exchange rates, interventions, and the predictability of stock returns in japan

J. of Multi. Fin. Manag. 17 (2007) 155–172

Exchange rates, interventions, and the predictabilityof stock returns in Japan

Daniel Hartmann, Christian Pierdzioch ∗Saarland University, Department of Economics, Germany

Received 4 April 2006; accepted 25 August 2006Available online 25 September 2006

Abstract

Using monthly Japanese data for the period 1991–2005, we examined the link between exchange ratemovements and stock returns. We found that exchange rate movements per se do not help to explain stockreturns. There is, however, evidence of in-sample predictability if one accounts for the interventions of theJapanese monetary authorities in the foreign exchange market. This evidence does not indicate a violationof market efficiency insofar as investors cannot use information on interventions to systematically improvethe performance of simple trading rules based on out-of-sample forecasts of stock returns.© 2006 Elsevier B.V. All rights reserved.

JEL classification: C53; E44; F37

Keywords: Foreign exchange market interventions; Predictability of stock returns; Japan

1. Introduction

It is a widely held view that exchange rate movements affect the value of firms and the compet-itiveness of industries which, in turn, should be reflected in stock returns. For this reason, muchresearch has been done to analyze whether exchange rate movements help to explain stock returns.The link between exchange rate movements and stock returns can depend on numerous factorslike a firm’s or an industry’s dependence on net foreign revenues, risk management practices, thecompetitive makeup of an industry, the location and flexibility of production, and the degree of

∗ Corresponding author at: Saarland University, Department of Economics, P.O. Box 151150, 66041 Saarbruecken,Germany. Tel.: +49 681 302 58195; fax: +49 681 302 58193.

E-mail addresses: [email protected] (D. Hartmann), [email protected](C. Pierdzioch).

1042-444X/$ – see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.mulfin.2006.08.004

mailto:[email protected]

mailto:[email protected]

dx.doi.org/10.1016/j.mulfin.2006.08.004

156 D. Hartmann, C. Pierdzioch / J. of Multi. Fin. Manag. 17 (2007) 155–172

exchange rate pass-through. Theoretical research on the factors that may affect the link betweenexchange rate movements and a firm’s value has been done by, for example, Adler and Dumas(1984), Booth (1996), and Bartram et al. (2005).

Empirical results on the link between exchange rate movements and stock returns are availablefor the link between exchange rate movements and (i) returns of aggregate stock market indexes(Roll, 1992), (ii) returns of industry-specific stock market indexes (Griffin and Stulz, 2001), and(iii) returns of stocks of individual firms (Jorion, 1990). There is evidence that the link betweenexchange rate movements and stock returns (i) is stronger when measured over longer horizons(Chow et al., 1997), (ii) has changed over time (Williamson, 2001), (iii) is nonlinear (Kanas,1997), and (iv) can be used to set up profitable trading rules (Bartov and Bodnar, 1994). Anoften reported finding, however, is that this link is small and hardly significant (Griffin and Stulz,2001).

Our results indicate that the link between exchange rate movements and stock returns signifi-cantly changes in months when central banks intervene in foreign exchange markets. A commonfinding in the literature is that interventions occur in times of large movements of exchange rates,where “large” exchange rate movements reflect significant exchange rate misalignments. Thisfinding is important because the link between stock returns and large movements of exchangerates can be different from the one between stock returns and small movements of exchange rates.The use of hedging instruments with nonlinear payoffs may imply a nonlinear link between cashflows and exchange rate movements (Bartram, 2004; Di Iorio and Faff, 2000). Moreover, due totransaction costs, only large movements of exchange rates may affect market structure (Dixit,1989; Booth, 1996).

When one studies the link between large exchange rate movements and stock returns, the prob-lem arises that measuring “large” exchange rate movements is difficult. The foreign exchangemarket interventions of central banks, however, can serve as an instrument for “large” movementsof exchange rates and significant exchange rate misalignments. Results documented in the liter-ature suggest that interventions are triggered by large deviations of exchange rates from centralbanks’ exchange rate targets, longer-term moving averages of exchange rates, and purchasingpower parity (Frenkel et al., 2005). While every single one of these deviations itself may indi-cate a significant exchange rate misalignment, interventions can be viewed as an easy-to-measuresingle summary statistic of all these deviations.

We used Japanese data to study the link between exchange rate movements and stock returns inintervention months. The Japanese monetary authorities heavily intervened in foreign exchangemarkets since the early 1990s. Many results on the interventions of the Japanese monetary authori-ties have been reported in the literature (Ito, 2002; Frenkel et al., 2005). Evidence of a link betweenexchange rate movements and stock returns in intervention months is not yet available. We foundthat neither contemporaneous nor lagged exchange rate movements per se help to predict stockreturns. Yet, there is evidence of in-sample predictability of 1-month-ahead stock returns if oneaccounts for interventions. The in-sample predictability of stock returns does not necessarilyindicate market inefficiency. Investors cannot use information on interventions to improve theperformance of simple trading rules based on out-of-sample forecasts of stock returns.

Our hypothesis is not that interventions per se are useful for predicting stock returns. Wesimply interpreted interventions as a summary statistic of large exchange rate movements or,for that matter, significant exchange rate misalignments. Moreover, rather than focusing on theeffectiveness of interventions, we focused on the informational content of interventions withregard to large exchange rate movements. Our empirical analysis should not be interpreted as atest of the effectiveness of interventions.

D. Hartmann, C. Pierdzioch / J. of Multi. Fin. Manag. 17 (2007) 155–172 157

In Section 2, we sketch the theoretical background of our empirical analyses. In Section 3,we describe our data. In Section 4, we report estimates of central bank reaction functions thatdocument the close link between large exchange rate movements and interventions. In Section5, we report evidence of in-sample predictability of stock returns. In Section 6, we describe themodeling approach we used to study the out-of-sample predictability of stock returns. We alsodiscuss how we analyzed the performance of simple trading rules. In Section 7, we report resultsof both tests of out-of-sample predictability of stock returns and of the performance of tradingrules. We also report results of tests of market timing to study the implications of our results formarket efficiency. In Section 8, we conclude.

2. Theoretical background

Many theories developed in the macroeconomics and finance literature imply that the linkbetween stock returns and exchange rate movements should be nonlinear. In order to make thetheoretical underpinnings of our research more explicit, we sketch the implications of theoriesbuilt on the assumption of frictions in international goods market arbitrage. These theories, whichhave received much attention in recent empirical research on exchange rate dynamics, imply thatlarge exchange rate movements can have implications different from those of small ones.

Baldwin (1988) has argued that only large exchange rate movements alter the structure of goodsmarkets if sunk costs imply that the market entry of foreign firms is costly. Foreign firms facesunk costs of market entry if, for example, they must establish a distribution and service networkbefore they can sell their products in a foreign market, or if they must bring their products intoconformity with local health and safety regulations. Therefore, foreign firms will establish a“beachhead” abroad only if large exchange rate movements imply that the marginal benefits ofmarket entry sufficiently exceed the marginal costs. Hence, only large exchange rate movements(significant exchange rate misalignments) change the competitive makeup of the market and, thus,the market value of firms and stock prices.

Extensions of Baldwin’s beachhead model have been studied, for example, by Baldwin andKrugman (1989) and Baldwin and Lyons (1994). Baldwin and Krugman have shown that sunkcosts of market entry may have persistent effects on the trade balance and, therefore, on theequilibrium exchange rate. These effects give rise to path dependencies in exchange rate dynam-ics. Baldwin and Lyons have further explored these effects, and they have traced out the policyimplications of these effects in a macroeconomic model of exchange rate determination. Pathdependencies in exchange rates suggest that it may be difficult for investors to find out how farexchange rates have moved away from their respective equilibrium values. Investors may, there-fore, appreciate having an easy-to-measure summary statistic of “large” exchange rate movementsthat are not in line with equilibrium exchange rate dynamics. Central banks’ interventions in for-eign exchange markets may serve as such a summary statistic.

Frictions in international goods market arbitrage arise if it is costly to ship goods between spa-tially separated goods markets. Shipping costs may involve transportation costs, insurance costs,and tariffs. Shipping costs may imply nonlinearities in exchange rate dynamics (Dumas, 1992).Sercu et al. (1995) have shown that shipping costs give rise to a no-trade region. In this region,the profits from international goods market arbitrage do not outweigh shipping costs even in thepresence of deviations from purchasing power parity (PPP). In consequence, small exchange ratemovements within the no-trade region do not affect international trade. Large exchange rate move-ments, in contrast, can make international goods market arbitrage profitable. As a result, shippingcosts create a band for the exchange rate within which exchange rate movements do not trigger


international goods market arbitrage, implying a strong persistence of deviations of the exchangerate from its long-run PPP value. At the boundaries of the band, in contrast, arbitrage starts tobecome heavy. The exchange rate should show an increasing mean-reverting tendency as it reachesthe boundaries of the band, resulting in nonlinear exchange rate dynamics (Taylor et al., 2001).

Nonlinearities in exchange rate dynamics may imply a nonlinear link between exchange ratemovements and the market value of firms and, thus, stock prices. Large exchange rate movementsand significant exchange rate misalignments, which imply that shipping costs or the sunk costs ofmarket entry become relatively unimportant, should have a stronger impact on stock prices thansmall exchange rate movements. In our empirical analysis, we used central bank interventions toidentify months of large exchange rate movements and significant exchange rate misalignments,and we report that the link between stock prices and exchange rate movements tends to be strongerin intervention months than in nonintervention months.

3. The data

The data we used in our empirical analyses are from Thomson Financial Datastream. We givethe Datastream codes in parantheses when we introduce a variable for the first time.

3.1. The interventions of the Japanese monetary authorities

Official data on the interventions of the Japanese monetary authorities in the yen/dollar marketwere released by the Japanese Ministry of Finance (2005) for the first time in 2001. The data setcovers the period 1991–2005. We aggregated the daily intervention data to monthly interventiondata by summing up the interventions that occurred in a given month. We counted a month asan intervention month when at least one intervention occurred in that month. Fig. 1 shows theinterventions of the Japanese monetary authorities. The Japanese monetary authorities intervenedin 65 months. The magnitude of the interventions of the Japanese monetary authorities variedwidely during our sample period. The interventions during the second half of the 1990s tendedto be larger on average than those during the first half of the 1990s. As discussed in detail by Ito(2002), this could be due to the fact that, in summer 1995, a new Director General of InternationalFinance Bureau was appointed who claimed to follow a different intervention philosophy basedon less frequent but larger interventions.

Fig. 1. The interventions of the Japanese monetary authorities, 1991–2005. The data are at a monthly frequency. Inter-ventions are measured in terms of billions of yen. Negative interventions denote sales of dollars. Positive interventionsdenote purchases of dollars.


3.2. Real-time information on interventions

An important issue concerning the intervention data is that these data have been made publiclyavailable by the Japanese Ministry of Finance only in 2001. Thus, when one uses the interventiondata to analyze the out-of-sample predictability of stock returns, it is important to be aware of thefact that official intervention data were not available to an investor in real time. Moreover, Frenkelet al. (2004) have documented that reports of Japanese interventions in the yen/dollar market inthe financial press were inaccurate. Thus, as regards our study of out-of-sample predictability ofstock returns, a natural concern is whether an investor, in real time, could have exploited a linkbetween exchange rate movements, interventions, and stock returns. This concern does not affectour study for three reasons. First, we did not use information on the exact number and the exacttiming of interventions. Second, we did not use information on the magnitude of interventionsin our empirical analysis because such information is hard to extract in real time when officialintervention data are not available. Third, even though reports of individual interventions in thefinancial press were not very accurate, reports of interventions disseminated by reporting serviceslike Reuters were more accurate (Galati et al., 2005).

3.3. The stock market data and macroeconomic and financial variables

We used end-of-month data of the MSCI stock market total-return index for Japan (MSJ-PANL(RI)) to measure the development of the Japanese stock market. (We obtained similar resultswhen we used a price index. The results are available upon request.) We rescaled the index such thatit assumed the value 100 in 1991/1. In order to compute stock returns, we computed the change inthe natural logarithm of the total-return index to calculate continuously compounded returns. Wethen subtracted from the continuously compounded returns a short-term interest rate (JPI60BS.).

We used a number of macroeconomic and financial variables as control variables. Our list ofcontrol variables contains 12 variables:

(1) The stochastically detrended short-term interest rate (RTB). We used the Japanese interbankmoney rate (JPI60BS.) as our short-term interest rate. We computed RTB as the differencebetween the short-term interest rate and its 12-month moving average (Rapach et al., 2005).(We also used the first difference of the interest rate. The results closely resemble those forRTB and are available upon request.)

(2) The term spread (TSP). TSP is the difference between the long-term government bond yield(JPI61. . .) and the short-term interest rate. TSP has been considered by, for example, Chenet al. (1986) as a predictor of stock returns.

(3) The change in the natural logarithm of the spot price of oil (OIL; UKI76AAZA). Theanalysis of OIL as an important source of business cycle fluctuations has a long tradition inthe literature (Chen et al., 1986; Pesaran and Timmermann, 2000).

(4) A January dummy (JAN). JAN plays an important role in the literature on financial marketanomalies and seasonalities in stock returns (Thaler, 1987).

(5) A dummy variable (DMA150) that assumes the value one if the difference between thestock market index and its 6-month (∼150 trading days) moving average is smaller than1% percent, and 0 otherwise. See Brock et al. (1992) for a study of moving average-basedtrading rules.

(6) The change in the natural logarithm of the narrowly defined money stock (DM0;JPOMA027B). The narrow money growth has been considered, for example, by Rapach


et al. (2005) as a predictor of returns. (We also used the change in the natural logarithm ofM2+certificates of deposit (JPM2. . .A). The results, available upon request, closely resem-bled those for DM0.)

(7) The inflation rate (INF), computed as the change in the natural logarithm of the consumerprice index (JPI64. . .F). The inflation rate can be used as a measure of monetary conditionsand business cycle fluctuations (Chen et al., 1986).

(8) The change in the natural logarithm of industrial production (DIPA; JPI66. . .IG). Variousstudies of return predictability using macroeconomic variables have used DIPA as a measureof the stance of the business cycle (Chen et al., 1986; Rapach et al., 2005).

(9) The change in the natural logarithm of the unemployment rate (DUP; JPOCSUN%E). Thevariable DUP as a predictor of stock returns has been studied by Rapach et al. (2005) andothers.

(10) The interest rate differential vis-a-vis the United States. We subtracted from the Japaneseshort-term interest rate the 3 month U.S. treasury bill rate (USI60C. . .).

(11) The default spread (RISK). We computed RISK as the difference between the OTC quo-tations for corporate bonds (JPQCBDMEA) and government guaranteed bonds (JPQGGB-MEA).

(12) The U.S. stock market returns (RETUS). RETUS denotes the returns on the MSCI index forthe U.S. stock market (MSUSAML(RI)).

We used the 12-month moving averages of DIPA, INF, OIL, DM0, and DUP to minimize theeffects of data revisions on our results. We accounted for a publication lag of 1 month.

4. Interventions and large exchange rate movements

In order to demonstrate that interventions can serve as an easy-to-measure instrument of “large”exchange rate movements, we estimated central bank reaction functions by means of a Probitmodel. We considered five explanatory variables. (1) The absolute deviation of the yen/dollarexchange rate from its PPP value. The PPP value serves as a proxy for the Japanese monetaryauthorities’ longer-run exchange rate target. In order to compute the PPP value, we used the factthat the yen/dollar exchange rate at the beginning of 1986 approximately represented its PPPvalue (Heston et al., 2002). Starting in January 1986, we used the ratio of Japanese and U.S.consumer prices to compute the exchange rate consistent with PPP. (2) The absolute deviationof the yen/dollar exchange rate from 125 yen/dollar. One hundred and twenty-five yen/dollarmay have been an “implicit” exchange rate target of the Japanese monetary authorities (Ito,2002). (3) The absolute deviation of the yen/dollar exchange rate from its 12-month movingaverage. The latter may capture a short-term exchange rate target. (4) A dummy variable forlagged interventions. The probability of an intervention was high given that an intervention hadoccurred in the previous month (Frenkel et al., 2005). (5) The volatility of the exchange rateestimated by means of an AR(1)-GARCH(1,1) model. This variable captures the fact that centralbanks often intervened to calm disorderly markets.

We present results for all interventions, and for interventions to strengthen the yen (sales) andinterventions to weaken the yen (purchases) (Table 1). The absolute deviation of the exchange ratefrom its implicit PPP value triggered interventions. The absolute deviation of the exchange ratefrom its moving average is significant in the case of sales. Absolute deviations of the exchange ratefrom 125 yen/dollar are significant when all interventions and purchases are analyzed. Laggedinterventions are highly significant. Exchange rate volatility is significant in the case of sales.

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Table 1Estimated reaction functions

Variable Interventions Sales Purchases First subsample Second subsample

Coef. t-Stat. Coef. t-Stat. Coef. t-Stat. Coef. t-Stat. Coef. t-Stat.

Deviations from PPPConstant −2.37 −1.85* −6.73 −4.38*** −1.74 −1.21 −59.17 −3.42*** −1.31 −0.81DEV PPP 0.01 2.00** −0.03 −2.08** 0.02 2.65*** 0.96 4.30*** 0.01 1.17DEV MA 0.03 1.29 0.15 3.22*** 0.01 0.46 0.86 4.59*** −0.01 −0.19INTER(−1) 1.37 5.53*** −7.69 −12.93*** 1.5 5.94*** −0.07 −0.09 1.45 5.19***

VOLA 20.06 0.54 111.1 2.94*** −2.21 −0.05 −340.07 −1.79* −3.95 −0.08

R2 0.2627 0.3536 0.3045 0.8631 0.225LL −72.5883 −9.5182 −67.1611 −2.6148 −54.4073

Deviations from targetConstant −2.57 −1.89* −7.07 −4.65*** −1.89 −1.18 −8.68 −1.04 −1.6 −0.95DEV TARGET 0.03 2.43** −0.01 −0.32 0.04 2.78*** 0.51 4.07*** 0.03 1.66*

DEV MA 0.03 1.23 0.15 3.63*** 0.01 0.44 0.89 3.92*** −0.01 −0.36INTER(−1) 1.27 5.03*** −7.5 −6.55*** 1.4 5.46*** 0.55 0.78 1.38 4.84***

VOLA 27.79 0.7 100.92 2.99*** 6.01 0.13 −332.7 0.17 6.22 0.13

R2 0.2695 0.3066 0.3065 0.8405 0.232LL −71.926 −10.2111 −66.9731 −3.045 −70.2041

The table presents estimation results for Probit models estimated by maximum likelihood. Asymptotic t-statistics (t-stat.) were computed using robust standard errors. Coef., estimated coefficient;DEV PPP, absolute deviation of the yen/dollar exchange rate from its implicit PPP value; DEV TARGET, absolute deviation of the yen/dollar exchange rate from 125 yen/dollar; DEV MA, absolutedeviation of the yen/dollar exchange rate from a 24-month moving average; INTER, intervention dummy; VOLA, volatility of the exchange rate computed by means of a GARCH (1,1) model; LL, valueof the maximized log-likelihood function; R2, adjusted coefficient of determination; (*) (**, ***) denote significance at the 10 (5, 1)% level. The first subsample covers the period of time 1991–1995/5,and the second subsample covers the period of time 1995/6–2005.


Because there is evidence of a change in the intervention strategy of the Japanese monetaryauthorities in the summer of 1995, we analyzed two subsamples. The first subsample ends in May1995, and the second subsample begins in June. Because of the small number of sales, we reportresults for purchases. The results for the first subsample indicate a significant impact of absolutedeviations from PPP, from 125 yen/dollar, and from the moving average on the probability of anintervention. Results for the second subsample reveal a significant impact of absolute deviationsfrom 125 yen/dollar on the probability of an intervention. The effects of the absolute deviationsfrom PPP and from the moving average were insignificant.

Our results support the result reported by Frenkel et al. (2005) that the importance of theexplanatory variables in the reaction function has changed over time. Thus, the definition of theJapanese monetary authorities of what constitutes a large exchange rate movement (a significantexchange rate misalignment) has changed over time. Even if the measure most important foridentifying large exchange rate movements may have changed over time, however, the interven-tions of the Japanese monetary authorities provide an easy-to-measure summary statistic of largeexchange rate movements. Moreover, the modeling approach that we shall describe in Section6 provides the flexibility that is necessary to capture the potentially time-varying link betweenexchange rate movements, interventions, and stock returns.

5. Exchange rates, interventions, and in-sample predictability of stock returns

We now present evidence of in-sample predictability of stock returns. To this end, we used theordinary least squares technique to estimate regressions of stock returns on a constant and variousmeasures of exchange rate movements and interventions. We present estimation results for thefull sample and two subsamples.

5.1. Definitions of variables

The variable NER denotes exchange rate returns defined as changes in the natural logarithmof the yen/dollar exchange rate. The variable NER PLUS (NER MINUS) is equal to NER if theyen/dollar exchange rate depreciated (appreciated), and zero otherwise. The variable NER BIG(NER SMALL) is equal to NER if exchange rate returns were larger (smaller) than 0.5 timesits recursively estimated unconditional standard deviation, and zero otherwise. In order to set upthe recursive estimation, we used data from 1990/1 up to the month in which NER is observed.The variables NER PLUS, NER MINUS, NER BIG, and NER SMALL capture a nonlinear linkbetween exchange rate movements and stock returns (Bartram, 2004). The variable INTER isequal to the value one in intervention months, and zero otherwise. The variable SALES (PURCH)is equal to the value one in months of sales (purchases). We computed the variable NER INTERby multiplying the variable NER with the variable INTER. The variable NER INTER is equal toNER in intervention months, and zero otherwise. The variables NER SALES and NER PURCHare defined in an analogous way.

5.2. Stock returns, contemporaneous exchange rate movements, and interventions

Table 2 summarizes results of regressions of stock returns on contemporaneous exchange ratemovements and interventions. The results indicate that, as reported in the earlier literature, the linkbetween NER and contemporaneous stock returns is weak. Irrespective of whether one considersthe full sample or the two subsamples, the coefficient of NER is never significant. The coefficient


Table 2Results for regressions of stock returns on contemporaneous exchange rate movements and interventions

Full sample First subsample Second subsample

Coef. t-Statistic Coef. t-Statistic Coef. t-Statistic

Only NERConstant −0.12 −0.30 −0.70 −0.80 0.00 0.01NER 0.01 0.10 −0.29 −1.09 0.08 0.70

R2 0.0008 0.0314 0.0019

NER BIG and NER SMALLConstant −0.12 −0.29 −0.84 −0.99 0.00 0.01NER BIG 0.02 0.15 −0.38 −1.37 0.11 0.93NER SMALL −0.20 −0.28 1.58 1.05 −1.15 −1.76*

R2 0.0023 0.0591 0.0193

NER PLUS and NER MINUSConstant −0.59 −0.99 −1.58 −1.22 −0.20 −0.30NER PLUS 0.24 1.08 0.43 0.64 0.17 0.70NER MINUS −0.15 −1.00 −0.57 −1.27 0.01 0.05

R2 0.0130 0.0459 0.0026

NER INTER and INTERConstant −0.31 −0.61 0.70 0.45 −0.59 −1.14NER 0.07 0.57 −0.13 −0.32 0.11 0.89NER INTER −0.13 −0.56 −0.30 −0.56 −0.03 −0.10INTER 0.43 0.50 −2.46 −1.35 2.09 2.11**

R2 0.0043 0.0505 0.0414

NER SALES and NER PURCHConstant −0.31 −0.60 0.70 0.44 −0.59 −1.13NER 0.07 0.57 −0.13 −0.31 0.11 0.88NER SALES 1.58 2.07** 1.46 1.55 1.72 3.05***

NER PURCH 0.06 0.30 0.12 0.24 0.01 0.04SALES −2.20 −1.47 −3.81 −1.63 0.29 0.23PURCH 1.35 1.53 −1.05 −0.54 2.37 2.27**

R2 0.0607 0.1199 0.0542

AllConstant −0.71 −0.98 −0.76 −0.37 −0.79 −1.02NER SALES −1.58 −2.10** −1.62 −1.76* −1.72 −2.56**

NER PURCH 0.06 0.30 0.53 0.78 −0.01 −0.05SALES 2.05 1.35 3.82 1.87* 0.26 0.17PURCH 1.36 1.55 −0.55 −0.27 2.30 2.18**

NER PLUS 0.29 0.37 2.93 1.80* −0.92 −1.20NER MINUS −0.03 −0.03 1.59 0.89 −1.08 −1.42NER BIG −0.04 −0.05 −2.41 −1.52 1.15 1.54

R2 0.1325 0.2664 0.0719

The regressions were estimated using the ordinary least squares technique. t-Statistics are based on heteroskedasticityconsistent standard errors; (*) (**, ***) denote significance at the 10 (5, 1)% level. The first subsample covers the periodof time 1991–1995/5, and the second subsample covers the period of time 1995/6–2005. For definitions of variables, seeSection 5.1.


of NER SMALL is significant in the second subsample. The coefficients of determination of theregressions are small. Thus, in line with results reported in much of the earlier literature, we foundthat the explanatory power of exchange rate movements for contemporaneous stock returns inJapan was limited. In some regressions, the coefficients are negative suggesting that depreciationsof the yen vis-a-vis the dollar were accompanied by decreases in stock prices (He and Ng, 1998).

The significance of coefficients and the magnitudes of the coefficients of determination improveif one considers regressions that feature our measures of interventions as explanatory vari-ables. The coefficient of NER INTER is significant in the second subsample. The coefficients ofNER SALES are always significant. In many regressions, the coefficients of SALES and PURCHare significant. It is also interesting to note that the coefficient of NER BIG is significant in abroader sense, but its sign changes from negative in the first subsample to positive in the secondsubsample. When we control for NER BIG, NER PLUS, and NER MINUS, the coefficients ofmany of our measures of interventions remain significant.

5.3. One-month-ahead stock returns, exchange rate movements, and interventions

Table 3 summarizes results of regressions of 1-month-ahead stock returns on our mea-sures of exchange rate movements and interventions. These regressions help to analyze thein-sample predictability of stock returns. The results indicate that NER INTER, NER SALES, andNER PURCH contain information that help to predict 1-month-ahead stock returns. The respec-tive coefficients are significant in many of the full-sample regressions and in the regressions forthe second subsample. In the first subsample, the respective coefficients are not significant, pos-sibly reflecting the change in the intervention policy that took place in 1995/6. We conductedtwo robustness checks. First, we used the control variables described in Section 3.3 as additionalexplanatory variables. Second, we accounted for the impact of anticipated interventions on stockreturns. To this end, we used lagged interventions. Our reaction function models have shownthat lagged interventions have significant predictive power for interventions. For both robustnesschecks, the results turned out to be qualitatively the same as the results reported in Table 3. Forthe sake of brevity, the results are not reported, but are available upon request.

5.4. The effectiveness of interventions

From our results, one should not draw conclusions regarding the effectiveness of interventions.Effectiveness of interventions is usually measured in terms of their effect on exchange rate returnsor on exchange rate volatility. One common practice is to rate interventions to weaken (strengthen)a currency as effective if they give rise to depreciations (appreciations) of the exchange rate. Panel(A) of Fig. 2 illustrates that there is no systematic link between sales (purchases) of dollars anddecreases (increases) of stock returns. The missing link can be due to a lack of effectiveness ofinterventions or, more likely, to the fact that the link between exchange rate movements and stockreturns is complex and nonlinear. As the regression lines also shown in panel (A) indicate thelink between exchange rate movements and stock returns changes from a small and negative linkin the full sample to a strong and positive in interventions months. In other words, our resultssimply suggest that the correlation between stock returns and exchange rate movements changesin intervention months. As shown in panel (B) of Fig. 2, the correlation between NER and 1-month-ahead stock returns increases from −0.07 to 0.19 in intervention months. The correlationbetween NER and contemporaneous stock returns does not change much, the respective correla-tions being −0.04 and 0.01. Taken together, our results suggest that interventions as a summary


Table 3Results of regressions of 1-month-ahead stock returns on exchange rate movements and interventions

Full sample First subsample Second subsample

Coef. t-Statistic Coef. t-Statistic Coef. t-Statistic

Only NERConstant −0.12 −0.30 −0.71 −0.76 0.10 0.23NER −0.11 −0.84 −0.19 −0.64 −0.11 −0.72

R2 0.0012 0.0164 0.0072

NER BIG and NER SMALLConstant −0.13 −0.32 −0.73 −0.78 0.10 0.23NER BIG −0.12 −0.92 −0.21 −0.66 −0.12 −0.81NER SMALL 0.31 0.44 0.05 0.04 0.48 0.60

R2 0.0017 0.0168 0.0116

NER PLUS and NER MINUSConstant −0.17 −0.30 −0.57 −0.55 0.09 0.14NER PLUS −0.08 −0.37 −0.30 −0.37 −0.10 −0.42NER MINUS −0.13 −0.58 −0.15 −0.44 −0.11 −0.39

R2 0.0030 0.0167 0.0074

NER INTER and INTERConstant −0.23 −0.45 −0.28 −0.17 −0.32 −0.62NER −0.31 −2.06** −0.80 −1.19 −0.24 −1.53NER INTER 0.61 2.60** 0.89 1.21 0.60 2.16**

INTER 0.64 0.78 −0.66 −0.33 1.76 1.90*

R2 0.0207 0.0350 0.0637

NER SALES and NER PURCHConstant −0.23 −0.45 −0.28 −0.16 −0.32 −0.61NER −0.31 −2.05** −0.80 −1.17 −0.24 −1.51NER SALES −0.92 −0.98 −1.16 −0.96 −2.63 −5.95***

NER PURCH 0.61 2.70** 0.89 1.24 0.58 2.06**

SALES −0.63 −0.35 −1.45 −0.51 1.51 1.50PURCH 0.98 1.21 −0.21 −0.11 1.66 1.68**

R2 0.0707 0.0948 0.0690

AllConstant −0.26 −0.41 −0.58 −0.33 −0.19 −0.27NER SALES −0.88 −0.92 −1.14 −0.92 −2.63 −5.87***

NER PURCH 0.61 2.72** 0.97 1.35 0.59 2.11**

SALES −0.64 −0.35 −1.43 −0.50 1.52 1.46PURCH 1.00 1.24 −0.11 −0.06 1.70 1.73*

NER PLUS 0.11 0.16 −0.39 −0.24 0.37 0.44NER MINUS 0.10 0.13 −0.67 −0.40 0.48 0.58NER BIG −0.43 −0.60 −0.25 −0.16 −0.69 −0.86

R2 0.0719 0.0968 0.0761

The regressions were estimated using the ordinary least squares technique. t-Statistics are based on heteroskedasticityconsistent standard errors; (*) (**, ***) denote significance at the 10 (5, 1)% level. The first subsample covers the periodof time 1991–1995/5, and the second subsample covers the period of time 1995/6–2005. For definitions of variables, seeSection 5.1.


Fig. 2. Stock returns, exchange rate movements, and interventions, 1991–2005. Panel (A) shows that our results shouldnot be used to draw conclusions regarding the effectiveness of interventions. Panel (B) shows the correlation of exchangerate movements and stock returns. The data are at a monthly frequency. In panel (A), we plot NER, SALES, and PURCHagainst 1-month-ahead stock returns (RETLEAD). The thin line denotes a regression line that obtains when RETLEADis regressed on a constant and NER. The thick line denotes a regression line that obtains when RETLEAD is regressedon a constant, NER, NER INTER, and INTER. For definitions of variables, see Section 5.1. In panel (B), we use thefollowing notation: (1) correlation of NER with RETLEAD (only intervention months), (2) correlation of NER withcontemporaneous stock returns (only intervention months), (3) correlation of NER with RETLEAD, and (4) correlationof NER with contemporaneous stock returns.

statistic of large exchange rate movements (significant exchange rate misalignments) rather thanthe effectiveness of interventions mattered for firms’ value and, therefore, stock returns.

6. Recursive modeling of out-of-sample predictability of stock returns

In order to simulate how an investor may have used information on interventions to predictstock returns out-of-sample in real time, we used a recursive modeling approach.

6.1. Recursive forecasting of stock returns in real time

We considered an investor whose problem, in every month, is to combine the then availabledata to predict stock returns. In every month, the investor must reach a decision under uncertainty


about the optimal forecasting model. In order to model the investor’s decision, we assumed thatthe investor applies the recursive modeling approach of Pesaran and Timmermann (1995, 2000).To this end, the investor identifies the optimal forecasting model by searching over all possiblepermutations of the variables introduced in Sections 3.3 and 5.1. This implies that the investormust search over a large number of models. In order to conduct this search in an efficient and timelymanner, the investor considers linear regression models estimated by the ordinary least squarestechnique. The regression models always include a constant. As time progresses, the investorrecursively restarts this search, implying a permanent updating of the optimal forecasting model.In order to start the recursive modeling approach, the investor considers the period 1991/1–1993/12as a training period.

In order to identify the optimal forecasting model, the investor needs a model-selection cri-terion. The model-selection criteria we considered are the adjusted coefficient of determination(ACD), the Akaike information criterion (AIC), and the Bayesian information criterion (BIC).The ACD, AIC, and BIC model-selection criteria have the advantages that: (i) an investor caneasily compute them, (ii) they are widely used in applied research, and (iii) they were readilyavailable to and investor at the beginning of our sample period. This is important because theinvestor can base decisions only on information which was available in the months in which thesedecisions had to be reached.

6.2. Measuring the performance of trading rules

In every month, the investor selects three models: one model that maximizes the ACD model-selection criterion, and two models that minimize the AIC and BIC model-selection criteria,respectively. This gives a sequence of optimal models, and a sequence of optimal 1-month-aheadstock-return forecasts. The stock-return forecasts can be used to set up a trading rule that requiresa switching between shares and bonds. For switching between shares and bonds, the investorcan use information on the optimal 1-month-ahead stock-return forecasts implied by the optimalforecasting models. We assumed that when the optimal 1-month-ahead stock-return forecastsare positive (negative), the investor only invests in shares (bonds), not in bonds (shares). Theinvestor does not make use of short selling, nor does the investor use leverage when setting up atrading rule. Trading in stocks and bonds involves transaction costs that are: (i) constant throughtime, (ii) the same for buying and selling stocks and bonds, and (iii) proportional to the value ofa trade.

We used Sharpe’s ratio (Sharpe, 1966) and Jensen’s α (Jensen, 1968) to assess the performanceof trading rules. We computed Sharpe’s ratio as SRS =(rS,T − RT)/S.D.(rS), where SRS is theSharpe’s ratio of trading rule S, rS,T the portfolio returns at the end of the investment horizon, T,obtained by following trading rule S, RT the short-term interest rate at the end of the investmenthorizon, and S.D.(rS) is the standard deviation of portfolio returns under trading rule S. Wecomputed Jensen’s α by estimating the regression equation: rS,T − Rt = αS + βS(rM,t − Rt) + εt,S,where αS is the Jensen’s α for trading rule S, rM,t the returns on the market portfolio, βS the β

coefficient of trading rule S, and εt,S is the trading-rule-specific disturbance term.

7. Empirical evidence of out-of-sample predictability of stock returns

We first present results that summarize how often our investor selects variables in the optimalforecasting models. We then report results that summarize the performance of the trading rules.Finally, we present results of tests of market timing.


Table 4Inclusion of variables in optimal forecasting models in percentage, 1994–2005

Variables Models with interventions Models without interventions

ACD AIC BIC ACD AIC BIC

Panel (A) inclusion of variables in the optimal forecasting modelDIPA 40.88 19.71 0.00 10.22 8.03 0.00INF 41.61 13.87 0.00 40.88 13.14 0.00RTB 1.46 11.68 0.00 4.38 2.92 0.00TSP 21.17 14.60 0.00 28.47 14.60 0.00RDIFF 6.57 0.00 0.00 6.57 0.00 0.00RISK 94.89 63.51 51.82 97.08 73.72 51.82JAN 0.00 0.00 0.00 0.00 0.00 0.00OIL 23.56 0.73 0.00 0.73 0.00 0.00DMA150 43.80 16.06 0.00 43.8 21.90 0.00DM0 27.01 18.98 16.06 26.28 21.17 16.06DUP 32.85 12.41 27.74 29.20 21.90 27.74RETUS 7.30 0.00 0.00 0.00 0.00 0.00NER 66.42 53.28 2.19 3.65 0.00 0.00NER BIG 32.12 24.09 2.19 22.63 4.38 4.38INTER 0.00 0.00 0.00 – – –NER INTER 98.54 77.37 2.19 – – –

With interventions Without interventions

Sharpe’s ratio Jensen’s α Terminal wealth Sharpe’s ratio Jensen’s α Terminal wealth

Panel (B) performance of simple trading rulesZero transaction costs

ACD 0.0504 0.0022 123.37 0.0314 0.0016 113.94AIC −0.0652 −0.0013 76.88 −0.0483 −0.0008 84.49BIC 0.0034 0.0003 101.13 0.004 0.0003 101.33

Medium-sized transaction costsACD −0.033 −0.0003 87.13 −0.0339 −0.0004 86.93AIC −0.1595 −0.0041 52.64 −0.1315 −0.0029 63.5BIC −0.0683 −0.0015 79.68 −0.068 −0.0015 79.76

High transaction costsACD −0.0975 −0.0023 66.38 −0.0826 −0.0018 71.06AIC −0.233 −0.0063 38.91 −0.1872 −0.0044 52.44BIC −0.1148 −0.0027 68.16 −0.1145 −0.0027 68.23

For definitions of variables, see Sections 3.3 and 5.1. ACD denotes the adjusted coefficient of determination, AIC denotesthe Akaike information criterion, and BIC denotes the Bayesian information criterion. In every month, the investor selectsthree optimal forecasting models according to the ACD, AIC, and BIC model-selection criteria. For switching betweenshares and bonds, the investor uses information on the optimal 1-month-ahead stock-return forecasts implied by theoptimal forecasting models. When the optimal 1-month-ahead stock-return forecasts are positive (negative), the investoronly invests in shares (bonds), not in bonds (shares). The investor does not make use of short selling, nor does the investoruse leverage when reaching an investment decision. We assumed medium-sized (high) transaction costs of 0.5 and 0.1 ofa percent (0.1 of a percent and 1%) for shares and bonds, respectively. Initial wealth is 100 yen.

7.1. Inclusion of variables in the optimal forecasting models

The results reported in panel (A) of Table 4 summarize how often an investor would haveincluded exchange rate movements, information on interventions, and the other control variables


in the optimal forecasting models under the ACD, the AIC, and the BIC model-selection criteria.We also report the results that we obtained when we dropped information on interventions fromthe list of variables that are of potential relevance for forecasting stock returns.

The variable NER is hardly included if information on interventions are not considered. Thevariable NER is included relatively often in the optimal forecasting model only if, at the sametime, the variable NER INTER is included in the optimal forecasting model. Under the BICmodel-selection criterion, the variables NER and NER INTER are hardly included in the optimalforecasting model. This is not surprising given that the BIC model-selection criterion selects par-simonious forecasting models. Under the ACD and the AIC model-selection criteria, the variableNER INTER is often included in the optimal forecasting model. The variable INTER is neverincluded in the optimal forecasting model, irrespective of the model-selection criterion being con-sidered. This implies that information on interventions matters for forecasting stock returns onlyinsofar as they revealed information about exchange rate movements to market participants. Asconcerns the other control variables, the variable RISK is often included in the optimal forecastingmodel. The variables DIPA, INF, DMA150, DM0, and DUP are often included in the optimalforecasting model under the ACD and AIC model-selection criteria. The variable JAN is neverand the variables OIL and RETUS are hardly included in the optimal forecasting model.

We conducted four robustness checks of our results. (1) We restarted our recursive modelingapproach in 1995/6 and produced out-of-sample forecasts of stock returns from then on. In thisway, we accounted for the change in the intervention strategy of the Japanese monetary authoritiesthat took place in 1995/5. (2) We restarted our recursive modeling approach in 1995/6, but nowwith the variables NER SALES, NER PURCH, SALES, and PURCH as predictors of stockreturns. (3) We analyzed the sample period 1991/1-1999/12, i.e., we excluded data for the periodduring which the Bank of Japan conducted a zero-interest-rate policy from our dataset. (4) Weanalyzed the potential impact of anticipated interventions on stock returns in real time by usinglagged interventions. The results were similar to those we report in this paper and are availableupon request.

7.2. Economic measures of out-of-sample predictability of stock returns

We compared the performance of trading rules based on forecasts that include information oninterventions with the performance of trading rules that neglect this information. Panel (B) ofTable 4 reports Sharpe’s ratios and Jensen’s α’s. Because of the well-known poor performanceof the Japanese stock markets during our sample period, some of the Sharpe’s ratios and someof the Jensen’s α’s assume negative values. We report results for zero, medium-sized, and hightransaction costs. As in Pesaran and Timmermann (1995), we assumed medium-sized (high)transaction costs of 0.5 and 0.1 of a percent (0.1 of a percent and 1%) for shares and bonds,respectively.

Under the ACD model-selection criterion, the performance of trading rules that account forinformation on interventions (NER INTER) tends to dominate the performance of trading rulesthat neglect this information. Under the AIC and BIC model-selection criteria, trading rulesthat do not account for information on interventions tend to dominate those that account forthis information. Under the BIC model-selection criterion, the differences between trading rulesthat account for information on interventions and those which do not account for this infor-mation is small. The reason for this is that, under the BIC model-selection criterion, exchangerate movements and information on interventions are hardly included in the optimal forecastingmodel.


Table 5Tests of market timing

ACD AIC BIC

Panel (A) regression-based tests of market timingWith interventions

Constant −0.50 0.07 −0.26−0.93 0.13 −0.45

Dummy 0.84 −0.50 0.291.04 −0.62 0.38

Without interventionsConstant −0.48 −0.02 −0.26

−0.79 −0.03 −0.46

Dummy 0.69 −0.43 0.300.86 −0.49 0.38

With interventions Without interventions

Panel (B) nonparametric tests of market timingACD 0.37 0.87AIC −0.15 −0.30BIC 0.39 0.22

ACD denotes the adjusted coefficient of determination, AIC denotes the Akaike information criterion, and BIC denotesthe Bayesian information criterion. In panel (A), we present results of a test of market timing developed by Cumby andModest (1987). This test requires estimating a regression of realized stock returns on a constant and a dummy variablethat assumes the value one if the forecast of stock returns is positive, and zero otherwise. We report t-statistics belowthe coefficients. t-Statistics are based on heteroskedasticity consistent standard errors. In panel (B), we report results ofnonparametric tests for market timing developed by Pesaran and Timmermann (1992). The Pesaran–Timmermann testhas asymptotically a standard normal distribution.

Transaction costs matter for terminal wealth (panel (B) of Table 4). In order to compute ter-minal wealth, we assumed that the investor starts with a financial wealth of 100 yen in 1994/1,the month in which forecasts of stock returns are being made for the first time. Accountingfor information on interventions tends to increase terminal wealth under the ACD model-selection criterion, but not under the AIC and BIC model-selection criteria. Thus, whether ornot an investor should use information on interventions for forecasting stock returns is not quiteclear.

7.3. Statistical measures of out-of-sample predictability of stock returns

We used the forecasts of stock returns implied by our recursive modeling approach to analyzethe implications of our results for market efficiency. To this end, we implemented results of testsof market timing. In panel (A) of Table 5, we report results of a test of market timing developedby Cumby and Modest (1987). The test results indicate that, irrespective of the model-selectioncriterion used to compute forecasts of stock returns, the null hypothesis of no market timingcannot be rejected. In panel (B), we report results of the nonparametric test of market timingdeveloped by Pesaran and Timmermann (1992). Our results reveal that the null hypothesis of nomarket timing cannot be rejected, irrespective of: (i) the model-selection criterion being used toset up a trading rule, and (ii) whether information on intervention is considered for forecastingstock returns.


8. Conclusions

We draw three main conclusions from our results. First, the link between exchange rate move-ments and stock returns changed in intervention months. Second, tests of in-sample-predictabilityof stock returns have revealed a significant link between exchange rate returns and 1-month-aheadstock returns if one accounts for interventions. Third, a recursive modeling approach and tests ofmarket timing have revealed that the evidence of in-sample predictability of stock returns doesnot necessarily constitute a violation of market efficiency.

One direction for future research would be to use our results to motivate industry-level andfirm-level-based studies of the link between exchange rate movements and stock returns in timesof central banks’ interventions. Many authors have reported that such studies can yield impor-tant insights into the link between exchange rate movements and stock returns. It would alsobe interesting to draw on our results to analyze in more detail the implications of the centralbanks’ interventions for the link between exchange rate variability, the riskiness of multina-tional firms, and the volatility of stock returns. Yet, another direction for future research wouldbe to analyze in detail whether interventions affect the pricing of currency risk in internationalstock markets. The reason for this is that deviations from PPP entail exposure to exchange raterisk and, at the same time, may trigger foreign interventions of monetary authorities. Therefore,interventions could affect the premium an investor requires for bearing currency risk. Becausethe intensity of interventions changed over time, a model with time-varying second conditionalmoments would be a natural candidate to analyze the link between interventions and exchangerate risk.

Acknowledgements

We would like to thank an anonymous referee for very helpful comments on an earlier draft ofthis paper. We also thank Volker Clausen and seminar participants at the University of Essen andat the 2006 Annual Meeting of the Council of International Economics of the German EconomicAssociation for many useful comments. The usual disclaimer applies.

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