No, the sum of two or more investment portfolios that contain a total of n securities does NOT correspond to the average total risk of a single portfolio consisting of the same n securities.
If one were to divide the risk of a portfolio of SIX securities into TWO portfolios of THREE securities each, then add the results and calculate their average, the result would be incorrect.
The overall risk results from the systematic and the non-systematic component, whereby the non-systematic component can be cancelled out by the correlation of a security or a financial asset that exists with the other n-1 securities or financial assets.
To learn more about the concept of systematic and non-systematic components, read this article:
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