Question

Consider the spot curve for hypothetical annual-coupon U.S. Treasury securities given in the table below (only the first 5 years of the curve are provided). Calculate the missing one-year forward rates f(T*,1) indicated by “????” and add them to the table. Show your work for all calculations in the space below the table.

Year 1.0 2.0 Spot Rate (%) 5.50 6.02 6.55 6.87 7.20 Forward Rate (%) 5.50 ???? ???? ???? ???? 3.0 4.0 5.0

Answer 1

1-year Forward rate would be:

$F[1,1] = \frac{(1+6.02\%)^2}{(1+5.5\%)} = 6.54\%$

$F[2,1] = \frac{(1+6.55\%)^3}{(1+6.02\%)^2} = 7.62\%$

$F[3,1] = \frac{(1+6.87\%)^4}{(1+6.55\%)^3} = 7.84\%$

$F[4,1] = \frac{(1+7.20\%)^5}{(1+6.87\%)^4} = 8.53\%$

Year	Spot rate	Forward rate
1	5.50%	5.50%
2	6.02%	6.54%
3	6.55%	7.62%
4	6.87%	7.84%
5	7.20%	8.53%

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.