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Bond Pricing and Yield to Maturity

One-line definition

The price of a bond is the present value of its future cash flows, discounted at its yield to maturity (YTM).

Formula

P = sum_t CF_t / (1 + ytm/frequency)^t

where CF_t is the coupon (or coupon + face at maturity) paid at period t.

Interpretation

A bond priced at par (P = face) has ytm = coupon_rate. Price and yield move inversely — this is the mechanism duration approximates linearly.

Why PMs care

Every other fixed-income sensitivity (duration, DV01, convexity) is a derivative of this pricing relationship.

Common mistakes

  • Reporting this price as what a buyer pays. It is the clean price; settlement adds accrued interest. See Accrued interest and settlement.
  • Mixing the yield's compounding frequency with the coupon frequency. ytm/frequency assumes they match; a semi-annual bond quoted on an annual yield needs converting first.
  • Assuming one yield is the right discount rate for every cash flow. YTM is a single internal rate; a curve-based present value discounts each flow at its own tenor and will not agree exactly. See Curve construction.
  • Treating price/yield as linear. It is convex — duration is only the first-order term, which is why convexity exists.