Consider the Arrow's portfolio model with one risky asset and one risk-free asset. The von Newmann-Morgenstern utility functions of an investor is: u(w) = In w, where w represents wealth, and In natural log. Denote as a the amount invested in the risky asset. Let the initial wealth be $10,000, the interest rate of the risk-free asset 5%, and the probability distribution of the return of the risky asset X = (1%, 5%; 0.55, 0.45). 1.1 Write the equation of the expected utility of final wealth 1.2 Take the first derivative of the expected utility with respect to a. 1.3 Now evaluate the first derivative, that you found in 1.2 above, at a = 0. What can you conclude about the optimal value of a? Why is that so?

Consider the Arrow's portfolio model with one risky asset and one risk-free asset. The von Newmann-Morgenstern utility functions of an investor is: u(w) = In w, where w represents wealth, and In natural log. Denote as a the amount invested in the risky asset. Let the initial wealth be $10,000, the interest rate of the risk-free asset 5%, and the probability distribution of the return of the risky asset X = (1%, 5%; 0.55, 0.45). 1.1 Write the equation of the expected utility of final wealth 1.2 Take the first derivative of the expected utility with respect to a. 1.3 Now evaluate the first derivative, that you found in 1.2 above, at a = 0. What can you conclude about the optimal value of a? Why is that so?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = . 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 Ro with probability q. We assume R₁ 0. Let A be the amount invested in the risky asset, so that w - A is invested in the safe asset. 1) What are risk preferences of this investor, are they risk-averse, risk neutral or risk-loving?
Hugo has a concave ubility function of U(W)=√W. His only asset is shares in an Internet start-up company. Tomorrow he will learn the stock's value. He belleves that it is worth $225 with probability 80% and $256 with probability 20%. What is his expected utsty? What risk premium would he pay to avoid bearing this risk? The stock's expected utility (EU) is EU = (Enter a numeric response using a real number rounded to two decimal places.) han fro
10. Which one of the following measures may be used to measure the risk of an investment on its own? a) Expected return of the investment. b) Expected utility of the investment for an investor. c) Standard deviation of the possible outcomes of the investment. d) The Bernoullian utility function's value of a good investment outcome.
The value of a successful project is $420,000; the probabilities of success are 1/2 with good supervision and 1/4 without. The manager is risk neutral, not risk averse as in the text, so his expected utility equals his expected income minus his disutility of effort. He can get other jobs paying $90,000, and his disutility for exerting the extra effort for good supervision on your project is $100,000. (a) Show that inducing high effort would require the firm to offer a compensation scheme with a negative base salary; that is, if the project fails, the manager pays the firm an amount stipulated in the scheme. (b) How might a negative base salary be implemented in reality? (c) Show that if a negative base salary is not feasible, then the firm does better to settle for the low-pay, low-effort situation.
Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.1) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?2) Find A as a function of w.
I need help with question d
(a) Calculate the risk-premium on this portfolio and provide a brief interpretation of it (b) Calculate the minimum sale price of the capital assets for the average investor.
advanced microeconomics, uncertainty
A widely used utility function in the economics literature is the constant rate of risk aversion utility function. It is given by: utc) = c*(1-n) (1-n) Assume that an agent lives tor three periods (t-0,1,2) and discounts future utity at rate B (per period), The agent is born with asset level ag and his/her labour market income is yo and y, for periods O and 1 respectively, the agent retire in the last period (no labour income). The interest rate in this economy is Please answer the following questions based on the information displayed here. Choose the best option avallable. Select one: O a. The budget constrain in period te2 is given by: C2 + ay = az(1+r) O b. The budget constrain in period te2 is given by: c2= az{1+1) O G. The budget constrain in period t=2 is glven by: ute, )+ ag = a;(1+1) +ya d. The budget constrain in period t=2 is given by: C2= az(1+r) +y3 e. The budget constrain in period te2 is given by: c, + ag = az(1+) +ya
Use the utility function u = E (r,) – 0.5 A o, where A is the risk aversion parameter and A = 3.5. Use the average annual return on the S&P 500 as E(r,). Use the average annual interest rate on the US Government 10-year treasury bond over the past decade as r Solve for the investor's optimal allocation between the risky and the risk-free asset.
Show that an investor with a quadratic utility function ranks portfolios only on the basis of the mean and variance of returns.