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Unformatted text preview: H AAS S CHOOL OF B USINESS U NIVERSITY OF C ALIFORNIA AT BERKELEY BA 103 Avinash Verma S OLUTION TO H OMEWORK 9 1. Stock A and Stock B are expected to return 6.3% and 3.15% respectively on an annual basis. The variance of returns on Stock A is 0.64 while the variance of returns on Stock B is 3025%%. Assuming that Stock A and Stock B have the smallest possible correlation, work out the price of a 1 year zero coupon with face value of 1000. [7 points] Given E A = 6.3%, E B = 3.15%, σ A = SQRT(0.64) = 0.8, σ B = SQRT(3025%%) = 55%, and ρ AB = –1. We know that because the correlation is –1, these two stocks can be combined into a risk free portfolio, and that the risk-eliminating portfolio weights are x A = σ B / ( σ A + σ A ) = 0.55/(0.55+0.8) = 0.407407, and x B = σ A / ( σ A + σ A ) = 0.8/(0.55+0.8) = 0.592593. The return on this risk free portfolio is E p = x A * E A + x B * E B = 0.407407*6.3% + 0.592593* 3.15% = 4.43%. If the risk free return for one-year 4.43%, the price of a ZCB with face value of $1000 is $1000/1.0443 = $957.55 2. [a]: Security 1 is expected to generate a return of 18% with a standard deviation of 0.45 over the next year. For the same period, security 2 is expected to return 21% with a variance of 3600%%. The correlation between the returns on the two securities is negative one-eighth. Investor A wants to form a portfolio of these two securities such that it has the minimum possible risk as measured by the portfolio...
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This note was uploaded on 09/11/2011 for the course UGBA 103 taught by Professor Berk during the Summer '07 term at University of California, Berkeley.
- Summer '07