Suppose that Ms.Lynch in Workouts can make up her portfolio using a risk-free asset that offers a surefire rate of return of 10% and a risky asset with an expected rate of return of 15%, with standard deviation 5.If she chooses a portfolio with an expected rate of return of 12.50%, then the standard deviation of her return on this portfolio will be

A) 5%.
B) 5.50%.
C) 2.50%.
D) 1.25%.
E) None of the above.

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Anirudh Vigneshwar · Accepted Answer

Final Answer : C, Explanation :  The standard deviation of a portfolio that combines a risk-free asset and a risky asset depends only on the portion of the portfolio invested in the risky asset. Since the risk-free asset has a 0% standard deviation, any standard deviation in the portfolio comes from the risky asset. The expected return of 12.50% is exactly halfway between the risk-free return of 10% and the risky asset's return of 15%, implying that the portfolio is composed of equal parts risk-free and risky assets. Therefore, the portfolio's standard deviation would be half of the risky asset's standard deviation, which is 2.50%.

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