T10 - UNIVERSITY OF TORONTO Joseph L. Rotman School of...

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Unformatted text preview: UNIVERSITY OF TORONTO Joseph L. Rotman School of Management RSM332 Tutorial #10 Problem Set Nov.24/Nov.25 2011 1. The stock market comprises two stocks, A and B, and a risk-free asset. The return on the risk-free asset is R f = 2%. The table below gives next periods returns of the two stocks, R A and R B , in each state of the world. State R A R B Probability Good 8% 1% 30% So-So 6% 2% 40% Bad- 2% 3% 30% What is the minimum-variance portfolio composed of stocks A and B. Solutions : Let x A be the weight of stock A in the portfolio. The variance of the portfolio is 2 P = x 2 A 2 A + (1- x A ) 2 2 B + 2 x A (1- x A ) A,B . To minimize the variance of the portfolio, we take the first order derivative of 2 P with respect to x A : 2 P x A = 2 x A 2 A- 2 (1- x A ) 2 B + 2 (1- 2 x A ) A,B . Setting the derivative equal to zero, we have x mvp A = 2 B- A,B 2 A + 2 B- 2 A,B = . 0077 2 + 0 . 0003 . 0414 2 + 0 . 0077 2 + 2 . 0003 = 0 . 1515 ....
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This note was uploaded on 12/20/2011 for the course RSM 332 taught by Professor Raymondkan during the Fall '08 term at University of Toronto.

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T10 - UNIVERSITY OF TORONTO Joseph L. Rotman School of...

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