ACTSC-372-1101-Test1_exam

# ACTSC-372-1101-Test1_exam - Currently your entire portfolio...

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Actsc 372: Test #1 - WINTER 2010 Name: Marks: /23 I.D.#: February 8, 2010 5:30-6:20pm 4 Questions Aids: Calculator Five pages in total; page 2 is a blank page for additional workspace. 1. [10 marks] Given initial wealth of \$10,000, you are exposed to a random loss X , where X is uniformly distributed on (0 , 6000). Your utility of wealth is given by u ( w ) = w γ ,w > 0 . (a) [2 marks] What is the condition on γ so that the above utility function can be used to describe a risk averse individual? (b) [4 marks] An insurance, which reimburses 75% of the incurred loss, is available to you at the cost of \$2,300. Justify if you are interested in such an insurance coverage given γ of your utility function is 0.8. (c) [4 marks] Suppose now γ of your utility function is 0.5, instead of 0.8, are you a more or a less risk averse individual? Justify your answer.

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3 2. [4 marks] The correlation coeﬃcients between pairs of stocks are as follows: Corr(A,B) = 0.85; Corr(A,C) = 0.60; Corr(A,D) = 0.45. Each stock has an expected return of 8% and standard deviation 20%.

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Unformatted text preview: Currently your entire portfolio is comprised of stock A but you are interested in adding one more stock to your portfolio. Would you choose stock B, C or D or would you need more information? Justify your answer. 4 3. [6 marks] An economy consists of N risky assets with mean vector μ and covariance matrix Σ . Provide three formulations of the optimization problems that enable you to determine the mean-variance eﬃcient frontier. (Note you do not need to derive the eﬃcient frontier) 5 4. [3 marks] It was established that under an economy with N risky assets, the optimal portfolio x * corresponds to the mean-variance eﬃcient frontier is given by x * = x MIN + τ z * for appropriate deﬁnitions of τ, x MIN , and z * . We also noted that the portfolio z * is a self-ﬁnancing portfolio. List (without proof) three additional properties associated with the portfolio z * ....
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ACTSC-372-1101-Test1_exam - Currently your entire portfolio...

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