Fixed Income Securities, 4th Edition

APPENDIX TO CHAPTER 3Returns, Yields, Spreads, and P&L Attribution

A3.1 YIELD TO MATURITY FOR SETTLEMENT DATES OTHER THAN COUPON PAYMENT DATES

Equations (3.6), (3.7), and (3.8) express the relationship between price and yield to maturity when settlement is on a coupon payment date. This appendix generalizes this relationship to other settlement dates. First, because accrued interest is zero when settlement falls on a coupon payment date, the full price in the equations in the text do not include any accrued interest. In this section, however, because settlement can fall on other dates, is taken to include accrued interest.

Second, the market convention for discounting cash flows that do not occur in regular six‐month intervals, using a semiannually compounded rate, is as follows. Let denote the semiannually compounded yield, and let denote the fraction of a semiannual period until the next coupon payment. For example, if the next coupon payment is in one month, taken to mean one‐sixth of a semiannual period, then . By convention, then, the present value of a unit of currency at ...