Moving Average Models for Volatility and Correlation, and Covariance Matrices

Abstract

The volatilities and correlations of the returns on a set of assets, risk factors, or interest rates are summarized in a covariance matrix. This matrix lies at the heart of risk and return analysis. It contains all the information necessary to estimate the volatility of a portfolio, to simulate correlated values for its risk factors, to diversify investments, and to obtain efficient portfolios that have the optimal trade-off between risk and return. Both risk managers and asset managers require covariance matrices that may include very many assets or risk factors. For instance, in a global risk management system of a large international bank all the major yield curves, equity indexes, foreign exchange rates, and commodity prices will be encompassed in one very large dimensional covariance matrix. Keywords: variances; covariances; volatility; correlation matrix; correlations; RiskMetrics; the standard error; equally weighted moving average; exponentially weighted moving average (EWMA); smoothing constant