Portfolio Performance of the SDR and Reserve Currencies: Tests Using the ARCH Methodology

In evaluating their foreign exchange exposure, international investors often compare actual portfolios with those calculated under the assumption that the variability of returns on various currency assets is time invariant. This paper uses autoregressive conditional heteroskedastic (ARCH) models to test that assumption. For major reserve currencies, including the SDR, we find evidence that the variances of returns do vary over time and that ARCH models that specify changing variances are superior to models that assume constant variance. By incorrectly assuming a constant variability of returns, the error introduced is smaller with the SDR than with any other national currency.