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"Problems_1 - MGMT41100 B-H Hwang Spring 2010 Practice Problems#1 Solutions 1 Toyota stock has the following probability distribution of

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MGMT41100 – B.-H. Hwang – Spring 2010 Practice Problems #1 - Solutions 1. Toyota stock has the following probability distribution of expected prices one year from now: a) If you buy Toyota today for $55 and it will pay a dividend during the year of $4 per share, what is your expected return on Toyota? Answer: E(r) = .25 (50-55+4)/55 + .40 (60-55+4)/55 + .35 (70-55+4)/55 = 18.18%. b) What is the standard deviation for Toyota stock? Answer: σ = [.25 (((50-55+4)/55) – 0.1818) 2 + .40 (((60-55+4)/55) – 0.1818) 2 + .35 (((70-55+4)/55) – 0.1818) 2 ] 1/2 = 14% 2. Stock A’s expected return and standard deviation are E[r A ] = 8% and σ A = 15%, while stock B’s expected return and standard deviation are E[r B ] = 12% and σ B = 21%. a. Determine the expected return and standard deviation of the return on a portfolio with weights w A =.35 and w B =.65 for the following alternative values of correlation between A and B: p AB =0.6 and p AB = -0.4. Answer: E[r P ] = ω A E[r A ] + ω B E[r B ] = 0.35(0.08)+0.65(0.12) = 0.106 regardless of the correlation. Using σ ωσ ωωρ σσ =++ 2 22 2 p A A B B A B AB A B , for ρ AB =0.6: σ p 2 = (.35) 2 (.15) 2 +(.65) 2 (.21) 2 +2(.35)(.65)(0.6)(.15)(.21) = 0.029988 or, σ p = 17.32% For ρ AB =-0.4: σ p 2 = (.35) 2 (.15) 2 +(.65) 2 (.21)
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This note was uploaded on 04/09/2011 for the course MGMT 411 taught by Professor Clarke during the Winter '09 term at Purdue University-West Lafayette.

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"Problems_1 - MGMT41100 B-H Hwang Spring 2010 Practice Problems#1 Solutions 1 Toyota stock has the following probability distribution of

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