Moving Average Models for Volatility and Correlation, and Covariance Matrices

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 indices, foreign exchange rates and commodity prices will be encompassed in one very large dimensional covariance matrix.