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Portfolio variance calculation for securities
October 18, 2020
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Portfolio variance calculation for securities

To calculate the portfolio variance for the stocks in the portfolio, multiply the square weight of each stock by the corresponding stock variance and add two times the weighted average of the stock multiplied by the covariance between the two stocks.

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

Calculation form

For example, suppose you have a portfolio that contains two assets, an inventory in company A and an inventory in company B. While 60% of your portfolio is invested in company A, the remaining 40% is invested in company B. The annual variance in the share of company "A" is 20%, while the variance in the share of company "B" is 30%.

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A wise investor seeks effective boundaries. This is the lowest level of risk at which a target return can be generated.

The relationship between the two assets is 2.04. To calculate the asset covariance, multiply the square root of the variance in company A's stock by the square root of the variance in 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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Portfolio variation and modern portfolio theory

Modern portfolio theory is a framework for building an investment portfolio. MPT takes its central premise the idea that rational investors want to maximize returns while minimizing risk, and it is sometimes measured using volatility.

Therefore, investors seek what are called effective limits, or the lowest level of risk and volatility, with which to achieve a target return.

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Measure the risks

After MPT, the risk in the portfolio can be reduced by investing in unrelated assets. That is, an investment that can be considered risky on its own can actually reduce the overall risk of the portfolio because it tends to rise when other investments go down.

This low correlation can reduce theoretical portfolio variance. In this sense, an individual's return on investment is less important than his total contribution to the portfolio in terms of risk, return and diversification.


The level of risk in a portfolio is often measured using the standard deviation, which is calculated as the square root of the variance. If the data points are far from average, the variance is high and the overall risk level in the portfolio is also high.

Standard Deviation is a key measure of risk used by portfolio managers, financial advisors, and institutional investors. Asset managers routinely include the standard deviation in their performance reports.

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