Question:

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.