Yield curve
What is Yield curve?
A yield curve shows yields across maturities for securities or modeled cash flows that share a defined issuer, currency, credit quality, and quotation basis.
Types of yield curve
Par curves show yields for hypothetical bonds priced at par, spot curves show discount rates for single cash flows, and forward curves show rates implied between future dates. Government, swap, corporate, and credit curves are distinct. Constant-maturity points are often interpolated estimates rather than yields on one currently traded security.
Curve shapes
An upward-sloping curve has higher long yields than short yields; a flat curve has similar yields; an inverted curve has lower long yields; and a humped curve peaks in the middle. Shape reflects expected future rates, term premium, inflation, policy, supply, demand, and market structure. No single interpretation is reliable in every regime.
Example
A two-year government yield is 4.5% and a ten-year yield is 4.0%, producing an inverted segment. A bond portfolio can gain or lose depending on where its key-rate exposures sit and how the curve changes. A parallel-shift duration estimate will miss a move in which short yields rise while long yields fall.
How curves are used
Curves discount cash flows, price bonds and derivatives, measure spreads, value liabilities, and support relative-value trades. Roll-down return depends on how a security moves along an unchanged curve, but the curve rarely stays unchanged. Analysts must use a curve consistent with currency, collateral, credit, tax, and instrument conventions.
Limitations
Curve construction requires instrument selection, cleaning, bootstrapping, and interpolation. Sparse or illiquid markets create model dependence. Official curves can use indicative quotes rather than transactions. A visually smooth curve can conceal uncertainty, and comparing curves from different providers without aligning conventions can produce false spread and valuation differences.
Practical checklist
Name the curve type, issuer, currency, collateral basis, instruments, timestamp, day count, and interpolation method. Distinguish observed inputs from fitted points. Measure key-rate rather than only parallel duration, test steepening and flattening, and reconcile pricing. Preserve methodology changes and avoid splicing historical series without documenting breaks, especially around missing maturities or revised construction methods. Retain the original input observations for audit.
Also known as: term structure of interest rates
Sources and further reading
- Treasury Yield Curve Methodology, U.S. Department of the Treasury