Please answer all parts of the questions clearly and show all calculations.

Question 4

You are given the following US Treasury Note yield curve data:

Years to Par Coupon Calculated Calculated

Maturity Yield to Maturity Spot Rate 1-year Forward Rate

1 5.00% 5.00% 5.00%

2 5.20% 5.21% 5.42%

3 6.00% 6.05% 7.75%

4 7.00% 7.16% 10.56%

5 7.00%

(a) Compute the five-year spot rate and forward rate assuming annual compounding.

(b) Explain why, for financial assets like coupon-paying bonds, it is not a good idea to value the asset using a single discount rate.

(c) You are given the following data for two bonds, ABC and XYZ:

Characteristic ABC XYZ

Market price 101.75 101.75

Maturity date June 1, 2025 June 1, 2025

Call date Noncallable June 1, 2020

Annual coupon 6.25% 7.35%

Interest payment Semiannual Semiannual

Effective duration 7.35 5.40

Yield to maturity 6.02% 7.10%

Credit rating AA AA

(i) Assess the magnitudes of the modified durations of ABC and XYZ, relative to their respective effective durations.

(ii) Compute the percentage price change forecasted for ABC and XYZ of an interest rate decline of 50 basis points over the next 6 months.

(iii) Suppose the actual prices at the end of 6 months were 105.55 and 104.14 for ABC and XYZ, respectively. Evaluate and explain why the actual price change would be greater for ABC and why the actual price change would be less for XYZ.