Suppose that Ms.Lynch can make up her portfolio using a risk-free asset that offers a surefire rate of return of 15% and a risky asset with an expected rate of return of 25%, with standard deviation 5.If she chooses a portfolio with an expected rate of return of 20%, then the standard deviation of her return on this portfolio will be
A)2.50%.
B)5%.
C)5.50%.
D)1.25%.
E)None of the above.

Question

Suppose that Ms.Lynch  can make up her portfolio using a risk-free asset that offers a surefire rate of return of 15% and a risky asset with an expected rate of return of 25%, with standard deviation 5.If she chooses a portfolio with an expected rate of return of 20%, then the standard deviation of her return on this portfolio will be
A)2.50%.
B)5%.
C)5.50%.
D)1.25%.
E)None of the above.

Quizplus · Accepted Answer

The standard deviation of a portfolio that combines a risk-free asset and a risky asset is proportional to the amount invested in the risky asset. Since the expected return of the portfolio (20%) is exactly in the middle of the risk-free rate (15%) and the risky asset's expected return (25%), it implies that the portfolio is composed of equal parts of the risk-free and risky assets. Therefore, the standard deviation of the portfolio will be half of the standard deviation of the risky asset alone, which is 5%/2 = 2.5%.

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