Question

Use the term structure below for problems 1 – 2:

Maturity	Spot Rate	Forward Rate
1	4.0%
2	4.25%
3	4.75%
4	5.25%
5	6.0%
6	6.75%

1. Calculate the 1-year forward rate as quoted today (year zero) for years 1, 2, 3, 4 & 5.  Show each of the spot and forward rates on the time line below. (For simplicity, you can use annual compounding.)

   0                    1                       2                       3                        4                      5 6    

|____________|____________|____________|____________|____________|____________|

2. Calculate the 2-year forward rate as quoted today (year zero) in year 1. Show the 2-year forward rate on a timeline and the relevant spot rates used to calculate the 2-year forward rate.

0                      1                       2                        3                       4                       5                       6    

          |____________|____________|____________|____________|____________|____________|

Answer 1

(a) One yer forward rate f quoted today are as follows:

For 1 year: 4.50%

For 2 years: 5.76%

For 3 years: 6.76%

For 4 years: 9.05%

For 5 years: 10.58%

Detailed working as follows:

(b) Two year forward rate as quoted today, in year 1 is as follows:

(1+st)^t

f = ------------- - 1

( 1+st-1)^t-1

Hence the rate required is for the period 1 to 3. (ie., t=3)

Substituting the values,

Forward rate f ={ [(1+S3)^3/(1+S1)]^1/2} -1

= [(1.0475^3/1.04)^1/2 ]-1 = 1.105169^1/2 = 1.05127-1 = 0.05127 = 5.127%