priceyield

Priceyield is a term used to describe the relationship between the price of a fixed-income instrument (such as a bond) and its yield to maturity. In this sense, priceyield captures how a security’s price responds to changes in yield and how yield moves when the price is adjusted. It is not a formal, universally defined metric in core finance texts, but practitioners commonly discuss priceyield to analyze price sensitivity and potential returns under shifting interest rates.

Calculation and interpretation

Priceyield can be treated as the price function P(y) of a bond with yield y. The slope of this function, dP/dy, represents the price’s sensitivity to small yield changes. In practice, this sensitivity is well approximated by the modified duration: dP/dy ≈ -D_mod × P, where D_mod is the modified duration. For small yield moves, the approximate price change is ΔP ≈ -P × D_mod × Δy. Convexity further refines this estimate for larger yield changes. Thus priceyield can be viewed as the quantitative expression of yield-induced price movement, linked directly to duration and convexity.

Applications and limitations

Priceyield is used in risk management, pricing, and scenario analysis to gauge how bond portfolios may react to interest-rate shifts. It helps traders understand potential gains or losses from yield changes and to compare price sensitivity across securities. However, the relationship assumes parallel shifts in the yield curve, ignores nonlinearity for large moves, and can be affected by embedded options or features that alter duration and convexity. In such cases, more sophisticated models and convexity adjustments are necessary.

See also

Duration, Modified duration, Convexity, Yield to maturity, Price/yield relationship, Yield curve.