Blaise Labriola
January 29, 2018
Blaise Labriola @ Zoonova.com
Managing Partner Zoonova.com.

Why is the risk of a portfolio always less or equal than the sum total of risks of individual assets in a portfolio?

This is because of the Covariance of the different securities in the Portfolio. Here is an easy way to understand how this works by the following calculations in  ZOONOVA

First here is a screenshot of the calculated Variance and Volatility of each security in a Portfolio with the weighted average at the top of the column.

Now we take the same portfolio and calculate a Covariance Matrix.

The diagonal of the Covariance matrix are the Variances of each individual security the other output is the Covariance output for each security against another security.

Using the Covariance output and matrix math we can calculate the Variance of the Portfolio and the Volatility from the SQRT of the Variance.

Here is the Portfolio output showing the Portfolio Variance and Volatility. If you compare this output with the weighted average output for Variance and Volatility you will see the actual Portfolio output is lower. This is because of the Covariance and Correlation relationship between the different securities which lowers the overall Volatility.

Cheers.

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