1. Consider the three state, two security example that we discussed in class. State Price Recession Normal Boom 90 100 100 100 80 0 100 200 Security 1 Security 2 Probability 0.2 0.5 0.3 (a) What is the risk-free rate that is implied by the price of security 1? (b) What is the expected return of security 2? (c) Suppose we introduce Security 3, which pays ( on both the Recession and Normal states and pays 300 in a boom. Is the market complete? (d) For what values of P3 is there no arbitrage? (e) For the remaining parts of the problem, assume that Pz = 50. Compute the state price vector. Is the state price vector unique? (f) Compute the stochastic discount factor. (g) Suppose that a fourth security is introduced that pays 200 in a recession, 100 in normal times, and 0 in a boom. What is the no-arbitrage price of Security 4? (h) What is the expected return of Security 4? Explain why it is lower than the expected return of Security 2. 1. Consider the three state, two security example that we discussed in class. State Price Recession Normal Boom 90 100 100 100 80 0 100 200 Security 1 Security 2 Probability 0.2 0.5 0.3 (a) What is the risk-free rate that is implied by the price of security 1? (b) What is the expected return of security 2? (c) Suppose we introduce Security 3, which pays ( on both the Recession and Normal states and pays 300 in a boom. Is the market complete? (d) For what values of P3 is there no arbitrage? (e) For the remaining parts of the problem, assume that Pz = 50. Compute the state price vector. Is the state price vector unique? (f) Compute the stochastic discount factor. (g) Suppose that a fourth security is introduced that pays 200 in a recession, 100 in normal times, and 0 in a boom. What is the no-arbitrage price of Security 4? (h) What is the expected return of Security 4? Explain why it is lower than the expected return of Security 2