c,d,e and f with explanation (working out) There are 2 future states 01 and 02. The probability of 01 and 02 eventuating are #1 andT2 respectively. Endowments differ by state. There are two agents with utility functionU(c) = co+1 ln(ci) + 2 ln(c2) There are 2 zero net supply AD securities (i.e. (1,0) and(0,1)). Denote demand for these securities as where k is agent 1 or 2 and i is state 1 or2. Assume the following:Agent 1 4Agent 2 4C01 C021 57 20.4 0.6Answer the following:(a) Set up the maximization problem for both agents.(b) Take the FOCs with respect to z, z, 2, and 3.(c) Solve for optimal zł, z, zỉ, and z.(d) Solve for qi and q2.(e) What are the post trade allocations?(f) What is the expected utility of both agents post and pre-trade.(g) Are the post trade allocations Pareto Optimal? Why?

Agent's ProblemThere are two agents and two states of the world, θ1 and θ2. Each agent maximizes…

Answered: There are 2 future states 01 and 02.…

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Suppose the demand functions for two products are q1 = f(p1, p2) and q2 = g(p1, p2) wherep1, p2, q1, and q2 are the prices (in dollars) and quantities for products 1 and 2. Consider thefour partial derivatives∂q1/∂p1,∂q1/∂p2,∂q2/∂p1and ∂q2/∂p2,State the sign of each of these partial derivatives if:(a) the products are complementary goods(b) the products are substitute goods.
Problem 4. Consider tuo scenarios, wi with probability and w with probability Suppose that the return on sonie security is K retum on another security is K uch that the tu0 socurities hane the same risk = -2% in the first scenario and K = 6% in the second scenario. If the = -3% in the first scenario, find the return K in the other scenario
Assuming your utility function U = E(r) - Ao². Consider the investments shown in the table. If your risk aversion coefficient is -2, which investment would you choose? Investment E[r] #1 #2 #3 #4 #2 #3 #4 #1 12% 15% 15% 24% σ 40% 40% 30% 40%
A forward contract has an underlying asset which, in Cox-RossRubenstein notation, has S=22,u=1.2 and d=0.9. This forward contract matures in one time step and the return over this time step is R=1.02. Assuming the forward price is calculated rationally, what is the value of the forward at node (1,1)? (Give your answer as a positive number.)
3.1 Show that for any portfolio w = equal to (wi,..., wn) the Beta of the portfolio is Bw = wiB1 + + wn Bn, !! ... where B; for i = 1,...,n are Betas of individual assets.
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Assume that security returns are generated by the single-index model,Ri = αi + βiRM + eiwhere Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 0.7 7 % 20 % B 0.9 9 6 C 1.1 11 15 a. If σM = 16%, calculate the variance of returns of securities A, B, and C. b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)
Consider a two-factor Arbitrage Pricing Theory (APT) model, T; = a; + b1,ifı + b2.i f2 + €i, with the following information Asset i Asset 1 0.07 0.50 0.25 Asset 2 0.15 1.10 0.75 Asset 3 0.20 b1,3 Hi b1i b2i 1.0 and the risk-free rate rp is 0.025. (a) Find the value of b13 to preclude arbitrage opportunity. (b) is an Asset 4 with 4 = 0.13, b14 = 0.8, and b2.4 = 0.4. Explain how you would exploit an arbitrage opportunity if there
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