Portfolio Volatility – Market Risk Metrics

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Volatility for a portfolio may be calculated using the statistical formula for the variance of the sum of two or more random variables which is then square rooted. Alternatively, the volatility for a portfolio may be calculated based on the weighted average return series calculated for the portfolio. Both of these methodologies are discussed below.

1. The portfolio volatility formula
Consider a portfolio of three assets X, Y and Z with portfolio weights of a, b and c respectively. The portfolio volatility is:

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Variance (X) = Variance in asset X’s returns, i.e. X’s returns volatility squared (σ_x²)

Variance (Y) = Variance in asset Y’s returns, i.e. Y’s returns volatility squared (σ_y²)

Variance (Z) = Variance in asset Z’s returns, i.e. Z’s returns volatility squared (σ_Z²)

_ρxy = correlation coefficient of X and Y returns

_ρxz = correlation coefficient of X and Z returns

_ρyz = correlation coefficient of Y and Z returns

If the assets in the portfolio are independent of each other the correlation coefficient terms in the equation above would be zero. If the assets in the portfolio are perfectly correlated with each other then the volatility of the portfolio would simply be the weighted average sum of the asset return volatility.

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