b. You are risk-averse investor with a risk-aversion coefficient of 5. If the risk free offers a rate of return of 5% will you accept this investment?
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- Consider an economy with a (net) risk-free return r1 = 0:1 and a market portfolio with normally distributed return, with ErM = 0:2 and 2M = 0:02. Suppose investor A has CARA preferences, with risk aversion coe¢ cient equal to 1 and an endowment of 10. a) Write down the maximization problem for the investor. b) Determine the amount invested in the risky portfolio and in the risk-free asset. c) Suppose another investor (B) has a coe¢ cient of absolute risk aversion equal to 2 (and the same endowment 10). Compute his optimal portfolio and compare it to that of investor A. Explain the di§erent results for investors A and B. d) Finally, consider Investor C with mean-variance preferences Ec V ar(c) (and endowment 10). Compute his optimal portfolio and compare it to that of investors A and B (as obtained in questions b and c). Compare your result with those obtained for investors A and B.Assuming two risk-free rates for lending and borrowing in the market: r(f) and r(b). Suppose your utility function is described by U = E(r) - 0.5A xo² with A> 0, and you are combining the risk-free asset with the optimal risky asset to maximize the utility. Consider the following two situations: 1. Suppose r(b) = r(f): you form the optimal complete portfolio C1 by borrowing money at r(f) and invest y1 (i.e., y1 represents portfolio weight) in the optimal risky portfolio (P1). Your utility score under this situation is denoted as U1; II. Suppose r(b) >r(f): you form another optimal complete portfolio C2 by borrowing money at r(b) and invest y2 (1.e., y2 represents portfolio weight) in the optimal risky portfolio (P2). Your utility score under this situation is denoted as U2. For simplicity, let's assume the optimal risky portfolios under these two situations are the same (i.e., E(P1)=E(P2) and o(P1) = o(P2)). What are the relationship between y1 and y2, U1 and U2: O a. y1=y2 and U1=U2 O…Given the utility function U = E(r) Ac€?o 0.5AA?A?2 and the fact that T-bill offer a risk-free rate of 4%, what is the minimum value for the risk-aversion coefficient A where an investor prefers the T-bills to an investment returning 10% with a standard deviation of 18%? (Hint: T-bills are risk-free)
- Assuming your utility function U = E(r) - Ao². Consider the investments shown in the table. If your risk aversion coefficient is -2, which investment would you choose? Investment E[r] #1 #2 #3 #4 #2 #3 #4 #1 12% 15% 15% 24% σ 40% 40% 30% 40%QUESTIONS: 1) Assuming that the risk-free rate of return is currently 3,2%, the market risk premium is 6% whereas the beta of HelloFresh SH. stock is 1.8, compute the required rate of return using CAPM. 2) Compute the value of each investment based on your required rate of return and interpret the results comparing with the market values. 3) Which investment would you select? Explain why using appropriate financial jargon (language). 4) Assume HelloFresh SH's CFO Mr. Christian Gaertner expects an earnings upturn resulting increase in growth (rate) of 1%. How does this affect your answers to Question 2 and 3? 5) AACSB Critical Thinking Questions: A) Companies pay rating agencies such as Moody's and S&P to rate their bonds, and the costs can be substantial. However, companies are not required to have their bonds rated in the first place; doing so is strictly voluntary. Why do you think they do it? (Textbook page: 198) B) What are the difficulties in using the PE ratio to value stock?…Which of the following investments does a rational investor prefer? a. Investment A: E(R) = 12%, σ = 5% b. Investment B: E(R) = 10%, σ = 5.5% c. Investment C: E(R) = 11%, σ = 6% d. Investment D: E(R) = 11.5%, σ = 6%
- 2. A local bank is offering a promotional deal where if you open a bank account for at least $1000, they will give you a $25 gift certificate card and pay 4% interest on the account. Does this promotion result in a higher or lower return on your account? If you invest $1000, maintain the balance for 1 year, and earn 4% on the account, what is your rate of O YrS return? annuiln front i Fhe discurriaa. Compute the expected rate of return on investment i given the following information: the market risk premium is 5%; Rf = 6%; βi = 1.2. b. Compute E(RM).Suppose the risk-free rate is 5%. The expected return and standard deviation of a risky asset are 10% and 20%, respectively. a. What is the slope of the capital allocation line (CAL) constructed using the risk-free asset and the risky asset? A. 0.30 B. 0.15 C. 0.25 D. 0.20 b. If an investor has a risk aversion coefficient of A=2, what is the optimal fraction of the money that she invests in the risky asset? A. 62.5% B. 42.5% C. 30% D. 20% c. If an investor invest 25% of her money in the risky asset, which is the investor’s risk aversion coefficient? a. 5 b. 1 c. 3 d. 4
- An investor has an opportunity to invest in two risky assets and a risk-free asset. Theexpected return of the two risky assets are μ1 = 0.12, μ2 = 0.15. Their standarddeviations are σ1 = 0.05 and σ2 = 0.1, and the correlation coefficient between theirreturn is 0.2. The risk-free rate is 0.05. Suppose the investor has $1000 and he wantsto hold a portfolio with expected return of 0.1. If the investor is risk averse, how muchshould he invest in the two risky assets and the risk-free asset?The risk-free rate is currently 3.3%, and the market return is 14.8%. Assume you are considering the following investments: Investment Beta A 1.54 B 1.16 C 0.51 D 0.11 E 2.14 . a. Which investment is most risky? Least risky? b. Use the capital asset pricing model (CAPM) to find the required return on each of the investments. c. Find the security market line (SML), using your findings in part b. d. On the basis of your findings in part c, what relationship exists between risk and return? Explain.Assume an investor with the coefficient of risk aversion A=5.5. To maximize her expected utility, she would choose the asset with an expected rate of return of _______ and a standard deviation of ________, respectively." a. 21%; 16% b. 24%; 21% c. 12%; 30% d. 15%; 5%