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: 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 consisting of asset A ? Why or why not? 6. What is the variance of a portfolio that consists of A and B together? 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