How do you calculate the standard deviation of a portfolio?

To calculate the standard deviation of a portfolio, you need to know the standard deviations and covariances of the individual assets in the portfolio. The standard deviation of a portfolio is a measure of the portfolio’s risk, or volatility. It is calculated using the following formula:

Standard Deviation of Portfolio = sqrt((w1^2 * s1^2) + (w2^2 * s2^2) + 2 * w1 * w2 * s1 * s2 * cov(1,2))

Where:

  • w1 and w2 are the weights of the first and second assets in the portfolio, respectively
  • s1 and s2 are the standard deviations of the first and second assets, respectively
  • cov(1,2) is the covariance between the first and second assets

If the portfolio contains more than two assets, you would add additional terms to the formula to account for the additional assets. For example, if the portfolio contains three assets, the formula would be:

Standard Deviation of Portfolio = sqrt((w1^2 * s1^2) + (w2^2 * s2^2) + (w3^2 * s3^2) + 2 * w1 * w2 * s1 * s2 * cov(1,2) + 2 * w1 * w3 * s1 * s3 * cov(1,3) + 2 * w2 * w3 * s2 * s3 * cov(2,3))

To calculate the standard deviation of a portfolio, you will need to know the standard deviations and covariances of the individual assets in the portfolio. You can typically find this information from financial websites or by consulting with a financial advisor.

It’s important to note that the standard deviation of a portfolio is not the same as the average standard deviation of the individual assets in the portfolio. The standard deviation of a portfolio takes into account the correlations between the assets in the portfolio, which can affect the overall risk of the portfolio.