Question

Answer the following questions using expectations theory:

A) The interest rate on a 1-year bond in period t is 5 percent; the interest rate on a 2-year bond in period t+1 is 9 percent. What is the implicit forward interest rate in t+1? Show your work and circle your final answer.

B) If the interest rate on a 1-year bond in period t is 4 percent, and the implicit forward interest rate on a 1-year bond in period t+1 is 6 percent, then what does the interest rate equal on a 2-year bond in period t+1? Show your work and circle your final answer.

C) The interest rate on a 1-year bond in period t is 6 percent, the implicit forward interest rate in t+1 is 7 percent, and the interest rate on a 3-year bond in period t+2 is 7 percent. What does the implicit forward interest rate equal in period t+2? Show your work and circle your final answer.

Answer 1

Based on the Pure Expectation Theory, short term rates are indicators of long term rates.

In simple words, if you invest an amount for two years in a bond, it would yield you the same result as if you would have invested in 1 year bond and then reinvested the proceeds from matured investments for another 1 year bond.

Part A

(1 + 2Yr bond)² = (1 + 1Yr Bond) * (1 + 1Yr Forward Rate)

(1 + 9%)² = (1 + 5%) * (1 + 1Yr Forward Rate)

(1 + 1Yr Forward Rate) = (1.09²)/1.05 = 1.1315

1Yr Forward Rate = 0.1315

1Yr Forward Rate = 13.15%

Part b

(1 + 2Yr bond)² = (1 + 1Yr Bond) * (1 + 1Yr Forward Rate)

(1 + 2Yr bond)² = (1 + 4%) * (1 + 6%)

(1 + 2Yr Bond)² = 1.04 * 1.06 = 1.1024

2Yr Bond = 1.0499 - 1

2Yr bond = 4.99%

Part c

(1 + 3Yr bond)³ = (1 + 1Yr Bond) * (1 + 1Yr Forward Rate1 Yr from now) * (1 + 1Yr Forward Rate2yr from now)

(1 + 7%)³ = (1 + 6%) * (1 + 7%) * (1 + 1Yr Forward Rate2yr from now)

(1 + 1Yr Forward Rate2yr from now) = 1.2250/(1.06 * 1.07) = 1.0801

1Yr Forward Rate2yr from now = 8.01%