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Unformatted text preview: UNIVERSITY OF TORONTO Joseph L. Rotman School of Management Dec. 14, 2009 Fang/Kan RSM332 FINAL EXAMINATION Pomorski/Yang SOLUTIONS 1. (a) The stock prices are equal to the present values of their expected future liquidation values: P A = E [DIV A ] 1 + E [ R A ] = $100 1 + 0 . 1 = 90 . 91 , P B = E [DIV B ] 1 + E [ R B ] = $100 1 + 0 . 15 = 86 . 96 . (b) The CAPM states that E [ R i ] R f = β i ( E [ R M ] R f ) . So applying this formula to stocks A and B, we have a system of two equations with two unknowns, E [ R M ] and R f : . 1 R f = 0 . 8( E [ R M ] R f ) , . 15 R f = 1 . 3( E [ R M ] R f ) . Solving the above system, we have R f = 0 . 02 and E [ R M ] = 0 . 12. (c) The investor will invest all her remaining wealth in the market portfolio. So we need to figure out the composition of the market portfolio. Let w A be the portfolio weight of stock A in the market portfolio. Then, E [ R M ] = w A E [ R A ] + (1 w A ) E [ R B ] ⇒ w A = E [ R M ] E [ R B ] E [ R A ] E [ R B ] . Given E [ R M ] = 0 . 12, E [ R A ] = 0 . 1 and E [ R B ] = 0 . 15, we have w A = E [ R M ] E [ R B ] E [ R A ] E [ R B ] = . 12 . 15 . 1 . 15 = 0 . 6 . Therefore, the investor will invest the following fraction of his wealth in stock A: (1 . 2) × . 6 = 0 . 48 . 1 (d) By R M = 0 . 6 R A + 0 . 4 R B (see part (c)) and the definition of β A :, β A = Cov[ R A ,R M ] σ 2 M = Cov[ R A , . 6 R A + 0 . 4 R B ] σ 2 M = . 6 σ 2 A + 0 . 4 σ AB σ 2 M . Recalling that β A = 0 . 8, ρ AB = 0 (which implies σ AB = 0) and σ 2 A = (0 . 25) 2 , we have . 6(0 . 25) 2 σ 2 M = 0 . 8 ⇒ σ 2 M = 0 . 046875 ⇒ σ M = 0 . 21651 . Using the fact that E [ R M ] R f = 0 . 1 (see part (b)), the Sharpe ratio of the market portfolio is SR M = E [ R M ] R f σ M = . 10 . 21651 = 0 . 46188 ....
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This note was uploaded on 04/26/2011 for the course RSM 332 taught by Professor Raymondkan during the Spring '08 term at University of Toronto.
 Spring '08
 RAYMONDKAN

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