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Estimating the Variance-Covariance (VCV) Matrix from Market Data
Team Latte
August 3, 2011
Quantitative equity analysts, fund managers and risk managers in bank need to have the variance covariance (VCV) matrix of asset returns almost on a real time basis. How do we estimate the VCV matrix from market data of stock (asset) prices?
The best, and the easiest way, to extract the VCV matrix from the market data is to estimate it via excess return. From a time series of stock price data we can calculate the mean return of the stock and hence determine the excess return for a particular period, i.e. the return of a particular period less the mean return. Let’s say that we have  risky assets (stocks or stock indices, etc.) and for each of these assets we have price data (which we can easily obtain in real time from Bloomberg) for  periods (say, 12 months, 52 weeks or 5 years, etc.)
Then, here's the algorithm for obtaining the VCV matrix of the portfolio of assets:
- Estimate the return on each of these assets over periods; ideally, all percentage asset returns should be annualized
- Calculate the mean return for each of the assets (stocks);
- Estimate the excess return matrix; the matrix of excess returns,
 is given by:
Note that the matrix of excess return, , will have a dimension of  and it will not be a square matrix as  . It is mostly likely that we may have many more periods. , over which return would be calculated than the number of assets, .
- Calculate the transpose of the matrix of excess returns,
 .
- Finally, the VCV matrix is given by the following matrix multiplication:
It is quite easy to implement the above algorithm in ExcelTM and we can generate real time VCV matrices for risk and portfolio analysis.
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