IX Arbitrage (30 points) Suppose the economy can be in one of the following three states: (i) Boom or good state, (ii) Neutral state, and (iii) Recession or "bad" state. Each state can occur with an equal probability. The following two risky securities are available at the beginning of a month: Security A: it is currently trading at $3 and at the end of the month, it is expected to yield a $4.50 net payoff in the good state, a $0 net payoff in the neutral state, and a $0 net payoff in the bad state. Security B: it is currently trading at $5 and at the end of th month, it is expected to yield a $15 net payoff in the good state, a $6 net payoff in the neutral state, and a $0 net payoff in the bad state. In addition, you can purchase a put option (Security C) on security B which expires at the end of the month and has a strike price (or an exercise price) of $11. The option is currently trading at $2. You are also allowed to short the two risky securities. 1. (10 points) Relative to the fundamental values, which of the three securities (A, B, and C) are fairly priced? Which securities are under-priced? Which securities are over-priced? For simplicity, please ignore the discount rate. 2. (20 points) Construct an arbitrage portfolio using these securities, which yields a pos- itive payoff in each state. Mention clearly which securities (and their quantities) you would long and/or short. Calculate the net payoffs of the arbitrage portfolio in the three states