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If a portfolio has a positive investment in every asset, can the standard deviation on the...

If a portfolio has a positive investment in every asset, can the standard deviation on the portfolio be less than that on every asset in the portfolio? What about the portfolio beta?

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Answer #1

Standard deviation of portfolio is a function of weight of each asset, their standard deviations, and correlation between them. Standard deviation of portfolio can be less than that on every asset in the portfolio by properly diversifying the investments.

Beta is a weighted average of beta of stocks in the portfolio. It can not be less than that of each asset in the portfolio because it is mean of the betas which can not be outside the betas of all other stocks.

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