Consider a world with 3 potential states of the economy: high growth, medium growth, and low growth (recession). The probability of the high state is 30%, of the medium state 40%, and of the low state 30%. There are 3 assets, and the payoff from each of them in each state of the world appears in the table below:

The price of asset A is 8, the price of asset B is 3, and the price of asset C is 16. Answer the following questions:

1. Find the expected payoff and the expected return from each asset.

2. Find the variance and the standard deviation of the payoff of assets A and B.

3. Find the variance and the standard deviation of the return of assets A and B.

4. What is the variance of payoffs of asset C? What is the variance of its return? (hint: use a shortcut from the formula sheet).

5. Can C be used to hedge a portfolio of asset A? Why or why not?

6. What is the variance of the payoff of a portfolio that of A and B together? What is the variance of returns of this portfolio?

7. What will be the sign (negative, positive, zero) of the covariance of A and B? Make an argument without explicitly calculating it.

8. Calculate the covariance of A and B.

9. Find the correlation between A and B.

10. What is the correlation between A and C? Show that they are linearly dependent.