Model-free evaluation of directional predictability in foreign exchange markets, страница 24

For the remainder of this section we focus on interest rate differentials ID_t. For reasons of space, we only report the results for the directions of joint negative changes in the spot market in Table V.^[27] As in to Table IV, the first section of Table V provides the GCS test statistics based on past interest rate differentials of two countries jointly (hereafter, ‘joint interest rate differentials’), while the remaining two sections of Table V list the GCS test statistics based on past individual interest rate differentials of each currency (hereafter, ‘individual interest rate differentials’).

First, our GCS tests M_ZID1ID₂1,0,0 and M_ZIDk 1,0 for k D 1,2 strongly suggest that the directions of joint changes with any threshold can be predicted using past joint and individual interest rate differentials. There is also strong evidence that the directions of greater co-movements (c D 0.5,1) are easier to predict. However, we find no clear descriptive pattern of their statistical significance.

Next, our remaining GCS tests based on interest rate differentials suggest that the level, volatility, skewness, kurtosis and direction of past joint and individual interest rate differentials are useful in predicting directional predictability of joint changes. For example, the directions of joint changes for the pairs BP&SF and BP&DM in both spot and futures markets (not shown here) are easily predictable and become more easily predictable with large threshold c D 0.5,1. Further, their directional predictability of joint changes can be well explained by the sources considered in this study.

To sum up, we observe that the directions of joint changes in both spot and futures markets are predictable, using joint and/or individual components of currency returns and interest rate differentials. These findings are more striking with greater co-movements (c D 0.5,1). Individual components of dependencies induced by currency returns are indeed important in exploring the direction of joint changes. Documented directional predictability of joint changes can be explained by various sources. In particular, the level of joint returns and the volatility of past individual returns are very helpful in predicting the directions of joint changes. These results can provide valuable information for financial risk management and portfolio diversification, as our study offers a possible link among the co-movement of returns, correlation and variance. For instance, a diversified portfolio is typically constructed among assets with negative or low correlation to each other. And, given a similar degree of correlation, overall risk can be further reduced by selecting assets with low volatility. Hence, when building a diversified portfolio, it seems natural to prefer assets with low volatility and low correlation to assets with greater volatility and/or high correlation. Meanwhile, comparative analytics of our GCS test for joint changes can provide the basis for a choice between assets with low correlation and greater volatility, and assets with high correlation and low volatility. In this regard, our GCS tests for joint changes will be useful in developing an effective composition of a portfolio.

6.  CONCLUSION

We have examined directional predictability in foreign exchange markets using a model-free statistical evaluation procedure. This method is developed to test whether the direction of the

Table V. GCS test statistics for negative joint changes in two currency spot rates (pD 21): using interest rate differentials