(a) Set up the maximization problem for both agents. (b) Take the FOCs with respect to z, z, z₁, and zz. (c) Solve for optimal z, z, z, and z. (d) Solve for qi and 92. (e) What are the post trade allocations? (f) Are the post trade allocations Pareto Optimal? There are 2 future states 01 and 02. The probability of 0₁ and 02 eventuating are #1 and #2, respectively. Endowments differ by state. There are two agents with utility function U(c) = co + 1 ln(c1) + 2 In(c2) There are 2 zero net supply AD securities. Denote demand for these securities as where k is agent 1 or 2 and i is state 1 or 2. Assume the following: eo €82 Agent 1 4 4 8 Agent 2 4 10 5 П 0.40 0.60

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%

Show that for an initial wealth w and a linear utility function u(w) = w, then P= E[X].

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.)

Think about whether a risk-free asset should earn a risk-premium beyond the risk-free rate.  Thinking about that should give you an idea of the beta for a risk-free asset.  Or, look again at the CAPM equation: E(Ri)=Rf+βi[E(RM)−Rf] Given this equation, what beta sets the E(R) of the risk free asset equal to the risk-free rate?  A) zero B) 0.5 C) 1.0 D) its random

State the decision criteria for each of the following. (2)   PI >   MIRR >   NPV >   IRR >   options;  0 1 PI MIRR NPV IRR Payback

6. Equilibrium pricing: Let the subscripts: j = 0 denote the risk-free asset, j = 1,...,n the set of available risky securities, and M the market portfolio. For the questions that follow, assume that CAPM provides an accurate description of reality. a. b. C. d. State the CAPM equation. (1) Use the CAPM equation to show that the following condition is true s; ≤ SM for any j. What is the significance of this condition when interpreted in the context of the capital market line? (5) Assume that B = 0.8, μM = 0.1 and r = 0.05. Using the CAPM, determine the expected return from holding one unit of asset j for one period. (2) Given your answer to c.), what could you conclude (from the perspective of the security market line) if a market survey indicated that the forecasted one- period return on asset j was 8 percent? Describe and motivate the rational trading response that is consistent with your conclusion. (4)

Consider the following securities: state Probability A B A B H M L 0.2 0.5 0.3 с 6 10 6 3 7 12 2 5 14 1. The expected payoff of A is: 2. The standard deviation of A is: 3. If the price of A is 3, its expected return is: 4. The covariance between A and B is: 5. The correlation coefficient between A and B is: 6. Is it possible to build a portfolio that has zero variance using A and C? YES/ NO

Consider the probability distribution p(s) of the returns rA and rB of two securities A and B: state p(s) rA rB роог 0.2 0.1 0.16 medium 0.5 0.2 0.1 доod 0.3 0.3 0.05 Calculate the covariance oAB between rA and rB. The correct answer (up to four decimals is) Select one: GAB = 0.0013 GAB = -0.0027 GAB = -0.0102 None of the above

Assuming two risk-free rates for lending and borrowing in the market: r(f) and r(b). Suppose your utility function is described by U = E(r) - 0.5A xo² with A> 0, and you are combining the risk-free asset with the optimal risky asset to maximize the utility. Consider the following two situations: 1. Suppose r(b) = r(f): you form the optimal complete portfolio C1 by borrowing money at r(f) and invest y1 (i.e., y1 represents portfolio weight) in the optimal risky portfolio (P1). Your utility score under this situation is denoted as U1; II. Suppose r(b) >r(f): you form another optimal complete portfolio C2 by borrowing money at r(b) and invest y2 (1.e., y2 represents portfolio weight) in the optimal risky portfolio (P2). Your utility score under this situation is denoted as U2. For simplicity, let's assume the optimal risky portfolios under these two situations are the same (i.e., E(P1)=E(P2) and o(P1) = o(P2)). What are the relationship between y1 and y2, U1 and U2: O a. y1=y2 and U1=U2 O…