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Yield curve

The yield curve orders rates or yields by maturity: distinguish par, spot and forward curves and read shape, moves and limits.

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In plain language — A yield curve is a chart: time runs across the horizontal axis and a rate or yield runs up the vertical axis. Before interpreting it, identify the securities and rate type used.

The yield curve describes how a market prices different maturities on one date for a coherent instrument family. A Treasury curve, swap curve and corporate curve are not the same. Par, spot and forward curves also answer different questions.

Four shapes, no automatic signal Always attach market, date, nodes and methodology. CYCLEPEDIA · TERM STRUCTURE Four shapes, no automatic signal Always attach market, date, nodes and methodology. 1 Normal Long yields above short yields in the segment. 2 Flat Small differences between selected nodes. 3 Inverted A short segment yields more than a long one. 4 Twist Nodes move by different amounts. CYCLEPEDIA · EDUCATIONAL MAP, NOT A FORECAST OR RECOMMENDATION
Shape describes a snapshot of the term structure; it does not determine growth, inflation or future returns by itself.

Basic shapes

A curve is called normal when long yields exceed short yields over the observed segment; inverted when a relevant segment shows the opposite; flat when differences are small. Local humps or troughs are possible.

These labels depend on selected nodes. Saying “the curve is inverted” without date, market and maturities may hide that only part is inverted. Spreads such as 2-year minus 10-year or 3-month minus 10-year summarise two points, not the entire curve.

Inversion has been studied as a macroeconomic indicator in specific markets and samples. It is not a certain recession clock or a direct instruction to trade an asset. Monetary policy, expectations, term premia, collateral demand and risk all influence yields.

Par, spot and forward curves

The par yield curve reports the coupon rate that would price a theoretical bond at par for each maturity under a methodology. Published Treasury series are official estimated curves, not necessarily executable prices of one security at every node.

The spot curve, or zero-coupon curve, assigns a discount rate to a single cash flow at each maturity. It lets valuation discount coupons and redemption separately:

Price = Σ cash flow_t × discount factor_t

The forward curve derives rates between future dates from the spot curve and compounding convention. An implied forward is consistent with today's curve under calculation assumptions; it is not an error-free forecast of a future fixing.

Bootstrap, smoothing and interpolation methods can produce different curves. Instruments, timestamp, day count and collateralisation belong to the definition.

How a curve moves

A parallel shift moves every node by the same scenario amount. Steepening increases slope between named nodes; flattening reduces it. A twist combines different directions or magnitudes. Bull and bear labels can indicate broad yield direction, but showing basis points by maturity is clearer.

Total duration mainly approximates a summarised move. Key-rate duration distributes sensitivity across nodes and reveals shape risk. Carry and roll-down often make the different assumption that the curve remains unchanged while a security's residual maturity shortens.

Five operational checks

Identify issuer or index and currency. Determine whether the display contains bond yields, zero rates, par rates or forwards. Record date and time because markets do not close together. Check methodology and which nodes are estimated. Finally, separate observation from interpretation: “the 10-year yield is 20 basis points above the 2-year” is a dataset fact; “growth will accelerate” is a hypothesis.

Use a curve consistent with cash flows and collateral in valuation. State shocks and interpolation in risk reports. Do not join historical series across methodology changes without documenting them.

Common error — Treating a published curve as executable prices, or its shape as a certain forecast. Curves are constructed estimates and interpretations remain conditional.

Questions this page answers

Which market does the curve represent? Is it par, spot or forward? Which nodes are observed or interpolated? Over which segment is the curve normal or inverted? Which movement scenario is applied to the portfolio?

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