Question

(1.) Consider the following annualized spot yields:

Maturity	Annualized Spot Rate
One Year	5.00%
Two Years	5.50%
Three Years	6.00%
Four Years	6.00%
Five Years	?

(a.) Assuming the expectations theory of the term structure is correct, calculate the expected one-year interest rate one year from now (i.e. 1f2).

(b.) Assuming the expectations theory of the term structure is correct, calculate the expected one-year interest rate three years from now (i.e. 3f4).

(c.) Suppose a forecasting service predicts that th eone-year interest rate four years from now will be 5.00%. Based on this forecast, ascertain what the five-year spot yield must be if bond prices permit no arbitrage.

Answer 1

(a) Expected one year interest rate one year Form now i.e, 1 F_2 = [(1 + r_02)^2/(1 + r_01)^1 - 1] times 100 where, r_02 = Two years spot rate r_01 = one year spot rate (given in Question) Hence, 1 F 2 = ((1 + 0.055)^2/(1 + 0.05)^1 - 1) times 100 tildeequalto 6% (b) Similarly 3 F 4 means one year interest rate after 3 = [(1 + r_04)^4/1 + r_03)^3 - 1] times 100 = [1 + 0.06)^4/1 + 0.06)^3 - 1] times 100 = 6% (c) given in Question that, one year interest rate for years From now = 5% i.e, 4 F 5 = 5% 5 = [(1 + r_05)^5/(1 + r_04)^4 - 1] times 100 = 5 = [(1 + r_05)^5/(1.06)^4 1.05 = (1 + r_05)^5/(1.06)^4 = (1 + r_05)^5 = 1.3256 Hence, r_05 = 5.8%