You are an analyst for a large public pension fund and you have been assigned the task of evaluating two different external portfolio managers (Y and Z). You consider the follow- ing historical average return, standard deviation, and CAPM beta estimates for these two managers over the past five years:
Portfolio Actual Avg. Return Standard Deviation Beta
Manager Y 10.20% 12.00% 1.2
Manager Z 8.80% 9.90 % 0.80
Additionally, your estimate for the risk premium for the market portfolio is 5.00 percent and the risk-free rate is currently 4.50 percent.
a. For both Manager Y and Manager Z, calculate the expected return using the CAPM. Express your answers to the nearest basis point (xx.xx percent).
b. Calculate each fund manager's average "alpha" (actual return minus expected return)
over the five-year holding period. Show graphically where these alpha statistics would plot on the security market line (SML).
c. Explain whether you can conclude from the information in part (b) if (1) either man-
ager outperformed the other on a risk-adjusted basis, and (2) either manager outper- formed market expectations in general.
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a. To calculate the expected return using the CAPM formula, we use the following formula:
Expected return = Risk-free rate + (Beta * Market risk premium)
For Manager Y:
Expected return = 4.50% + (1.2 * 5.00%) = 4.50% + 6.00% = 10.50%
For Manager Z:
Expected return = 4.50% + (0.80 * 5.00%) = 4.50% + 4.00% = 8.50%
Therefore, the expected return for Manager Y is 10.50% and for Manager Z is 8.50%.
b. To calculate the average alpha, we subtract the expected return from the actual average return for each manager.
For Manager Y:
Average alpha = Actual Avg. Return - Expected return = 10.20% - 10.50% = -0.30%
For Manager Z:
Average alpha = Actual Avg. Return - Expected return = 8.80% - 8.50% = 0.30%
The average alpha for Manager Y is -0.30% and for Manager Z is 0.30%.
To plot these alpha statistics on the security market line (SML), we need to determine the beta-adjusted alpha. This can be done by multiplying the alpha by the respective manager's beta.
For Manager Y:
Beta-adjusted alpha = -0.30% * 1.2 = -0.36%
For Manager Z:
Beta-adjusted alpha = 0.30% * 0.80 = 0.24%
c. From the information in part (b), we can conclude the following:
(1) Neither manager outperformed the other on a risk-adjusted basis. Both managers have average alphas close to zero, indicating that their performance does not deviate significantly from what is expected based on their betas.
(2) On a risk-adjusted basis, both managers have alphas close to zero, indicating that they did not consistently outperform market expectations over the five-year holding period. However, it is important to note that the average alpha only captures performance over a specific time period and may not fully reflect the managers' long-term performance.
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