Question

Please use the the following information for a and b: The current four-year interest rate is 6.25%The current one-year interest rate is 3.0%The expected one-year rate for one year from now is 5.0%The expected one-year rate for two years from now is 6.5%a. Assuming the Expections Hypothesis is correct, what is the expected one-year rate for three years from now

Answer 1

10.65%

Step-by-step explanation:

To prevent arbitrage, investing in a 1-year security in each of the 1st, 2nd, 3rd and 4th years should yield the same return as investing in a 4-year security from the 1st year.

Accordingly,

`[(1+r_(1))(1+r_(2)) (1+r_(3))(1+r_(4))]^{(1)/(4)} = 1+R_(4)`

Where r = the 1-year rate of return for each given year

R = the 4-year rate of return

`[(1.03)(1.05) (1.065)(1+r_(4))]^{(1)/(4)} = 1.0625\\=1.151798(1+r_(4))=1.0625^(4) \\=1.151798(1+r_(4))=1.274429\\=(1+r_(4))=1.106469\\=r_(4)=0.106469`

Therefore, the expected one-year rate three years from now is 10.65%.