Mom(f, h) for di�erent formation period f and holding period h 5.

[Table 1 about here]

The left-hand panel of Table 1 shows the annualized excess return of our momentum portfolio

('winner minus loser') for di�erent combinations of formation f and holding periods h from 1 to

12 months. We also report in brackets the t-statistic based on Newey-West standard errors, the

sample standard deviation, the skewness and the Sharpe ratio. Momentum strategies provide a

signi�cant positive return with the highest being 5.96% for Mom(9,3) and a Sharpe ratio of 0.93

for Mom(6,6).6

5Following Menkho� et al. (2012b) we do not use the equity momentum portfolio convention where the mostrecent month is not considered in the formation period to avoid short-term reversal (see for example, Jegadeesh &Titman (1993), Fama & French (1996), Daniel & Moskowitz (2016)). Indeed foreign exchange markets su�er lessfrom liquidity issues (Asness et al. 2013).

6Menkho� et al. (2012b) �nd higher return and Sharpe ratios (9.46% per annum with Sharpe ratio 0.95) butthey use a di�erent time-span which does not include the period of �nancial crisis.

5

We observe that, as the holding period h increases, currency momentum returns gradually de-

clines. Thus, momentum returns �rst increase and then decline with the formation period f . This

result is di�erent from what is reported by Menkho� et al. (2012b) who �nd a decreasing currency

momentum return with longer formation period f . Currency momentum returns are mostly neg-

atively skewed. This result is in line with the equity momentum literature; Daniel & Moskowitz

(2016) show that equity momentum strategies experience a huge loss during the recovery period

from a �nancial crisis.

In the right-hand panel of table 1, we assess the contribution of spot rates to momentum excess

return. We follow Menkho� et al. (2012b) to report negative of the equation 1 that re�ect an

appreciation of foreign currencies. The spot rate changes show a continuity pattern as most

annualized mean returns are positive, thus spot rate does contribute to momentum strategies.

However, compared with currency excess returns, the contribution of the spot rate is smaller and

less signi�cant in most cases.

Even though the Sharpe ratio is the highest for 6-month holding period strategies, the 1-month

holding period strategy is more stable across the di�erent formation periods. We follow the conven-

tion in the literature and focus on the 1-month holding period strategy: Mom(6,1) and Mom(9,1).

We plot the cumulative excess return of Mom(6,1) and Mom(9,1) in �gure 2 along with the dollar

risk factor (DOL) and US equity market excess return (Mkt − rf) for comparison. The shaded

areas are the period �nancial crisis corresponding to the bursting of the dot-com bubble (in 2001),

the subprime debt crisis (in 2008) and the European sovereign debt crisis (in 2012).

From �gure 2, currency momentum strategies underperform the US-equity market portfolio but

earn a higher return than DOL. Large drawdowns of currency momentum strategies can be viewed

in the subprime debt crisis and European sovereign debt crisis.

3 Momentum crash and the currency market

It has been well documented in equity literature that momentum portfolios are subject to occasional

large losses. For example, Daniel & Moskowitz (2016) show that momentum crash is largely due

to time-varying beta, which introduces asymmetry into the momentum portfolio payo�. As a

consequence, they carry positive loading on factors which, in the past, had a positive realisation

and negative loading on factors which had a negative realisation. This dynamic induces a pattern

in the momentum strategy betas and leads to an asymmetric payo� in the bear market. That is,

6

momentum strategy earns a moderate pro�t in bear market conditions but faces signi�cant losses

when the market recovers. The currency market is one of the largest markets and yet it is largely

unregulated. It is interesting to investigate whether this feature is also a characteristic of this

market and shed some light on the economic sources driving it. This next section will look at this

critical issue.

3.1 Time-varying betas of currency momentum strategies

To link the idea of asymmetric momentum portfolio payo� to bear markets, we start with a simple

graphic analysis showing the relationship between currency momentum betas and the carry trade

factor HML. Figure 3 shows the dynamic betas estimated using rolling 48-month regressions.7

It is clear from �gure 3 that currency momentum risk exposure to carry trade changes over time.

During the period of �nancial crisis, currency momentum betas are more volatile. The momentum

beta to HML factor increases during the dot-com crisis and European sovereign debt crisis but

decreases in the subprime debt crisis period. Meanwhile, outside the �nancial crisis period betas

also change signi�cantly. For example, the beta exposure to HML has been gradually increasing

from 2016 until the end of the sample. In this paper we claim that it is this time-varying beta

pattern that introduces asymmetry in the momentum portfolio and leads to crash risk. In the next

sections, we shall investigate this behaviour and its economic drivers in more detail.

3.2 The econometric strategy

In this section, we explain our econometric strategy. We link momentum portfolio return to carry

trade via the carry trade factor (HML) of Lustig et al. (2011). HML is the return di�erence between

highest interest rate portfolio and lowest interest rate portfolio. Burnside et al. (2011) show that

DOL and HML together fail to explain currency momentum returns. We show in the next sections

that a possible explanation for this could be that the models used do not consider time-varying

risk exposure. In this paper, we follow Daniel & Moskowitz (2016) and set the dependent variable

as the return of currency momentum strategy MOM(6,1) or MOM(9,1), denoted as RMom. We

�rst estimate the full sample unconditional beta to the HML by performing a simple univariate

regression.

7Dynamic betas to HML are estimated jointly with DOL in a two-variable regression: RMomt = α0 + β0 ×

RDOLt + γ0 × RHML

t + εt. Where α0 and βm0 are the regression coe�cients; and εt is the error term. R

DOLt and

RHMLt are factor returns for DOL and HML.

7

RMomt = α0 + γ0 ×RHML

t + εt (2)

Where RMomt is the currency momentum return; RHML

t is the carry trade factor return; α0 and γ0

are the regression coe�cients; εt is the error term.

The second regression (equation 3) �ts a conditional regression with a bear HML indicator variable

IHMLB,t−1 that equals 1 if cumulative HML returns in the past six months are negative and 0 otherwise.

This model helps us to test if there is a signi�cant beta change (γB) and return level change (αB)

in bear HML conditions.

RMomt = α0 + αHML

B × IHMLB,t−1 + (γ0 + γB × IHML

B,t−1)RHMLt + εt (3)

In the third regression (equation 4), we add a factor return indicator IHMLU,t which equals to1 if the

contemporaneousRHMLt is positive and 0 otherwise. This regression is designed to test whether

there is signi�cant beta change (βB,U) when carry trade rebounds from a bear market condition.

This model is also used by Henriksson & Merton (1981) to assess fund managers' market timing

ability.

RMomt = α0 + αHML

B × IHMLB,t−1 + (γ0 + IHML

B,t−1(γB + IHMLU,t × γB,U))RHML

t + εt (4)

3.3 Is carry trade important to explain momentum crash?

This section discusses the key results. Table 2 shows the OLS estimators, the Newey-West t-

statistics in parenthesis and the adjusted R2 for equations 2, 3 and 4.

We start by considering the unconditional model and �t the currency momentum risk exposure to

carry trade. The risk coe�cientγ0 is small and insigni�cant for both MOM(6,1) and MOM(9,1).

This result is consistent with Burnside et al. (2011) and Menkho� et al. (2012b) who �nd an

insigni�cant correlation between currency carry trade and currency momentum returns.

In the second model, we add the interaction terms which re�ect bear HML market conditionIHMLB,t−1

in the slope and intercept coe�cients. Indicator variable IHMLB,t−1 splits the market into two states:

bear carry trade market (when IHMLB,t−1=1) and bull carry trade market (when IHML

B,t−1=0). The second

column of table 2 shows that momentum strategy has a signi�cant decreasing risk exposure (γB)

in a bear market carry trade state while in a bull carry trade state (i.e. when the carry trade

8

strategy recovers from losses), currency momentum beta is positively exposed to carry trade (i.e.

it su�ers signi�cant losses).

In the �nal speci�cation, the bear market is further split into contemporaneous up/down carry

trade states by introducing IHMLU,t . In the third column of table 2, the betas to HML of currency

momentum in a bull HML market (γ0) are still signi�cantly positive as in the second model.

The time-varying exposure causes the momentum strategies to have a written call option-like

payo� in the bear carry trade state. That is, when carry trade portfolio return decreases, the

momentum earns little; when the carry trade portfolio return increases, the momentum strategy

su�ers signi�cant losses. 8


3.4 Can the DOL factor explain momentum crash?

The results above show that carry trade and momentum strategy are linked in a bear market and,

as for the equity market, fx momentum strategy payo� re-call that of an option, and this type of

payo� can explain momentum crash. Daniel & Moskowitz (2016) investigated this issue for the

equity market. In the next sections, we run a battery of robustness checks to further investigate

the economic sources driving the �option-like� payo� for fx momentum portfolios. We start running

a horse race between HML and DOL to empirically assess their joint contribution. The collective

e�ects of the two currency factors are indeed interesting. We de�ne the market state DOL dummy

variables IDOLB,t−1 and IDOLU,t . IDOLB,t−1 = 1 if the cumulative DOL factor return in the past six months

is negative and 0 otherwise. IDOLU,t = 1 if the contemporaneous factor returnRDOLt is positive and

0 otherwise. In this section, we �rst test the unconditional models for DOL and HML:

RMomt = α0 + β0 ×RDOL

t + γ0 ×RHMLt + εt

Secondly, we test the models when all interaction terms associated with DOL have been added to

equations 3 and 4.

8The intercepts α0 in all three models of table 2 are signi�cant with low adj. R2s which possibly suggests amissing variable. However, our main objective here is to investigate the dynamic risk patterns to carry trade factor.

9

RMomt = α0 + αDOLB × IDOLB,t−1 + αHML

B × IHMLB,t−1

+ (β0 + IDOLB,t−1(βB + βB,U × IDOLU,t ))RDOLt

+ (γ0 + γB × IHMLB,t−1)R

HMLt + εt

RMomt = α0 + αDOLB × IDOLB,t−1 + αHML

B × IHMLB,t−1

+ (β0 + IDOLB,t−1(βB + βB,U × IDOLU,t ))RDOLt

+ (γ0 + IBHMLt−1 (γB + γB,U × IHML

U,t ))RHMLt + εt

Estimation results are reported in Table 3, with the Newey-West t-statistics and the adjusted

time series R2. We �nd results consistent with Daniel & Moskowitz (2016) in terms of currency

momentum's negative exposure to DOL. The momentum betas to carry trade are small and posi-

tive. In model 2 and model 3, dynamic risk patterns of momentum betas to HML is robust even

if we include DOL. Currency momentum strategies are negatively exposed to carry trade when

carry trade recovers from previous drawdowns. Overall the inclusion of DOL cannot explain the

asymmetric payo� pattern and momentum crash that we have observed in the previous section.9


3.5 Hedging the unconditional risk exposure

In this section we show that excess momentum return is mainly driven by the dynamic risk pattern

to HML portfolio and use risk-adjusted currency momentum returns ex-post information as in

(Grundy & Martin 2001) or ex-ante information as in (Daniel & Moskowitz 2016). Under a two

factor model, the following regression is used to estimated the dynamic risk exposure at time t:

RMomτ = α0 + β0,t ×RDOL

τ + γ0,t ×RHMLτ + ετ

If τ = t, t − 1, t − 2, t − 3, ... then ex-ante information is used. If τ = t, t + 1, t + 2, t + 3, ... ,

the ex-post information is used. We run the regression each time to dynamically estimate the risk

9βB,U is not signi�cant.

10

exposure β0,t and ˆγ0,t. The risk adjusted momentum returns at time t is calculated as RMomt −β0,t×

RDOLt − ˆγ0,t × RHML

t . We use the 36/5 months ex-ante or ex-post information to form the risk

adjusted portfolios based on strategy Mom(6,1) and Mom(9,1). The annualized return, t-statistics,

annualized standard deviation, sample skewness and Sharpe ratios are reported in Table 4.


None of the risk-adjusted portfolios outperforms the strategies in table 1. Most of the strategies in

table 4 do not have signi�cant positive returns. One exception is ex-ante betas adjusted Mom(6,1)

based on 36-month rolling data, but the Sharpe ratio of this strategy is decreasing due to increasing

standard deviation. This section further con�rms that the dynamic beta pattern to HML factor

reported in the previous sections is the main driver of the momentum portfolio return.

3.6 Currency momentum and HML volatility

We pointed out that currency momentum strategy behaves like a written call-option to HML factor

in a bear HML market. One consequence of this result is that due to the dynamic risk exposure, we

would expect the return from momentum strategy to be negatively correlated with the volatility of

the HML factor when carry trade experiences losses (IHMLB,t−1=1) but no correlation with carry trade

when the market rebounds (IHMLB,t−1=0).

10 Due to the positive correlation between volatility of DOL

and HML, we would also expect a similar pattern to be observed on the volatility of DOL.11 We

�rst model the conditional volatility of HML and DOL by using ARMA(1,1)-GARCH(1,1) with

Normal error term. The estimation results are reported in Table 5.


The associated ARCH and GARCH coe�cients are all signi�cant, which indicates that an ARMA(1,1)-

GARCH(1,1) could properly model the volatility. From this model, the implied in-sample con-

ditional volatility h2t,DOL and h2t,HML is obtained, along with the down-HML indicator IHMLB,t−1 .We

specify three regression models to investigate the momentum return and currency market factor

volatility. The empirical results are listed in table 6.


10The higher the volatility, the higher the call option value the lower the expected return of currency momentumportfolio.

11Variance of DOL is the variance of HML plus the variance of middle portfolios and all the covariance terms.

11

In the �rst model, we regress returns from Mom(6,1) and Mom(9,1) portfolios to the conditional

variance of DOL, h2t,DOL and the interaction with IHMLB,t−1, R

Momt = α0+(κo+κB×IHML

B,t−1)×h2t,DOL+εt.

In the second model the conditional variance is replaced by h2t,HML : RMomt = α0 + (λo + λB ×

IHMLB,t−1) × h2t,HML + εt. The �rst two colums of Table 6 show that the estimated coe�cients κB and

λB are negative but κ0 and λB are not signi�cantly di�erent from 0. Thus, only when the previous

6-month HML factor return is negative do momentum portfolios behave like written call options.

When the previous 6-month HML return is positive, there is no signi�cant correlation between

currency momentum return and factor volatility. In the last model of Table 6, the two conditional

volatilities are added together RMomt = α0+(κo+κB×IHML

B,t−1)×hDOLt +(λo+λB×IHMLB,t−1)×hHML

t +εt.

In this case, only the coe�cient λB is signi�cant, probably due to the colinearity issue.

4 Economic implication

The main results in the previous section indicate that momentum crash is predictable. In this

section we propose two modi�ed currency momentum strategies to mitigate momentum crash.

Both strategies are implementable in practice and use results from momentum risk analysis to

adjust portfolio weights. We show that hedged currency momentum strategies outperform the

momentum strategy discussed in the previous sections.

4.1 Mitigating crash risk strategy

The simplest way to mitigate currency momentum crash is to close the position when the previous

6-month cumulative HML return is negative. Since the asymmetric payo� or momentum crash is

conditioned on IHMLB,t−1 < 0, we modify the currency momentum strategy Mom(6,1) and Mom(9,1)

by allocating zero weight at time t when IHMLB,t−1 = 1. This strategy is denoted as mitigating crash

risk strategy (MCR). Note that the information needed to make the investment decision is ex-ante.

4.2 Dynamic weighting strategy

To further implement our strategy as, although it outperforms the momentum strategies discussed

in the previous sections, it also misses the investment opportunity as momentum crash happens

(i.e. when IHMLB,t−1 = IHML

U,t = IDOLU,t = 1). We employ the dynamic weighting strategy (DWS) of

12

Daniel & Moskowitz (2016). To maximize the in-sample unconditional Sharpe ratio, the optimal

weight for risky assets at time t− 1 is:

wt−1 = (1

2λ)µt−1σ2t−1

Where µt−1 ≡ Et−1[RMomt ] is the conditional expected return given time t− 1 information. σ2

t−1 ≡Et−1[(R

Momt − µt−1)

2] is the conditional expected variance of the coming month given time t − 1

information. λ is a time-invariant scalar that controls the unconditional risk. When expected

returns are constant in proportion to expected variance overtime, this strategy is equivalent to the

constant volatility strategy of Barroso & Santa-Clara (2015).

To work out the dynamic weight, the conditional variance σ2t−1 is proxied by the previous 72-month

sample variance of Mom(6,1) and Mom(9,1). Following the insight that currency momentum is

e�ectively a written call option, the expected return µt−1 is then estimated in two stages: i) we em-

ployed a dynamic 36-month rolling window ARMA(1, 1)−GARCH(1, 1) to make one-step-ahead

forecasts for the factors' conditional variance h2t−1,DOL and h2t−1,HML given t − 1 information; ii)

we use the insights of the �rst and second regressions in table 6 to estimate conditional expected

return µt−1 in which the regressions relate currency momentum to factor conditional variances

and the bear carry trade market indicator. One di�erent thing is that we replace the contempo-

raneous variance of h2t,DOL and h2t,HML by the one-step-ahead forecast from the �rst stage. Due

to the colinearity issue between conditional variance of DOL and HML, expected return µt−1 is

estimated separately by using variance of DOL and HML respectively. Meanwhile, the conditional

expectation cannot be estimated through coe�cients from the full sample regression as it was in

table 6. A dynamic regression is performed in a 36-month rolling window. That is, each time t,

we use the previous 36 months up to time t − 1 to get estimations of the parameter set [α0, λo,

λB, κ0, κB]. Thus this strategy is subject to information at time t − 1. λ is chosen such that

the annualized standard deviation of this strategy is 19%. Hence, two strategies, namely dynamic

weighting strategy inferred by DOL (DWSD) and dynamic weighting strategy inferred by HML

(DWSH), are proposed.

This strategy exploits the momentum crash. When IHMLB,t−1 = 0, factors' conditional variances do

not correlate with momentum return, which results in around 0 estimate for µt−1 and thus 0 for

wt−1. When IHMLB,t−1 = 1, momentum returns are negatively correlated with the factor's conditional

variance. High volatility of HML or DOL suggests a large negative value of wt−1. When currency

crashes, a large positive return would be achieved.

13


4.3 Performance of momentum strategies

To make the long-short currency momentum strategies comparable with each other, we normalized

the in-sample annualized volatility to 19% by multiplying a time-invariant constant to weights.12

We compare the pro�tability of hedging crash risk and dynamic weighting strategies with the main

momentum strategy discussed in the previous sections, using a smaller sample from Nov. 2003 to

Feb. 2018 as the �rst 72 months have been used for a rolling estimate of the conditional returns

for the dynamic weighting strategy. Table 8 shows the annualized average return, t-statistic based

on Newey-West standard error, annualized standard deviation, sample skewness and annualized

Sharpe ratio. In �rst panel of Table 8, no transaction costs are considered. The second and third

panels report the statistics with 50% of quoted spreads and full quoted spreads, respectively.13 The

average return and Sharpe ratio from the hedge momentum strategy are signi�cantly improved.

The sample skewness is around 0 for MCR strategy and positive for DWS, which indicates that

the currency momentum crash has been hedged out. Unlike the momentum strategies discussed

in the previous sections, the hedged strategies show signi�cant positive returns after transaction

costs.


Figure 4 plots the cumulative return of the plain currency momentum strategy, the MCR strategy

and dynamic weighting strategy for Mom(6,1) and Mom(9,1).

5 Conclusion

We show that, in the currency market, momentum strategies are subject to dynamic (beta) risk

exposure to currency market speci�c pricing factors, for example the carry trade factor HML.

Momentum payo� reseambles the payo� of a written call option in the bear market: when carry

trade crashes, momentum strategy gains a little. When carry trade recovers from previous crash,

12To achieve the same level of returns and standard deviations in Table 8, the ex post multiplier is required. Ourstandardized strategies serve the purpose of showing the risk-return di�erence between strategies.

13Lyons et al. (2001) suggest that full quoted bid-ask spread overestimates the e�ective spread and transactioncost. Following Goyal & Saretto (2009), 50% of full quoted spread is a proper estimate for transaction costs oncurrency market.

14

momentum strategy crashes. We report this empirical fact for the fx market. Thus, due to

this asymmetric payo� pattern, under a down-HML market, currency momentum strategies work

e�ectively as a written call option. In so doing we report robust evidence that, in the bear market,

momentum and carry trade strategies are linked. We use this empirical insight and propose two

strategies to mitigate momentum crash risk.

15

References

Asness, C. S., Moskowitz, T. J. & Pedersen, L. H. (2013), `Value and momentum everywhere', The

Journal of Finance 68(3), 929�985.

Barroso, P. & Santa-Clara, P. (2015), `Momentum has its moments', Journal of Financial Eco-

nomics 116(1), 111�120.

Brunnermeier, M. K., Nagel, S. & Pedersen, L. H. (2008), `Carry trades and currency crashes',

NBER macroeconomics annual 23(1), 313�348.

Burnside, C. (2011), Carry trades and risk, Technical report, National Bureau of Economic Re-

search.

Burnside, C., Eichenbaum, M. & Rebelo, S. (2011), `Carry trade and momentum in currency

markets', Annual review of �nancial economics 3, 511�535.

Carhart, M. M. (1997), Òn persistence in mutual fund performance', The Journal of �nance

52(1), 57�82.

Chan, K., Hameed, A. & Tong, W. (2000), `Pro�tability of momentum stragegies in the interna-

tional equity markets', Journal of �nancial and quantitative analysis 35(2), 153�172.

Cooper, M. J., Gutierrez Jr, R. C. & Hameed, A. (2004), `Market states and momentum', The


Daniel, K. & Moskowitz, T. J. (2016), `Momentum crashes', Journal of Financial Economics

122(2), 221�247.

Fama, E. F. & French, K. R. (1996), `Multifactor explanations of asset pricing anomalies', The

journal of �nance 51(1), 55�84.

Goyal, A. & Saretto, A. (2009), `Cross-section of option returns and volatility', Journal of Financial

Economics 94(2), 310�326.

Grundy, B. D. & Martin, J. S. M. (2001), Ùnderstanding the nature of the risks and the source

of the rewards to momentum investing', The Review of Financial Studies 14(1), 29�78.

Henriksson, R. D. & Merton, R. C. (1981), Òn market timing and investment performance. ii.

statistical procedures for evaluating forecasting skills', Journal of business pp. 513�533.

16

Jegadeesh, N. & Titman, S. (1993), `Returns to buying winners and selling losers: Implications for

stock market e�ciency', The Journal of �nance 48(1), 65�91.

Jostova, G., Nikolova, S., Philipov, A. & Stahel, C. W. (2013), `Momentum in corporate bond

returns', The Review of Financial Studies 26(7), 1649�1693.

Korajczyk, R. A. & Sadka, R. (2004), Àre momentum pro�ts robust to trading costs?', The


Kothari, S. P. & Shanken, J. (1992), `Stock return variation and expected dividends: A time-series

and cross-sectional analysis', Journal of Financial Economics 31(2), 177�210.

Lesmond, D. A., Schill, M. J. & Zhou, C. (2004), `The illusory nature of momentum pro�ts',

Journal of �nancial economics 71(2), 349�380.

Lustig, H., Roussanov, N. & Verdelhan, A. (2011), `Common risk factors in currency markets',

The Review of Financial Studies 24(11), 3731�3777.

Lyons, R. K. et al. (2001), The microstructure approach to exchange rates, Vol. 12, MIT press

Cambridge, MA.

Menkho�, L., Sarno, L., Schmeling, M. & Schrimpf, A. (2012a), `Carry trades and global foreign

exchange volatility', The Journal of Finance 67(2), 681�718.

Menkho�, L., Sarno, L., Schmeling, M. & Schrimpf, A. (2012b), `Currency momentum strategies',

Journal of Financial Economics 106(3), 660�684.

Menkho�, L. & Taylor, M. P. (2007), `The obstinate passion of foreign exchange professionals:

technical analysis', Journal of Economic Literature 45(4), 936�972.

Mi�re, J. & Rallis, G. (2007), `Momentum strategies in commodity futures markets', Journal of

Banking & Finance 31(6), 1863�1886.

Okunev, J. & White, D. (2003), `Do momentum-based strategies still work in foreign currency

markets?', Journal of Financial and Quantitative Analysis 38(2), 425�447.

Rouwenhorst, K. G. (1998), Ìnternational momentum strategies', The Journal of Finance

53(1), 267�284.

Shen, Q., Szakmary, A. C. & Sharma, S. C. (2007), Àn examination of momentum strategies in

commodity futures markets', Journal of Futures Markets: Futures, Options, and Other Deriva-

tive Products 27(3), 227�256.

17

Stivers, C. & Sun, L. (2010), `Cross-sectional return dispersion and time variation in value and

momentum premiums', Journal of Financial and Quantitative Analysis 45(4), 987�1014.

18

Figure 1 � Cross-sectional sample size of currencies available. The sample period spans fromJan. 1997 to Mar. 2018

19

Figure 2 � Cumulative excess return of currency momentum strategiesMom(6, 1),Mom(9, 1),'Dollar risk factor' DOL and US value-weighted equity portfolio. The shaded areas indicatethe recent �nancial crisis which is the bursting of the dot-com bubble (from Jan. 2001 to Apr.2002); the subprime debt crisis (from Jan. 2008 to May 2009); and the European sovereigndebt crisis (from Jun. 2011 to Dec. 2012). The sample period starts from Jan. 1997 to Mar.2018.

20

Figure 3 � Dynamic carry trade risk exposure of two currency momentum strategies Mom(6,1)

and Mom(9,1) which are estimated by using a ex-ante rolling 48-month window. Note that dynamic

exposures to carry trade 'high minus low' HML are estimated jointly with DOL in a two-variable

regression. The shaded aeras indicate recent market drawdowns of the bursting of dot-com bubble

(from Jan. 2001 to Apr. 2002); the subprime debt crisis (from Jan. 2008 to May 2009); and the

European sovereign debt crisis (from Jun. 2011 to Dec. 2012).

21

Figure 4 � This �gure plots the cumulative return of mitigate crash strategies (MCR), dy-namic weighting strategies (DWS) and their base currency momentum strategies Mom(6,1)and Mom(9,1). The shaded aera correponds to the US subprime debt crisis and Europeansovereign debt crisis. The sample period starts from Nov. 2003 to Feb. 2018.

22

Table

1�Currency

Mom

entum

Returns

Currency

momentum

excess

return

Spotrate

changes

hh

f1

36

912

f1

36

912

Mean

2.90

2.78

1.52

1.54

1.45

4.46

3.55

1.84

1.22

1.07

1(1.56)

(2.24)

(1.85)

(1.86)

(2.05)

1(1.60)

(2.05)

(1.88)

(1.72)

(1.60)

Std.dev

10.25

6.52

4.67

3.54

3.15

11.98

6.87

4.40

3.30

3.08

Skewness

0.04

-0.15

0.35

-0.19

0.03

1.08

1.50

1.44

0.56

0.01

Sharperatio

0.28

0.43

0.32

0.43

0.46

0.37

0.52

0.42

0.37

0.35

Mean

4.36

2.26

2.03

2.41

1.55

4.99

2.10

1.37

1.10

0.39

3(2.16)

(1.41)

(1.51)

(1.81)

(1.30)

3(1.92)

(1.30)

(1.23)

(1.15)

(0.42)

Std.dev

11.23

6.53

4.70

3.78

3.47

12.65

6.49

4.33

3.49

3.17

Skewness

0.10

-0.09

-0.33

-0.24

-0.02

1.11

0.36

-0.10

-0.28

-0.29

Sharperatio

0.39

0.35

0.43

0.64

0.45

0.39

0.32

0.32

0.32

0.12

Mean

5.15

4.47

3.99

3.09

1.93

3.50

2.59

1.68

0.60

-0.31

6(2.37)

(2.36)

(2.25)

(1.93)

(1.36)

6(1.63)

(1.52)

(1.30)

(0.51)

(-0.26)

Std.dev

11.58

6.51

4.28

3.63

3.26

12.72

6.58

4.12

3.36

3.10

Skewness

0.08

-0.15

-0.58

-0.24

-0.15

0.97

0.32

0.06

0.01

-0.37

Sharperatio

0.44

0.69

0.93

0.85

0.59

0.28

0.39

0.41

0.18

-0.10

Mean

5.81

5.96

3.57

2.24

1.30

5.52

3.96

1.73

0.53

-0.58

9(2.25)

(2.68)

(1.82)

(1.36)

(0.90)

9(2.20)

(2.04)

(1.08)

(0.39)

(-0.46)

Std.dev

12.19

6.82

4.50

3.57

3.12

13.55

6.76

4.20

3.19

2.94

Skewness

-0.29

-0.23

-0.25

-0.17

0.02

0.80

0.22

-0.25

-0.33

-0.73

Sharperatio

0.48

0.87

0.79

0.63

0.42

0.41

0.59

0.41

0.16

-0.20

Mean

3.49

2.45

1.17

0.40

0.41

3.04

1.93

-0.02

-1.29

-1.42

12(1.44)

(1.23)

(0.65)

(0.26)

(0.29)

12(1.20)

(1.02)

(-0.01)

(-0.88)

(-1.07)

Std.dev

11.84

6.53

4.39

3.47

3.08

13.00

6.60

3.98

3.34

3.00

Skewness

-0.46

0.16

0.02

-0.08

-0.10

0.38

0.07

-0.18

-0.09

-0.35

Sharperatio

0.29

0.38

0.27

0.12

0.13

0.23

0.29

0.00

-0.39

-0.47

Note:Thistable

show

stheportfoliostatisitcsforcurrency

momentum

strategies.

Theleftpanel

reportstheannualized'winner

minusloser'

momentum

excess

return

fordi�erentform

ationperiodandholdingperiodin

1,3,6,9,12months.

Numbersin

bracketsare

t-statisticsbasedon

New

ey-W

eststandard

errors.Thepotfoliosamplestandard

deviations,Sharperatiosandskew

nessare

alsoreported

asfollow

s.Therightpanel

show

sthecoorespondingstatisticsforchanges

ofexchangerates.

23

Table 2 � Dynamic Exposures to HML

Coe�cient 1 2 3Mom(6,1) Mom(9,1) Mom(6,1) Mom(9,1) Mom(6,1) Mom(9,1)

α0 0.34 0.42 0.65 0.86 0.65 0.86(1.87) (1.88) (3.58) (4.30) (3.57) (4.29)

αHMLB -1.04 -1.50 1.02 0.56

(-2.06) (-2.80) (2.08) (0.95)γ0 0.10 0.08 0.25 0.20 0.25 0.20

(1.04) (0.75) (2.48) (2.13) (2.47) (2.13)γB -0.43 -0.37 0.37 0.43

(-1.79) (-1.63) (1.02) (1.44)γB,U -1.53 -1.53

(-3.73) (-4.22)

Adj.R2 0.01 0.00 0.07 0.07 0.14 0.13

Note: This table reports results of estimated coe�cients, t-statistics in the brackets and adjusted R2 for

three speci�cations of monthly times series regression.(1)RMom

t = α0 + γ0 ×RHMLt + εt;

(2)RMomt = α0 + αHML

B × IHMLB,t−1 + (γ0 + γB × IHML

B,t−1)RHMLt + εt;

(3)RMomt = α0 + αDOL

B × IHMLB,t−1 + (γ0 + IHML

B,t−1(γB + IHMLU,t × γB,U ))R

HMLt + εt.

The denpendent variables are monthly returns of momentum strategies Mom(6,1) and Mom(9,1), respec-

tively. The independent variables are: an intercept α0; the ex-ante down-HML indicator IHMLB,t−1; the

contemporaneous HML factor return RHMLt ; the contemporaneous up-HML indicator, IHML

U,t ; and inter-

action terms. The sample runs from December 1997 to Feburary 2018.

24

Table 3 � Collective E�ects on Currency Market Pricing Factors


α0 0.35 0.42 0.33 0.49 0.35 0.51(1.93) (1.87) (1.37) (1.97) (1.48) (2.11)

αDOLB 0.52 1.02 0.38 0.88(1.23) (1.87) (0.91) (1.68)

αHMLB -0.53 -0.98 0.76 0.27

(-1.37) (-2.30) (1.79) (0.50)β0 -0.38 -0.37 0.34 0.36 0.32 0.34

(-2.51) (-2.08) (2.14) (1.79) (2.19) (1.88)βB -1.15 -0.97 -1.12 -0.94

(-3.46) (-2.12) (-3.39) (-2.08)βB,U -0.57 -0.98 -0.43 -0.84

(-1.18) (-1.44) (-0.92) (-1.30)γ0 0.17 0.14 0.33 0.27 0.33 0.27

(1.69) (1.36) (3.49) (2.80) (3.43) (2.75)γB -0.52 -0.44 -0.01 0.06

(-3.05) (-2.42) (-0.02) (0.23)γB,U -0.99 -0.96

(-2.79) (-2.85)

Adj.R2 0.30 0.27 0.30 0.28 0.32 0.30

Note: This table reports results of estimated coe�cients, t-statistics in the brackets and adjusted R2 for

three speci�cations of monthly times series regression.(1)RMom

t = α0 + β0 ×RDOLt + γ0 ×RHML

t + εt;(2)RMom

t = α0 + αDOLB × IDOL

B,t−1 + αHMLB × IHML

B,t−1 + γ0 ×RHMLt + (β0 + IDOL

B,t−1(βB + IDOLU,t × βB,U ))R

DOLt + (γ0 +

γB × IHMLB,t−1)R

HMLt + εt;

(3)RMomt = α0 + αDOL

B × IDOLB,t−1 + αHML

B × IHMLB,t−1 + γ0 ×RHML

t + (β0 + IDOLB,t−1(βB + IDOL

U,t × βB,U ))RDOLt + (γ0 +

IHMLB,t−1(γB + IHML

U,t × γB,U ))RHMLt + εt.

The dependent variables are monthly returns of bottom ten percent losser portfolio for momentum strate-

gies Mom(6,1) and Mom(9,1), respectively. The independent variables are: an intercept α0; the ex ante

down-DOL indicator IDOLB,t−1; the ex-ante down-HML indicator IHMLB,t−1; the contemporaneous DOL factor

return RDOLt ; the contemporaneous HML factor return RHMLt ; the contemporaneous up-DOL indicator,

IDOLU,t ; the contemporaneous up-HML indicator, IHMLU,t ; and interaction terms. The sample runs from

December 1997 to Feburary 2018.

25

Table 4 � Dynamic Risk Hedged Portfolios

ex-ante estimation betas5-month rolling 36-month rolling

Mom(6,1) Mom(9,1) Mom(6,1) Mom(9,1)Mean 0.00 -2.18 4.64 4.45

(0.00) (-0.69) (1.81) (1.46)Std. dev 52.58 50.99 38.26 40.35Skewness -0.17 -0.22 -0.14 -0.00Sharpe ratio 0.00 -0.04 0.12 0.11

ex-post estimation betas5-month rolling 36-month rolling

Mom(6,1) Mom(9,1) Mom(6,1) Mom(9,1)Mean -4.88 -2.72 0.32 -0.97

(-2.37) (-1.36) (0.17) (-0.49)Std. dev 28.38 27.71 31.57 32.46Skewness 0.08 -0.14 0.07 -0.34Sharpe ratio -0.17 -0.10 0.01 -0.03

Note: This table reports the annualized return, t-statistics based on Newey-West standard errors in brack-

ets, annualized standard deviation, sample skewness and Sharpe ratios of the risk adjusted portfolio based

on Mom(6,1) and Mom(9,1). For comparison, the corresponding statistics for Mom(6,1) and Mom(9,1) are

listed in the �rst column. Note that annualized return and standard deviation are reported in percentages.

26

Table 5 � ARMA(1,1)-GARCH(1,1) Model for Currency Factors

ARMA(1,1)-GARCH(1,1)DOL HML

Parameters Coe�cients T-stats Parameters Coe�cients T-statsC 0.10 (0.67) C 0.10 (0.55)AR1 0.52 (0.61) AR1 0.88 (4.25)MA1 -0.43 (-0.46) MA1 -0.82 (-3.06)K 0.01 (1.43) K 0.02 (2.06)ARCH1 0.15 (1.96) ARCH1 0.12 (2.83)GARCH1 0.57 (2.41) GARCH1 0.69 (7.36)

Note: This table reports estimated coe�cients and t-statistics in brackets of ARMA(1,1)-GARCH(1,1)

models for currency market pricing factors DOL and HML.

27

Table 6 � Currency Momentum Return and Factor Volatility


α0 0.03 0.43 0.19 0.61 0.17 0.68(0.05) (0.59) (0.35) (1.10) (0.25) (0.92)

κo 19.13 12.62 6.56 3.50 -1.11 -3.07(1.19) (0.68) (1.24) (0.62) (-0.06) (-0.13)

κB -32.61 -38.40 -13.84 -15.44 7.18 4.04(-3.16) (-3.12) (-3.75) (-3.17) (1.25) (0.54)

λo 8.79 -1.71(0.42) (-0.06)

λB -17.09 -14.70(-2.26) (-1.49)

Adj.R2 0.03 0.05 0.04 0.06 0.04 0.05

Note: This table reports results of the estimated coe�cients, t-statistics in brackets and adjusted R2 for

four speci�cation of monthly times series regression.(1)RMom

t = α0 + (κo + κB × IHMLB,t−1)× hDOL

t + εt(2)RMom

t = α0 + (λo + λB × IHMLB,t−1)× hHML

t + εt(3)RMom


t + (λo + λB × IHMLB,t−1)× hHML

t + εtThe dependent variables are monthly returns of momentum strategies Mom(6,1) and Mom(9,1), respec-


contemporaneous conditional volatility of DOL hDOLt ; the contemporaneous conditional volatility of HML

hHMLt . The sample runs from December 1997 to Feburary 2018.

28

Table 7 � Forecasting Conditional Momentum Returns

Coe�cient 1 2Mom(6,1) Mom(9,1) Mom(6,1) Mom(9,1)

α0 0.33 0.32 α0 0.39 0.44(1.61) (1.36) (1.90) (1.83)

κo 0.09 0.11 λo 0.04 0.02(5.76) (6.26) (0.99) (0.38)

κB -0.13 -0.14 λB -0.11 -0.12(-7.72) (-6.11) (-2.26) (-1.79)

Adj.R2 3.15 3.66 -0.18 -0.07

Note: This table reports results of the estimated coe�cients, t-statistics in the brackets and adjusted R2

for four speci�cation of monthly times series regression.(1)RMom


t−1 + εt;

(2)RMomt = α0 + (λo + λB × IHML

B,t−1)× hHMLt−1 + εt.

The dependent variables are monthly returns of momentum strategies Mom(6,1) and Mom(9,1), respec-


ex-ante conditional volatilities of DOL and HMLhDOLt−1 , hHML

t−1 which are from 1-step ahead forecast based

on ARMA(1,1)-GARCH(1,1).

29

Table 8 � Optimized Momentum Strategies

Mom(6,1) MCR(6,1) DWS(6,1) Mom(9,1) MCR(9,1) DWS(9,1)

No transaction cost appliedMean 4.80 11.60 15.10 3.10 13.55 10.39

(1.05) (2.53) (2.69) (0.61) (2.99) (2.28)Std.dev 19.00 19.00 19.00 19.00 19.00 19.00Skewness -0.55 -0.06 5.00 -0.47 0.00 2.63Sharpe ratio 0.25 0.61 0.79 0.16 0.71 0.55

Transcation cost 50% of full quoted bid-ask spread appliedMean 2.01 9.04 14.75 0.51 11.12 9.81

(0.44) (2.00) (2.61) (0.10) (2.48) (2.12)Std.dev 19.00 19.00 19.00 19.02 19.10 19.00Skewness -0.57 -0.13 4.87 -0.49 -0.07 2.23Sharpe ratio 0.11 0.47 0.78 0.03 0.58 0.52

Transcation cost full quoted bid-ask spread appliedMean -0.78 6.37 14.38 -2.06 8.60 9.21

(-0.17) (1.44) (2.53) (-0.40) (1.95) (1.96)Std.dev 19.00 19.00 19.00 19.00 19.00 19.00Skewness -0.58 -0.20 4.74 -0.51 -0.13 1.81Sharpe ratio -0.04 0.33 0.76 -0.11 0.45 0.48

Note: This table reports results of the annualized average return, t-statistics based on Newey-West stan-

dard errors in brackets, annualized sample standard deviation, skewness and Sharpe ratio for plain currency

momentum strategies Mom(6,1) and Mom(9,1), and optimized momentum strategies 'MCR' and 'DWS'

based on Mom(6,1) and Mom(9,1). The �rst panel shows the results without transaction costs. The

second panel shows the results with 50% of full quoted bid-ask spread. The third panel shows the results

with full bid-ask spread. Data sample starts from December, 2003 to Feb 2018.

30

can we predict currency momentum crashes?strategies. in particular, when carry trade is recovering...

Documents