Stephanie Dell is evaluating two stocks (X and Y) using the capital asset pricing model. Dell predicts that the betas for the two stocks will be identical, but that the unsystematic risk for Stock X will be much higher than for Stock Y. Using the capital asset pricing model, determine which of the following statements is correct.
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A. B. C.Explanation
To determine which statement is correct, let's first understand the components of the capital asset pricing model (CAPM).
The CAPM is a financial model used to calculate the expected return on an investment. It takes into account the risk-free rate of return, the beta of the investment, and the market risk premium. The formula for the CAPM is as follows:
Expected Return = Risk-Free Rate + Beta × (Market Risk Premium)
Now, let's analyze the given information. Stephanie Dell predicts that the betas for both stocks X and Y will be identical. Beta measures the systematic risk of a stock, indicating how much the stock's price tends to move in relation to the overall market. If the betas are identical, it means that both stocks have the same systematic risk.
However, Dell predicts that the unsystematic risk for Stock X will be much higher than for Stock Y. Unsystematic risk is the risk that is specific to an individual stock and can be diversified away by holding a portfolio of different stocks. This means that Stock X has higher idiosyncratic or company-specific risk compared to Stock Y.
Now, let's evaluate the given statements:
A. Stock X will have a higher expected return than Stock Y, but a standard deviation less than or equal to Stock Y.
Since the betas are identical, the systematic risk is the same for both stocks. However, Stock X has higher unsystematic risk. According to the CAPM, expected return is positively related to beta. If the betas are the same, Stock X and Stock Y should have the same expected return. Therefore, statement A is incorrect.
B. Stock X will have a higher standard deviation than Stock Y, but an expected return less than or equal to Stock Y.
Standard deviation measures the total risk of an investment, including both systematic and unsystematic risk. Since Stock X has higher unsystematic risk compared to Stock Y, it will have a higher standard deviation. If the betas are the same, the expected return should also be the same. Therefore, statement B is correct.
C. Both the expected return and standard deviation for Stock X will be higher than Stock Y.
As explained earlier, if the betas are identical, the expected return should be the same for both stocks. Therefore, statement C is incorrect.
In conclusion, the correct statement is:
B. Stock X will have a higher standard deviation than Stock Y, but an expected return less than or equal to Stock Y.