Question

4. Which forward rate cannot be computed from the 1-, 2-, 3-, and 4-year spot rates? The rate for a:

A. 1-year loan beginning in 2 years

B. 2-year loan beginning in 2 years

C. 3-year loan beginning in 2 years

Answer 1

Forward rate is an interest rate which can be obtained today for a loan in future.

The idea behind computation of forward rates using spot rates is based on no arbitrage condition.

Let r(1), r(2), r(3) and r(4) be 1-year,2-year, 3-year and 4-year spot rates respectively.

f(2,1) be forward rate of one year loan issued 2 years from now

f(2,2) be forward rate of two year loan issued two years from now

f(2,3) be forward rate of three year loan beginning in two years time.

Forward rate for one year loan starting in 2 years as be computed as

[1+r(3)]^3 = [1+r(2)]^2 * [1+f(2,1)]

Forward rate for two year loan starting in 2 years can be computed as under

[1+r(4)]^4 = [1+r(2)]^2 * [1+f(2,2)]^2

But for calculating 3 year loan beginning in two years, spot rate for year 5 would be required. Thus, it cannot be computed.

C. Is the correct answer.