W998AMMT.5

5. The yield curve currently looks like this:

[graph showing that r1=0.06, r2=0.08 and r3=0.09]

• What should the price of a two-year, $1000 par, 9% coupon bond with annual coupons be? (The next coupon is due in one year.) (3)

9% coupons means $90 per year, so the cash flows look like this:

The price of the bond is the present value of the cash flows:

Examples of pricing a bond from such a description can be found in the bond topic section of the notes. Pricing a bond with different spot rates is also shown in that section.

• What should the price of a one-year STRIP be? (2)

A one-year strip pays off $100 in one year. Thus, its price is just the present value of $100:

PV=$100 / (1.06)=$94.34

SEE W98 8AM MIDTERM, 1a, FOR ANOTHER EXAMPLE OF THIS QUESTION.

• Which should have the higher yield-to-maturity? WHY? (Do not do any computations for this!) (3)

The bond should have the higher YTM. It’s YTM will be a weighted average of the two spot rates (0.06 and 0.08), so its YTM must be greater than 0.06. The STRIP’s YTM will be a weighted average of its spot rates, as well. However, it only has one spot rate (0.06), so its YTM will be 0.06.

OTHER EXAMPLES OF YTM COMPARISON QUESTIONS CAN BE SEEN IN PREVIOUS MIDTERMS (e.g. W98 8am 1e, AND IN QUIZ 2, FALL 1997.

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