Question

Assume the expectations hypothesis. (And, please give your answers in xx.xxx % format and circle them.) a) The current yield curve is given by: y1 = 1% , y2 = 2% , y3 = 3% , y4 = 4%. Derive the yield curve expected to be in effect two years from now. b) The yield curve expected to be in effect two years from now is given by y1 = 4.5% , y2 = 5.5% . The current market prices of 1-year and 2-year zero coupon bonds are $982.12 and $961.29 , respectively. By reverse engineering, derive the current yield curve.

Answer 1

a) from Expectation hypothesis,

Spot rate for one year after two years from now

= 1.03^3/1.02^2 -1

=0.050295 or 5.03%

Spot rate for two years after two years from now

= (1.04^4/1.02^2)^0.5 -1

=0.06039 or 6.04%

So, the yield curve two years from now is given below

Year	Rate
1	5.03%
2	6.04%

b) One year Spot rate (r1) is given by

1000/(1+r1) =982.12

=> r1 = 0.0182 or 1.82%

Two year Spot rate (r2) is given by

1000/(1+r2)^2 =961.29

=> r2 = 0.0199356 or 1.99%

So, the yield curve is as given below

Year	Rate
1	1.82%
2	1.99%
3	4.50%
4	5.50%