332final09a - UNIVERSITY OF TORONTO Joseph L. Rotman School...

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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 = 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 A :, A = Cov[ R A ,R M ] 2 M = Cov[ R A , . 6 R A + 0 . 4 R B ] 2 M = . 6 2 A + 0 . 4 AB 2 M . Recalling that A = 0 . 8, AB = 0 (which implies AB = 0) and 2 A = (0 . 25) 2 , we have . 6(0 . 25) 2 2 M = 0 . 8 2 M = 0 . 046875 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 M = . 10 . 21651 = 0 . 46188 ....
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332final09a - UNIVERSITY OF TORONTO Joseph L. Rotman School...

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