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Tut9_2009+Solutions - BUS3026W Finance II 2009 Tutorial 9...

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BUS3026W Finance II 2009 - Tutorial 9 Due: Monday 11 May ______________________________________________________________ Question One Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 6% and the market’s average return was 14%. Performance is measured using an index model regression on excess returns. Stock A Stock B Index model regression estimates 1% + 1.2 (r M -r f ) 2% + 0.8 (r M -r f ) R-Square 0.576 0.436 Residual standard deviation 10.3% 19.1% Standard deviation of excess returns 21.6% 24.9% a. Calculate the following statistics for each stock: i. Alpha ii. Information Ratio iii. Sharpe Measure iv. Treynor Measure b. Which stock is the best choice under the following circumstances? Justify your answer. i. This is the only risky asset to be held by the investor. ii. This stock will be mixed with the rest of the investor’s portfolio, currently composed solely of holdings in the market index fund. iii. This is one of many stocks that the investor is analyzing to form an actively managed stock portfolio. Answer a. i. Alpha A = 1% Alpha B = 2% ii. IR A = [1/10.3] = 0.097 IR B = [2/19.1]= 0.105 iii. S A = [(1.2 x 8 + 1)/ 21.6] = 0.49 S B = [(0.8 x 8 + 2)/ 24.9] = 0.34 iv. T A = [1.2 x 8 + 1)/1.2 = 8.83 T B = [0.8 x 8 + 2)/0.8 = 10.5 b. i. Compare Sharpe Ratios since both assets have unsystematic risk present and therefore Treynor would be inappropriate. Therefore we’d select A. [2] ii. If we have a market index portfolio as a base we have already achieved optimal diversification. Both stocks are mispriced so both are candidates for inclusion. Since the unsystematic risk of either stock would be diversified away if it was added to the portfolio, the only aspect that is important in evaluating which one to add is the alpha. Since B has a higher alpha than A, it would therefore be included in the portfolio. [4] iii. Both would be included in the actively managed portfolio, depending on how many stocks are needed to achieve full diversification. If it was possible to construct the actively managed portfolio from just mispriced stocks that would be ideal. We couldn’t
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