ANSWER E PLEASE ONLY Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = (x^n) / n. There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 − q and R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A is invested in the safe asset. a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving? b) Find A as a function of w. c) Does the investor put more or less of his portfolio into the risky asset as his wealth increases? d) Now find the share of wealth, α, invested in the risky asset. How does α change with wealth? e) Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?

ANSWER E PLEASE ONLY Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = (x^n) / n. There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 − q and R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A is invested in the safe asset. a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving? b) Find A as a function of w. c) Does the investor put more or less of his portfolio into the risky asset as his wealth increases? d) Now find the share of wealth, α, invested in the risky asset. How does α change with wealth? e) Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.9P

See similar textbooks

Similar questions

Millicent’s utility function is U(w) = W0.5 , where W is her wealth. She owns a “pure water” producing firm that will be worth GH100 or 0 Ghana cedis next year with equal probability. a. Suppose her firm is the only asset she has. What is the lowest price at which she will agree to sell her pure water? (Hint: price=amount that will give her the same expected utility) b. Assume that she has GH200 safely stored under her mattress, find the new lowest price at which she will agree to sell her “pure water” producing firm c. From your answers in parts (a) and (b), what is the relationship between her wealth and her degree of risk aversion?
Suppose XYZ Corporation's stock price rises or falls with equal probability by $25 each month, starting where it ended the previous month. What is the value of a three month at the-money European call option on XYZ's stock if the stock is priced at $100 when the option is purchased?$______
**Practice** I have been trying to practcie this question but I always seem to get it wrong What is the expected final wealth of each agent? Pay attention to the names in each option!A. Anna’s expected final wealth is 1440 and Bob’s expected final wealth is 980B. Anna’s expected final wealth is 1020 and Bob’s expected final wealth is 1380C. Anna’s expected final wealth is 1460 and Bob’s expected final wealth is 1105D. Anna’s expected final wealth is 1140 and Bob’s expected final wealth is 1200E. None of the options above
A risk-averse investor will: a. Always accept a greater risk with a greater expected return b. Only invest in assets providing certain returns c. Sometimes accept a lower expected return if it means less ri d. Never accept lower risk if it means accepting a lower expected return
3. Assume W(F)=F². Probability of sun is 2/3 and hurricane, 1/3. Plot the IC that runs through Fs, Fh=(400, 400). Plot the constant expected consumption line that run through the same point. Is this person risk neutral or risk averse?
A risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his wealth within the next year. a. What is the consumer's expected wealth one year from now? b. An insurance company offers our consumer full insurance against the possible loss. What premium must the consumer be charged for the insurance company to expect to break even? c. Suppose our risk-averse consumer is indifferent between getting $85,000 wealth with certainty and facing the above described uncertain situation. What is the maximum premium that the insurance company will be able to charge this consumer for its full insurance policy?
The risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standard deviation of 20%. Answer the following questions. Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition of A to make the investors prefer the optimal risky portfolio than the risk free asset?
Suppose Real Option Inc. has a product that generates the following cash flow. At t=1, the demand can be high or low. There is a probability of 0.6 that demand is high. If demand is high (low) the cash flow is CFH=400 (CFL=200). At t=2, the demand can also be high or low. If demand was high at t=1, then a high demand at t=2 arises with probability 0.7. If demand was low at t=1, then a high demand at t=2 arises with probability 0.2. If demand is high (low) at t=2 then CFH=400 (CFL=200). The interest rate for this project is 20%. (a) Draw the event and decision tree. (b) What is the market price (expected value) of Real Option Inc. at t=0? Now suppose Real Option Inc. can rent a platform to run a marketing campaign. For this purpose Real Option Inc. must sign a two year contract with the platform provider. The costs for using the platform are 180 per period. Marketing itself does not cost anything and has the following effect. In the high demand state, marketing doubles the demand. In…
Only typed answer Assume the correlation of returns between KO and the market portfolio equals 0.80, the standard deviation of KO equals 0.60, and the standard deviation for the market portfolio equals 0.30. What is the beta for KO.
Consider the constant relative risk aversion utility of wealth function from Chapter 3 for an investor with gamma parameter equal to 0.25: U(W) = W^(0.25)/(0.25) = 4W^(0.25). Suppose this investor is faced with a 50-50 bet to receive nothing or to receive 1000 dollars. What's a fair price for this bet to the investor? I.e., what is the certainty equivalent wealth (CEW) associated with this bet, for this investor
Suppose that the consumer is asked to contemplate a gamble with a probability of 60% of winning Birr 10,000 with a utility of 10 utils, and a 40% probability of winning Birr 15,000 with a utility of 12 utils. A. What will be the expected income and expected utility of the consumer? B. If the utility of this consumer from a risk free alternative which gives him an income equal to the expected income of the risky alternative given above is equal to 11 utils, is this consumer risk lover or risk averse? Why? Illustrate your answer with the help of a diagram
You've estimated the following expected returns for a stock, depending on the strength of the economy: State (s) Probability Expected return Recession 0.3 -0.03 Normal 0.5 0.08 Expansion 0.2 0.13 What is the expected return for the stock? What is the standard deviation of returns for the stock?