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T3 2011

T3 2011 - Fina 3104 L2 T3 Practice Problems Homework 1 Fina...

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Fina 3104 T2 1 Fina 3104 L2 T3 § Practice Problems § Homework 1

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Fina 3104 T2 2 Practice Problem 1(TAPPS) Portfolio Mathematics and Capital Allocation True or False (Briefly Explain) The utility indifference curves of two different risk-averse investors cannot intersect.
Fina 3104 T2 3 Solution FALSE . Different risk-averse investors can have different levels of risk aversion, and their indifference curves can intersect. (Note: The utility indifference curves of the same investor (with the same risk aversion A) cannot intersect. This is because a return-risk combination (a point in the return-risk graph) can only give one utility score. Different indifference curves correspond to different utility scores, and if they intersect that would mean a single point corresponds to more than one utility score, which cannot happen.)

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Fina 3104 T2 4 Practice Problem 2(castcolt) Risk and Return for Security Portfolios Suppose you have \$100 to invest in two assets, A and B. A and B are the only assets available. A is a risky asset and B is a risk-free asset. Neither A nor B pays dividends/interests. The expected return on A is 5%, and B earns a risk-free rate of 3%. The standard deviations of returns on A and B are 10% and 0%, respectively. The covariance between the returns on the two assets is 0. (a) If you invest \$30 in A and \$70 in B, what is the expected return on your portfolio? (b) What is the standard deviation of return for the portfolio in (a)?
Fina 3104 T2 5 Solution (a) The expected return on the portfolio, E(rP) = wAE(rA) + wBrB = 0.3 x 5% + 0.7 x 3% = 3.6% (b) The standard deviation of return for the portfolio, E(rP) = ( wA A 2 + wB B 2 + 2wAwBσAB )1/2 = (0.32(10%)2 + 0 + 0)1/2 = 3%

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Fina 3104 T2 6 Practice Problem 2 (c) If you want to invest \$130 in A, how much do you have to short sell B? Assume you can fully use the proceeds from the short sale, and ignore margin and collateral requirements.
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