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 securities are available to you at the beginning of a month: Risky Security: It is currently trading at $50. At the end of the month, it is expected to yield a net payoff of $10 in the good state, a $5 payoff in the neutral state, and a $2 payoff in the bad state. Riskfree Security: It is currently trading at $4. At the end of the month, it is expected to yield a net payoff of $4 in all three states.

1. Please draw the payoff trees for the risky and the riskfree securities. Please label the trees clearly. 8

Combine the riskfree and the risky asset to construct a portfolio that generates a positive payoff of $1 in the bad state. Compute the percentage of your total allocation that should be in the riskfree asset.

3. Compute the mean/expected net payoff of the portfolio you constructed