Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 62. Moving Average Models for Volatility and Correlation, and Covariance Matrices

CAROL ALEXANDER, PhD

Chair of Risk Management and Director of Research, ICMA Centre, Business School, The University of Reading

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

Keywords: variances, volatility, correlation, covariances, correlation matrix, equally weighted moving average, exponentially weighted moving average (EWMA), smoothing constant, RiskMetrics, standard error

Variances and covariances are parametersof the joint distribution of asset (or risk factor) returns. It is important to understand that they are unobservable. They can only be estimated or forecast within the context of a model. Continuous-time models, used for option ...