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Unformatted text preview: UNIVERSITY OF TORONTO Joseph L. Rotman School of Management RSM332 PROBLEM SET #2 SOLUTIONS 1. (a) The expected returns on each security are all equal to 17%. As an example of how to calculate this, E [ R 1 ] = 0 . 4(0 . 3) + 0 . 4(0 . 1) + 0 . 1(0 . 1) + 0 . 1(0 . 0) = 0 . 17 or 17% . The standard deviations on each security are respectively, σ 1 = 11%, σ 2 = 46 . 05%, and σ 3 = 10 . 3%. As an example of how to calculate this, σ 1 = h . 4(0 . 3 . 17) 2 + 0 . 4(0 . 1 . 17) 2 + 0 . 1(0 . 1 . 17) 2 + 0 . 1(0 . . 17) 2 i 1 2 = 0 . 11 . (b) The covariances between the returns are respectively, Cov[ R 1 ,R 2 ] = . 0479, Cov[ R 1 ,R 3 ] = . 0084, and Cov[ R 2 ,R 3 ] = 0 . 043. As an example of how to calculate this, Cov[ R 1 ,R 2 ] = 0 . 4(0 . 3 . 17)( . 3 . 17) + 0 . 4(0 . 1 . 17)(0 . 3 . 17) + 0 . 1(0 . 1 . 17)(0 . 5 . 17) + 0 . 1(0 . . 17)(1 . 2 . 17) = . 0479 . The correlations between the returns of different securities are respectively, Corr[ R 1 ,R 2 ] = 0.9456, Corr[ R 1 ,R 3 ] = 0.7414 and Corr[ R 2 ,R 3 ] = 0.9195. As an example of how to calculate this, Corr[ R 1 ,R 2 ] ≡ Cov[ R 1 ,R 2 ] σ 1 σ 2 = . 0479 (0 . 11)(0 . 4605) = . 9456 . (c) The expected return and standard deviation of a portfolio with equal proportions in two securities ( i and j ) is given by μ p = 0 . 5 E [ R i ] + 0 . 5 E [ R j ] , σ p = q . 25 σ 2 i + 0 . 25 σ 2 j + 0 . 5Cov[ R i ,R j ] . Substituting in the values in parts (a) and (b) above gives us the same mean return on each of the portfolios, i.e. 17%. Substituting in the values in parts (a) and (b), 1 the standard deviations of the portfolios are (i) σ p = 0 . 1792 for the equally weighted portfolio of assets 1 and 2, (ii) σ p = 0 . 0384 for the equally weighted portfolio of assets 1 and 3, and (iii) σ p = 0 . 2778 for the equally weighted portfolio of assets 2 and 3....
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This note was uploaded on 11/29/2011 for the course RSM 332 taught by Professor Raymondkan during the Winter '08 term at University of Toronto Toronto.
 Winter '08
 RAYMONDKAN

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