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Tom's portfolio consists solely of an investment in Merck stock.Merck has an expected return of 13% and a volatility of 25%.The market portfolio has an expected return of 12% and a volatility of 18%.The risk-free rate is 4%.Assume that the CAPM assumptions hold in the market.
-Assuming that Tom wants to maintain the current volatility of his portfolio,then the maximum expected return that Tom could achieve by investing in the market portfolio and risk-free investment is closest to:
A)13%.
B)15%.
C)16%.
D)12%.

Question

Quizplus · Accepted Answer

According to the CAPM, the expected return on a portfolio can be calculated as the risk-free rate plus the product of the portfolio's beta (volatility) and the excess return of the market portfolio over the risk-free rate. To maintain the same volatility as his current portfolio, Tom will need to invest a portion of his funds in the risk-free asset and the remainder in the market portfolio. Let x be the fraction of his funds invested in the market portfolio, and (1-x) be the fraction invested in the risk-free asset.

Given Merck's volatility of 25%, we have:

0.25^2 = x^2 * 0.18^2 + (1-x)^2 * 0

Solving this equation, we get x = 0.726.

Thus, Tom will need to invest 72.6% of his funds in the market portfolio and the remaining 27.4% in the risk-free asset.

The expected return on his new portfolio will be:

0.274 * 0.04 + 0.726 * (0.12 - 0.04 * 1.25) = 0.15

Therefore, the maximum expected return that Tom could achieve by investing in the market portfolio and risk-free investment while maintaining the same volatility as his current portfolio is 15%.

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