Question

7. The yield to maturity on a seven-year government bond is 8% and the yield to maturity on a six-year government bond is 7%. Provide an estimate of the one-year interest rate during year 7. If both the six and seven year bonds have built into their yields a premium for interest rate risk, how would this change your answer?

Answer 1

7-year bond rate (S7) = 8%
6-year bond rate (S6) = 7%
One year interest rate during year 7 = x%

(1 + S7)7 = (1+S6)6 * (1+x%)
(1+x%) = (1+0.08)7 / (1+0.07)6
(1+x%) = 1.713824 / 1.50073
x% = 1.14199 - 1
x% = 0.14199
x = 14.199%

One year interest rate during year 7 = 14.199%

2) My answer would not change because interest rate risk is captured by the duration of the bond
Duration = Change in bond prices/change in yields of bond

And also, according to Malkiel's theorem, the bond yields are essentially the interest rates i.e. as the interest rate changes the bond yield also changes.