Consider an agent/investor who has a wealth of 100TL and can buy either of the following two assets for a price. The first asset is risky and when the state of the economy is state H (state is L) it delivers 3 TL (0 TL, resp.) for every one of the first asset the investor owns. The first asset is traded at a price 711 > 0. On the other hand, the second asset is risk-free and delivers 1 TL for every risk-free asset the investor has, while the price of the risk-free asset is normalized to 1, i.e. T2 = 1. (That is, the risk-free asset is the same as keeping your money in your pocket provided that the real interest rates are normalized to 1.) There are two states H and L and the probability of state H is 0.40. Moreover, the money utility of the agent is given by u(x) = VT. A. Suppose that 71 = 1. The agent considers buying x amount of the risky asset while the rest, 100 21, will be invested into the risk-free asset. Compute the expected utility and certainty equivalence figures for the following portfolio choices of the agent, and indicate which one is the best: i. x1 = 50, investing half of the wealth into the risky asset; ii. x1 = 25, investing a quarter of the wealth into the risky asset; iii. x1 = 0, not investing into the risky asset. B. Show that the optimal portfolio with #1 = 1 is given by x1 = 10. 350 C. Show that the optimal portfolio is given by *** 14200 1463 9.7061 when 711 = 1.1. C. Suppose 711 > 0 and 12 = 1. Then, formulate agent's optimal portfolio identification problem and characterize the solution (identifying the related equations and solve them if possible; if not, discuss in detail why it is not possible). Identify the relation between 71 > 0 and optimal portfolio choice x1(71) for a fixed level of T2 = 1 (possibly using Wolfram Alpha or Excel or Mathematica)? What you identify is agent's demand (function) of the risky asset! Consider an agent/investor who has a wealth of 100TL and can buy either of the following two assets for a price. The first asset is risky and when the state of the economy is state H (state is L) it delivers 3 TL (0 TL, resp.) for every one of the first asset the investor owns. The first asset is traded at a price 711 > 0. On the other hand, the second asset is risk-free and delivers 1 TL for every risk-free asset the investor has, while the price of the risk-free asset is normalized to 1, i.e. T2 = 1. (That is, the risk-free asset is the same as keeping your money in your pocket provided that the real interest rates are normalized to 1.) There are two states H and L and the probability of state H is 0.40. Moreover, the money utility of the agent is given by u(x) = VT. A. Suppose that 71 = 1. The agent considers buying x amount of the risky asset while the rest, 100 21, will be invested into the risk-free asset. Compute the expected utility and certainty equivalence figures for the following portfolio choices of the agent, and indicate which one is the best: i. x1 = 50, investing half of the wealth into the risky asset; ii. x1 = 25, investing a quarter of the wealth into the risky asset; iii. x1 = 0, not investing into the risky asset. B. Show that the optimal portfolio with #1 = 1 is given by x1 = 10. 350 C. Show that the optimal portfolio is given by *** 14200 1463 9.7061 when 711 = 1.1. C. Suppose 711 > 0 and 12 = 1. Then, formulate agent's optimal portfolio identification problem and characterize the solution (identifying the related equations and solve them if possible; if not, discuss in detail why it is not possible). Identify the relation between 71 > 0 and optimal portfolio choice x1(71) for a fixed level of T2 = 1 (possibly using Wolfram Alpha or Excel or Mathematica)? What you identify is agent's demand (function) of the risky asset