Question

Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that the current rate on 10-year Treasury bonds is 3.25 percent and on 20-year Treasury bonds is 5.50 percent. Assume that the maturity risk premium is zero. Calculate the expected rate on a 10-year Treasury bond purchased ten years from today, E(10r10).

Answer 1

As per Interest expectation theory, on the basis of long term interest rates, short term interest rates in futures can be predicted.
Current rate on 10-Year Treasury bonds					3.25%	0.0325
Current rate on 20-Year Treasury bonds					5.50%	0.055
Maturity risk premium is zero.
So, as per expectation theory, Expected rate (forward rate) on a 10-Year bonds purchased ten years from today can be calculated by below :
(1 + Forward interest rate)^n = (1 + Longer time Spot rate)^n / (1+ Shorter time Spot rate)^n
(1+F)^10 = (1 + 0.055)^20 / (1+0.0325)^10
(1+f)^10 =	2.917757	/	1.376894
(1+F)^10 =	2.119086
1+F =	1.07799
F =	0.07799 or		7.80%
So, Expected rate on a 10-Year Treasury bond purchased ten years from today is 7.80%.