FRM: Covariance matrix





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Published on Feb 18, 2009

A covariance matrix, in finance, is a square matrix that contains covariances between portfolio assets. Because, for example, the element in row 2/column 2 is an assets covariance with itself, the diagonal of the covariance matrix contains asset variances. Recall that COV[A,A] = correlation[A,A]*Volatility[A]*Volatility[A], and since Correlation[A,A] = 1, it follows that COV[A,A] = 1*Variance[A]. The brief video reviews a spreadsheet in Carol Alexanders Market Risk Analysis: Quantitative Methods in Finance (v. 1). It is a simple but key idea: the covariance matrix embed a correlation matrix. So, if matrix D is the diagonal matrix of return volatilities, and matrix C is the correlation matrix, then the covariance matrix is a matrix product: DCD.

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