Bond Pricing, Duration, and Convexity

1. Using the following data, plot (graph) the corporate A-rated yield and Treasury

yield curves and calculate the default premium spread (in basis points) for each

instrument.

a) 2 year corporate with a yield of 2.01% and treasury with a 1.39% yield

b) 5 year corporate with a yield of 3.06% and treasury with a 1.83% yield

c) 10 year corporate with a yield of 4.02% and treasury with a 2.23% yield

d) 20 year corporate with a yield of 4.94% and treasury with a 2.70% yield

2. Find the prices for the Treasuries in problem 1 given the following coupon

information.

a) 2 year treasury has a 1.25% coupon

b) 5 year treasury has a 1.63% coupon

c) 10 year treasury has a 2.25% coupon

d) 20 year treasury has a 2.70% coupon

3. For the Treasury instruments in question 2,

a) Calculate the modified duration

b) Calculate the convexity

4. For a 0.60% increase in interest rates, what is the percentage change in the price

of the instruments in question 2?

a) Using the duration approximation

b) Using the convexity approximation

c) Calculate the actual percentage change in prices.

5. Given the bonds in question 2 (Treasuries only) and if you have a six year

investment horizon for $100,000, what bond portfolio would you create and why?

Give portfolio weights in percent and dollars amounts.

Table 1 2 10 20 Q1 Default Spread (b Q2 Price Q3a M. Duration Q3b Convex Q4a Dur. Approx Q4b Conv Q4c Actual Q5 Treasury $ Treasury % Figure 1 Example Corp A and Treasury Yield Curves 6.0% 5.0% 4.0% 3.0% 2.0% 1.0% 0.0% 0 5 10 15 20 25 Time to Maturity I reasury Corp. A