Single Index Model – Practice Problems 1. Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds. If the σ of your portfolio was 0.14 and σ M was 0.19, the β of the portfolio would be approximately ________. 2. Suppose the following equation best describes the evolution of β over time: β t = 0.30 + 0.70 β t-1 If a stock had a β of 0.82 last year, you would forecast the β to be _______ in the coming year. 3. The index model has been estimated for stocks A and B with the following results: R A = 0.03 + 0.7R M + e A R B = 0.01 + 0.9R M + e B σ M = 0.35 σ (e A ) = 0.20 σ (e B ) = 0.10 The covariance between the returns on stocks A and B is ___________. 4. The beta of a stock has been estimated as 0.85 by Merrill Lynch using regression analysis on a sample of historical returns. The Merrill Lynch adjusted beta of the stock would be ___________. 6. The index model has been estimated for stocks A and B with the following results:
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