Question

The yield curve is as follows:  

2 yr interest rate        3%

3 yr interest rate        4%

5 yr interest rate         5%

What is the 2 yr forward 3 yr interest rate?

Under pure expectations theory, what should the three year interest rate be in two years?

（show the process）

Answer 1

So, the 3 year interest rate in 2 years, means we will hold the security at the end of the 5th year.

According to the pure expectations theory, holding a 5 year bond is equal to holding a 2 year bond that will yield 3 % and a 3 year bond.. under pure expectations theory you are indifferent holding the 5 year bond, or a 2 year bond plus purchasing a 3 Year interest rate bond after 2 years

So, the 3 year interest rate is

(1.05)^5 = (1.03)^2 (1+x )^3

1.2763 = 1.0609 * (1+x)^3

1.0629 = (1+x)

x = 6.29%