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.
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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)?
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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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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. (d) Calculate the expected return and the
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This note was uploaded on 11/27/2011 for the course FINA 3104 taught by Professor Darwin during the Spring '11 term at HKUST.

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

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