Question

Problem in Forecasting Interest Rates based on unbiased expectations theory:

These are the rates today (June 15, 2018) for loans of equal risk.
R1 = 2%;
R2 = 3%
R3 = 4%
R4 = 5%

A. Given this information, calculate one-year forward rate for a one-year loan beginning 6/15/19 and ending on 6/15/20

B. Calculate the two-year forward rate for a one-year loan beginning 6/15/20 and ending on 6/15/21

C. Calculate the three-year forward rate for a one-year loan beginning 6/15/21 and ending on 6/15/22

D. Calculate the two-year forward rate for a two-year loan beginning 6/15/20 and ending on 6/15/22

Answer 1

a

Annualized Forward rate of 1 years 1 years from now =((1+2 Year rate)^2/(1+1 Year rate)^1)-1

Annualized Forward rate of 1 years 1 years from now=((1+0.03)^2/(1+0.02)^1)-1

Annualized Forward rate of 1 years 1 years from now % = 4.01

b

Annualized Forward rate of 1 years 2 years from now =((1+3 Year rate)^3/(1+2 Year rate)^2)-1

Annualized Forward rate of 1 years 2 years from now=((1+0.04)^3/(1+0.03)^2)-1

Annualized Forward rate of 1 years 2 years from now % = 6.03

c

Annualized Forward rate of 1 years 3 years from now =((1+4 Year rate)^4/(1+3 Year rate)^3)-1

Annualized Forward rate of 1 years 3 years from now=((1+0.05)^4/(1+0.04)^3)-1

Annualized Forward rate of 1 years 3 years from now % = 8.06

d

Annualized Forward rate of 2 years 2 years from now =((1+4 Year rate)^4/(1+2 Year rate)^2)^1/2-1

Annualized Forward rate of 2 years 2 years from now=((1+0.05)^4/(1+0.03)^2)^1/2-1

Annualized Forward rate of 2 years 2 years from now % = 7.04