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Problem in forecasting interest rates based on unbiased expectations theory
Problem in forecasting interest rates based on unbiased expectations theory. These are spot rates today (Oct. 9, 2020)
R1= 12%, R2=13%, R3=14%, R4=15%
A. Given this information calculate one year forward ratefor a one yr loan beginning 10/9/21 and ending 10/9/22.
B. calculate two year forward ratefor a one yr loan beginning 10/9/22 and ending 10/9/23.
C. calculate three year forward ratefor a one yr loan beginning 10/9/23 and ending 10/9/24.
D. calculate two year forward ratefor a two yr loan beginning 10/9/22 and ending 10/9/24.
Expert Solution
a.)
Annualized Forward rate of 1 years 1 years from now =((1+2 Year rate)^2/(1+1 Year rate)^1)-1
=((1+ 13%)^2/ (1+ 12%)^1)-1
= 14.01%
b.)
Annualized Forward rate of 1 years 2 years from now =((1+3 Year rate)^3/(1+2 Year rate)^2)-1
=((1+ 14%)^3/(1+13%)^2)-1
= 16.03%
c.)
Annualized Forward rate of 1 years 3 years from now =((1+4 Year rate)^4/(1+3 Year rate)^3)-1
=((1+15%)^4/ (1+14%)^3)-1
= 18.05%
d.)
Annualized Forward rate of 2 years 2 years from now =((1+4 Year rate)^4/(1+2 Year rate)^2)^1/2-1
=((1+15%)^4/(1+13%)^2)^1/2-1
= 17.04%
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