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# WUSTL FIN 441 - Textbook Assignment 4

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Department of Finance Olin Business School Washington University in St. Louis Spring 2022 FIN 441-Investments Textbook Assignment 4 Due Feb 23rd, 2022 1. (Bodie, Kane & Marcus 2021, Chapter 5, CFA Problems 2) Based on the Scenarios below, what is the expected return for a portfolio with the following return profile? Bear Market Normal Market Bull Market Probability 0.2 0.3 0.5 Rate of return -25% 10% 24% 2. (Bodie, Kane & Marcus 2021, Chapter 5, CFA Problems 3,4) Use the following scenario analysis for Stocks X and Y to answer CFA the following questions (round to the nearest percent) Bear Market Normal Market Bull Market Probability 0.2 0.5 0.3 Stock X -20% 18% 50% Stock Y -15% 20% 10% a. What are the expected rates of return for Stocks X and Y? b. What are the standard deviations of returns on Stocks X and Y? 3. (Bodie, Kane & Marcus 2021, Chapter 6, Problem 5) Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 18%. T-bills offer a risk-free 7% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to T-bills?4. (Bodie, Kane & Marcus 2021, Chapter 6, Problem 19) You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. Your client’s degree of risk aversion is A = 3.5. a. What proportion, y, of the total investment should be invested in your fund? b. What are the expected value and standard deviation of the rate of return on your client’s optimized portfolio? 5. (Bodie, Kane & Marcus 2021, Chapter 6, Problem 21) Consider the following information about a risky portfolio that you manage and a risk-free asset: E(rP) = 11%, σP= 15%, rf= 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? b. What will be the standard deviation of the rate of return on her portfolio? 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

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