Term Structure of Interest Rates › Yield Curve Shapes and Their Interpretation

Yield-curve shapes contain economic information, but they combine expected rate paths with premia and other market effects. The examples below illustrate possible interpretations, not a unique explanation for each shape.

An upward-sloping curve has higher rates at longer maturities. Possible contributors include:

• An expected rise in future short-term rates, which can be associated with growth or inflation pressures.
• A positive term premium for bearing longer-duration interest-rate risk.
• Compensation for expected inflation and a separate premium for inflation uncertainty in nominal yields.

Upward curves are often steep near the end of recessions or early in expansions, when short rates are relatively low. Later tightening can flatten them. The slope alone does not identify which contributor dominates.

An inverted curve has short-term rates above long-term rates. Specified US Treasury spreads have been useful historical recession indicators, with false positives and varying lead times. Possible contributors to inversion include:

• Expectations of falling short-term rates, possibly because of anticipated weakness and policy easing.
• Demand for long-term government bonds that raises prices and lowers yields.
• Low or negative term premia, which can also lower long yields relative to short yields.

A Federal Reserve Bank of San Francisco study examined the 10-year minus 1-year Treasury spread from January 1955 through February 2018. All nine recessions in that sample were preceded by inversion, with leads of 6 to 24 months and one false positive. This is a dated statistical association, not a guarantee about any particular inversion.

A flat curve has similar rates across the maturities being compared. It may appear during a transition in slope, but can also arise from stable expected rates or offsetting premia. Possible interpretations include:

• A central bank nearing the end of a tightening or easing cycle.
• Offsetting effects of expected growth, inflation and policy; flatness alone does not measure disagreement.
• Changes in term premia that offset the expected-rate component.

Intermediate-term rates can exceed both ends of the curve, creating a "humped" shape. Several mechanisms can contribute:

• Short-term rates are expected to rise temporarily before declining.
• A concentration of bond supply affects particular maturities.
• Investor demand differs across maturity segments.

These mechanisms can overlap. A schematic hump cannot establish their relative contributions.

Several theories attempt to explain why yield curves take different shapes:

Pure expectations theory treats today's forward as the expected future spot rate after abstracting from term premia and the relevant convexity adjustment. We can write this simplifying economic hypothesis as:

$$f_0(T_1,T_2) = E_0^{P}\!\left[z_{T_1}(T_2-T_1)\right]$$

Here $f_0$ is the forward observed today, $z_{T_1}(\tau)$ is the spot rate observed at future time $T_1$ for tenor $\tau$, and $E_0^P$ is today's physical, or real-world, expectation. The observation time and tenor are different quantities. Under these simplifying assumptions, rising forwards suggest rising expected future spot rates. The equality is not a general no-arbitrage identity, and risk-neutral pricing under a specified measure does not imply that real-world expected rates equal forwards. The Federal Reserve's term-structure model notes explain why premium definitions and convexity conventions matter.

Liquidity Preference Theory adds a positive maturity-related premium to the expectations component. In this hypothesis, a preference for less volatile short-maturity claims creates extra compensation for holding long bonds, so the curve can slope upward even with flat rate expectations. This is a proposed mechanism, not a guarantee that every estimated term premium is positive or increasing.

Strict Market Segmentation Theory treats supply and demand within maturity segments as independent, assuming little effective substitution across them. Liability matching can motivate different maturity preferences: an insurer and a money market fund need not seek the same cash-flow dates.

Preferred Habitat Theory combines elements of the previous theories. Investors have preferred maturities but will shift if the yield premium is sufficiently attractive. This allows expectations to influence the entire curve while acknowledging institutional preferences.