This paper tests the common assumption used in portfolio theory that returns on various currency fixed-income investments do not vary over time. This assumption underlies most optimal portfolio models investors use in managing their financial assets. If this assumption does not hold, the resulting allocation of assets is not necessarily optimal, and the obtained measure of the riskiness of a portfolio may not be accurate. Suboptimal allocations may have significant implications for the hedging approaches necessary to control the implied interest and exchange rate risk and may thus expose investors to greater risk of loss than they are willing to accept. If estimates of changing variances can be made with reasonable accuracy, appropriate portfolio shifts can be made over time. Such a strategy can help central banks manage their foreign exchange reserves.
The tests employ the autoregressive conditional heteroscedasticity (ARCH) methodology. The existence of heteroscedasticity makes it difficult to base inferences and predictions on least-squares estimation. When the conditional variances of returns are not constant through time, they can be calculated with the estimation procedure used in ARCH models. Estimation is possible because the autoregressive (AR) representation of a time series with ARCH disturbances allows for the changing variances of investment returns to be forecast, even though the level of returns cannot be predicted. For this study, the standard univariate ARCH model was estimated using weekly data on short-term investment returns on various currencies, including composites such as the ECU and the SDR, for February 1982 to December 1991.
The empirical results indicate that the returns on nine currency investments exhibit statistically significant and persistent changes over time. Specifically, the estimated constant term in an autoregressive specification for returns is positive for all currencies, implying an upward trend in total returns, although the process is generally not explosive. The estimated ARCH parameter for SDR returns is the smallest among all currency returns exhibiting one lag of ARCH effects, indicating that SDR investments provide greater insulation from unexpected shocks. Finally, the statistical tests presented in the paper indicate that the conventional assumption of a standard normal distribution for the errors of the underlying portfolio model is not consistent with the data for the 1982-91 period.