spillovers of currency carry trade returns, market risk sentiment, and u.s. market returns

North American Journal of Economics and Finance 26 (2013) 197– 216

Contents lists available at ScienceDirect

North American Journal ofEconomics and Finance

Spillovers of currency carry trade returns,market risk sentiment, and U.S. market returns

Hsiu-Chuan Lee ∗, Shu-Lien Chang

Department of Finance, Ming Chuan University, No. 250, Sec. 5, N. Rd. ZhongShan, Taipei, Taiwan

a r t i c l e i n f o

Article history:Received 14 May 2013Received in revised form 7 October 2013Accepted 9 October 2013

JEL classification:E40F30G15

Keywords:Currency carry trade marketsSpillover effectsMarket risk sentimentGeneralized VAR modelMarkov-switching model

a b s t r a c t

This paper examines the link between spillovers of currency carrytrade returns and U.S. market returns. Following Tse and Zhao(2012), this paper hypothesizes that the magnitude of spilloversof currency carry trade returns is positively correlated with mar-ket risk sentiment and, therefore, has an impact on market returns.Using the G10 currencies and S&P 500 index futures, the empiri-cal results present a high magnitude of spillover effects of currencycarry trade markets. The empirical findings also show a significantlypositive relationship between spillovers of currency carry tradereturns and subsequent market returns. Furthermore, the resultsindicate that this relationship is stronger in bear markets than inbull markets. Finally, our findings show that spillovers of currencycarry trade returns significantly affect the subsequent transitionprobabilities of market returns.

© 2013 Elsevier Inc. All rights reserved.

1. Introduction

A large volume of research has focused on the critical issue of uncovered interest rate parity (UIP).Tests of the efficiency of a foreign exchange market are typically based on an assessment of the relevantUIP. The UIP hypothesis postulates that the interest rate differential between two currencies shouldbe offset by the expected appreciation of the low-yielding currency. The empirical failure of the UIPoccurs when the currencies of countries whose interest rates are higher tend to appreciate, whichthereby demonstrates the rejection of the UIP hypothesis.1

∗ Corresponding author. Tel.: +886 2 2882 4564x2188; fax: +886 2 2880 9796.E-mail addresses: [email protected] (H.-C. Lee), [email protected] (S.-L. Chang).

1 The violation of the UIP hypothesis is also referred to as the “forward premium puzzle”.

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198 H.-C. Lee, S.-L. Chang / North American Journal of Economics and Finance 26 (2013) 197– 216

One strand of the literature has shown that the UIP hypothesis tends to hold over the long runor under fixed exchange-rate regimes. Lothian and Wu (2011) indicate that the UIP hypothesis holdsmuch better over the long-run than suggested by the evidence over short-run samples. Flood and Rose(1996) and Coleman (2012) provide evidence that the UIP hypothesis holds much better under fixedthan flexible exchange-rate regimes. Despite significant efforts to provide empirical support for theUIP hypothesis, its rejection has been documented in many studies. Previous literature suggests thatthe violation of the UIP hypothesis is precisely what makes currency carry trades profitable on average.Brunnermeier, Nagel, and Pedersen (2009), Clarida, Davis, and Pedersen (2009), Darvas (2009), Baillieand Chang (2011), and Tse and Zhao (2012), among others, show that the rejection of the UIP hypothesisis associated with currency carry trade returns.

Tse and Zhao (2012) explain that the failure of the UIP hypothesis that is associated with currencycarry trade returns can be attributed to investor risk appetite sentiment (or so-called market risksentiment).2 More specifically, Tse and Zhao (2012) suggest that the returns of currency carry tradesare positively correlated with investor risk appetite sentiment.3 In addition, Diebold and Yilmaz (2012)suggest that the degree of spillovers of asset returns might be associated with sentiment.4 Motivatedby the argument of Tse and Zhao (2012), this paper employs the approach suggested by Diebold andYilmaz (2012) to measure the magnitude of spillovers of currency carry trade returns, and hypothesizesthat these spillovers are positively associated with market risk sentiment. As documented by Frijns,Koellen, and Lehnert (2008), when market risk sentiment is higher (lower), investors have a greaterpreference for investing in (selling) risky assets. Accordingly, if the spillovers of currency carry tradereturns reflect market risk sentiment, it is likely that the total spillover index of currency carry tradereturns is positively correlated with subsequent market returns.

The purpose of this study is to take a fresh look at the relationship between currency carry tradereturns and the behavior of market returns. The contributions of this study are two-fold. First, thispaper examines whether the impact of spillovers of currency carry trade returns on subsequent marketreturns is asymmetric during bull and bear markets. Prior research has explored the impact of currencycarry trades on market returns (Cheung, Cheung, & He, 2012; Tse & Zhao, 2012).5 Using the Japaneseyen as the funding currency and the Australian dollar, British pound, Canadian dollar, New Zealanddollar, and Mexican peso as target currencies, Cheung et al. (2012) indicate that currency carry tradespositively affect stock market returns in target currency countries. Utilizing data from the G10 (Groupof ten countries) currencies, Tse and Zhao (2012) present that the returns of currency carry trades andfutures returns are positively correlated with no Granger-causality in either direction. To the best ofour knowledge, however, no study has been conducted on the influence of spillovers of currency carrytrade returns on market returns under bull and bear market regimes. This paper attempts to fill thisgap. Second, under the framework of nonlinear models, this study explores whether the increase inthe extent of spillovers of currency carry trade returns leads to a bullish market regime. Overall, theempirical findings of this study complement the previous literature by providing an additional linkbetween the spillovers of the currency carry trade markets and the behavior of market prices.

Following Tse and Zhao (2012), this paper uses the G10 currencies quoted against the U.S. dollarto examine the link between spillovers of currency carry trade returns and market returns. Becausethis study utilizes the U.S. as its domestic country, the S&P 500 futures index is employed as the proxyfor market prices.6 Our sample period covers January 3, 1994 to March 28, 2012. The empirical results

2 This paper uses “investor risk appetite sentiment” and “market risk sentiment” interchangeably to represent “investorsentiment regarding risk appetite”.

3 Burnside, Han, Hirshleifer, & Wang (2011) show that currency carry trade returns are indicative of investor overconfi-dence. More specifically, as indicated by Burnside et al. (2011), the failure of the UIP hypothesis can be attributed to investoroverconfidence on monetary policy, which increases currency carry trade profits.

4 As indicated by Diebold and Yilmaz (2012), the total spillover index of asset returns might be associated with the existenceof sentiment, e.g., contagion from panic selling or herd behavior.

5 Christiansen et al. (2011) show that a typical currency carry trade strategy is significantly and positively exposed to currentand lagged stock returns. Additionally, the exposure to the current and lagged stock market returns is much greater in turbulentthan in normal markets.

6 The empirical ability of U.S. financial indicators to predict excess foreign returns is well documented (see Galsband, 2012).Compared with stock indices, the information can be incorporated into futures prices fairly when the market experiences bullish

H.-C. Lee, S.-L. Chang / North American Journal of Economics and Finance 26 (2013) 197– 216 199

are summarized as follows. First, the magnitude of spillover effects from currency carry trade returnsis greater in bull markets than in bear markets. Second, spillovers of currency carry trade returnsGranger-cause market returns, but not vice versa. Third, the impact of spillovers of currency carrytrade returns on subsequent market returns is significantly positive, and this effect is stronger in bearmarkets than in bull markets. Finally, a higher magnitude of spillovers of currency carry trade returnsleads to a higher (lower) probability of bull (bear) markets.

The remainder of the paper is organized as follows. Section 2 develops testable hypotheses. Section3 describes the data and presents econometric models. Section 4 reports the empirical results. Finally,concluding remarks are presented in Section 5.

2. Testable hypotheses

This paper expects that the spillover effect of currency carry trade returns is positively associatedwith investor risk appetite sentiment. Tse and Zhao (2012) document that the (portfolio) returns ofcurrency carry trades positively reflect investor risk appetite sentiment. Baker, Wurgler, and Yuan(2012) provide evidence that sentiment may be contagious, implying that there are co-movementand spillover effects across countries for sentiment. Diebold and Yilmaz (2012) indicate that the totalspillover index of asset returns might be positively associated with the extent of sentiment. Takentogether, this paper hypothesizes that spillovers of the currency carry trade returns are positivelycorrelated with investor risk appetite sentiment. As suggested by Frijns et al. (2008), when the marketis bullish, investors are more willing to invest in risky assets, suggesting that investor risk appetitesentiment is higher in bull markets.7 Thus, if spillovers of currency carry trades returns positivelyreflect market risk sentiment, Hypothesis 1 is stated as follows:

Hypothesis 1. The magnitude of spillover effects of currency carry trade returns is greater in bullmarkets than in bear markets.

When market sentiment regarding risk appetites is higher (lower), investors have a greater pref-erence for investing in (selling) risky assets. As suggested by Tse and Zhao (2012), a high investor riskappetite sentiment induces investors to invest in stock markets and currency carry trades, and a lowinvestor risk appetite sentiment results in selling stocks and unwinding carry trades. More specifi-cally, as documented by Frijns et al. (2008), when the sentiment with regard to risk appetites is high,investors have a preference for investing in risky assets. By contrast, a low investor risk appetite sen-timent results in selling stocks. Accordingly, if an increase in the total spillover index for currencycarry trade returns reflects an increase in the investor risk appetite sentiment, the change in the totalspillover index is positively correlated with subsequent market returns. Thus, Hypothesis 2 states asfollows:

Hypothesis 2. A change in the spillovers of currency carry trade returns is positively correlated withsubsequent market returns.

As indicated by Chen (2011), financial constraints are more likely to bind investors in bear markets.Substantial financial constraints can greatly decrease investor risk appetite sentiment. Therefore, whenmounting fears of liquidation squeeze the stock market, a low investor risk appetite sentiment mayhave a greater impact on stock returns during bear markets. Moreover, Chen (2011) suggests that, inprospect theory, investors are more concerned about market downturns than upturns, in part becauseof loss aversion, i.e., the strong tendency to prefer loss avoidance over gain acquisition. When themarket is not performing well, investor sentiment is expected to have a greater effect in bear markets.Thus, Hypothesis 3 is posited as follows:

and bearish regimes because futures indices have low transaction costs and no constraints on short selling. Therefore, followingTse and Zhao (2012), this paper uses S&P 500 index futures to approximate stock market prices.

7 Baker and Wurgler (2006) also provide empirical results that investor sentiment is higher during bull markets than bearmarkets.


Hypothesis 3. The positive relationship between a change in spillovers of currency carry trade returnsand market returns is stronger in bear markets than in bull markets.

Finally, the paper expects that the increase in spillovers of currency carry trade returns will leadto a bullish market. Chen (2011) suggests that investor sentiment affects the market regime and thata lack of consumer confidence leads to a higher probability of switching to (or maintaining) a bearmarket regime. Gervais and Odean (2001) indicate that a bull market may also attract more investmentcapital, in part because investors grow more confident in their personal investment abilities. In a sense,because high investor risk appetite sentiment leads to the purchase of stocks, this causes market pricesto rise even higher and increase the probability of a bull market. Thus, Hypothesis 4 is postulated asfollows:

Hypothesis 4. A higher magnitude of spillovers of currency carry trade returns will lead to a higher(lower) probability of bull (bear) markets.

3. Data and methodology

3.1. Data

Following Tse and Zhao (2012), this paper uses the G10 currencies for the following analysis. TheG10 currencies include the U.S. dollar (USD), Australian dollar (AUD), Canadian dollar (CAD), Swissfranc (CHF), German mark (GE) or euro (EUR), British pound (GBP), Japanese yen (JPY), Norwegiankrone (NOK), New Zealand dollar (NZD), and Swedish kronor (SEK). For the period after the intro-duction of the euro on January 1, 1999, the GE and German three-month interbank interest ratesare replaced by the euro dollar and three-month euro interbank interest rates, respectively.8 Dailyexchange rates and three-month interbank interest rates are collected from Datastream. The datacover the period from January 3, 1994 to March 28, 2012.

Following Brunnermeier et al. (2009), Christiansen, Ranaldo, and Söderlind (2011), and Tse and Zhao(2012), this study denotes the return of an investment in a foreign currency financed by borrowing inthe domestic (U.S.) currency by:

Zt = (iFt−1 − iDt−1) − �St (1)

where iFt is the log foreign interest rate at time t, iDt is the logarithm of the domestic U.S. interest rate attime t, and St is the log exchange rate at time t. Each exchange rate is quoted as foreign currency unitsper U.S. dollar (USD). �St is the depreciation of the foreign currency. As indicated by Brunnermeieret al. (2009), if the UIP holds, E(Zt) equals zero. Thus, Zt can be regarded as the abnormal return to acurrency carry trade strategy in which the foreign currency is the investment currency and USD is thefunding currency.

3.2. Measure of spillover effects

This paper uses the generalized VAR framework suggested by Diebold and Yilmaz (2012) to examinethe spillover effects of currency carry trade returns.9 The approach is constructed as follows. Let Xt

denote an N-dimensional time-series vector following a VAR(p) as:

Xt =p∑i=1

�iXt−i + εt, t = 1, 2, . . ., T (2)

8 This paper uses the approach suggested by Bai and Perron (2003) to test the potential structural breaks for currency carrytrade returns of German mark (GE) or euro (EUR). The results of structural break test provide evidence for no structural breakfor German mark (GE) or euro (EUR).

9 Prior research has found that the forward rate premium can be attributed to investor sentiment and trend behavior. Burnsideet al. (2011) and Tse and Zhao (2012) show that investor sentiment can explain the forward premium puzzle. Conversely, Zhou(2002) shows that the trend factor can explain the forward premium. This paper also finds a significant time trend in ourcurrency carry trade returns. Thus, this paper removes the time trend from returns of currency carry trades to explore the UIPwith regard to investor sentiment.


where ε ∼ (0,˙) is a vector of independently and identically distributed disturbances. Provided thatthe VAR process is covariance stationary, the moving-average representation exists and is given by:

Xt =∞∑i=0

Aiεt−i (3)

where the N × N coefficient matrices Ai obey the following recursive relations:

Ai = �1Ai−1 + �2Ai−2 + · · · + �pAi−p (4)

where A0 = IN and Ai = 0 for i < 0. Diebold and Yilmaz (2009), Diebold and Yilmaz (2012) employ variancedecompositions to investigate spillover effects.10 Because the variance decomposition, which usesthe Cholesky factorization to achieve orthogonality, depends on the ordering of variables, Dieboldand Yilmaz (2012) use the generalized VAR framework to estimate variance decompositions that areinvariant to the ordering (see also Koop, Pesaran, & Potter, 1996; Pesaran & Shin, 1998).

Diebold and Yilmaz (2012) define own variance shares as the fractions of the H-step-ahead error vari-ances in forecasting Xi that are due to shocks to Xi, for i = 1, 2, . . ., N. Cross variance shares, or spillovers,are defined as the fraction of the H-step-ahead error variances in forecasting Xi that are due to shocksto Xj, for i, j = 1, 2, . . ., N, such that i /= j. Hence, the H-step-ahead error variance decomposition, �g

i,j(H),

of the generalized VAR framework can be calculated as follows11:

�gi,j

(H) =�−1jj

∑H−1h=0 (e′

iAh˙ej)

2∑H−1h=0 (e′

iAh˙A

′hei)

(5)

where is the variance matrix for the error term vector ε, �jj is the standard deviation of the errorterm for the jth equation, and ei is the selection vector with unity as its ith element and zeros else-where. According to the characteristics of the generalized VAR, the sum of the elements in each rowof the variance decomposition matrix is not equal to 1,

∑Nj=1�

gi,j

(H) /= 1. Diebold and Yilmaz (2012)normalized each entry of the variance decomposition matrix by the row sum as follows:

�gi,j

(H) =�gi,j

(H)∑Nj=1�

gi,j

(H)(6)

such that∑N

j=1�gi,j

(H) = 1 and∑N

i,j=1�gi,j

(H) = N. After obtaining �gi,j

(H), the total spillover index can beconstructed as follows:

Sg(H) =

N∑i, j = 1

i /= j

�gi,j

(H)

N∑i,j=1

�gi,j

(H)

=

N∑i, j = 1

i /= j

�gi,j

(H)

N(7)

Following Diebold and Yilmaz (2009, 2012), this paper uses dynamic spillover matrices to measurethe spillover effects.12 The generalized VAR model with a 120-day rolling sample is used to estimate thedynamic spillover matrices. This paper utilizes the Schwarz Information Criterion (SIC) to determine

10 Variance decompositions assess the fraction H-step-ahead error variance in forecasting Xi , that is due to shocks to Xj , ∀ j /= ifor each i.

11 Eq. (5) is the so-called generalized forecast error variance decomposition (GVDC). As indicated by Lee, Huang, and Yin(2013) the GVDC is likely to be regarded as an out-of-sample causality analysis that provides information regarding the relativeimportance of each random innovation in affecting the variables in the VAR system.

12 As indicated by Diebold and Yilmaz (2009, 2012), financial market conditions will vary over time, and it seems unlikely thatany single fixed-parameter model would apply over the entire sample.


the number of optimal lags, and the generalized variance decompositions of 10-day-ahead forecasterrors are employed for the following analysis.

3.3. Markov-switching models

The paper uses a Markov-switching model to measure the magnitude of spillovers of currencycarry trade returns and the impact of these spillovers on market returns under bull and bear marketregimes. Maheu and McCurdy (2000), Perez-Quiros and Timmermann (2000), and Chen (2011) haveshown that the Markov-switching model has well identified bull and bear markets in stock returns.Thus, a simple two-state mean/variance Markov-switching model of market returns is estimated asfollows:

Rett = uSt + εt, εt∼i.i.d N(0, �2St

) (8)

where uSt and �2St

are the state-dependent mean and variance of Rett, respectively. Rett is the marketreturn at time t. The study employs the returns of the S&P 500 index futures as the proxy for marketreturns. The unobserved state variable St is a latent dummy variable set at either 0 or 1. Let St = 0indicate the bull market and St = 1 represent the bear market. Futures returns are assumed to follow atwo-state Markov process with a fixed transition probability matrix:

P =[

p00 1 − p11

1 − p00 p11

](9)

where p00 = P(St = 0|St−1 = 0) and p11 = P(St = 1|St−1 = 1). Once the market regimes are identified, themagnitude of spillovers of currency carry trade returns under different market conditions can becalculated.

To measure the impact of spillovers of currency carry trade returns on market returns under bulland bear markets, a two-state Markov-switching model is estimated as follows:

Rett = uSt + ˛St dSpillt−1 + ˇStRett−1 + ϕSt

(∑ni=2dSpillt−in − 1

)+ �St

(∑ni=2Rett−in − 1

)

+ εt, εt∼i.i.d N(0, �2St

), n = 1, 4, 7, 10 (10)


are the state-dependent mean and variance of Rett, respectively. Rett is the return ofthe S&P 500 index futures at time t and dSpillt is the difference in the total spillover index of currencycarry trade returns at time t. The unobserved state variable St is a latent dummy variable set at either0 or 1. Let St = 0 indicate the bull market and St = 1 represent the bear market. As mentioned above,futures returns are assumed to follow a two-state Markov process with a fixed transition probabilitymatrix. Following Lewellen and Nagel (2006), this paper imposes the constraint that lags 2 ∼ n havethe same slope, which reduces the number of parameters in the Markov-switching model with dailydata. If the spillovers of currency carry trade returns have a larger effect on market returns in bearmarkets than in bull markets, the regression coefficient of ˛1 (or ˛1 + ϕ1) should be positive and largerthan ˛0 (or ˛0 + ϕ0).

Finally, to investigate the impact of spillovers of currency carry trade returns on the probabilitiesof market regimes, the paper follows Perez-Quiros and Timmermann (2000) and allows the transitionprobabilities to vary with the lagged spillover index of currency carry trade returns as the following(see Alizadeh & Nomikos, 2004):

p00t = Pt(St = 0|St−1 = 0) = ˚

[ω +

(∑nj=1Spillt−jn

)], n = 1, 4, 7, 10 (11)

p11t = Pt(St = 1|St−1 = 1) = ˚

[ + �

(∑nj=1Spillt−jn

)], n = 1, 4, 7, 10 (12)


Table 1Forward premium regressions and descriptive statistics for currency carry trade returns.

AUD CAD CHF GE/EUR GBP JPY NOK NZD SEK

Panel A: Forward premium regressions, �St = + × (iFt−1 − iD

t−1) + εt 0.004 −0.006** −0.031*** −0.0070* −0.008** −0.030*** −0.003 −0.004 −0.002ˇ −2.426* −1.855** −4.370*** −3.264*** 2.414* −3.072*** −0.855 −0.361 −2.224***

H0: = 0 0.742 5.334** 25.385*** 3.260* 4.665** 36.362*** 0.660 0.264 0.341H0: = 1 7.591*** 13.567*** 38.774*** 20.059*** 0.956 42.809*** 5.551** 0.990 20.301***

H0: = 0, = 1 5.214*** 7.736*** 19.502*** 10.619*** 2.656* 22.933*** 3.290** 4.737*** 10.188***

Pane B: Currency carry trade returns, Zt = (iFt−1 − iD

t−1) − �StMean 0.012*** 0.006*** 0.004*** 0.001 0.004*** −0.002** 0.007*** 0.013*** 0.004***

Median 0.015*** 0.003*** 0.004*** 0.005*** 0.006*** −0.007*** 0.007*** 0.023*** 0.010***

Std 0.077 0.047 0.066 0.064 0.054 0.070 0.068 0.080 0.070Max 0.242 0.167 0.231 0.162 0.178 0.231 0.203 0.256 0.206Min −0.449 −0.255 −0.271 −0.232 −0.299 −0.216 −0.352 −0.350 −0.339

This table reports forward premium regression analyses and summary statistics of currency carry trade returns for the G10(Group of Ten countries) currencies quoted against the U.S. dollar (USD): Australian dollar (AUD), Canadian dollar (CAD), Swissfranc (CHF), German mark (GE)/EUR, British pound (GBP), Japanese yen (JPY), Norwegian krone (NOK), New Zealand dollar(NZD), and Swedish kronor (SEK). The forward-premium regression is estimated as follows:

�St = + × (iFt−1 − iDt−1) + εt

where iFt is the log foreign interest rate at time t. iDt is the logarithm of the domestic U.S. interest rate at time t. St is the logexchange rate at time t. Each exchange rate is quoted as foreign currency units per US dollar. The Newey–West heteroskedasticitycorrection is employed in the regression model. The F-statistics are reported for H0 : = 0, H0 : = 1, and H0 : = 0, = 1. Thesample period is from January 3, 1994 to March 28, 2012. The overlapping daily currency carry trade return is from May 9, 1994to March 28, 2012.

* Indicate statistical significance at the 0.10 level.** Indicate statistical significance at the 0.05 level.

*** Indicate statistical significance at the 0.01 level.

where is the cumulative density function of a standard normal variable, and Spillt is the total spilloverindex of currency carry trade returns at time t. If the higher magnitude of spillovers of currency carrytrade returns sends the market into a bull regime, the regression coefficient of should be positiveand significantly different from zero. In addition, if the higher magnitude of spillovers of currencycarry trade returns reduces the probability of bear regimes, the regression coefficient of � should benegative and significantly different from zero.

4. Empirical results

4.1. Forward premium regressions and descriptive statistics for currency carry trade returns

Table 1 reports the results of forward premium regressions and the summary statistics for currencycarry trade returns. Panel A of Table 1 reports the results of forward premium regressions.13 Under theUIP hypothesis, if the return on a foreign n-period zero coupon bond is one percentage point higher perannum than that of a domestic bond, one would expect, on average, the foreign currency to depreciateby one percent over the next n periods. Thus, the UIP hypothesis implies = 0 and = 1 (see Lothian& Wu, 2011). Panel A of Table 1 shows that all the regression coefficients for are negative, exceptGBP. Furthermore, the hypothesis for = 1 is rejected for most of the currencies, except for the GBPand NZD. Finally, the results show that the hypothesis, = 0 and = 1, is rejected for all currencies,indicating that the UIP hypothesis fails in our sample period.

13 The most popular method to assess whether UIP holds has been to estimate the regression as:

�St = + × (iFt−1 − iDt−1) + εt

where iFt is the log foreign interest rate at time t, iDt is the logarithm of the domestic U.S. interest rate at time t, and St is the logexchange rate at time t. Each exchange rate is quoted as foreign currency units per USD.


Table 2The magnitude of the total spillover index under different market regimes.

Panel A: Results of market regimes

St = 0, Bull St = 1, Bear

uSt × 100 0.090*** −0.080***

�2St

× 100 0.005*** 0.036***

State probability (p00/p11) 0.984*** 0.971***

Average duration (days) 61.285 34.514

Panel B: Descriptive statistics of total spillover index under different market regimesFull sample Bull Bear Bull–bear

Mean 0.688 0.692 0.682 0.010***

Median 0.693 0.700 0.680 0.020***

Std 0.063 0.066 0.055 –Max 0.822 0.822 0.786 –Min 0.526 0.526 0.526 –

This table presents the total spillover index under different market conditions, which are determined by a simple Markov-switching model. A simple two-state mean/variance Markov-switching model of market returns is estimated as follows:

Rett = uSt + εt, εt∼i.i.d. N(0, �2St

)


are the state-dependent mean and variance of Rett , respectively. Rett is the return of the S&P 500 index futuresat time t. The unobserved state variable St is a latent dummy variable set at either 0 or 1. Let St = 0 indicate the bull marketand St = 1 represent the bear market. Futures returns are assumed to follow a two-state Markov process with a fixed transitionprobability matrix:

P =[

p00 1 − p11

1 − p00 p11

]where p00 = P(St = 0|St−1 = 0) and p11 = P(St = 1|St−1 = 1). The sample period is from October 21, 1994 to March 28, 2012.* Indicate statistical significance at the 0.10 level.** Indicate statistical significance at the 0.05 level.


Panel B of Table 1 reports the summary statistics for the currency carry trade returns. The meanvalues of the currency carry trade returns are all significant at the 10% level, except for the meanvalue of GE/EUR. The largest mean value for currency carry trade returns is NZD, at 0.013. The smallestmean value of currency carry trade returns is JPY, at −0.002. Similarly, the median values of currencycarry trade returns are all significant at the 10% level. The largest median value of currency carrytrade returns is NZD, at 0.023. The smallest median value of currency carry trade returns is JPY, at−0.007. Overall, the findings are in line with the results from Brunnermeier et al. (2009) in that thecurrency carry trade return is the largest for NZD and the smallest for JPY. The results indicate that aninvestment in NZD financed by borrowing in USD can obtain a positive abnormal return. By contrast,a currency carry trade strategy in which USD is the investment currency and the JPY is the fundingcurrency would obtain a positive return in currency carry trade markets.

Overall, because the hypothesis, = 0 and = 1, is rejected for all currencies and the currency carrytrade returns are all significant at the conventional level, the finding supports the failure of the UIPhypothesis. Our empirical results are consistent with Brunnermeier et al. (2009), Clarida et al. (2009),Baillie and Chang (2011), and Tse and Zhao (2012), among others. As indicated by Tse and Zhao (2012),the failure of the UIP hypothesis associated with significant currency carry trade returns might reflectmarket risk sentiment.

4.2. Test for the hypotheses

4.2.1. The magnitude of spillovers for currency carry trade returns under different regimesTable 2 displays the magnitude of spillover effects from currency carry trade returns. The paper uses

the total spillover index suggested by Diebold and Yilmaz (2012) to measure the total spillover effects


Fig. 1. Total spillover index. This figure plots the time series of dynamic matrices of total spillovers.

of currency carry trade returns. If the spillovers of currency carry trade returns reflect the investorrisk appetite sentiment, the magnitude of the total spillover index will be higher in a bull market thanin a bear market. The results are presented in Table 2, in which Panel A presents the market regimesusing the Markov-switching model. As shown in the panel, the Markov-switching model identifies aregime with a higher mean (0.090) with a lower variance (0.005) and a lower mean (−0.080) witha higher variance (0.036). This result is consistent with the findings of Maheu and McCurdy (2000),Perez-Quiros and Timmermann (2000), and Chen (2011) in that a high return is accompanied with alow variance and a low return is accompanied with a high variance. The high-return stable and low-return volatile regimes in market returns are conventionally labeled as bull markets and bear markets,respectively. Obviously, the Markov-switching model has well identified the bull and bear markets inthe market returns. The fixed transition probabilities for bull and bear regimes are 0.984 and 0.971,respectively, indicating that both the bull and bear market states are highly persistent. The bull marketpersists on average for 61.285 days, whereas the bear market regime will persist for 34.514 days, onaverage.

Panel B of Table 2 presents the magnitude of spillovers for currency carry trade returns under bulland bear markets. The empirical results show that the mean value of the total spillover index is 0.692under a bull market. The mean value of the total spillover index is 0.682 under a bear market. The meanvalue of the difference in total spillover index for the bull and bear regimes is 0.010 and is significant atthe 1% level. Additionally, the median values of the total spillover indices for the bull and bear regimesare 0.700 and 0.680, respectively. The median of the difference in the total spillover index for the bulland bear regimes is 0.020 and is significant at the 1% level. These empirical findings are consistent withHypothesis 1 because the degree of spillovers of currency carry trade returns contains information onmarket risk sentiment. Thus, the total spillover index of currency carry trade returns is higher in a bullmarket than in a bear market.

Fig. 1 shows the time-series patterns for the total spillover index of currency carry trader returns.The figure presents that the magnitude of the total spillover index is relatively high, from 0.53 to 0.82.This finding implies that the spillover effects from currency carry trade returns are important andcannot be ignored by practitioners. Furthermore, Fig. 1 reports that the total spillover index generallyreaches a local peak surrounding the relatively high stock prices accompanied with a sharp declinein the stock market. The values of the total spillover index reach local peaks surrounding the Asianfinancial, the dot-com bubble, and the subprime crises. The results of Fig. 1 are consistent with Table 2


in that the total spillover index of currency carry trade returns is positively related to the magnitudeof the investor risk appetite sentiment, and the findings shown in Fig. 1 support Hypothesis 1.

4.2.2. The impact of spillovers for carry trade returns on subsequent market returns under differentmarket regimes

Christiansen et al. (2011) provide empirical evidence that a typical carry trade strategy is signif-icantly and positively exposed to current and lagged stock returns. However, Tse and Zhao (2012)conclude that currency carry trades and stock returns are positively correlated with no Granger-causality in either direction. Thus, the lead–lag relationship between currency carry trades and marketreturns is inconclusive. Therefore, this paper first examines the lead–lag relationship between the totalspillover index of currency carry trade returns and the market returns of S&P 500 index futures.14 Next,the Markov-switching model is used to investigate whether the impact of the total spillover index ofcurrency carry trade returns on market returns is asymmetric during bull and bear markets.

To test the lead–lag relationship, the VAR model is applied as follows:

Rett = ˛1 +n∑k=1

ˇ1kRett−k +n∑k=1

�1kdSpillt−k + ε1,t

dSpillt = ˛2 +n∑k=1



, n = 1, 4, 7, 10 (13)

where Rett is the return of the S&P 500 index futures at time t and dSpillt is the difference in the totalspillover index of currency carry trade returns at time t. In the Rett equation, the total spillover indexof currency carry trade returns Granger-causes the market returns of the S&P 500 index futures ifthe null hypothesis that the lagged coefficients, �1k’s, are zero is rejected. In the dSpillt equation, themarket returns of the S&P 500 index futures Granger-causes the total spillover index of currency carrytrade returns if the null hypothesis that the lagged coefficients, ˇ2k’s, are zero is rejected. In additionto Granger-causality tests, we also examine the cumulative effects for Eq. (13). In the Rett equation, forinstance, if the null hypothesis that the sum of the lagged coefficients �1k’s,

∑nk=1�1k, is zero is rejected,

the total spillover index of currency carry trade returns has a cumulative effect on the market returns.In the dSpillt equation, if the null hypothesis that the sum of the lagged coefficients ˇ2k’s,

∑nk=1ˇ2k, is

zero is rejected, the market returns have a cumulative effect on the total spillover index of currencycarry trade returns. The tests on the sum of the lagged coefficients allow us to identify the dynamicnet effect for Eq. (13). To ensure that the results are robust to the different number of lags, this paperreports the VAR results for up to ten lags to distinguish the causality and predictability for short- orlong-term horizons (see Dufour & Renault, 1998).

The empirical results are shown in Table 3, in which Panel A reports the results of the Granger-causality tests. In the Rett equation, the results show that the null hypothesis, �11 = �12 = · · · = �1k = 0,can be rejected for one lag up to ten lags. In the dSpillt equation, the null hypothesis,ˇ21 = ˇ22 = · · · = ˇ2k = 0, cannot be rejected for one lag up to ten lags. This finding indicates that thetotal spillover index of currency carry trade returns Granger-causes the market returns, but not viceversa. Panel B of Table 3 presents the sum of the coefficients for VAR. In the Rett equation, for example,the results of the sum of the coefficients tests,

∑nk=1�1k, are positively significant at the 5% level for all

lags, which indicates that the total spillover index of currency carry trade returns has a cumulativelypositive effect on the market returns. In the dSpillt equation, the results of the sum of the coefficientstests,

∑nk=1ˇ2k, are not significant at the conventional level for all lags, which suggests that the market

returns have an insignificantly cumulative effect on the total spillover index of currency carry tradereturns. Overall, the tests of the cumulative effects for

∑nk=1�1k and

∑nk=1ˇ2k support Hypothesis

2 that the spillovers of currency carry trade returns reflect the investor risk appetite sentiment andthus have a positive effect on subsequent market returns, but not vice versa. Our empirical resultsare different from previous findings of Christiansen et al. (2011) and Tse and Zhao (2012) and provide

14 The authors would like to thank the referee for bringing this point to our attention.


Table 3Relationship between the futures returns and the total spillover index.

Rett dSpillt∑n

i=1ˇ1k

∑n

i=1�1k

∑n

k=1ˇ2k

∑n

i=1�2k

Panel A: Causality testn = 1 19.867*** 11.905*** 0.120 7.119***

n = 4 8.659*** 4.298*** 0.875 3.472***

n = 7 6.780*** 5.114*** 0.978 2.456**

n = 10 5.573*** 3.791*** 1.139 1.834**

Panel B: Sum of coefficients testn = 1 −0.066*** 0.111*** 0.002 0.040***

n = 4 −0.152*** 0.153** −0.000 0.075***

n = 7 −0.251*** 0.249*** −0.018 0.109***

n = 10 −0.229*** 0.208** −0.042* 0.088**

This table reports the results of causality and sum of coefficients tests for the returns on the S&P 500 index futures and the totalspillover index of currency carry trade returns with the VAR. The VAR is estimated as follows:

Rett = ˛1 +n∑k=1



dSpillt = ˛2 +n∑k=1


�2kdSpillt−k + ε2,t , n = 1, 4, 7, 10

where Rett is the return of the S&P 500 index futures at time t, and dSpillt is the difference in the total spillover index of currencycarry trade returns at time t. The sample period is from October 21, 1994 to March 28, 2012.



additional evidence for the relationship between spillovers of currency carry trade returns and marketreturns.

To investigate whether the impact of spillovers of currency carry trade returns on subsequentmarket returns is asymmetric during bull and bear markets, the fixed-transition-probability Markov-switching model is used in this paper. Following the VAR model, the total spillover index with one,four, seven, and ten lags is used to test the relations. If the spillovers of currency carry trade returnscontain information about the sentiment with regard to risk appetites, the regression coefficient of˛1 (or ˛1 + ϕ1) should be positive and larger than ˛0 (or ˛0 + ϕ0). The results are reported in Table 4.15

For the one-lag Markov-switching model, the empirical results show that ˛0 and ˛1 are 0.054 and0.180, respectively, and the regression coefficients are all significant at the 5% level. Furthermore, thenull hypothesis, H0 : ˛0 = ˛1, is rejected at the 5% level. Similarly, for the Markov-switching modelwith four, seven, and ten lags, the results show that the regression coefficients of ˛0 and ˛1 are allpositive and significant at the 10% level, and the null hypothesis, H0 : ˛0 = ˛1, is rejected for all lags. Forthe regression coefficients ˛0 + ϕ0 and ˛1 + ϕ1, the results of the Markov-switching model with four,seven, and ten lags show that ˛0 + ϕ0 and ˛1 + ϕ1 are positive and that ˛1 + ϕ1 is significant at the 1%level. Moreover, the results also indicate that the null hypothesis, H0 : ˛0 + ϕ0 = ˛1 + ϕ1, is rejected forall lags, which indicates that ˛1 + ϕ1 is larger than ˛0 + ϕ0.

Overall, the empirical evidence of Table 4 is consistent with Hypothesis 3 that the spillovers of cur-rency carry trade returns have a positive effect on subsequent market returns and that this positive

15 Table 4 shows that the Markov-switching model identifies a regime with a higher mean (u0) and a lower variance (�20 ) and

a regime with a lower mean (u1) and a greater variance (�21 ). This result is consistent with the findings in Maheu and McCurdy

(2000), Perez-Quiros and Timmermann (2000), and Chen (2011). The high-return stable and low-return volatile states in marketreturns are conventionally labeled as bull markets and bear markets, respectively. Obviously, the Markov-switching model haswell identified bull and bear markets in market returns. Overall, the market regime identification results from Table 4 areconsistent with those in Table 2.


Table 4Impact of the total spillover index on futures returns under different market regimes.

n = 1 n = 4 n = 7 n = 10

OLS MS OLS MS OLS MS OLS MS

u × 100 0.026 0.027 0.030 0.003u0 × 100 0.090*** 0.100*** 0.110*** 0.110***

u1 × 100 −0.100** −0.110** −0.140*** −0.140***

�20 × 100 0.005*** 0.005*** 0.005*** 0.006***

�21 × 100 0.036*** 0.036*** 0.036*** 0.036***

0.111*** 0.109*** 0.107*** 0.107***

˛0 0.054** 0.050** 0.048* 0.049**

˛1 0.180*** 0.1800*** 0.177*** 0.172***

−0.066*** −0.070*** −0.073*** −0.070***

ˇ0 −0.000 −0.002 −0.007 −0.005ˇ1 −0.090*** −0.098*** −0.105*** −0.101***

ϕ 0.039 0.139* 0.090ϕ0 −0.041 −0.005 0.009ϕ1 0.157 0.375** 0.272� −0.081* −0.180*** −0.163**

�0 −0.099*** −0.211*** −0.212***

�1 −0.108*** −0.254*** −0.274***

P00 0.984*** 0.983*** 0.983*** 0.983***

P11 0.971*** 0.970*** 0.970*** 0.970***

H0: + ϕ = 0 5.335** 8.945*** 4.933**

H0 : ˛0 = ˛1 4.134** 4.312** 4.463** 3.875**

H0 : ϕ0 = ϕ1 2.511 4.683*** 1.474H0 : ˛0 + ϕ0 = 0 0.070 0.839 1.161H0 : ˛1 + ϕ1 = 0 11.946*** 19.951*** 8.691***

H0 : ˛0 + ϕ0 = ˛1 + ϕ1 5.022** 7.463*** 2.929*

This table presents the impact of the total spillover index of the currency carry trade returns on the futures returns on the S&P500 under different market conditions. A two-state Markov-switching model is estimated as follows:


(∑n

i=2dSpillt−i

(n − 1)

)+ �St

(∑n

i=2Rett−i

(n − 1)

)+ εt, εt∼i.i.d N(0, �2

St), n = 1, 4, 7, 10


are the state-dependent mean and variance of Rett , respectively. Rett is the return of the S&P 500 indexfutures at time t and dSpillt is the difference in the total spillover index of currency carry trade returns at time t. The unobservedstate variable St is a latent dummy variable set at either 0 or 1. Let St = 0 indicate the bull market and St = 1 represent the bearmarket. Futures returns are assumed to follow a two-state Markov process with a fixed transition probability matrix:

P =[

p00 1 − p11

1 − p00 p11

]where p00 = P(St = 0|St−1 = 0) and p11 = P(St = 1|St−1 = 1). The F-statistic is reported for null hypothesis H0. The sample period isfrom October 21, 1994 to March 28, 2012.



effect is larger in bear market than in bull market regimes (at least from the perspective of the regres-sion coefficients of ˛0 and ˛1). This finding is consistent with the argument of financial constraintsand prospect theory that the impact of the market risk sentiment on financial markets is greater whenthere are financial constraints or when the market is not doing well.

4.2.3. The impact of spillovers for currency carry trade returns on transition probabilitiesIf spillovers of currency carry trade returns are positively related to the investor risk appetite

sentiment, a higher degree of spillovers of currency carry trade returns leads to a higher (lower)probability of a bull (bear) market. To examine this hypothesis, a Markov-switching model with


Table 5Impact of the total spillover index on futures returns and state transition probabilities under different market regimes.

n = 1 n = 4 n = 7 n = 10

j = 1 to n j = 1 to 1 j = 1 to n j = 1 to 1 j = 1 to n j = 1 to 1 j = 1 to n

u0 × 100 0.086*** 0.098*** 0.098*** 0.112*** 0.112*** 0.112*** 0.112***

u1 × 100 −0.095* −0.114** −0.114** −0.136** −0.135** −0.134** −0.134**

�20 × 100 0.005*** 0.005*** 0.005*** 0.005*** 0.005*** 0.005*** 0.005***

�21 × 100 0.036*** 0.036*** 0.036*** 0.036*** 0.036*** 0.036*** 0.036***

˛0 0.056** 0.052** 0.053** 0.051* 0.052** 0.052** 0.053**

˛1 0.178*** 0.179*** 0.178*** 0.174*** 0.173*** 0.170*** 0.169***

ˇ0 −0.005 −0.007 −0.007 −0.012 −0.012 −0.010 −0.010ˇ1 −0.089*** −0.097*** −0.097*** −0.103*** −0.103*** −0.099*** −0.099***

ϕ0 −0.037 −0.037 0.001 0.003 0.012 0.014ϕ1 0.154 0.154 0.368** 0.364** 0.270 0.263�0 -0.099*** −0.099*** −0.212*** −0.212*** −0.218*** −0.216***

�1 −0.108*** −0.108*** −0.251*** −0.251*** −0.267*** −0.268***

ω −0.701 −0.725 −0.719 −0.762 −0.690 −0.757 −0.723 4.113*** 4.132*** 4.120*** 4.171*** 4.063*** 4.156*** 4.104***

1.281 1.363* 1.324* 1.385* 1.152 1.309* 1.045� −4.626*** −4.723*** −4.664*** −4.741*** −4.396*** −4.630*** −4.237***

H0 : ˛0 = ˛1 3.737* 3.955** 3.889** 3.850** 3.763* 3.378* 3.281*

H0 : ϕ0 = ϕ1 2.254 2.248 4.189** 4.050** 1.348 1.257H0 : ˛0 + ϕ0 = 0 0.182 0.189 1.201 1.298 1.354 1.480H0 : ˛1 + ϕ1 = 0 11.517*** 11.461*** 18.797*** 18.440*** 8.275*** 8.007***

H0 : ˛0 + ϕ0 = ˛1 + ϕ1 4.588** 4.555** 6.629** 6.419** 2.641 2.492

This table presents the impact of the total spillover index of the currency carry trade returns on futures returns and statetransition probabilities on the S&P 500 under different market conditions. A two-state Markov-switching model is estimatedas follows:


(∑n

i=2dSpillt−i

n − 1

)+ �St

(∑n

i=2Rett−i

n − 1

)+ εt, εt∼i.i.d N(0, �2

St), n = 1, 4, 7, 10.


are the state-dependent mean and variance of Rett , respectively. Rett is the return of the S&P 500 indexfutures at time t and dSpillt is the difference in the total spillover index of currency carry trade returns at time t. The unobservedstate variable St is a latent dummy variable set at either 0 or 1. Let St = 0 indicate the bull market and St = 1 represent the bearmarket. Futures returns are assumed to follow a two-state Markov process with a transition probability matrix:

Pt =[

p00t 1 − p11

t

1 − p00t p11

t

],

where p00t = Pt(St = 0|St−1 = 0) = ˚

[ω +

(n∑j=1

Spillt−j/n

)]

and p11t = Pt(St = 1|St−1 = 1) = ˚

[ + �

(n∑j=1

Spillt−j/n

)]. is the cumulative density function of a standard normal vari-

able. Spillt is the total spillover index of currency carry trade returns at time t. The F-statistic is reported for null hypothesis H0.The sample period is from October 21, 1994 to March 28, 2012.



time-varying transition probability is employed in conjunction with the total spillover index withone lag and n-lag for the function of the time-varying transition probability. The empirical results,which are reported in Table 5, are similar when using the total spillover index with one lag and n-lagin the time-varying transition probability.

The results show that the regression coefficient of is significantly positive for all lags, whichsuggests that a larger value for the total spillover index leads to a higher probability of a bull regime.


Table 6Robustness analyses for descriptive statistics of total spillover index under different market regimes: 150-day rolling sample.

Descriptive statistics of total spillover index under different market regimes

Full sample Bull Bear Bull–bear

Mean 0.680 0.685 0.673 0.012***

Median 0.689 0.697 0.673 0.024***

Std 0.066 0.071 0.057Max 0.814 0.814 0.780Min 0.515 0.515 0.536

This table displays the descriptive statistics for the total spillover index under different market conditions. The generalized VARmodel with a 150-day rolling sample is used to estimate the dynamic volatility spillover matrices. The first dynamic spillovermatrix is estimated during the period from May 9, 1994 to December 2, 1994, the second spillover matrix is estimated duringthe period from May 10, 1994 to December 5, 1994, etc. Thus, a total of 4519 spillover matrices are obtained for the periodfrom December 2, 1994 to March 28, 2012 in this rolling window estimation. This paper uses the Schwarz Information Criterion(SIC) to select the lag order of the generalized VAR model. The market conditions are determined by a simple Markov-switchingmodel. A simple two-state mean/variance Markov-switching model of market returns is estimated as follows:

Rett = uSt + εt, εt∼i.i.d N(0, �2St

)


are the state-dependent mean and variance of Rett , respectively. Rett is the return of the S&P 500 index futuresat time t. The unobserved state variable St is a latent dummy variable set at either 0 or 1. Let St = 0 indicate the bull marketand St = 1 represent the bear market. Futures returns are assumed to follow a two-state Markov process with a fixed transitionprobability matrix:

P =[

p00 1 − p11

1 − p00 p11

]where p00 = P(St = 0|St−1 = 0) and p11 = P(St = 1|St−1 = 1). The sample period for estimating market regimes is from December 2,1994 to March 28, 2012.* Indicate statistical significance at the 0.10 level.** Indicate statistical significance at the 0.05 level.


On the contrary, the regression coefficient of � is significantly negative, which indicates that a highervalue of the total spillover index leads to a lower probability of a bear market. This finding is consistentwith our prediction for Hypothesis 4. For example, in the model with n = 4 and j = 1, the regressioncoefficients for and � are 4.132 and −4.723, respectively, and are significant at the 1% level. Inaddition, the results for ˛0 and ˛1 that are displayed in Table 5 are similar to those in Table 4, whichindicates that the spillovers of currency carry trade returns have a greater effect on subsequent marketreturns in a bear market than in a bull market. In sum, the empirical results of Table 5 suggest that thetotal spillover index of currency carry trade returns contains information on the investor risk appetitesentiment and thus a high total spillover index leads to stock buying and causes market prices torise even higher, which increases the likelihood of a bull market. This finding is consistent with theargument by Chen (2011) that investor sentiment affects the transition probabilities of market regimes.

4.3. Robustness check

4.3.1. Empirical evidence for 150-day rolling windowFor a robustness check, this paper uses a 150-day rolling window to calculate dynamic spillover

matrices and the total spillover index and to examine Hypotheses 1–4. Table 6 displays the descriptivestatistics for the total spillover index with a 150-day rolling window under bull and bear marketconditions. Table 6 shows that the mean values of the total spillover index for bull and bear marketsare 0.685 and 0.673, respectively. The mean value of the difference in the total spillover index for thebull and bear regimes is 0.012 and is significant at the 1% level. Similarly, the results for the medianvalues also show that the degree of spillovers of carry trade returns is larger in bull markets than inbear markets. Thus, the empirical findings are consistent with Hypothesis 1.

Table 7 presents the results for the effects of spillovers of currency carry trade returns on subse-quent market returns and on transition probabilities. The empirical results show that the regression


Table 7Impact of the total spillover index on futures returns and state transition probabilities under different market regimes: 150-dayrolling sample.

n = 1 n = 4 n = 7 n = 10

j = 1 to n j = 1 to 1 j = 1 to n j = 1 to 1 j = 1 to n j = 1 to 1 j = 1 to n

u0 × 100 0.088*** 0.101*** 0.101*** 0.114*** 0.114*** 0.113*** 0.113***

u1 × 100 −0.097* −0.115** −0.115** −0.138** −0.138** −0.134** −0.135**

�20 × 100 0.005*** 0.005*** 0.005*** 0.005*** 0.005*** 0.005*** 0.005***

�21 × 100 0.036*** 0.036*** 0.036*** 0.036*** 0.036*** 0.036*** 0.036***

˛0 0.062* 0.060* 0.060* 0.061* 0.061* 0.062* 0.062*

˛1 0.213*** 0.214*** 0.214*** 0.202*** 0.203*** 0.202*** 0.202***

ˇ0 −0.003 −0.005 −0.005 −0.009 −0.009 −0.008 −0.008ˇ1 −0.091*** −0.098*** −0.098*** −0.103*** −0.103*** −0.100*** −0.100***

ϕ0 −0.078 −0.077 −0.116 −0.116 −0.105 −0.105ϕ1 0.035 0.034 0.235 0.235 0.091 0.090�0 −0.099*** −0.099*** −0.220*** −0.221*** −0.222*** −0.222***

�1 −0.107*** −0.106*** −0.241*** −0.241*** −0.256*** −0.257***

ω −0.126 −0.060 −0.019 −0.041 0.040 −0.124 −0.047 3.293*** 3.194*** 3.135*** 3.154*** 3.039*** 3.269*** 3.158***

0.465 0.344 0.230 0.351 0.064 0.461 0.131� −3.450*** −3.268*** −3.099*** −3.256*** −2.834** −3.418*** −2.931***

H0 : ˛0 = ˛1 3.774* 3.854** 3.860** 3.202* 3.228* 3.105* 3.116*

H0 : ϕ0 = ϕ1 0.491 0.480 2.612 2.624 0.563 0.560H0 : ˛0 + ϕ0 = 0 0.167 0.158 0.928 0.931 0.428 0.422H0 : ˛1 + ϕ1 = 0 4.296** 4.276** 8.409*** 8.447*** 2.780* 2.782*

H0 : ˛0 + ϕ0 = ˛1 + ϕ1 2.159 2.145 4.613** 4.648** 1.571 1.575

This table displays the robustness check for the impact of the total spillover index of currency carry trade returns on S&P 500futures returns and state transition probabilities. The generalized VAR model with a 150-day rolling sample is used to estimatethe total spillover index of currency carry trade returns. A two-state Markov-switching model is estimated as follows:


(∑n

i=2dSpillt−i

n − 1

)+ �St

(∑n

i=2Rett−i

n − 1

)+ εt, εt∼i.i.d N(0, �2

St), n = 1, 4, 7, 10.


are the state-dependent mean and variance of Rett , respectively. Rett is the return of the S&P 500 indexfutures at time t and dSpillt is the difference in the total spillover index of currency carry trade returns at time t. The unobservedstate variable St is a latent dummy variable set at either 0 or 1. Let St = 0 indicate the bull market and St = 1 represent the bearmarket. Futures returns are assumed to follow a two-state Markov process with a transition probability matrix:

Pt =[

p00t 1 − p11

t

1 − p00t p11

t

],

where p00t = Pt(St = 0|St−1 = 0) = ˚

[ω +

(n∑j=1

Spillt−j/n

)]

and p11t = Pt(St = 1|St−1 = 1) = ˚

[ + �

(n∑j=1

Spillt−j/n

)]. is the cumulative density function of a standard normal vari-

able. Spillt is the total spillover index of currency carry trade returns at time t. The F-statistic is reported for the null hypothesisH0. The sample period is from December 2, 1994 to March 28, 2012.



coefficients of ˛0 and ˛1 are all positively significant at the 10% level. This finding is consistent withHypothesis 2, in that the spillovers of currency carry trade returns have a positive effect on subsequentmarket returns. Furthermore, the hypothesis H0 : ˛0 = ˛1 is rejected for all models, which indicatesthat the empirical evidence supports Hypothesis 3 that the relationship between spillovers of cur-rency carry trade and subsequent market returns is asymmetric. Specifically, the empirical results


provide evidence that spillovers of currency carry trade returns have a greater effect on subsequentmarket returns in a bear market than in a bull market. Finally, the results also indicate that theregression coefficient of is significantly positive and that the regression coefficient of � is signifi-cantly negative for all models. This finding is consistent with Hypothesis 4 in that a higher magnitudeof spillovers of currency carry trade returns leads to a higher (lower) probability of bull (bear) mar-kets. Overall, our empirical results show that the spillover effect of currency carry trade returns, ifany, reflects the sentiment with regard to risk appetites. Thus, Hypotheses 1–4 are supported by ourresults.

4.3.2. The results of the Markov-switching VAR modelAlthough the VAR results of Table 3 show that market returns insignificantly affect spillovers of

currency carry trade returns, it is likely that the market returns cause the currency carry trade spillovereffects under bull or bear market regimes.16 To examine this issue, the Markov-switching VAR modelis estimated as follows:

Rett = Ret,St + ˛Ret,St dSpillt−1 + ˇRet,StRett−1 + εRet,St

dSpillt = dSpill + ˛dSpill,St dSpillt−1 + ˇdSpill,StRett−1 + εdSpill,t(14.1)

(εRet,St

εdSpill,t

)∼i.i.d.

([0

0

],

[�2

Ret,St0

0 �2dSpill

])(14.2)

Pt =[

p00t 1 − p11

t

1 − p00t p11

t

](14.3)

p00t = Pt(St = 0|St−1 = 0) = ˚

[ω + Spillt−1

](14.4)

p11t = Pt(St = 1|St−1 = 1) = ˚

[ + �Spillt−1

](14.5)

where uRet,St and �2Ret,St

are the state-dependent mean and variance of Rett, respectively. dSpill and

�2dSpill

are the mean and variance of dSpillt, respectively. Rett is the return of the S&P 500 index futuresat time t, and dSpillt is the difference in the total spillover index of currency carry trade returns at timet. The unobserved state variable St is a latent dummy variable set at either 0 or 1. Let St = 0 indicate thebull market and St = 1 represent the bear market. is the cumulative density function of a standardnormal variable. Spillt is the total spillover index of currency carry trade returns at time t. If the totalspillover index of currency carry trade returns reflects the investor risk appetite sentiment, ˛Ret,Stshould be positively significant. By contrast, if market returns affect the subsequent total spilloverindex of currency carry trade returns, ˇdSpill,St should be significant.

The results are reported in Table 8. Regardless of whether the total spillover index of currency carrytrade returns is constructed by a 120- or 150-day rolling window, the empirical results show that theregression coefficients of ˛Ret,0 and ˛Ret,1 are all positively significant at the 5% level. By contrast, theregression coefficients of ˇdSpill,0 and ˇdPill,1 are not significant at the 10% level. This result suggeststhat the market price behavior does not cause the currency carry trade spillover effects under bulland bear market regimes. This finding is consistent with the results of Table 3. Moreover, the resultsof Table 8 show that ˛Ret,0 and ˛Ret,1 are all positively significant, that ˛Ret,1 is larger than ˛Ret,0, andthat (�) is positive (negative). These findings also support Hypotheses 2–4.

4.3.3. Impact of the total spillover index of currency carry trade returns on investor sentimentIf the total spillover index of currency carry trade returns reflects market risk sentiment, it would

be interesting to examine the relationship between the total spillover index of currency carry trade

16 The authors would like to thank the referee for bringing this point to our attention.


Table 8Relationship between futures returns and total spillover index under different market regimes.

120-Day rolling 150-Day rolling

i = Reti i = dSpillt i = Reti i = dSpillt

Ret,0 × 100 0.087*** 0.086***

Ret,1 × 100 −0.102* −0.105**

dSpill × 100 0.003 0.004�2Ret,0 × 100 0.005*** 0.005***

�2Ret,1 × 100 0.037*** 0.037***

�2dSpill

× 100 0.003*** 0.002***

˛Ret,0 0.058** 0.058*

˛Ret,1 0.179*** 0.228***

˛dSpill,0 0.101*** 0.106***

˛dSpill,1 −0.038*** −0.040***

ˇRet,0 −0.008 −0.003ˇRet,1 −0.090*** −0.093**

ˇdSpill,0 −0.021 −0.021ˇdPill,1 0.009 0.001ω −1.049 −0.318 4.557*** 3.528***

2.060** 0.952� −5.668*** −4.069***

This table reports the Markov-switching VAR model for the relationship between futures returns on the S&P 500 and the totalspillover index. A two-state Markov-switching VAR model is estimated as follows:

Rett = Ret,St + ˛Ret,St dSpillt−1 + ˇRet,StRett−1 + εRet,StdSpillt = dSpill + ˛dSpill,St dSpillt−1 + ˇdSpill,St Rett−1 + εdSpill,t

,

(εRet,StεdSpill,t

)∼i.i.d.

([00

],

[�2

Ret,St0

0 �2dSpill

])where uRet,St and �2

Ret,Stare the state-dependent mean and variance of Rett , respectively. dSpill and �2

dSpillare the mean and

variance of dSpillt . Rett is the return of the S&P 500 index futures at time t and dSpillt is the difference in the total spillover indexof currency carry trade returns at time t. The unobserved state variable St is a latent dummy variable set at either 0 or 1. LetSt = 0 indicate the bull market and St = 1 represent the bear market. Futures returns are assumed to follow a two-state Markovprocess with a transition probability matrix:

Pt =[

p00t 1 − p11

t

1 − p00t p11

t

],

where p00t = Pt(St = 0|St−1 = 0) = ˚

[ω + Spillt−1

]and p11

t = Pt(St = 1|St−1 = 1) = ˚[ + �Spillt−1

]. is the cumulative den-

sity function of a standard normal variable. Spillt is the total spillover index of currency carry trade returns at time t. The 120-dayrolling sample period is from October 21, 1994, to March 28, 2012. The 150-day rolling sample period for estimating marketregimes is from December 2, 1994 to March 28, 2012.



returns and investor sentiment proposed by Baker and Wurgler (2006). This paper expects that thetotal spillover index of currency carry trade returns should be positively correlated with subsequentinvestor sentiment, as proposed by Baker and Wurgler (2006). As mentioned above, when the senti-ment regarding risk appetite is high, investors have a preference for investing in risky assets. Accordingto the sentiment index proposed by Baker and Wurgler (2006), high investor sentiment periods areassociated with a large number of IPOs with high average first-day returns, high NYSE share turnover,and lower discounts from closed-end funds. These market characteristics may be driven by investors’high-risk appetites and may thus determine bull stock markets. As a result, this study expects that ifthe spillover effect of currency carry trade returns reflects the investor risk appetite sentiment, thetotal spillover index of currency carry trade returns has effects on subsequent investor sentiment, assuggested by Baker and Wurgler (2006).


Table 9Impact of the total spillover index of currency carry trade returns on investor sentiment.

120-Day rolling sample 150-Day rolling sample

−0.024 −0.024ˇ −0.096* −0.103*

� 5.480* 7.955**

Adj-R2 0.020 0.032DW 2.032 2.016Sample period 1994/11–2010/12 1995/01–2010/12

This table reports the impact of the total spillover index of currency carry trade returns on investor sentiment. The relationshipbetween investor sentiment and the total spillover index is estimated as follows:

dSentimentt = + × dSentimentt−1 + � × dSpillt−1 + εt

where dSentimentt is the difference in investor sentiment at time t, and dSpillt–1 is the difference in the total spillover index ofcurrency carry trade returns. The monthly data are used for analyses. The monthly data for the sentiment index are availablefrom Jeffrey Wurgler’s website: http://pages.stern.nyu.edu/∼jwurgler/. Following Baker and Wurgler (2006), the monthly datafrom the total spillover index takes the daily spillover value at the beginning of that month. The Newey–West autocorrelationand heteroskedasticity-consistent standard errors are used in the paper.



To explore this argument, the regression model is estimated as follows:17

dSentimentt = + × dSentimentt−1 + � × dSpillt−1 + εt (15)

where dSentimentt is the difference in investor sentiment at time t and dSpillt is the difference in thetotal spillover index of currency carry trade returns at time t. Monthly data are used for the analysis.18

The results are shown in Table 9. The empirical findings indicate that the total spillover indices ofcurrency carry trade returns for the 120- and 150-day rolling windows are significantly and positivelycorrelated with subsequent investor sentiment. The regression coefficients are 5.480 and 7.955 for the120- and 150-day rolling windows, respectively. The empirical results provide interesting evidence forthe relationship between the sentiment with respect to risk appetites for currency carry trade marketsand investor sentiment that was proposed by Baker and Wurgler (2006). The empirical results implythat investor sentiment extracted from the stock market can be affected by market risk sentiment.

5. Concluding remarks

This paper investigates the impact of spillovers of currency carry trade returns on market returns.As suggested by Tse and Zhao (2012), the violation of the UIP hypothesis associated with currencycarry trade returns is related to market risk sentiment. Diebold and Yilmaz (2012) have developed aframework to measure the magnitude of spillover effects and indicate that the total spillover index ofasset returns might be associated with the extent of sentiment. Taken together, this paper hypothesizesthat the magnitude of the total spillover index of currency carry trade returns is positively correlatedwith market risk sentiment and has an impact on subsequent market returns.

The current study takes a fresh look at the relationship between currency carry trade returns andU.S. market returns. Instead of studying the impact of portfolios of currency carry trade returns on

17 This paper also uses the VAR to examine the relationship between the total spillover index of currency carry trade returnsand the sentiment index by Baker and Wurgler (2006). The empirical results show that the lagged total spillover index ofcurrency carry trade returns has positively significant effects on investor sentiment. By contrast, the lagged investor sentimenthas no significant effects on the total spillover index of currency carry trade returns. These empirical findings imply that marketrisk sentiment estimated from currency trade markets is different from that of investor sentiment extracted from the stockmarket.

18 The monthly data for the sentiment index are available for from Jeffrey Wurgler’s website: http://pages.stern.nyu.edu/∼jwurgler/. Following Baker and Wurgler (2006), the monthly data of the total spillover index takes the daily spillovervalue at the beginning of that month.

http://pages.stern.nyu.edu/~jwurgler/




market returns in a linear framework, this paper investigates whether the magnitude of the totalspillover index of currency carry trade returns has asymmetric effects on market returns throughoutbull and bear market regimes. In particular, this paper examines whether the impact of the totalspillover index of currency carry trade returns on market returns is larger in bear markets than in bullmarkets. Moreover, the paper also investigates whether a higher magnitude of spillovers of currencycarry trade returns leads to a higher (lower) probability of bull (bear) markets.

Using data over the period January 3, 1994 to March 28, 2012, this paper constructs the totalspillover index for currency carry trade returns and uses this index to measure the extent of marketrisk sentiment. The results show that the magnitude of spillovers of currency carry trade returns ishigher in bull markets than in bear markets. The results also show that the total spillover index ofcurrency carry trade returns Granger-causes market returns, but not vice versa. Furthermore, theempirical results show that the total spillover index of currency carry trade returns positively andsignificantly affects subsequent market returns, and this relationship is stronger in bear markets thanin bull markets. Moreover, the empirical results indicate that a larger value of the total spillover indexleads to a higher (lower) probability of a bull (bear) market regime. Finally, as a robustness check,our results indicate that the total spillover index of currency carry trade returns contains informationon subsequent investor sentiment, as suggested by Baker and Wurgler (2006), which indicates thatinvestor sentiment extracted from the stock market can be affected by market risk sentiment.

The empirical findings of the current study provide valuable information for practitioners. As sug-gested by the empirical findings, investors should pay more attention to spillovers of currency carrytrade markets in a bear regime because these spillovers have a large effect on market returns in a bearmarket. The results also show that the relatively high stock prices accompanied with a sharp decline inthe stock market will likely occur under a relatively high total spillover index of currency carry tradereturns, which reflects a high investor risk appetite sentiment. This finding might provide additionalinformation for traders and risk managers that will allow them to avoid potential downside risks.

Whereas our empirical results present a significantly positive relationship between market risksentiment and subsequent (aggregate) U.S. market returns, Baker and Wurgler (2006) provide empir-ical evidence that the impact of sentiment on portfolio returns varies with firm characteristics. Hence,it is of interest to further explore the linkages between market risk sentiment and portfolio returnswith regard to different firm characteristics. This paper leaves this research topic for future works.

Acknowledgments

The authors would like to thank two anonymous referees and the editor, Hamid Beladi, for theirconstructive comments and suggestions.

References

Alizadeh, A., & Nomikos, N. (2004). A Markov regime switching approach for hedging stock indices. Journal of Futures Markets,24, 649–674.

Bai, J., & Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18,1–22.

Baillie, R. T., & Chang, S. S. (2011). Carry trades, momentum trading and the forward premium anomaly. Journal of FinancialMarkets, 14, 441–464.

Baker, M., & Wurgler, J. (2006). Investor sentiment and the cross-section of stock returns. Journal of Finance, 61, 1645–1680.Baker, M., Wurgler, J., & Yuan, Y. (2012). Global, local, and contagious investor sentiment. Journal of Financial Economics, 104,

272–287.Brunnermeier, M. K., Nagel, S., & Pedersen, L. H. (2009). Carry trades and currency crashes. NBER Macroeconomics Annual,

313–347.Burnside, C., Han, B., Hirshleifer, D., & Wang, T. Y. (2011). Investor overconfidence and the forward premium puzzle. Review of

Economic Studies, 78, 523–558.Chen, S. S. (2011). Lack of consumer confidence and stock returns. Journal of Empirical Finance, 18, 225–236.Cheung, Y. L., Cheung, Y. W., & He, A. W. W. (2012). Yen carry trades and stock returns in target currency countries. Japan and

the World Economy, 24, 174–183.Christiansen, C., Ranaldo, A., & Söderlind, P. (2011). The time-varying systematic risk of carry trade strategies. Journal of Financial

and Quantitative Analysis, 46, 1107–1125.Clarida, R., Davis, J., & Pedersen, N. (2009). Currency carry trade regimes: Beyond the Fama regression. Journal of International

Money and Finance, 28, 1375–1389.

http://refhub.elsevier.com/S1062-9408(13)00076-4/sbref0005





































































































































































































Coleman, A. (2012). Uncovering uncovered interest parity during the classical gold standard era, 1888–1905. North AmericanJournal of Economics and Finance, 23, 20–37.

Darvas, Z. (2009). Leveraged carry trade portfolios. Journal of Banking and Finance, 33, 944–957.Diebold, F. X., & Yilmaz, K. (2012). Better to give than to receive: Predictive directional measurement of volatility spillovers.

International Journal of Forecasting, 28, 57–66.Diebold, F. X., & Yilmaz, K. (2009). Measuring financial asset return and volatility spillovers, with application to global equity

markets. Economic Journal, 119, 158–171.Dufour, J., & Renault, E. (1998). Short run and long run causality in time series: Theory. Econometrica, 66, 1099–1125.Flood, R. P., & Rose, A. K. (1996). Fixes: Of the forward discount puzzle. Review of Economics and Statistics, 78, 748–752.Frijns, B., Koellen, E., & Lehnert, T. (2008). On the determinants of portfolio choice. Journal of Economic Behavior & Organization,

66, 373–386.Galsband, V. (2012). Downside risk of international stock returns. Journal of Banking and Finance, 36, 2379–2388.Gervais, S., & Odean, T. (2001). Learning to be overconfident. Review of Financial Studies, 14, 1–27.Koop, G., Pesaran, M. H., & Potter, S. M. (1996). Impulse response analysis in non-linear multivariate models. Journal of Econo-

metrics, 74, 119–147.Lee, C. C., Huang, W. L., & Yin, C. H. (2013). The dynamic interactions among the stock, bond and insurance markets. North

American Journal of Economics and Finance, 26, 28–52.Lewellen, J., & Nagel, S. (2006). The conditional CAPM does not explain asset-pricing anomalies. Journal of Financial Economics,

82, 289–314.Lothian, J. R., & Wu, L. (2011). Uncovered interest-rate parity over the past two centuries. Journal of International Money and

Finance, 30, 448–473.Maheu, J. M., & McCurdy, T. H. (2000). Identifying bull and bear markets in stock returns. Journal of Business and Economic

Statistics, 18, 100–112.Perez-Quiros, G., & Timmermann, A. (2000). Firm size and cyclical variations in stock returns. Journal of Finance, 55, 1229–1262.Pesaran, H. H., & Shin, Y. (1998). Generalized impulse response analysis in linear multivariate models. Economics Letter, 58,

17–29.Tse, Y., & Zhao, L. (2012). The relationship between currency carry trades and U.S. stocks. Journal of Futures Markets, 32, 252–271.Zhou, S. (2002). The forward premium anomaly and the trend behavior of the exchange rates. Economics Letters, 76, 273–279.


















































































































































































































































































































































spillovers of currency carry trade returns, market risk sentiment, and u.s. market returns

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