Portfolio Mathematics and Capital Allocation Solution

Portfolio Mathematics and Capital Allocation Solution -...

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1 FINA 3104 Practice Problems Fall 2011 Portfolio Mathematics and Capital Allocation 1. True or False (Briefly Explain) (a) The utility indifference curves of two different risk-averse investors cannot intersect. 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.) (b) If you invest y of your wealth in a risky asset ( y > 1), and the borrowing rate r b is higher than the riskfree rate r f , the expected return on your complete portfolio is given by E( r C ) = r b + y [E( r P ) - r b ], where r P is the return on the risky asset. Solution: TRUE. When you buy on margin you are borrowing at rate r b (equivalently, you are short selling the riskfree asset at rate r b ). The expected return on your complete portfolio is given by E( r C ) = (1-y) r b + y E( r P ) = r b + y [E( r P ) - r b ]. 2. 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 riskfree asset. The expected return on A is 5%, and B earns a riskfree rate of 3%. The standard deviations of returns on A and B are 10% and 0%,
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Portfolio Mathematics and Capital Allocation Solution -...

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