The expected return and standard deviation of Stock A are 12% and 24%, respectively. The expected return and standard deviation of Stock B are 5% and 19%, respectively. The correlation between the two stocks is 0.4. The risk-free rate in the economy is 1%. A. What is the Sharpe ratio for Stock A and Stock B? Show your calculation steps briefly and clearly. B. Calculate the optimal risky portfolio P*. You do not need to show your calculation steps for this subquestion. C. Now suppose that the correlation between the two stocks is -0.2 (instead of 0.4). Re-calculate the optimal risky portfolio P* and compare it to your answer in Part B. What do you observe? You do not need to show your calculation steps for this subquestion. D. Using the results above, briefly explain why investors might still consider investing in stocks with a (relatively) low Sharpe ratio as a part of their portfolio.
Risk and return
Before understanding the concept of Risk and Return in Financial Management, understanding the two-concept Risk and return individually is necessary.
Capital Asset Pricing Model
Capital asset pricing model, also known as CAPM, shows the relationship between the expected return of the investment and the market at risk. This concept is basically used particularly in the case of stocks or shares. It is also used across finance for pricing assets that have higher risk identity and for evaluating the expected returns for the assets given the risk of those assets and also the cost of capital.
The expected return and standard deviation of Stock A are 12% and 24%, respectively. The expected return and standard deviation of Stock B are 5% and 19%, respectively. The correlation between the two stocks is 0.4. The risk-free rate in the economy is 1%.
A. What is the Sharpe ratio for Stock A and Stock B?
-
- Show your calculation steps briefly and clearly.
B. Calculate the optimal risky portfolio P*.
-
- You do not need to show your calculation steps for this subquestion.
C. Now suppose that the correlation between the two stocks is -0.2 (instead of 0.4). Re-calculate the optimal risky portfolio P* and compare it to your answer in Part B. What do you observe?
-
- You do not need to show your calculation steps for this subquestion.
D. Using the results above, briefly explain why investors might still consider investing in stocks with a (relatively) low Sharpe ratio as a part of their portfolio.
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