The performance benchmark then is the unmanaged

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risk) of the managed portfolio. The performance benchmark then is the unmanaged portfolio. The typical proxy for this unmanaged portfolio is an aggregate stock market index such as the S&P 500. b. The benchmark error might occur when the unmanaged portfolio used in the evaluation process is not “optimized.” That is, market indices, such as the S&P 500, chosen as benchmarks are not on the manager’s ex ante mean/variance efficient frontier. c. Your graph should show an efficient frontier obtained from actual returns, and a different one that represents (unobserved) ex-ante expectations. The CML and SML generated from actual returns do not conform to the CAPM predictions, while the hypothesized lines do conform to the CAPM. d. The answer to this question depends on one’s prior beliefs. Given a consistent track record, an agnostic observer might conclude that the data support the claim of superiority. Other observers might start with a strong prior that, since so many managers are attempting to beat a passive portfolio, a small number are bound to produce seemingly convincing track records. e. The question is really whether the CAPM is at all testable. The problem is that even a slight inefficiency in the benchmark portfolio may completely invalidate any test of the expected return-beta relationship. It appears from Roll’s argument that the best guide to the question of the validity of the CAPM is the difficulty of beating a passive strategy. 14. The effect of an incorrectly specified market proxy is that the beta of Black’s portfolio is likely to be underestimated (i.e., too low) relative to the beta calculated based on the “true” market portfolio. This is because the Dow Jones Industrial Average (DJIA), and other market proxies, are likely to have less diversification and therefore a higher variance of returns than the “true” market portfolio as specified by the capital asset pricing model. Consequently, beta computed using an overstated variance will be underestimated. This result is clear from the following formula: 2 Proxy Market Proxy Market Portfolio Portfolio ) r , r ( Cov σ = β An incorrectly specified market proxy is likely to produce a slope for the security 13-9
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13-10 market line (i.e., the market risk premium) that is underestimated relative to the “true” market portfolio. This results from the fact that the “true” market portfolio is likely to be more efficient (plotting on a higher return point for the same risk) than the DJIA and similarly misspecified market proxies. Consequently, the proxy- based SML would offer less expected return per unit of risk.
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