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. What are risk preferences of this investor, are they risk-averse, risk- neutral or risk-loving? Find A as a function of w. Does the investor put more or less of his portfolio into the risky asset as his wealth increases? Now find the share of wealth, α, invested in the risky asset. How does α change with wealth

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. What are risk preferences of this investor, are they risk-averse, risk- neutral or risk-loving? Find A as a function of w. Does the investor put more or less of his portfolio into the risky asset as his wealth increases? Now find the share of wealth, α, invested in the risky asset. How does α change with wealth

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter2: Fundamental Economic Concepts

Section: Chapter Questions

Problem 6E

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Suppose you visit with a financial adviser, and you are considering investing some of your wealth in one of three investment portfolios stocks, bonds, or commodities. Your financial adviser provides you with the following table, which gives the probabilities of possible returns from each investment To maximize your expected return, you should choose: Stocks Bonds Probability Return Probability Return 0.15 20% 0.15 16.7% 06 10% T 04 7.5% 0.25 8% 0.45 3.3% OA bonds OB stocks OC. commodities OD. All of the portfolios have the same expected return. If you are risk-averse and had to choose between the stock or the bond investments, you would choose OA the stock portfolio because there is less uncertainty over the outcome OB. the bond portfolio because there is less uncertainty over the outcome. OC. the stock portfolio because of greater expected return. OD. the bond portfolio because of greater expected return. Commodities Probability Return 02 20% 0.2 15% 0.2 8% 02 02 5% 0%
ANSWER E PLEASE ONLY 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.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 assetas his wealth increases? d) Now find the share of wealth, α, invested in the risky asset. How doesα change with wealth? e) Calculate relative risk aversion for this investor. How does relativerisk aversion depend on wealth?
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?
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) Find A as a function of w
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.a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?b) Find A as a function of w.
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. Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?
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.
19. An individual has initial wealth Wo = 3 and has the opportunity to invest some quantity of money x in an extremely risky corporate bond. With probability p= 1/4, the bond will be worth 10x at maturity. With probability 1 – p, it will be worth zero. The individual's utility function over final wealth is u(W) = W0.5. What is the level of investment x that maximizes expected utility? (а) 0 (b) 1 (c) 4/3 (d) V3 (e) 2
You have $1,000 that you can invest. If you buy Ford stock, you face the following returns and probabilities from holding the stock for one year: with a probability of 0.2 you will get $1,500; with a probability of 0.4 you will get $1,100; and with a probability of 0.4 you will get $900. If you put the money into the bank, in one year’s time you will get $1,100 for certain. a) What is the expected value of your earnings from investing in Ford stock? b) Suppose you are risk-averse. Can we say for sure whether you will invest in Ford stock or put your money into the bank?
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.
3) A risk-loving individual has $1000 to invest. The individual maximizes his/her expected utility and has a monotonic utility function. Show that he/she will never choose a diversified portfolio - that is, show that he/she will either keep the entire $1000 in a safe, or invest the entire $1000 in a risky assesst, for which each $1 invested yields $] with probability p, and SB with probability (1-p), where $B<$1<$J.
Questions 18 through 20 refer to the following information: Shawn's consumption is subject to risk. With probability 0.75 he will enjoy 10000 in consumption, but with probability 0.25 he will have only 3600. His utility function for consumption is given by v(c) = vc. Question 18 What is the expected value of Shawn's consumption? Question 19 What is his expected utility?