What is Portfolio Variance?

Portfolio variance measures the degree to which a portfolio’s returns vary around their average return. It incorporates both the individual volatility of assets and the correlation between their returns. 

For a two-asset portfolio, the “portfolio variance” can be calculated as follows:

Portfolio Variance = w1212 +w2222  + 2 w1w212 12

Where:

• w1, w2 = Portfolio weights
• 1, 2 = Standard deviations of asset returns
• 12 = Correlation between the two assets

Furthermore, using the portfolio variance, we can also calculate the standard deviation of the portfolio as follows:

• Standard Deviation of the Portfolio = Portfolio Variance x 100 

Portfolio Variance Calculation India Example

Suppose a portfolio contains two assets:

Assume that the correlation between these two assets is 0.20. Now, 

Portfolio Variance = (0.6² × 0.15²) + (0.4² × 0.10²) + 2(0.6)(0.4)(0.15)(0.10)(0.20)

Portfolio Variance = 0.009684

Standard Deviation of Portfolio = 0.009684 x 100 = 9.84%

The portfolio has an estimated standard deviation of 9.84%, which potentially indicates that its returns have historically varied around the portfolio’s average return by about 9.84 percentage points, based on the assumptions used.

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