Question

Suppose 1-year, 2 year and 3 -year interest rates today are 2.2%, 2.2% and 2.0%, respectively. What's the expected 1-year interest rate two years from now according to the expectations theory?

1.3 percent.

1.6 percent.

1.36 percent.

1.8 percent.

Answer 1

According to expectation theory we have:

I_n = (i₀ + i₁ + ------+ i_n-1)/n

where I_n = interest rate on 4-year bond today and i_n = expected 1-year interest rate n years from now.

Using above data we have :

I₁ = (i₀)/1 => 2.2 = (i₀)/1 => i₀ = 2.2%

Also, I₂ = (i₀ + i₁)/2

=> 2.2 = (2.2 + i₁)/2

=> i₁ = 4.4 - 2.2 = 2.2%

Now,

I₃ = (i₀ + i₁ + i₂)/3 where i₂ = one year interest rate 2 year from now that we have to calculate

=> 2 = (2.2 + 2.2 + i₂)/3

=> i₂ = 3*2 - 2.2 - 2.2 = 1.6%

So, Expected one year interest rate 2 years from now = 1.6%

Hence, the correct answer is (b) 1.6 percent.