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Applied HW - EMH

# Applied HW - EMH - Siming Zhu AEM 4230 Applied Finance EMH...

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Siming Zhu AEM 4230 – Applied Finance October 16, 2008 EMH Homework 1. Consider the following information about a risky portfolio that you manage, and a risk-free asset: E(r p ) = 11%, σ p = 15%, r f = 5%. a. Your client wants to invest a proportion of her total investment budget in your risky fund to provide an expected rate of return on her overall or complete portfolio equal to 8%. What proportion should she invest in the risky portfolio, p, and what proportion in the risk-free asset? E[R] = .08 = (.11)(X) + (.05)(Y) X+Y = 1. Thus, X = 1-Y E[R] = .08 = (.11)(1-Y) + (.05)(Y) E[R] = .08 = .11 - .11Y + .05Y .06Y = .03 Y = .03/.06 E[R] = (.5)(.11) + (.5)(.05) = .08 [or 8%] The investor should invest 50% of her total investment budget in the risky portfolio and 50% on the risk-free portfolio. b. What will be the standard deviation of the rate of return on her portfolio? Standard Deviation [ σ ] = (.5)(.15) + (.5)(0) = .075 [or 7.5%] c. Another client wants the highest return possible subject to the constraint that you limit his standard deviation to be no more than 12%. Which client is more risk averse? The client in A is more risk averse because he is not willing to tolerate as high of a

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Applied HW - EMH - Siming Zhu AEM 4230 Applied Finance EMH...

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