
Explanation:
When constructing a blended benchmark to evaluate a portfolio manager's performance, the benchmark should match the systematic risk (beta) of the portfolio but exclude the alpha, as alpha represents the manager's active value added. The CAPM regression provides a market loading (beta) of $0.79. To replicate this risk profile using the S&P 500 and risk-free T-bills, the weight allocated to the market index must be `0.79$. Because benchmark weights must sum to , the remaining weight allocated to the risk-free asset is $1 - 0.79 = 0.210.21`R_{\text{Tbill}} + 0.79R_{\text{SP500}}$.
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Q.31 James is a portfolio manager of the ABC Fund. He is trying to construct a blended benchmark using the S&P 500 and a risk-free portfolio, T-bills. The estimates for the CAPM regression yields the coefficients shown in the table below:
| Coefficient | t-statistic | |
|---|---|---|
| Alpha | 0.65% | 2.45% |
| MKT Loading | 0.79 | 6.70 |
| Adjusted R² | 0.17 |
Which of the following best describes the benchmark?
A
$0.65 + 0.79R_{\text{Tbill}} + 0.79R_{\text{SP500}}$
B
$0.65 + 0.21R_{\text{Tbill}} + 0.79R_{\text{SP500}}$
C
$0.21R_{\text{Tbill}} + 0.79R_{\text{SP500}}$
D
$0.79R_{\text{Tbill}} + 0.79R_{\text{SP500}}$
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