All rates should be calculated to 3 decimal places in % (e.g. 1.234%), the discount factors to 5 decimal places (e.g. 0.98765), and the bond prices to 3 decimal places (e.g. 99.999).
You are given the following yields-to-maturity for semi-annually coupon paying Treasury Bonds on 31st December 2007 and 31st December 2008:
Term 0.5yr 1yr 2yr 3yr 5yr 7yr 10yr
31 Dec 2007 3.49% 3.34% 3.05% 3.07% 3.45% 3.70% 4.04%
31 Dec 2008 0.27% 0.37% 0.76% 1.00% 1.55% 1.87% 2.25%
(1) Using linear interpolation to estimate any other required rates, find the discount factors D(t) for t = 0.5, 1.0, 1.5, ..., 10.0 for both dates.
(2) From your answers to (1), calculate the price of a constant-maturity 3-year semi-annual coupon bond1 with an annual coupon rate of 3% and the face value 100, for both 31 December 2007 and 31 December 2008. Hence analyse the price change.
(3) Again from your answers to (1), find the 6-month forward rates f(t,t+½) for t = 0.5, 1.0, 1.5, ... , 9.5 for both dates.2 (See Appendix for the explanation for forward rates.)
You are also given the following historical data on the spot 6-month rate:
Date 31/12/07 30/06/08 31/12/08 30/06/09 31/12/09
6m Rate 3.49% 2.17% 0.27% 0.35% 0.20%
30/06/10 31/12/10 30/06/11 30/12/11 29/06/12 31/12/12
0.22% 0.19% 0.10% 0.06% 0.16% 0.11%
(4) Using a graph, comment on how well the market predicted the future moves of the spot 6-month rate on both dates.
(5) In general, are forward rates a good predictor of future interest rates? Briefly discuss.