Portfolio variance measures the dispersion of returns of a portfolio. It is calculated using the standard deviation of each security in the portfolio and the correlation between securities in the portfolio.

Calculating the Portfolio Variance of Securities

To calculate the portfolio variance of securities in a portfolio, multiply the squared weight of each security by the corresponding variance of the security and add two multiplied by the weighted average of the securities multiplied by the covariance between the securities.

To calculate the variance of a portfolio with two assets, multiply the square of the weighting of the first asset by the variance of the asset and add it to the square of the weight of the second asset multiplied by the variance of the second asset. Next, add the resulting value to two multiplied by the weights of the first and second assets multiplied by the covariance of the two assets.

For example, assume you have a portfolio containing two assets, stock in Company A and stock in Company B. Sixty percent of your portfolio is invested in Company A, while the remaining 40% is invested in Company B. The annual variance of Company A's stock is 20%, while the variance of Company B's stock is 30%.

The correlation between the two assets is 2.04. To calculate the covariance of the assets, multiple the square root of the variance of Company A's stock by the square root of the variance of Company B's stock. The resulting covariance is 0.50.

The resulting portfolio variance is 0.36, or ((0.6)^2 * (0.2) + (0.4)^2 * (0.3) + (2 * 0.6 * 0.4 * 0.5)).

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