
Explanation:
A benchmark should represent an investable, passive alternative that mimics the systematic risk (beta) of the portfolio, without including the active return (alpha). The manager's market loading (beta) is 0.79, meaning that 79% of the portfolio's systematic risk is equivalent to investing in the market index (S&P 500). To create a fully invested blended benchmark, the remaining 21% (which 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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