### CORRELATION ANALYSIS

#### Introduction

The correlation analysis section of V-Lab presents measures of correlation for major firms, equity indices, currencies, commodities, and other asset classes both globally and in the United States. The Correlation Analysis section of V-Lab provides 45 correlation analyses on 135 assets using various econometric models.

Correlations are critical inputs for many of the common tasks of financial management. Hedges require estimates of the correlation between the returns of assets in the hedge. If the correlations and volatilities are changing, then the hedge ratio should be adjusted to account for the most recent information. Similarly, structured products such as rainbow options that are designed with more than one underlying asset have prices that are sensitive to the correation between the underlying returns. A forecast of future correlations and volatilities is the basis of any pricing formula.

Asset allocation and risk assessment also rely on correlations, however in this case a large number of correlations are often required. Construction of an optimal portfolio with a set of constraints requires a forecast of the covariance matrix of returns. Similarly, the calculation of the standard deviation of today's portfolio requires a covariance matrix of all the assets in the portfolio. These functions entail estimation and forecasting of large covariance matrices, potentially with thousands of assets.