Suppose the economy can only be in one of the following two states: (i) Boom or good state and (ii) Recession or bad state. Each of the states can occur with an equal probability. At the beginning of a month, you can purchase the following two securities in the market:

- Security 1: It is currently trading at $4. At the end of the month, the stock price is expected to increase by $10 in the good state and expected to remain unchanged in the bad state.

- Security 2: It is also currently trading at $5. This asset has payoffs that are like an insurance contract. It yields a positive return when the economic conditions are poor. At the end of the month, the price of security 2 is expected to remain unchanged in the good state and expected to increase by $10 in the bad state.

a) 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.

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

c) Compute the standard deviations of returns for securities 1 and 2.

d) Compute the covariance and the correlation between the returns of two securities