# Finding the Standard Deviation of a Portfolio Using Beta

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Suppose that the expected return on the market is 12% and the risk free rate is 7%. The standard deviation of the return on the market is 15%. One investor creates a portfolio on the efficient frontier with an expected return of 10% and another creates a portfolio on the efficient frontier with an expected return of 20%. What is the standard deviation of the return of the two portfolios?

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##### Solution Summary

This solution illustrates how to find a portfolio's standard deviation using the Capital Asset Pricing Model,.

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The Capital Asset Pricing Model tells us that:

Required return on a security (or portfolio) = Risk-free rate + (Beta*(Expected return on the market - risk-free rate))

Furthermore, the Beta on the market is always 1.0 and the beta is the ratio of the standard deviation of a security or portfolio to that of the market. (Thus, Beta = standard deviation of security or portfolio / Standard deviation of ...

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