Penny Linn, CFA, predicts that both Stock X and Y will return 20% next year. The Treasury bill rate is 5% and the market risk premium is 8%. The beta for Stock X is 1.5 and for Stock Y is 2. The standard deviation for Stock X is 20% and for Stock Y is 30%. Determine if Linn's predictions lie above or below the security market line.
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A. B. C.B
To determine if Penny Linn's predictions lie above or below the security market line (SML), we need to compare the expected returns of the stocks with their respective required returns according to the Capital Asset Pricing Model (CAPM).
The CAPM is represented by the following equation:
Required Return = Risk-Free Rate + Beta × Market Risk Premium
Let's calculate the required returns for Stock X and Stock Y using the given information:
For Stock X: Beta (β) = 1.5 Market Risk Premium = 8% Risk-Free Rate = 5%
Required Return for Stock X = 5% + 1.5 × 8% = 5% + 12% = 17%
For Stock Y: Beta (β) = 2 Market Risk Premium = 8% Risk-Free Rate = 5%
Required Return for Stock Y = 5% + 2 × 8% = 5% + 16% = 21%
Now, let's compare the required returns with Penny Linn's predictions of 20% for both stocks:
For Stock X: Required Return = 17% Predicted Return = 20%
Since the predicted return for Stock X (20%) is higher than the required return (17%), it lies above the security market line (SML).
For Stock Y: Required Return = 21% Predicted Return = 20%
Since the predicted return for Stock Y (20%) is lower than the required return (21%), it lies below the security market line (SML).
Based on the calculations, we can conclude that only Stock Y lies below the SML, so the correct answer is:
B. Only Stock Y lies below the SML.