Market news co-moments and currency returns

Abstract

We propose three co-moments of the market returns’ cash-flow, and discount-rate shocks and examine empirically an intertemporal capital asset pricing model using the co-moments on currency returns as well as stock returns during Dec. 1983 to Dec. 2017. We find that our proposed model has explanatory power for both currency and stock portfolios. We find several common sources of market risk in currency and stock returns that are reflected in market news. Our findings show that the co-moments are related to currency risk premiums and outperform the well-known liquidity, dollar and HML risk factors.

Appendices

Appendix A: Market news co-moments and liquidity risk

There are two reasons to examine the relationship between market news co-moments and liquidity risk. First, Brunnermeier et al. (2009) believe that liquidity plays an important role in understanding risk premia in the exchange market. Second, Menkhoff et al. (2012) believe that it is difficult to disentangle the effects of risk co-moments and liquidity, because these concepts are related closely. This subsection links the market news co-moments and the liquidity proxies to examine whether they can affect the relative pricing power of our suggested models.

To examine these relationships, we use the three liquidity proxies of bid-ask spread (BAS), TED spread and Pastor and Stambaugh (2003) (PS).The BAS illiquidity factor which is the classical measure of market microstructure is:

$$\psi_{t} = \frac{1}{{T_{t} }}\sum\limits_{{\tau \smallint T_{t} }} {\left[ {\sum\limits_{{k\smallint J_{\tau } }} {\left( {\frac{{\psi_{\tau }^{k} }}{{k_{\tau } }}} \right)} } \right]}$$

(A.1)

where $\psi_{\tau }^{k}$ is the currency $k$’s percentage BAS in month τ, $T_{t}$ and $k_{\tau }$ are all of the months and currencies under study respectively, and $\psi_{t}$ is an illiquidity factor. A higher BAS shows lower liquidity.

The TED illiquidity factor is the spread in interest rate between the three-month Euro interbank deposits and the three-month Treasury bills (Brunnermeier et al. 2009). It explains the willingness of a bank to provide funds in the interbank market. A large spread is directly associated with lower liquidity.

The PS liquidity factor is based on price reversals. It allows stocks with low liquidity to be characterized by a greater price effect of order flow. Liquidity-induced movements of asset prices should be eventually reversed, so that stronger pricing reversals reflect lower liquidity. Unlike the above two illiquidity factors, this measure is a liquidity factor, so that its higher values reflect higher liquidity.

1.1 A.1: Relationship between liquidity factors and market news co-moments

How strongly are liquidity factors and market news co-moments related? There are low correlations between the market news co-moments and the liquidity risk proxies for both samples. During 1983–2017, we find that the total market betas, the market cash-flow betas and the market discount-rate betas are positively correlated to BAS with the values of 20%, 18% and 10% respectively, negatively correlated to TED with the values of − 25%, − 21%, and − 8% respectively, and negatively correlated to PS with the values of − 33%, − 20% and − 9% respectively. During the same period, the total market co-kurtosis, the market cash-flow co-kurtosis and the market discount-rate co-kurtosis are positively correlated to BAS with the values of 25%, 21% and 5% respectively, negatively correlated to TED with the values of − 31%, − 10% and − 9% respectively, and negatively correlated to PS with the values of − 34%, − 30% and − 19% respectively. During this period, we find that the total market co-skewness, the market cash-flow co-skewness and the market discount-rate co-skewness are negatively correlated to BAS with the values of − 18%, − 10% and − 6% respectively, positively correlated to TED with the values of 18%, 12% and 2% respectively and positively correlated to PS with the values of 26%, 14% and 10% respectively. Not surprisingly, the relationship between these liquidity proxies and market news co-moments is far from perfect. For example, the BAS and TED measures are only mildly correlated (14%), and none of the correlation coefficients is larger than 31% in absolute value.

1.2 A.2: Empirical findings for liquidity risk

To shed further light on the role of liquidity risk factors for currency returns and to examine the relative importance of market news co-moments and liquidity as risk factors, we include market news co-moments and one of the liquidity factors jointly in (35) and (36). To estimate the pricing of the liquidity factors using the FMB methodology, we obtain the betas of the liquidity risk proxies for meeting the first stage of the regression (See Sect. 5). For each liquidity proxy, we use the following equation to construct the liquidity beta $\beta^{l}$.

$$\beta^{l} = \frac{{\rho_{\emptyset ,l} \times \sigma_{\emptyset } }}{{\sigma_{l} }}$$

(A.2)

where $\rho_{\emptyset ,l}$ is the correlation between currency excess return and the liquidity proxy, $\sigma_{\emptyset }$ is the standard deviation of currency excess returns, and $\sigma_{l}$ is the standard deviation of the liquidity proxy. According to Sect. 5, we then add the betas to (35) and (36) for estimating the pricing of liquidity risk.

The results are reported in Table 8. The important message from these results is that total market beta and co-skewness, as well as cash-flow beta and co-skewness, can be seen as dominant risk factors, confirming the Menkhoff et al. (2012) findings. For example, Panel A shows our results when jointly using market news co-moments and BAS in both samples: both the total market beta and co-skewness factors and the cash-flow beta and co-skewness factors are significantly different from zero, whereas BAS is found to be insignificant in the joint specification. We also find the same results for TED in Panel B. For the PS liquidity factor (Panel C), we find significant results for the risk in both samples, where economic and statistical significance of the co-moments remain higher than for PS.

Table 8 Asset pricing tests: market news co-moments and liquidity risk

Overall, the liquidity factors often become insignificant when jointly used with market news co-moments. We conclude that the total market beta and co-skewness factors and the cash-flow beta and co-skewness factors are more important than each of the single liquidity proxies. However, we are not able to rule out a description based on our suggested co-moments just being summary measures of different dimensions of liquidity that are not considered by the three (il)liquidity factors.

Appendix B: Horse races among co-moments, DOL and HML

Lustig et al. (2011) and Menkhoff et al. (2012) show that currency returns can be understood by linking them cross-sectionally to the two risk factors of DOL and HML. We need to know whether these two currency proxies can price the cross section of currency returns using our risk-based models. We run horse races between our suggested co-moments and the DOL and HML portfolios in eight different scenarios. First, we simply use our co-moments and HML jointly in the SDF; second, we use the factor-mimicking portfolios for our suggested co-moments, as constructed in subsection (5.2), and HML ; third, we use all factors, but orthogonalize the factor-mimicking portfolio for our suggested co-moments with respect to HML ; and fourth, we use all factors, but orthogonalize HML with respect to the factor-mimicking portfolio for our suggested co-moments. The latter four scenarios are similar to the prior four scenarios, except that we replace HML by DOL. To estimate the pricing of the HML factor using the FMB methodology, we use the following ratio to construct betas of the first stage of the methodology:

$$\beta^{ {\text{HML}} } = \frac{{\rho_{\emptyset , {\text{HML}} } \times \sigma_{\emptyset } }}{{\sigma_{ {\text{HML}} } }}$$

(A.3)

where $\rho_{\emptyset , {\text{HML}} }$ is the correlation between currency excess return and HML , $\sigma_{\emptyset }$ is the standard deviation of currency excess returns and $\sigma_{ {\text{HML}} }$ is the standard deviation of HML. According to Sect. 5, we then add the betas to (35) and (36) for estimating the pricing of HML.

To estimate the pricing of DOL using the FMB methodology, we follow Menkhoff et al. (2012) and construct the DOL proxy as $DOL_{t} - \mu_{DOL}$, where $DOL_{t}$ is the average return of the five currency portfolios in month $t$ and $\mu_{DOL}$ is the average of DOL, which is calculated from $t - 35$ to $t$. We use the following ratio to construct the beta of this factor:

$$\beta^{DOL} = \frac{{\rho_{\emptyset ,DOL} \times \sigma_{\emptyset } }}{{\sigma_{DOL} }}$$

(A.4)

where $\rho_{\emptyset ,DOL}$ is the correlation between currency excess return and DOL, and $\sigma_{DOL}$ is the standard deviation of DOL. We then add the betas to (35) and (36) for estimating the pricing of DOL.

The results of these analyses are reported in Panels A-H of Table 9. Panel A shows that HML dominates our suggested co-moments when HML and our co-moments are contained jointly in the SDF. Non-return factors (i.e., risk co-moments) cannot beat their own factor-mimicking portfolios in a horse race (see chapter 7 in Cochrane 2005). Panel B presents the results involving HML and the factor-mimicking portfolio of our suggested co-moments. These factors have high correlations.⁸ We find that the $\lambda$ s are significant, but the results do not allow us to make a decision due to multicollinearity issues. More interestingly, Panels C and D report the results when we orthogonalize either the factor-mimicking portfolio with respect to HML (Panel C) or HML with respect to the factor-mimicking portfolio of our suggested co-moments (Panel D). These are reliable findings since, by estimating whether the orthogonal components of either factor are priced, we avoid the statistical problems that limit the earlier findings. Panel C shows that the orthogonalized components of the factor-mimicking portfolios still have significantly negative (positive) factor pricings for total co-skewness and cash-flow co-skewness (total beta and cash-flow beta) in the joint specification. This finding, especially for market news covariance (beta), is consistent with Menkhoff et al. (2012) who found that the factor-mimicking portfolios pick up some parts of the second principal component of the cross-section of currency returns that is not considered by HML. In contrast, Panel D shows that the orthogonalized component of HML is not priced when it is jointly contained with the factor-mimicking portfolio of market news co-moments.

We also compare our basic models, as shown in Table 4, with the models that include both market news co-moments and HML based on their economic significance. From Table 4, we observe that market news co-moments generate cross-sectional $R^{2}$ s of 84.09% and 95.25%, MSEs of 0.75 and 0.42 and MAEs of 0.64 and 0.38 for the whole sample period. For the subsample, we also see that market news co-moments generate cross-sectional $R^{2}$ s of 84.78% and 96.29%, MSEs of 0.74 and 0.41 and MAEs of 0.63 and 0.37. When we estimate the same model using both market news co-moments and HML (Panels A-D of Table 9), we find that (1) the cross-sectional $R^{2}$ s of the models reduce and their MSE and MAE pricing errors increase, (2) the pricings of the total market betas, the market cash-flow betas, the total market co-skewness and the market cash-flow co-skewness retain their significance, whereas the pricings of the HML factors are not significant in all models, (3) the magnitude of the pricings of the market news co-moments are larger than the HML factors. Thus, these reasons show that the co-moments outperform HML.

Table 9 Asset pricing tests: market news co-moments, DOL, and HML

Panels E through H report the results when we add the DOL factor to our basic models. We see still significantly negative (positive) factor pricings for total market co-skewness and cash-flow co-skewness (total market beta and cash-flow beta) in the joint SDF specification, while DOL is not significant. The pricings of the DOL factors in the SDFs are larger than those found in Lustig et al. (2011) and Menkhoff et al. (2012). Compared to our basic models in (35) and (36), the DOL-based models have lower cross-sectional $R^{2}$ s, higher MSEs and MAEs, and less significant and economic pricings. Thus, these reasons show that the co-moments outperform DOL.

In summary, we can conclude that when “market news co-moments and HML ” and “market news co-moments and DOL” are considered jointly in the SDF, HML and DOL do not outperform our co-moments in currency portfolios. In addition, the total market betas, the market cash-flow betas, the total market co-skewness and the market cash-flow co-skewness dominate HML and DOL in terms of higher $R^{2}$ s and lower pricing errors.