Difficulty moderate short answer questions 49 discuss

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distribution of the squared information ratio of in the universe of securities. Difficulty: Moderate Short Answer Questions 49. Discuss the Treynor-Black model . The Treynor-Black estimates the alpha, beta, and residual risk of securities under consideration for a portfolio. The model uses these estimates to determine the optimal weights of each of these securities in the portfolio. These composite estimates for the active portfolio and the macroeconomic forecasts for the passive index portfolio are used to determine the optimal risky portfolio, which will be a combination of the passive and active portfolios. Feedback: The purpose of this question is to ascertain if the student understands the basic concepts behind this model, which allows the portfolio manager to utilize both active and passive components of portfolio building to obtain an optimal portfolio. Difficulty: Moderate 27-26
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Chapter 27 - The Theory of Active Portfolio Management 50. You have a record of an analyst's past forecasts of alpha. Describe how you would use this information within the context of the Treynor-Black model to determine the forecasting ability of the analyst. You can use the index model and valid estimates of beta, you can estimate the ex-post alphas from the average realized return and the return on the market index. The equation is . Then you would estimate a regression of the forecasted alphas on the realized alphas as in the equation . The coefficients a 0 and a 1 reflect the bias in the forecasts. If there is no bias a 0 =0 and a 1 =1. The forecast errors are uncorrelated with the true alpha, so the variance of the forecast is . To measure the value of the forecast, you would use the squared correlation coefficient between the forecasts and the realizations. This can also be determined by the formula . If the analyst has perfect forecasting ability the correlation coefficient will be 1. If the analyst has no ability then the correlation coefficient will be 0. For values in between 0 and 1 you can adjust the forecasts by multiplying by the correlation. Feedback: The value of active management depends on the analyst's ability to forecast accurately. The best way to exploit analysts' forecasts is with the Treynor-Black model. Difficulty: Difficult 27-27
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