Investors can choose one of the two independent investment assets, A an B. The payoff per unit invested in each asset is uniformly distributed wit parameters as given below. A U(1, 1.1) B U(0.9, 1.2) Suppose that an investor with initial wealth of 1 chooses one of these assets based on the utility function u(x) = - exp(-3x). Calculate the expected utilities of investing in A and B.
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Expected utility in portfolio theory
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- An investor has utility function U = 10 + 5P – 0.02P2. What is the expected utility of the following investment option? Probability Payoff (P) 0.4 10 0.3 20 0.2 30 0.1 40You are considering a $500,000 investment in the fast-food industry and have narrowed your choice to either a McDonald's or a Penn Station East Coast Subs franchise. McDonald's indicates that, based on the location where you are proposing to open a new restaurant, there is a 25 percent probability that aggregate 10-year profits (net of the initial investment) will be $16 million, a 50 percent probability that profits will be $8 million, and a 25 percent probability that profits will be -$1.6 million. The aggregate 10-year profit projections (net of the initial investment) for a Penn Station East Coast Subs franchise is $48 million with a 2.5 percent probability, $8 million with a 95 percent probability, and -$48 million with a 2.5 percent probability. Considering both the risk and expected profitability of these two investment opportunities, which is the better investment? Explain carefully.Buying and selling prices for risky investments obviously are related to certain equivalents. This problem, however, shows that the prices depend on exactly what is owned in the first place. Suppose that your utility for wealth (A) can be represented by the utility function u(A) = In [(A)] You currently have R1000 in cash. A business deal of interest to you yields a reward of R100 with probability 0,5 and RO with probability 0,5. 2.1 If you own this business deal in addition to the R1000, what is the smallest amount for which you would sell the deal? 2.2 Suppose you do not own the deal. Formulate an appropriate equation and solve with algebra to find the largest amount you would be willing to pay for the deal. 2.3 Explain why the amounts in 2.1 and 2.2 are slightly different.
- Suppose you have an exponential utility function given by U(x) =1- exp(-x/R) where, for you, R = 1000. Further, suppose you have an investment with a 50/50 chance of returning either 0 or 2000 dollars. Note U(0) = 0 and U(2000) = 0.865, so the utility of the lottery is 0.432. What is the certain equivalent of that investment?An investor with capital x can invest any amount between0 and x; if y is invested then y is eitherwon or lost, with respectiveprobabilities p and 1− p. If p > 1/2, how much should be invested byan investor having a exponential utility function u(x) = 1 − e −bx ,b > 0.An aggressive investment in Industry 4.0 next-generation technology has the potential to save your company $7M if it is very successful, or $3M if it is moderately successful, but it will cost $2M if it fails. The relative risk for the project is $1.25M. The company has a risk tolerance of $1 million and has assigned a utility value of .777 based on an exponential utility function for this investment. What is the value of a safe investment that the company would just as soon choose rather than investing in the IT project? A. $2M B. $1.5M C. 52.75 D. $1.25M
- Using the normal table or software, find the value of z that makes the following probabilities true. You might find it helpful to draw a picture to check your answers (a) P(Zz) =0.01 (e) P(Z|Leo owns one share of Anteras, a semiconductor chip company which may have to recall millions of chips. The stock currently trades at $100/share. Leo believes the probability that they have to recall the chips is 50%. If the chips have to be recalled, the stock price will be cut in half, but otherwise it will remain $100. The expected value of Leo's share is ______ Assume Leo has the utility function, U(X)=√X. The minimum price Leo would accept to sell his share is _______ Leo's risk premium is ________Two stocks are available. The corresponding expectedrates of return are r¯1 and r¯2; the corresponding variances and covariances areσ12, σ22, and σ12. What percentages of total investment should be invested ineach of the two stocks to minimize the total variance of the rate of return ofthe resulting portfolio? What is the mean rate of return of this portfolio?Mr Usu has an expected utility function with u(x) = x0.5. He is analyzing an investment opportunity that promises to pay out $1,160 with prob. 0.6 and $2,800 with prob. 0.4. What is the expected utility of this opportunity?A Real estate investor has the opportunity to purchase a small apartment complex. The apartment complex costs $4 million and is expected to generate net revenue (that after all operating and finance costs) of $60,000 per month. Course, the revenue can vary because the occupancy rate is uncertain. Considering the uncertainty, the revenue could vary from a low -$10,000 To a high of $100,000 per month. Assume that the investors objective is to maximize the value of the investment in the 10 years. The city Council is currently considering an application to rezone a nearby empty parcel of land. The owner of that land wants to build a small electronics assembly plant. Was plant does not really conflict with the city’s overall land use plan, but it may have a substantial long-term negative effect on the value the nearby residential district in which the apartment complex is located. Because the city Council currently is divided on the issue and will not make a decision until next month, the…You plan to invest $1,000 in a corporate bond fund or in a common stock fund. The following table represents the annual return (per $1,000) of each of these investments under various economic conditions and the probability that each of those economic conditions will occur. Compute the expected return for the corporate bond and for the common stock fund. Show your calculations on excel for expected returns. Compute the standard deviation for the corporate bond fund and for the common stock fund. Would you invest in the corporate bond fund or the common stock fund? Explain. If choose to invest in the common stock fund and in (c), what do you think about the possibility of losing $999 of every $1,000 invested if there is depression. Explain.SEE MORE QUESTIONS