Suppose that the yield to

maturity of zero-coupon treasury bond from today up to year 1, year 2, and year 3 is 2%, 4%, and 6%, respectively. Yield to maturity is an annualized simple interest rate compounded annually.

(a) What are the annualized zero rates from today up to year 1, year2, and year 3, i.e., z

01, z02, z03, respectively?

(b) If the expectations hypothesis holds, what are the expected future 1-year spot rate for the next two years, i.e., E[r1,2] and E[r2,3]? What is the expected future annualized spot rate from year 1 to year 3, i.e., E[r1,3]?