Consider a mean-variance optimizer that wants to invest in bonds for two periods. In order for them to be indifferent (i.e., get the same utility) between a two year bond and rolling over two one year bonds, what must the liquidity premium equal? What if they want to invest for N periods and are indifferent between an N period bond and an N 1 period bond rolled over into a one period bond? What must the liquidity premium equal then?

HINT: Recall mean-variance utility is given by U(r) = E[r] A/2 V ar(r)

and think about what the returns on the different investment strategies are, and what parts of those returns are risky. Also recall the liquidity premium is the difference between the forward rate and the expected short rate.