Standard Deviation and Variance of a Portfolio

Covariance reflects the degree to which two securities vary or change together, and is represented as Cov (Ri,Rj). The problem with covariance is that it has no units, and is difficult to compare across assets. Using covariance, we can calculate the correlation between the assets using the following formula:

Correlation

After incorporating covariance, the standard deviation of a two-asset portfolio can be calculated as follows:

Standard Deviation of a two Asset Portfolio

In general as the correlation reduces, the risk of the portfolio reduces due to the diversification benefits. Two assets a perfectly negatively correlated provide the maximum diversification benefit and hence minimize the risk.

Let’s take an example to understand the calculation. Assume we have a portfolio with the following details:

Example

The standard deviation can be calculated as follows:

This portfolio has an expected return of 16.80% and portfolio risk of 11.09%.