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Portfolio Variances Calculation Examples Concept

Variance is a statistical term. Variance in accounting and financial analysis refers to the deviation of actual expenses from the budgeted or forecast amount.
Portfolio variance refers to the measurement of fluctuation of actual returns of a set of investments over a period of time. Portfolio variance is calculated using the standard deviations of each security in the portfolio as well as the correlations of each security pair in the portfolio.

The formula for portfolio variance is as follows

Variance = (w(1)^2 x o(1)^2) + (w(2)^2 x o(2)^2) + (2 x (w(1)o(1)w(2)o(2)q(1,2))
Where,
w(1) = the portfolio weight of the first asset
w(2) = the portfolio weight of the second asset
o(1) = the standard deviation of the first asset
o(2) = the standard deviation of the second asset
Cov(1,2) = the covariance of the two assets, which can be sampled to: q(1,2)o(1)o(2), where q(1,2) is the correlation between the two assets.

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Portfolio Variances Calculation Examples Explanation

Let’s take an example and understand the calculation of portfolio variances.
Example: Assume there is a portfolio that consists of two stocks. Stock A is worth $5,000 and has a standard deviation of 20%. Stock B is worth $10,000 and has a standard deviation of 10%. Given Cov is 0.85, w(1)is 33.3% and w(2) is 66.7%. Calculating the portfolio variance by using the formula
Variance = (33.3%^2 x 20%^2) + (66.7%^2 x 10%^2) + (2 x 33.3% x 20% x 66.7% x 10% x 0.85) = 1.64%

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