Consider the following utility function introduced in the lecture.
U = E(r) − 1/2 Aσ2
Suppose there are 3 types of financial securities one can choose to invest in. Expected return and standard deviation of each of these securities are as follows.
E(r1) = .13; σ1 = .3
E(r2) = .15; σ2 = .5
E(r3) = .20; σ3 = .2
(a) Which of these three securities would a risk averse investor with A = 4 choose to invest, given that she can only invest in one of these three securities?
(b) For the same investor (with A = 4), if there is also a risk free asset with expected return 5%, will she invest in the risk free asset or one of those three securities?
(c) Which of these three securities would a risk neutral investor choose to invest, given that she can only invest in one of these three securities?
Consider the following utility function introduced in the lecture. U = E(r) − 1/2 Aσ2 Suppose...
John has a utility function given by the expression U(x) = E(r) -½A(s²). Where E(r) is the expected return on an asset and s is the standard deviation of returns on that asset.John has the opportunity to purchase the XJKsecurity that returns 25.9% with 23% probability and returns 8.6% the remainder of the time. The security has a price of $33 and A=11 a) What is the risk-neutral valuation of the XJK security? Recall the risk-neutral value is simply the...
Consider an investor with preferences given by the utility function U = E(r) - 0.5A0- and there are two portfolios with the following characteristics: Portfolio A Portfolio B E(r) = 0.148 O=0.16 E(T) = 0.082 o= 0.068 (a) Suppose that the investor has a level of risk aversion of A = 4. Which portfolio should the investor choose? [3 Points] (6) Suppose that the investor has a level of risk aversion of A = 6. Which portfolio should the investor...
Will sellr 6. Suppose the utility is U- E(r) -0.5Ao2 for all the questions im an standard deviation risk sider a portfolio that offers an expected rate of return of 15% and a of 30%. T-bills offer a risk-free 10% rate of return. What is aversion for which the risky portfolio the maximum level of is still preferred to bills? 7. Suppose you are given the following information regarding several investments: Utility Formula Data Investment Bxpected Return E) Standard Deviation...
answer all. For the next question, assume an investor with the following utility function U-E)-3/2) 12. To maximize her expected uility, she would choose the set with an espect rate of return of and a standard deviation ofrspectively A. 1296; 20% B. 10%; 15% C. 1056; 1056 D, 8%, 10% Е.none ofthe above 13. Which of the following statements regarding the Capital Allocation Line (CAL) false? A. The CAL shows risk-return combinations. B. The slope of the CAL equals the...
2. Company A's stock has a beta of BA 1.5, and Company B's stock has a beta of βΒ-2.5. Expected returns on this two stocks are E [rA]-9.5 and E rB 14.5. Assume CAPM holds. At age 30, you decide to allocate ALL your financial wealth of $100k between stock A and stock B, with portfolio weights wA + wB1. You would like this portfolio to be risky such that Bp- 3 (a) Solve for wA and wB- (b) State...
An investor’s utility function for expected return and risk is U = E(r) − 4σ2. Which of the following would this investor prefer to invest in: A risk-free security offering a return of 8 percent per year A risky portfolio with expected return of 14 percent per year and standard deviation of 25 percent per year Select one: a. Risk-free security b. Risky portfolio
The universe of available securities includes two risky stocks A and B, and a risk-free asset. The data for the universe are as follows: Assets Expected Return Standard Deviation Stock A 6% 25% Stock B 12% 42% Risk free 5% 0 The correlation coefficient between A and B is -0.2. The investor maximizes a utility function U=E(r)−σ2 (i.e. she has a coefficient of risk aversion equal to 2). Assume that to maximize his utility when there is no available risk-free...
Consider a Treasury bill with a rate of return of 5% and the following risky securities: Security A: E(r) = .15; variance = .0400 Security B: E(r) = .10; variance = .0225 Security C: E(r) = .12; variance = .1000 Security D: E(r) = .13; variance = .0625 The investor must develop a complete portfolio by combining the risk-free asset with one of the securities mentioned above. The security the investor should choose as part of her complete portfolio to...
2. (Understanding optimal portfolio choice) Consider two risky assets, the expected return of asset one is μ-0.1, the expected return of asset two is μ2-0.15, the risk or standard deviation of asset one is σ1-0.1, the risk or standard deviation of asset two is σ2-02. The two assets also happen to have zero correlation. An investor plans to build a portfolio by investing w of his investment to asset one and the rest of his investment to asset two. Calculate...
Question 1 Consider two risky assets A and B with E(rA)= 15%, Sigma_A= 32%, E(rB)= 0.09, Sigma_B= 23%, corrA,B= 0.2. The risk free rate is 5%. The optimal risky portfolio of comprised of the two risky assets is to allocate 64% to A and the rest to B. What is the standard deviation of the optimal risky portfolio ? Select one: a. 20.75% b. 23.61% c. 22.86% d. 23.00% Question 2 Continued with previous question. What is the Sharpe ratio...