Asset C has expected return of 14%, standard deviation of 7%, and beta of 0.4. Asset D has expected return of 17%, standard deviation of 10%, and beta of 0.7. The market portfolio has a standard deviation of 6%. The market risk premium is 2%. The risk-free rate is 5%. Assuming that Assets C and D are perfectly negatively correlated, which of the following has the lowest Sharpe ratio? _____"Question 62Answera.A portfolio consisting of 50% Asset C and 50% Asset Db.Asset Dc.Asset C
Question
Asset C has expected return of 14%, standard deviation of 7%, and beta of 0.4. Asset D has expected return of 17%, standard deviation of 10%, and beta of 0.7. The market portfolio has a standard deviation of 6%. The market risk premium is 2%. The risk-free rate is 5%. Assuming that Assets C and D are perfectly negatively correlated, which of the following has the lowest Sharpe ratio? _____"Question 62Answera.A portfolio consisting of 50% Asset C and 50% Asset Db.Asset Dc.Asset C
Solution
The Sharpe ratio is a measure of risk-adjusted return. It is calculated as the difference between the expected return of the investment and the risk-free rate, divided by the standard deviation of the investment's returns.
Let's calculate the Sharpe ratio for each option:
a. A portfolio consisting of 50% Asset C and 50% Asset D
Since the assets are perfectly negatively correlated, the standard deviation of the portfolio will be 0. This is because the positive and negative movements in the assets will cancel each other out. The expected return of the portfolio will be the average of the expected returns of the two assets, which is (14% + 17%) / 2 = 15.5%.
The Sharpe ratio will be (15.5% - 5%) / 0 = undefined (since we cannot divide by zero).
b. Asset D
The Sharpe ratio for Asset D will be (17% - 5%) / 10% = 1.2.
c. Asset C
The Sharpe ratio for Asset C will be (14% - 5%) / 7% = 1.29.
Therefore, the portfolio consisting of 50% Asset C and 50% Asset D has the lowest Sharpe ratio, since its Sharpe ratio is undefined.
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