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# ps2sol - Financial Economics V 3025 Rajiv Sethi Phone 854...

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Financial Economics V 3025 Fall 2009 Rajiv Sethi 5B Lehman Phone: 854 5140 [email protected] Problem Set 2: Solutions Due Date: Monday, October 19 1. An investor has access to two risky assets P and Q with the following statistical properties: E ( r p ) = 7% ; ° p = 6% ; E ( r q ) = 8% ; ° q = 8% : The correlation coe°cient between the two asset returns is zero and the risk-free rate of interest is 5% : (a) The reward-to-variability ratios are 1 3 for asset P and 3 8 for asset Q; so Q has the higher ratio. (b) The expected return of a portfolio consisting of equal weights in the two risky assets is E ( r ) = 1 2 (0 : 07) + 1 2 (0 : 08) = 0 : 075 = 7 : 5% and the standard deviation is ° = s 1 4 (0 : 0036) + 1 4 (0 : 0064) = 0 : 05 = 5% (c) No, this is not possible. For every combination of bills and P; there exists a combination of bills and Q that has a higher expected return for the same risk. 2. See spreadsheet 3. If the risk-free rate falls then (i) the expected return and standard deviation of the optimal risky portfolio both fall, (ii) the share of bonds in the optimal risky portfolio rises while the share of equities falls, and (iii) the slope of the optimal CAL increases. An investor whose preferences are such that she would have borrowed (to buy risky assets on margin) at the original risk-free rate is clearly better o±: for any point beyond

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ps2sol - Financial Economics V 3025 Rajiv Sethi Phone 854...

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