Foreign currency returns and systematic risks Victoria Galsband1

Thomas Nitschka

Deutsche Bundesbank

Swiss National Bank

October 11, 2011

1 E-Mail:

[email protected], [email protected]. We gratefully acknowledge comments by Mathias Ho¤mann, Claudia Lambert (discussant) and an anonymous referee of the SNB working paper series. This paper also bene…tted from comments and suggestions from participants in the 14th Conference of the Swiss Society for Financial Market Research and the 2011 Macro and Financial Econometrics Conference at the University of Heidelberg. We also thank Adrien Verdelhan for graciously providing us with data on currency portfolios. Parts of this research have been conducted while both authors were at the University of Zurich and Nitschka enjoyed …nancial support from the Fonds zur Förderung des akademischen Nachwuchses (FAN) of the University of Zurich sponsored by the Ecosciencia donation. The views expressed in this paper are those of the authors and do not necessarily re‡ect the stance of the Bundesbank or the Swiss National Bank.

Abstract Growing evidence suggests that deviations from uncovered interest rate parity re‡ect risk premia on foreign currencies. Hence, general pricing models of asset returns should explain the cross-sectional di¤erences in returns on high and low interest rate di¤erential currencies. We apply an empirical approximation of the intertemportal CAPM to show that cross-sectional dispersion in currency returns can be explained by di¤erences in currency excess returns’ sensitivities to the market return’s cash-‡ow news component. This …nding echoes recent explanations of the value and growth anomaly on stock markets but is more robust in terms of variation of sample period and state variables used to back out the market return’s cash-‡ow and discount-rate news. JEL classi…cation: F31, F37, G15 Keywords: CURRENCY RETURNS, CASH-FLOW NEWS, DISCOUNTRATE NEWS, MARKET RETURN, UIP

1

Introduction

Sensitivities of asset returns to the return on the market portfolio should explain their cross-sectional dispersion. This is one basic insight from the standard, two-period version of the CAPM (Sharpe, 1964; Lintner, 1965). The intertemporal version of the CAPM (Merton, 1973) additionally reveals that sensitivity to the market return’s cash-‡ow news should be awarded with a higher price of risk than sensitivity to the market return’s discount rate news. This theoretical result o¤ers valuable guidance for evaluations of empirical asset pricing anomalies. For instance, Campbell and Vuolteenaho (2004) show that the value and growth anomaly - signi…cant di¤erences in average returns on high and low book-to-market ratio sorted stock portfolios despite similar sensitivities to the CAPM market return - can be explained via the di¤erences in the sensitivity to the market’s cash-‡ow news. Value stocks have higher sensitivities to the riskier cash-‡ow news components of the market return than growth stocks even though their total market return sensitivities, i.e. the sum of their sensitivities to cash-‡ow and discount-rate news, are of similar size. This paper uses the vector autoregressive framework of Campbell (1991) and Campbell and Vuolteenaho (2004) to examine if the logic of the intertemporal CAPM applies to asset classes other than equities. More speci…cally, we apply the Campbell and Vuolteenaho (2004) "bad" cash-‡ow and "good" discount-rate beta CAPM version to excess returns, i.e. ex post deviations from the uncovered interest rate parity condition (UIP), on foreign currency portfolios. We …nd that in the sample period from December 1983 to June 2010, di¤erences in the sensitivity to the market return’s cash-‡ow news explain cross-sectional di¤erences in average foreign currency excess returns. Our results are robust to the choice of sample period as well as the state variables employed to back out the cash-‡ow and discount-rate news. This robustness stands in marked contrast to the evidence provided by Chen and Zhao (2009) who highlight that the success of the vector autoregressive approach of Campbell and Vuolteenaho (2004) in explaining the value and growth anomaly on stock markets depends crucially on the particular set of 1

state variables and the sample period length. Our main results should nonetheless raise a number of questions. First, why should foreign currency excess returns be related to the return on the market portfolio or the di¤erent news components of the stock market return at all? Second, empirical tests of the CAPM typically rely on the use of stock market returns as empirical proxy for the return on the market portfolio. Why should foreign currency excess returns be related to stock market returns? Finally, why should average foreign currency returns be related to cash-‡ow news? What is the economic rationale? The answer to the …rst question is related to a growing literature, both theoretical (e.g. Bansal and Shaliastovich, 2010; Farhi and Gabaix, 2011; Verdelhan, 2010) and empirical (Lustig and Verdelhan, 2006 and 2007; Ranaldo and Söderlind, 2010; Lustig et al., 2011; Menkho¤ et al., 2011), showing that deviations from UIP re‡ect compensation for risk, i.e. risk premia. Hence, as for other asset classes in a standard CAPM setup, the sensitivity of foreign currency risk premia to the di¤erent market return news components should at least partly explain their cross-sectional dispersion. This paper strongly supports the asset pricing view on exchange rates. Speci…cally, it provides empirical evidence on the success of the two-beta CAPM in pricing foreign currency returns, on the one hand, and foreign currency and stock returns simultaneously, on the other hand. The answer to the second question is related to the fact that the use of stock market returns as approximation of the market return is based on the extensive study of di¤erent market return proxies by Stambaugh (1982). He …nds that broad stock market indexes are the best empirical proxies of the market portfolio. It is an empirical question if this holds true when empirical versions of the CAPM are confronted with foreign currency returns. Rejection of a notion that a stock market return is a good approximation of the market return would stand in stark contrast to the growing evidence on tight links between di¤erent asset markets, especially equity and currency markets. Asness et al. (2009) show that value and momentum strategies for di¤erent asset classes, ranging from stock portfolios to commodity and currency markets, are closely related to each other. Lustig et al. (2011) and 2

Brunnermeier et al. (2008) show that typical foreign currency carry trades, i.e. long positions in high forward discount/interest rate di¤erential currencies and short positions in low forward discount/interest rate di¤erential currencies, are strongly correlated with the US stock market return in the 2007/2008 …nancial turmoil. Recently, Verdelhan (2011) shows that countries’systematic equity risk is associated with systematic bond and currency risk over the period from 1999 to 2010. Finally, we are not aware of a particular economic rationale for why foreign currency returns should react more sensitively to cash-‡ow news than to discount-rate news. As Campbell and Vuolteenaho (2004) point out, news about higher future discount rates is "bad" news because the market’s cash ‡ows are discounted at a higher rate but at the same time this news re‡ects better future investment opportunities. This kind of news is less "bad" than new information about lower expected cash ‡ows as the latter is supposed to alleviate the present value of the market portfolio in a permanent or at least persistent manner. Hence, sensitivities to both news components can be compensated with a risk premium. It seems rather an empirical question what news component predominantly rationalizes average asset returns. Our …ndings indicate that the cash-‡ow innovations are decisive to explain average foreign currency returns in the intertemporal CAPM framework. The remainder of the paper is organized as follows. Section 2 brie‡y sketches the decomposition of stock returns into cash-‡ow and discount-rate shocks to break the single CAPM beta of foreign currencies into a cash-‡ow and a discount-rate beta. Section 3 describes the data. Section 4 presents our empirical results for the U.S. stock market and foreign currency returns and Section 5 concludes.

2

Stock Market Return Decomposition

A standard present value relation states that changes in asset prices must be associated with changes in expected future cash ‡ows or discount rates. This section brie‡y sketches the log-linear approximate relation which allows to empirically break the returns on the market portfolio into cash-‡ow and 3

discount-rate components. Using a …rst-order Taylor expansion, Campbell and Shiller (1988a) approximate the log one-period return, rt+1 = ln (Pt+1 + Dt+1 ) ln (Pt ), around the mean log dividend-price ratio, (dt pt ), where Pt is price, Dt is the dividend, and lower-case letters are used for logs. The resulting log-linear relation can be applied to any asset return: rt+1

k + pt+1 + (1

) dt+1

(1)

pt

where k and are parameters1 in the linearization, and is strictly less than unity. Using Equation (1), one can show2 that the log price-dividend ratio is determined by the expected value of future discounted dividend growth and returns pt

dt =

k 1

+ Et

1 X

s

[ dt+1+s

(2)

rt+1+s ]

s=0

where Et denotes a rational expectation formed at the end of period t and denotes a one-period backward di¤erence. Intuitively, a high stock price today is either associated with high dividends or low returns in the future. Further applying Equation (2) to substitute pt and pt+1 out of the approximate Equation (1), Campbell (1991) shows that the unexpected stock return at any time can be decomposed into news about future cash ‡ows (i.e., dividends or consumption) and news about future discount rates (i.e., expected returns). Following Campbell (1991), we write the unpredicted component 1

More speci…cally, the parameters are de…ned by

1 1+exp (dt pt )

and k

ln

(1 ) ln (1= 1). Interestingly, the interpretation of the discount coe¢ cient should not necessarily be linked to the time-series average of the log dividend yield. For example, Campbell (1993, 1996) links it to the average log consumption-wealth ratio. 2 Speci…cally, relation (2) results from rearranging (1) for the current stock price, solving it forward iteratively, imposing the standard transversality condition, lims!1 s (dt+s pt+s ) = 0, and subtracting the current dividend.

4

of return on a stock market index as (1 X M M = (Et+1 Et ) Et rt+1 rt+1

s

dM t+1+s

1 X s=1

s=0

s M rt+1+s

)

(3)

where the cash-‡ow news M NCF;t+1

(Et+1

Et )

1 X

s

dM t+1+s

(4)

s=0

corresponds to revision in expectations about future dividend growth and the discount-rate news M NDR;t+1

(Et+1

Et )

1 X

s M rt+1+s

(5)

s=1

corresponds to revision in expectations about future discount rates. Even though Equations (1)-(3) hold only as approximations, we follow the literature3 and treat them as exact. While an increase in expected cash ‡ows must be associated with a capital gain, a rise in discount rates leads to a capital loss. Furthermore, as argued by Campbell and Vuolteenaho (2004), returns caused by cash-‡ow news are never reversed since the shock is permanent. By contrast, returns generated by discount-rate news pertain their mean reverting feature due to the transitory nature of a shock. Hence, the cash-‡ow news component could be interpreted as permanent, the discount-rate component as transitory part of the stock market return. In order to identify market cash-‡ow and discount-rate news, we follow Campbell (1991) and assume that the data are generated by a …rst-order4 vector autoregressive (VAR) model zt+1 = a + zt +ut+1 3

(6)

Campbell and Shiller (1988a) and Campbell (1991) …nd that the approximation error is small enough and does not a¤ect the results signi…cantly. 4 As discussed by Campbell and Shiller (1988a), the assumption that the VAR is …rstorder is not restrictive, since this formulation also allows for higher-order VAR models by stacking lagged values into the state vector.

5

M where zt+1 is a m-by-1 state vector with rt+1 as its …rst element, a and are m-by-1 vector and m-by-m companion matrix of constant parameters, and ut+1 is an i.i.d. m-by-1 vector of shocks. The model in Equation (6) produces future market returns forecasts s+1

M = e10 Et rt+1+s

(7)

zt

where e1 denotes a m-by-1 vector whose …rst element is one and the remaining elements are all zero. Provided that the data are generated by the process in Equation (6), the discounted sum of changes in future return expectations (i.e., the discount-rate news) can be written as M NDR;t+1

= e1

0

1 X

s

s

ut+1

s=1

= e10

(I

)

1

ut+1

= e10 ut+1

(8)

where (I ) 1 and e10 captures the e¤ect of each VAR state variable shock on discount-rate expectations.5 Since the identity e10 ut+1 = M M NCF;t+1 NDR;t+1 holds true, t + 1 cash-‡ow news can be identi…ed as M NCF;t+1 = (e10 + e10 ) ut+1 :

(9)

The decomposition in Equation (3) might be useful in several ways. First, it allows us to study the relative importance of permanent and transitory news components of the stock market index. Secondly, it allows us to understand how currency portfolio returns react to equity market news arrival. In particular, we can investigate how currency returns interact with changes in market discount rates and cash ‡ows. Empirical evidence suggests that the uncovered interest parity condition fails to hold with the exception of high in‡ation countries (Hansen and Ho5

As discussed by Campbell and Vuolteenaho (2004), the weight of the variable in Equation (8) depends on its persistence and on the absolute value of a variable’s coe¢ cient in the …rst regression of the VAR.

6

drick, 1980; Fama, 1984; Bansal and Dahlquist, 2000). We therefore de…ne it ekt+1 where ikt denotes country k the currency return as crtk = ikt interest rate, it the home country, here United States, equivalent and ekt+1 the change in the log spot exchange rate of country k relative to the home currency. Alternatively one could de…ne crtk = ftk ekt+1 exploiting that it , holds at daily or lower the covered interest rate parity, ftk ekt = ikt frequencies (Akram et al., 2008). At the end of each period t, Lustig et al. (2011) allocate all currencies in a sample of 37 countries to six portfolios on the basis of their forward discounts observed at the end of period t. The receptiveness of currency excess return i of portfolio i to stock market cash-‡ow news is referred to as cash-‡ow crt+1 beta of portfolio i i M Cov crt+1 ; NCF;t+1

i M CF

M V ar rt+1

M Et rt+1

(10)

;

the discount-rate beta6 is de…ned analogously i M Cov crt+1 ; NDR;t+1

i M DR

M V ar rt+1

M Et rt+1

:

(11)

Both betas obviously add up to the traditional CAPM market beta i M

=

i M CF

+

i M DR :

(12)

Please note that this de…nition of sensitivities is di¤erent from regression coe¢ cients which would normalize the covariance of the currency returns with the variance of the respective news components.

3

Data

This section …rst describes the state variables used in the estimation of the VAR. Then we present details about the Lustig et al. (2011) currency port6

Note that we follow Campbell and Vuolteenaho (2004) in de…ning discount-rate news as "better-than-expected" news.

7

folio returns.

3.1

VAR State Variables

Bianchi (2010) points out that the unexpected market return decomposition into two news components and the subsequent "bad beta, good beta" analysis of Campbell and Vuolteenaho (2004) depend strongly on the use of the small stock value spread and the extraction of news series over a sample period that includes the stock market crash that preceded the Great Depression. Bianchi (2010) shows that the value spread inherits important information from the great depression, such that the original VAR of Campbell and Vuolteenaho (2004) can also be described as a two-state Markov-switching process. One regime is closely related to the Great Depression, the other is not. The former regime receives a large weight when agents form their expectations according to the ICAPM. Hence, as Campbell and Vuolteenaho (2004) exploit basic insights of the ICAPM, their results strongly depend on this Great Depression regime. In addition, Chen and Zhao (2009) show that not only the sample period but also the choice of state variables strongly in‡uences the results of Campbell and Vuolteenaho (2004). Against this backdrop, we de…ne a baseline setup that follows as closely as possible Campbell and Vuolteenaho (2004) in specifying the VAR model. We additionally work with the same state variables as Campbell and Vuolteenaho (2004) but over a shorter sample period that runs from November 1983 to June 2010 and corresponds to the available currency return data. Finally, we consider the sensitivity of our conclusions to a variety of combinations of di¤erent state variables in the VAR following Chen and Zhao (2009). The state variables for the baseline speci…cation are de…ned as follows. First, the excess market return rM is measured as the log excess return on the CRSP value-weight index. Second, the yield spread ty between long-term and short-term bonds in annualized percentage points measured in line with Campbell and Vuolteenaho (2004) as the di¤erence between the ten-year constant maturity taxable bond yield and the yield on short-term taxable notes is available up to December 2001. Since 2002 we measure the spread

8

by the di¤erence between the market yield on U.S. Treasury securities at ten-year constant maturity7 , quoted on investment basis from the Federal Reserve8 and the annualized three-month U.S. Treasury bill rate. Third, the market’s smoothed price-earnings ratio pe is constructed as the log ratio of the S&P 500 price index9 to a ten-year moving average of S&P 500 earnings. Finally, the fourth variable, the small-stock value spread vs, is computed from the Kenneth R. French data library10 as the di¤erence between the log book-to-market ratios of small value and small growth stocks. In addition, we follow Chen and Zhao (2009) and consider the following alternative state variables: the one-year price-earnings ratio de…ned as the log ratio of the S&P500 price index to a one year moving average of S&P500 earnings, the dividend yield de…ned as the dividend-price ratio of S&P500, the book-to-market spread de…ned as the log di¤erence between book-to-market equity on value over growth portfolios, in‡ation de…ned as the monthly rate of change in the consumer price index and the stock variance de…ned as the cross-sectional variance of the 25 book-to-market ratio and size sorted Fama-French stock portfolios.

3.2

Currency Portfolio Returns

We use a monthly data set consisting of six foreign currency portfolio returns from a perspective of a U.S. investor constructed by Lustig et al. (2011).11 The sample contains 37 countries, including both developed and emerging markets for which forward contracts are traded. At the end of month t + 1, all currencies in the sample are allocated into six portfolios on the basis of their forward discounts12 observed at the end of period t, net of transaction 7

To check how closely our measure of yield spread is related to that of Campbell and Vuolteenaho (2004) we have calculated it also for the period prior to 2002. The correlation between both spread measures for the period 1928-2001 turned out highly signi…cant. 8 http://www.federalreserve.gov/releases/h15/data.htm 9 Online data is available on http://www.econ.yale.edu/~shiller/data.htm. 10 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html 11 Monthly foreign currency excess return data are available on Adrien Verdelhan’s website http://web.mit.edu/adrienv/www/Data.html 12 Under the covered interest rate parity, the forward discount is equal to the interest rate di¤erential. The cross-section of foreign currency portfolio returns formed on the

9

costs. The portfolios are rebalanced at the end of every month, so that the …rst portfolio always contains currencies with smallest forward discounts and portfolio six always contains the largest forward discount currencies. The i currency excess return crt+1 for portfolio i is computed as the average of the currency excess returns in portfolio i. The currency portfolio returns take into account transaction costs, i.e. bid and ask spreads. Lustig et al. (2011) provide further details on portfolio building methodology. Table 1 presents annualized mean returns (in percentage points) as well as Sharpe ratios on the six forward discount rate sorted currency portfolios over the time span13 from December 1983 to June 2010. Portfolio F1 contains currencies with lowest forward discounts. Portfolio F6 contains currencies with the highest forward discounts. The pattern in average currency excess returns and Sharpe ratios strongly resembles the results obtained by Lustig and Verdelhan (2007), who study risk premia across currency portfolios sorted on past interest rates. Average returns increase from low to high forward discounts and vary from -0.95 up to 4.29 percent p.a.

[about here: Table 1]

4

Empirical Results

This section …rst presents the estimates from a VAR model to obtain the market return’s cash-‡ow and discount-rate news components for di¤erent sample periods using the state variables proposed by Campbell and Vuolteenaho (2004). We then present the currency portfolios’sensitivities to these news components. Finally, we present our main cross-sectional pricing results and robustness checks with respect to the choice of state variables to obtain the cash-‡ow and discount-rate news components. basis of the foreign interest rates has been studied deeply by Lustig and Verdelhan (2007). 13 Note that the respective sample period for the …rst-order VAR model needs to start in November 1983.

10

4.1

VAR Dynamics

Panel A of Table 2 reports the basic characteristics of the …rst-order VAR model described above when using the state variables proposed by Campbell and Vuolteenaho (2004) for the sample period from December 1928 to June 2010. Panel B of this table gives the corresponding estimates for the sample period from November 1983 to June 2010. The VAR is estimated using OLS and employing = 0:951=12 for monthly data. The results do not alter qualitatively for other plausible parameter values. Each row of the table corresponds to a di¤erent dependent variable listed in the header of the row. OLS t-statistics are reported in parentheses below the coe¢ cient estimates. The …rst …ve columns give coe¢ cients on the explanatory variables listed in 2 the column header; the last column shows the adjusted R statistics. The top row of Panel A of Table 1 gives the results of the stock market return forecasting equation when lags of returns, price-earnings ratio, value spread, and term yield are applied as regressors. All four state variables exhibit some forecasting potential. In line with previous …ndings, the momentum property is strongly pronounced for monthly returns. The past smallstock value spread negatively forecasts the stock market with a t-statistic of 2.28. Consistent with the literature, the coe¢ cient on term yield is positive and statistically signi…cant. Finally, similar to Campbell and Shiller (1988b), Campbell and Vuolteenaho (2004), and Campbell et al. (2010), a higher price-earnings ratio is statistically signi…cantly associated with lower 2 returns. The R statistic for the return equation is 2.13% over the full sample. The next rows summarize the forecasting power of the VAR system for 2 the remaining state variables. Overall, R statistics are relatively high and the autoregressive coe¢ cients of the price-earnings ratio, value spread, and term yield are all very close to unity. The shocks to cash ‡ows are almost unrelated to shocks to expected returns with a correlation coe¢ cient of -0.01. Panel B of Table 2 shows that the forecasting power of the state variables for the stock market returns is considerably lower. The autocorrelation of the market return explains most of the forecasting power of the VAR for this sample period while the value spread is marginally insigni…cant at con-

11

ventional signi…cance levels and the term yield as well as the price-earnings ratio exhibit no predictive power for the market return over this particular sample period. Such estimates are in line with the criticism of the returns decomposition approach by Chen and Zhao (2009).

[about here: Table 2]

4.2

Cash-Flow and Discount-Rate Betas of Foreign Currencies

If the pattern of increasing excess returns on currencies from low to high forward discount sorted currency portfolios re‡ects compensation for risk, then we should expect that their sensitivities to systematic risk factors, such as the news components, will also increase from low to high forward discount currencies. Table 3 displays the cash-‡ow and discount-rate betas of the currency portfolio returns as de…ned in Equations (10) and (11). Panel A delivers the betas for the news components obtained from the VAR over the sample period from December 1928 to June 2010. Panel B provides the corresponding betas obtained from the VAR over the November 1983 to June 2010 span length corresponding to the available currency portfolio data sample. Since the de…nition of cash-‡ow and discount-rate betas is di¤erent from regression coe¢ cients, the sum of the cash-‡ow and discount-rate betas represents the total market return beta of a respective currency portfolio. A comparison between the betas in Panel A and Panel B of Table 3 reveals three major insights. First, total market return betas do not vary across the sample periods. They are of similar size. Second, even though the sum of cash-‡ow and discount-rate betas remains rather constant, the importance of the di¤erent news components, i.e. the size of cash-‡ow and discount-rate components in the total market beta, varies. Over the full sample period presented in Panel A, the market betas of currency portfolio returns are dominated by the discount rate news components. By contrast,

12

over the subsample period considered in Panel B, the cash-‡ow news component dominates the total market beta. Third, across both sample periods we observe an increasing pattern in cash-‡ow as well as discount-rate betas from low to high forward discount sorted currency portfolios. Hence, a priori, both news components could be responsible for the di¤erences in average returns on the currency portfolios under study. [about here: Table 3]

4.3

Cross-Sectional Pricing Results

This section presents our cross-sectional …ndings. The …rst subsection presents our evaluation of the explanatory power of the two-beta CAPM variety for currency portfolio returns alone. The second subsection provides an update on the performance of the two-beta CAPM when confronted with the 25 size and book-to-market sorted Fama-French stock portfolio returns. The third subsection presents our results when we vary both the sample period as well as the state variables to back out the two news components of the market return. 4.3.1

Two-Beta CAPM and foreign currency returns: the baseline speci…cation

We use the cash-‡ow and discount-rate betas from the previous subsection, presented in Table 3, to assess the explanatory power of the two-beta version of the CAPM when confronted with returns on foreign currencies. Therefore, we follow Fama and MacBeth (1973) and run cross-sectional regressions of the Lustig et al. (2011) average currency portfolio excess returns on their estimated cash-‡ow and discount-rate betas from either the full restricted sample period, i.e. E cri =

i M CF

M CF

+

i M DR M DR ;

(13)

where cri denotes excess return on currency portfolio i as de…ned in previous sections. We do not consider constant terms in the cross-sectional regressions 13

as we deal with excess returns. Our cross-sectional pricing exercises over the sample period from December 1983 to June 2010 are summarized in Table 4. Panel A of Table 4 provides the results for the two-beta variety of the CAPM when the cash-‡ow and discount-rate news are obtained from the full sample VAR covering the time period from December 1928 to June 2010. Panel B of Table 4 gives the corresponding results for the two-beta CAPM when the cash-‡ow and discount-rate news are obtained from the currency return sample. The main result is easily summarized. Even though both cash-‡ow and discount-rate betas increase from low to high forward discount portfolios, it is the di¤erence in the cash-‡ow news betas that is associated with average foreign currency portfolio returns. This is true for both sample periods presented in Panel A and Panel B of Table 4. According to the R2 statistic, about 80% of the cross-sectional variation is explained by the two news components. This good …t, however, comes at a cost of a relatively high estimate of the price of cash-‡ow risk of almost 67 % p.a. for the full sample period and about 80% for the restricted sample period. The intertemporal CAPM predicts that the price of cash-‡ow risk should be 2M and the price of discount-rate risk should re‡ect 2M with 2M being the variance of the unexpected return on the market portfolio and denoting the coe¢ cient of relative risk aversion. Given the variance of the unexpected market return for the two sample periods, the risk price estimates imply a relatively high risk aversion coe¢ cient of between 26 and 31.

[about here: Table 4] 4.3.2

Two-beta CAPM and the 25 Fama-French portfolios

General asset pricing models such as the empirical interpretation of the intertemporal CAPM employed in this paper should be useful for pricing returns on di¤erent asset classes at the same time. Before we assess whether the two-beta CAPM explains both foreign currency and stock portfolio returns simultaneously, we present the pricing results when we consider only 14

the 25 book-to-market and size sorted stock portfolio returns as test assets. The estimate equation obeys E rj;ex =

i M CF

M CF

+

j M DR M DR

(14)

where rj;ex denotes the return on one of the 25 Fama-French book-to-market and size sorted equity portfolios in excess of the one-month T-bill rate. Table 5 summarizes the results of this evaluation. Panel A of Table 5 provides the results for the two-beta variety of the CAPM when the cash‡ow and discount-rate news are obtained from the full sample VAR. Panel B of Table 5 gives the corresponding results for the two-beta CAPM when the cash-‡ow and discount-rate news are obtained from the currency return sample. These estimates reveal two main …ndings. First, we con…rm the main …nding of Campbell and Vuolteenaho (2004) when we use information from 1928 to 2010 to derive the two news components of the market returns. Average excess returns on book-to-market and size sorted portfolios mirror di¤erences in their sensitivities to the market return’s cash-‡ow news. Di¤erences in sensitivities to the discount-rate news component play a negligible role. Second, the restriction of the time period used to back out the two news components leaves the explanatory power of di¤erences in the sensitivity to cash-‡ow news una¤ected. However, the discount-rate news seems to be priced as well albeit with a negative sign. This …nding re‡ects one of the criticisms by Chen and Zhao (2009) of the Campbell and Vuolteenaho (2004) framework. The variation of the sample period has the potential to alter considerably the conclusions drawn by Campbell and Vuolteenaho (2004).

[about here: Table 5] 4.3.3

Two-beta CAPM and the pricing of both stock and currency portfolios across di¤erent sample periods

This subsection presents risk price estimates of cash-‡ow and discount-rate risk when both foreign currency portfolio returns and stock portfolio returns 15

are considered jointly as test assets in the two-beta CAPM. Table 6 presents the results. As before, Panel A of Table 6 provides the results for the twobeta variety of the CAPM when the cash-‡ow and discount-rate news are obtained from the full sample VAR (December 1928 to June 2010). Panel B of Table 6 gives the corresponding results for the two-beta CAPM when the cash-‡ow and discount-rate news are obtained from the currency return sample, i.e. November 1983 to June 2010. The results leave the conclusions drawn from the previous two subsections unaltered. Di¤erences in cash-‡ow news explain the cross section of both foreign currency and stock portfolio returns. A general asset pricing model, such as the empirical implementation of the intertemporal CAPM considered in this paper, is able to explain cross-sectional di¤erences in asset returns irrespective of a speci…c asset class. However, the particular sample period seems to be important when determining which of the market return’s news component is important in pricing asset returns. This …nding re‡ects one of the criticisms of the Campbell and Vuolteenaho (2004) approach raised by Chen and Zhao (2009). Another source of their criticism is the dependence of the explanation of the value and growth anomaly provided by Campbell and Vuolteenaho (2004) on the choice of state variables. We address this point of concern in the next subsection.

[about here: Table 6] 4.3.4

Pricing stock and currency returns in the two-beta CAPM: variation in state variables

So far we have presented empirical evidence supporting the view that di¤erences in the sensitivities of foreign currency returns to the market return’s cash-‡ow news component can explain the cross-sectional dispersion in average foreign currency returns. In contrast to the evidence on the cross section of stock portfolio returns, this …nding holds irrespective of the particular sample period used to back out the two news components of the market return. Yet, hitherto our analysis has relied on state variables employed in Campbell 16

and Vuolteenaho (2004). Chen and Zhao (2009) show that the Campbell and Vuolteenaho (2004) framework depends heavily on the particular choice of state variables. To address this concern in our setup, we consider seven di¤erent combinations of potential state variables to obtain the market return’s news component as in Chen and Zhao (2009). The sample period for these VARs spans the period from November 1983 to June 2010. We regard again the three test asset cases presented in the previous subsections, i.e. the six forward discount rate sorted currency portfolios, the 25 Fama-French equity portfolios and the combination of foreign currency and stock portfolio returns. It turns out that our main conclusion with regard to the relation of foreign currency returns and the market return’s news components is almost una¤ected by the variation in the VAR state variables. Di¤erences in sensitivities to the cash-‡ow news rationalize the cross-sectional dispersion in foreign currency portfolio returns albeit at a cost of relatively high risk price estimates.

[about here: Table 7] Table 7 presents the details of these pricing exercises. The …rst panel gives an overview of the di¤erent combinations of state variables that we consider. Model 1 denotes the baseline case which uses the speci…cation of Campbell and Vuolteenaho (2004). The cross-sectional results of Model 1 have been presented in the previous subsections. Model 2 di¤ers from the baseline model in considering additionally dividend growth as a state variable. The variables regarded as state variables in the eight models under consideration are indicated by the plus sign. The following panels of the table provide an overview of the risk price estimates for the di¤erent models when confronted with three sets of test assets. The …rst set consists of the six forward discount sorted currency portfolios. These estimates are presented in column A. The second test asset set consists of the 25 book-to-market and size sorted FamaFrench portfolios. These estimates are displayed in column B. The third test

17

asset set regards the foreign currency and stock portfolio returns in column C. These results are provided in column C. The results in column A across all models show that average foreign currency returns are explained by their sensitivities to the market’s cash‡ow news components. Sensitivity to the discount-rate news is not priced in any of the VAR speci…cations under study. Only Model 4, featuring the value spread, dividend growth and the one-year price-earnings ratio besides the market return as state variables in the VAR delivers insigni…cant results, i.e. none of the two risk price components is economically and statistically signi…cantly related to average foreign currency portfolio returns. The results in column B show that for the particular sample period and the regarded combinations of state variables, both cash-‡ow and discountrate news seem to be priced in the book-to-market and size sorted stock portfolio returns. This evidence re‡ects the point made by Chen and Zhao (2009) that the proposed explanation of the value and growth anomaly by Campbell and Vuolteenaho (2004) depends critically on both sample period and state variables used to estimate the market return’s news components. Column C con…rms these conclusions.

5

Conclusions

Empirical speci…cations of general asset pricing models, such as the CAPM with its concept of the market portfolio, should be able to explain average returns on a variety of asset classes at the same time. We …nd evidence that supports this hypothesis. An empirical proxy of the intertemporal version of the CAPM explains excess returns on both foreign currency and stock portfolios. The results for the foreign currency portfolios are more robust with regard to variations of the sample period or state variables used to back out cash-‡ow and discount-rate news components. Our main result contributes to two strands of the literature. First, our main results support that an asset pricing model is able to rationalize excess returns on foreign currencies thus providing further support for the view that ex post deviations from the uncovered interest parity condition re‡ect 18

compensation for risk. Second, we contribute to a growing literature that highlights the links between di¤erent asset classes. Systematic risk, proxied by the excess return on a broad stock market index, is related to risk premia on foreign currency markets.

19

6

References 1. Akram, Q. Farooq, Dag…nn Rime, and Lucio Sarno, 2008, "Arbitrage in the Foreign Exchange Market: Turning on the Microscope," Journal of International Economics, 76(2): 237-253. 2. Asness, Cli¤ord S., Tobias J. Moskowitz and Lasse H. Pedersen, 2009, "Value and Momentum Everywhere," working paper. 3. Bansal, Ravi and Magnus Dahlquist, 2000, "The Forward Premium Puzzle: Di¤erent Tales from Developed and Emerging Markets," Journal of International Economics, 51(1): 115-144. 4. Bansal, Ravi and Ivan Shaliastovich, 2010, "A Long-Run Risks Explanation of Predictability Puzzles in Bond and Currency Markets," working paper Duke University. 5. Bianchi, Francesco, 2010, "Rare Events, Financial Crises, and the Cross-Section of Asset Returns," working paper. 6. Brunnermeier, Markus K., Stefan Nagel, and Lasse H. Pedersen, 2008, "Carry Trades and Currency Crashes," NBER Macroeconomics Annual 2008. 7. Campbell, John Y., 1991, "A Variance Decomposition for Stock Returns," Economic Journal, 101(405): 157-179. 8. Campbell, John Y., 1993, "Intertemporal Asset Pricing Without Consumption Data," American Economic Review, 83(3): 487-512. 9. Campbell, John Y., 1996, "Understanding Risk and Return," Journal of Political Economy, 104(2): 298-345.

10. Campbell, John Y., Stefano Giglio, and Christopher Polk, 2010, "Hard Times," mimeo. 11. Campbell, John Y. and Robert J. Shiller, 1988a, "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Review of Financial Studies, 1(3): 195-228. 20

12. Campbell, John Y. and Robert J. Shiller, 1988b, "Stock Prices, Earnings, and Expected Dividends," Journal of Finance, 43(3): 661-676. 13. Campbell, John Y. and Tuomo Vuolteenaho, 2004, "Bad Beta, Good Beta," American Economic Review, 94(5): 1249-1275. 14. Chen, Long and Xinlei Zhao, 2009, "Return Decomposition," Review of Financial Studies, 22(12): 5213-5249. 15. Fama, Eugene F., 1984, "Forward and Spot Exchange Rates," Journal of Monetary Economics, 14(3): 319-338. 16. Fama, Eugene F. and Kenneth R. French, 1993, "Common Risk Factors in the Returns on Stock and Bonds," Journal of Financial Economics, 33(1): 3-56. 17. Fama, Eugene F. and James D. MacBeth, 1973, "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, 81(3): 607-636. 18. Farhi, Emmanuek and Xavier Gabaix, 2011, "Rare Disasters and Exchange Rates," working paper NBER, NYU Stern and Harvard University. 19. Hansen, Lars P. and Robert J. Hodrick, 1980, "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy 88(5): 829-853. 20. Lintner, John, 1965, "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets," Review of Economics and Statistics, 47(1): 13-37. 21. Lustig, Hanno, Nikolai Roussanov, and Adrien Verdelhan, 2011, "Common Risk Factors in Currency Markets," forthcoming in Review of Financial Studies.

21

22. Lustig, Hanno and Adrien Verdelhan, 2006, "Investing In Foreign Currency Is Like Betting On Your Intertemporal Marginal Rate Of Substitution," Journal of the European Economic Association, 4(2-3): 644655. 23. Lustig, Hanno and Adrien Verdelhan, 2007, "The Cross Section of Foreign Currency Risk Premia and Consumption Growth Risk," American Economic Review, 97(1): 89-117. 24. Menkho¤, Lukas, Lucio Sarno, Maik Schmeling and Anderas Schrimpf, 2011, "Carry Trades and Global Foreign Exchange Volatility," forthcoming in Journal of Finance. 25. Merton Robert C., 1973, "An Intertemporal Capital Asset Pricing Model," Econometrica, 41(5): 867-887. 26. Nitschka, Thomas, 2010, "Cash‡ow News, the Value Premium and an Asset Pricing View on Stock Market Integration," Journal of International Money and Finance, 29(7): 1406-1423. 27. Ranaldo, Angelo and Paul Söderlind, 2010, "Safe Haven Currencies," Review of Finance, 10: 385-407. 28. Shanken, Jay, 1992, "On the Estimation of Beta-Pricing Models," Review of Financial Studies, 5(1): 1-55. 29. Stambaugh, Robert F., 1982, "On the Exclusion of Assets from Tests of the Two-Parameter Model: A Sensitivity Analysis," Journal of Financial Economics, 10: 237-268. 30. Sharpe, William F., 1964, "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk," Journal of Finance, 19(3): 425442. 31. Verdelhan, Adrien, 2010, "A Habit-Based Explanation of the Exchange Rate Risk Premium," Journal of Finance, 65(1): 123-146.

22

32. Verdelhan, Adrien, 2011, "The Share of Systematic Risk in Bilateral Exchange Rates," working paper.

23

7

Tables Table 1: Descriptive Statistics of Forward Discount Sorted Foreign Currency Portfolios

The table shows the mean returns, standard deviations and Sharpe ratios of the six forward discount sorted currency portfolio returns from Lustig et al. (2011) for the sample period from December 1983 to June 2010. All moments are expressed in percentage points per annum. F1 is the portfolio consisting of lowest forward discount currencies. Portfolio F6 consists of the highest forward discount currencies.

F1

F2

F3

F4

F5

F6

Mean

-0.65 -0.95 0.01 2.37 2.29 4.29

Standard deviation

2.37

Sharpe ratio

-0.28 -0.44 0.00 1.07 0.94 1.55

2.13

24

2.19 2.20 2.44 2.78

Table 2: VAR Characteristics The table shows the OLS parameter estimates for a …rst-order VAR model including a constant, the market return (rM ), price-earnings ratio (pe), smallstock value spread (vs) and term yield spread (ty). OLS t-statistics are in parentheses. Each row corresponds to a di¤erent dependent variable. The …rst …ve columns report coe¢ cients on the explanatory variables listed in 2 the column header; the last column shows the adjusted R statistics. Panel A presents the results for the sample period 1928:12 - 2010:06. The correlation between the implied cash-‡ow and discount-rate news is -0.01. Panel B presents the corresponding results for the sample period 1983:11 - 2010:06. The correlation between the implied cash-‡ow and discount-rate news is 0.36.

constant

rtM

tyt

pet

vst

2

R (%)

Panel A: Sample period December 1928 - June 2010 M rt+1

tyt+1 pet+1 vst+1

0.06 (3.38) 0.02 (0.22) 0.03 (2.03) 0.02 (1.08)

0.11 0.01 -0.02 -0.01 (3.46) (1.77) (-3.04) (-2.27) 0.04 0.89 -0.03 0.08 (0.27) (62.40) (-1.06) (2.97) 0.52 0.00 0.99 -0.00 (24.43) (0.73) (294.19) (-0.84) -0.02 0.00 -0.00 0.99 (-0.62) (0.05) (-0.23) (203.80)

2.36 83.46 99.03 98.22

Panel B: Sample period November 1983 - June 2010 M rt+1

tyt+1 pet+1 vst+1

0.07 (2.11) 0.03 (0.19) 0.06 (2.54) 0.09 (2.37)

0.12 -0.00 -0.01 (2.13) (-0.51) (-0.71) -0.38 0.91 -0.09 (-1.21) (38.47) (-1.73) 0.47 -0.00 1.00 (12.35) (-1.28) (160.49) -0.06 -0.01 0.08 (-0.84) (-1.17) (0.80) 25

-0.03 (-1.54) 0.22 (2.01) -0.01 (-0.81) 0.92 (41.54)

1.54 84.87 99.07 86.36

Table 3: Betas of Currency Portfolios Panel A of the table shows the estimated cash-‡ow and discount-rate betas for six forward-discount rate sorted currency portfolios obtained from the VAR system estimated over 1928:12-2010:06 and presented in Panel A of Table 1. Panel B gives the corresponding betas from the VAR system estimated over 1983:11-2010:06 and presented in Panel B of Table 1. Portfolio

F1

F2

F3

F4

F5

F6

F6-F1

Panel A: Sample period December 1928 - June 2010 i M CF i M DR

-0.014 -0.010 -0.010 0.004 0.023 0.042 0.014 0.035 0.038 0.034 0.071 0.118

0.056 0.104

Panel B: Sample period November 1983 - June 2010 i M CF i M DR

-0.003 0.009

0.008 0.018

0.010 0.019

26

0.027 0.063 0.103 0.016 0.041 0.061

0.106 0.052

Table 4: Asset Pricing Tests with Currency Portfolios The table reports the Fama-MacBeth (1973) estimates of the risk prices using six forward discount rate sorted currency portfolios as test assets. Shanken (1992) corrected t-statistics are in parentheses. Estimates are for the 1983:12-2010:06 period for forward discount sorted portfolios. The underlying news series for the estimates in Panel A are obtained from a VAR system estimated over 1928:12-2010:06 reported in Table 1. The underlying news series for the estimates in Panel B are obtained from a VAR system estimated over 1983:11-2010:06 reported in Table 1. Mean squared pricing error (MSE) and mean absolute pricing error (MAE) are in percentage points per annum. M CF

M DR

R2 (%) M SE

M AE

Panel A: Sample period December 1928 - June 2010 67.05 (1.83)

14.02 (1.12)

80.99

0.55

0.50

Panel B: Sample period November 1983 - June 2010 79.11 (2.69)

-60.99 (-1.33)

88.40

27

0.33

0.44

Table 5: Asset Pricing Tests with Stock Portfolios The table reports the Fama-MacBeth (1973) estimates of the risk prices using the 25 book-to-market and size sorted Fama-French stock portfolios. Shanken (1992) corrected t-statistics are in parentheses. Estimates are for the 1983:12-2010:06 period that spans the time period for which data on forward discount sorted foreign currency portfolios is available. The underlying news series for the estimates in Panel A are obtained from a VAR system estimated over 1928:12-2010:06 reported in Table 1. The underlying news series for the estimates in Panel B are obtained from a VAR system estimated over 1983:112010:06 reported in Table 1. Mean squared pricing error (MSE) and mean absolute pricing error (MAE) are in percentage points per annum. M CF

M DR

R2 (%) M SE

M AE

Panel A: Sample period December 1928 - June 2010 40.19 (5.13)

1.16 (0.72)

32.43

4.93

1.78

Panel B: Sample period November 1983 - June 2010 29.91 (5.05)

-20.23 (-2.84)

26.07

28

5.39

1.85

Table 6: Asset Pricing Tests with Stock and Currency Portfolios The table reports the Fama-MacBeth (1973) estimates of the risk prices using the 25 book-to-market and size sorted Fama-French stock portfolios as well as the six forward discount sorted currency portfolio returns jointly as test assets. Shanken (1992) corrected t-statistics are in parentheses. Estimates are for the 1983:12-2010:06 period that spans the time period for which data on forward discount sorted foreign currency portfolios is available. The underlying news series for the estimates in Panel A are obtained from a VAR system estimated over 1928:12-2010:06 reported in Table 1. The underlying news series for the estimates in Panel B are obtained from a VAR system estimated over 1983:11-2010:06 reported in Table 1. Mean squared pricing error (MSE) and mean absolute pricing error (MAE) are in percentage points per annum. M CF

M DR

R2 (%) M SE

M AE

Panel A: Sample period December 1928 - June 2010 40.56 (5.55)

1.11 (0.74)

65.71

4.39

1.67

Panel B: Sample period November 1983 - June 2010 30.28 (5.52)

-20.63 (-3.12)

26.07

29

4.73

1.71

Table 7: Asset Pricing Tests with Di¤erent State Variables: VAR system estimated over 1983:12-2010:06 The table reports the Fama-MacBeth (1973) estimates of the risk prices using (A) six forward discount rate sorted currency portfolios; (B) 25 FamaFrench portfolios; and (C) six forward discount rate sorted currency portfolios and 25 Fama-French portfolios as test assets. Shanken (1992) t-statistics are in parentheses. Estimates are for the sample period from 1983:12-2010:06. The underlying news series are obtained from a VAR system estimated over 1983:12-2010:06. Model 1 is the benchmark case. Excess return is the log excess return on the CRSP value-weight index; term yield is the spread of the long-term over short-term bonds; 10-year PE ratio is the log ratio of the S&P500 price index to a ten year moving average of S&P500 earnings; value spread is the small stock value spread; real dividend growth is the growth rate in real S&P500 dividends; 1-year PE ratio is the log ratio of the S&P500 price index to a one year moving average of S&P500 earnings; dividend yield is the dividend-price ratio of S&P500; book-to-market spread is the log di¤erence between book-to-market equity on value over growth portfolios; in‡ation is the monthly rate of change in consumer price index; stock variance is the cross-sectional variance of 25 Fama-French portfolios.

30

Models

1

2

3

Excess return

+ + + +

+ + + + +

+ + +

Term yield 10-year PE ratio Value spread Dividend growth

4

5

+ + + + + + + +

1-year PE ratio Dividend yield

+

BM spread In‡ation

6

7

8

+ + + + + + + + + + + + + +

Stock variance

(A)

(B)

(C)

31.73 (4.76) 22.47 (2.80) 22.23 5.67 1.89

32.12 (5.22) 22.90 (3.08) 61.29 4.96 1.75

Model 2 M CF

M DR

R2 (%) M SE M AE

70.04 (2.04) 45.34 (0.85) 83.58 0.47 0.48

31

Model 3 M CF

M DR

R2 (%) M SE M AE

69.93 (2.22) 39.25 (0.88) 84.80 0.44 0.46

30.10 (4.88) 19.41 (2.71) 22.84 5.63 1.89

30.42 (5.32) 19.73 (2.97) 61.34 4.96 1.75

Model 4 M CF

M DR

R2 (%) M SE M AE

14.58 (0.85) 43.48 (0.42) 77.84 0.74 0.69

7.43 (10.41) 11.43 (2.41) 17.72 6.00 1.94

7.46 (11.26) 11.67 (2.36) 58.96 5.26 1.82

Model 5 M CF

M DR

R2 (%) M SE M AE

61.74 (1.84) 10.35 (0.31) 80.88 0.55 0.54

30.47 (5.42) 11.49 (2.55) 32.67 4.91 1.78

32

30.72 (5.84) 11.65 (2.76) 65.61 4.41 1.68

Model 6 M CF

M DR

R2 (%) M SE M AE

97.93 (3.34) 53.36 (1.69) 92.48 0.32 0.39

31.50 (4.62) 11.84 (2.21) 19.53 5.87 1.96

31.94 (5.07) 12.14 (2.46) 72.45 5.11 1.80

Model 7 M CF

M DR

R2 (%) M SE M AE

63.24 (1.76) 13.33 (0.37) 80.43 0.56 0.55

30.91 (5.42) 12.08 (2.60) 32.98 4.89 1.79

31.18 (5.84) 12.26 (2.82) 69.32 4.38 1.68

Model 8 M CF

M DR

R2 (%) M SE M AE

84.41 (2.46) 73.39 (1.31) 87.39 0.36 0.47

36.12 (5.42) 28.51 (3.48) 24.56 4.68 1.77

33

36.61 (5.94) 29.07 (3.83) 67.97 4.10 1.63