Suppose the economy can only be in one of the following three states: (i) Boom or good state, (ii) Neutral state, and (iii) Recession or bad state. Good and bad states can occur with a probability of 0.25 and the neutral state can occur with a probability of 0.50. At the beginning of a month, you can purchase the following two securities in the market: Security 1: It is currently trading at $5. At the end of the month, the stock price is expected to increase by $15 in the good state, expected to remain unchanged in the neutral state, and expected to decrease by $5 in the bad state. Security 2: It is currently trading at $6. At the end of the month, the price of security 2 is expected to decrease by $6 in the good state, expected to remain unchanged in the neutral state, and expected to increase by $18 in the bad state. Please answer the following questions. Show all your calculations clearly.

1. Draw the payoff trees for securities 1 and 2 if you purchase them at the beginning of the month and sell them at the end of the month. Use percentage returns (and not prices) to draw the payoff trees. Please label the trees clearly. 4

2. Compute the expected returns (not prices) of securities 1 and 2.

3. Compute the standard deviations of returns for securities 1 and 2. 5

4. Compute the covariance and the correlation between the returns of two securities.