Robust conditional variance estimation and value-at-risk

ABSTRACT The exponentially weighted moving average (EWMA) estimator is widely used to forecast the conditional volatility of short-horizon asset returns. The EWMA estimator is appropriate when returns are drawn from a normal conditional distribution, but when the conditional distribution of returns is fat-tailed – as is commonly found in practice – the EWMA estimator is inefficient in the sense that it attaches too much weight to extreme returns. In this paper we propose a simple generalization of the EWMA estimator that nests both the standard EWMA estimator and other EWMA estimators that are robust to leptokurtosis in the conditional distribution of returns. We illustrate the new estimator by forecasting the value-at-risk (VAR) of aggregate equity portfolios for the US, the UK and Japan using historical simulation. Back-testing results show that a robust EWMA estimator based on the absolute value of returns rather than their squares offers an improvement over the standard EWMA estimator.