124 PA R T I I Financial Markets We can conduct the same steps for bonds with a longer maturity so that we can examine the whole term structure of interest rates Doing so, we will find that the interest rate of int on an n-period bond must equal int * i t + i te + + i te + + + i et + (n - 1) n (2) Equation states that the n-period interest rate equals the average of the oneperiod interest rates expected to occur over the n-period life of the bond This is a restatement of the expectations theory in more precise terms.1 APP LI CAT IO N Expectations Theory and the Yield Curve The one-year interest rate over the next five years is expected to be 5%, 6%, 7%, 8%, and 9% Given this information, what are the interest rates on a two-year bond and a five-year bond? Explain what is happening to the yield curve Solution The interest rate on the two-year bond would be 5.5% i t + i et + + i et + + + i te + (n - 1) int * n where it * year interest rate * 5% i te+ * year interest rate * 6% n * number of years *2 Thus i 2t * 5% + 6% * 5.5% The interest rate on the five-year bond would be 7% it + ite+ + ite+ + + ite+ (n - 1) int * n where it * year interest rate * 5% i te+ * year interest rate * 6% i et + * year interest rate * 7% i et + * year interest rate * 8% i et + * year interest rate * 9% n * number of years * The analysis here has been conducted for discount bonds Formulas for interest rates on coupon bonds would differ slightly from those used here but would convey the same principle