Question

Assume a yield curve that has a 1 year rate of 4%, a 2 year rate of 5%, a 3 year rate of 5.5% and a 4 year rate of 6%.

1. How many forward rates can you find from this yield curve.

2. Attempt to calculate them.

Answer 1

The formula for calculating Forward rates is:

where f_n is the forward rate over the nth year, r_n is the n-year spot rate, and r_n-1 is the spot rate
for n-1 years.

Assuming yield curve rates as spot rates:

1-year rate of 4%, 2-year rate of 5%, 3-year rate of 5.5%, 4-year rate of 6%.

1) Using the above data 4 forward rates can be calculated.

2)

By definition, the forward rate over the first year is equal to the one-year spot rate.

So,

f₁=4%

f₂=(1.05)²/(1.04) = 1.0600-1 =0.0600 = 6%

f3=(1.055)³/(1.05)² = 1.0651-1 =0.0651 = 6.51%

f4=(1.06)⁴/(1.055)³ = 1.0751-1 =0.0751 = 7.51%