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The finance committee of an endowment has decided to shift part of its investment in an index fund to one of two professionally managed portfolios. Upon examination of past performance, a committee member proposes to choose the portfolio that achieved a greater alpha value/
a- Do you agree? Why or why not?
b- Could a positive alpha be associated with inferior performance? Explain |
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1. a. Possibly. Alpha alone does not determine which portfolio has a larger Sharpe ratio. Sharpe measure is the primary factor, since it tells us the real return per unit of risk. We only invest if the Sharpe measure is higher. The standard deviation of an investment and its correlation with the benchmark are also important. Thus positive alpha is not a sufficient condition for a managed portfolio to offer a higher Sharpe measure than the passive benchmark.
b. Yes. It is possible for a positive alpha to exist, but the Sharpe measure decline. Thus, we would experience inferior performance. |
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| The board of a large pension fund noticed that the alpha value of the portfolio of one of its contract managers has recently increased. Should the fund increase the allocation to this portfolio? |
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| 2. Maybe. Provided the addition of funds creates an efficient frontier with the existing investments, and assuming the Sharpe measure increases, the answer is yes. Otherwise, no. |
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| Could portfolio A Show a higher Sharpe ratio than that of B and at the same time is a lower M2 measure? Explain |
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| 3. The M-squared is an equivalent representation of the Sharpe measure, with the added difference of providing a risk-adjusted measure of performance that can be easily interpreted as a differential return relative to a benchmark. Thus, it provides the same information as the Sharpe measure. But in a different format. |
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| Two portfolio managers use different procedures to estimate alpha. One uses a single-index model regression, the other the Fama-French model. Other things equal, would you prefer the portfolio with the larger alpha based on the index model or the FF model? |
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| 4. Definitely, the FF model. Research shows that passive investments (e.g., a market index portfolio) will appear to have a zero alpha when evaluated using the multi-index model but not using the single-index one. The nonzero alpha appears even in the absence of superior performance. Thus, the single-index alpha can be misleading. |
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| Does the use of universes of managers with similar investment styles to evaluate relative investment performance overcome the statistical problems associated with instability of beta or total variability? |
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| During a particular year, the T-bill rate was 6%, the market return was 14%, and portfolio manager with beta of .5 realized a return of 10%. Evaluate the manager based on the portfolio alpha. |
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