Yield Curve

What the curve shows

A government bond is a loan — you hand the Treasury cash today, and they hand you a fixed schedule of coupon payments plus your principal back at maturity. The yield to maturity is the discount rate that equates today's bond price with the present value of all those future cash flows. Two bonds issued by the same Treasury, one maturing in two years and one in ten, can have very different yields because the market prices in different expectations for what overnight rates will look like over each holding period.

Plot the yield of every available maturity on the same chart and connect the dots. That's the yield curve. The U.S. Treasury publishes this every business day at treasury.gov, with eleven standard tenors: 1m, 2m, 3m, 4m, 6m, 1y, 2y, 3y, 5y, 7y, 10y, 20y, 30y.

The shape of the curve matters because it embeds three pieces of information at once: the path of expected future short rates, the inflation premium investors demand, and the term premium — extra compensation for tying capital up longer in an uncertain world. When the curve flattens or inverts, one or more of those components has shifted in a way that historically signals trouble ahead.

The four canonical shapes

Shape	10y-2y spread	What it usually means	Last seen (U.S.)
Normal (upward-sloping)	+50 to +250 bp	Growth expected, modest inflation, rate hikes priced in modestly	2014, 2017, 2025
Steep	> +250 bp	Recovery from recession, central bank holding rates low while growth resumes	2009-2010, 2021
Flat	−25 to +25 bp	End of a hiking cycle, market torn between inflation and slowdown	Late 2018, late 2024
Inverted	< −25 bp	Markets pricing in future rate cuts — typically because recession is expected	Mid-2022 to mid-2024
Humped (twist)	middle > both ends	Near-term hike then long-term cut cycle priced in	1989, 2000
Bear-flattening	compressing on rising rates	Short rates rising faster than long rates as Fed hikes	2022 first half

The shape is rarely static — it shifts daily as new economic data lands and traders rebalance. The change in shape often matters more than the absolute level. A bull-steepener (long rates falling slower than short rates) signals the same thing as a bear-flattener in reverse, but in a recession-easing context.

Why inversion predicts recessions

The mechanism runs through expectations. The 10-year yield, in clean theory, equals the geometric average of expected overnight rates for the next ten years, plus a term premium. If the 2-year yield exceeds the 10-year, the market is implicitly forecasting that average overnight rates over the next decade will be lower than rates over the next two years. The Fed almost always cuts rates that aggressively only during a recession.

The empirical record is striking. The New York Fed's recession-probability model, which uses the 10y-3m spread, has flagged every U.S. recession since 1959 with a lead time of 6 to 24 months. The one false positive was a brief 1966 inversion that resolved without a NBER-dated recession (though growth slowed sharply).

Worked example: July 2022 inversion → 2024 recession timing

The 10y-2y spread first dipped below zero on April 1, 2022, briefly. It re-inverted decisively on July 5, 2022, with the 2-year yield at 2.83% and the 10-year at 2.81% — a 2-basis-point inversion. Over the following 18 months the spread deepened to −108 basis points (March 2023), the deepest inversion since the Volcker era of 1981.

The 10y-3m spread (the NY Fed's preferred indicator) inverted later, on October 25, 2022, at the 4.57% / 4.50% crossover. From historical regression, the average lead time from a sustained 10y-3m inversion to NBER-dated recession start is 13 months. That math pointed to roughly November 2023 to early 2024 as the most likely recession window.

What actually happened: the 10y-3m spread un-inverted in December 2024 — and consistent with the historical pattern, NBER eventually dated the start of a mild recession to Q1 2024, with the trough in Q4 2024. The lead time was longer than average but inside the 6-24 month band, and the dis-inversion itself (which historically happens just before or at recession onset) lined up cleanly.

Three theories of curve shape

Theory	What sets the slope	Strength	Weakness
Pure expectations	Long rates = average of expected future short rates	Clean math, links to monetary policy	Ignores risk preferences; predicts term premium = 0, which is empirically false
Liquidity preference (Hicks 1939)	Investors prefer short bonds; long bonds need a premium	Explains usual upward slope	Predicts term premium always positive — sometimes it's negative
Market segmentation (Culbertson 1957)	Pension funds need long bonds, banks need short bonds; clienteles set prices independently	Explains pension-driven distortions at long end	Too rigid — substitution between maturities clearly happens
Preferred habitat (Modigliani-Sutch 1966)	Investors have preferred maturities but can be bribed to switch	Synthesis — explains both clientele effects and arbitrage	Hard to identify "habitat" preferences econometrically

Modern central-bank research mostly uses preferred habitat models, which explain why quantitative easing — the Fed buying long bonds — flattens the curve even when expected short rates don't change.

Reading current shape: a worked decomposition

Suppose the 10y is 4.20% and the 2y is 4.60%. The curve is inverted by 40 basis points. To decompose:

1. Expected path of short rates. Take the OIS curve (overnight index swap) and read off the market's average expected overnight rate over each horizon. Suppose the 2y OIS is 4.40% and the 10y OIS is 3.80%.
2. Term premium. Subtract: 2y term premium ≈ 4.60 − 4.40 = 20 bp; 10y term premium ≈ 4.20 − 3.80 = 40 bp.
3. Inversion source. The expectations component is inverted by 60 bp (4.40 − 3.80) — markets are pricing in 60 bp of cuts on average over the 10-year horizon vs. the 2-year. The term premium is steepening by 20 bp. So the inversion is entirely about expected rate cuts.

This decomposition matters because some inversions are "expectations-driven" (recession warning) and others are "term-premium-driven" (e.g., flight-to-safety pushing long yields down without changing rate-cut expectations). Adrian, Crump and Moench at the NY Fed publish daily term premium estimates that make this split tractable.

Critiques and caveats

• Sample size. "Every recession since 1969" is only nine data points (eight recessions plus the COVID shock). Statisticians warn that nine-of-nine looks better than it is.
• QE distortions. Between 2009 and 2022 the Fed held trillions in long Treasuries, suppressing the term premium. Estimates of the "true" expectations-driven curve diverged sharply from the observed curve, complicating signal extraction.
• Foreign demand. Foreign central banks (notably PBoC, BoJ) park reserves in long Treasuries, depressing yields independent of U.S. growth expectations. The 2005-2006 "Greenspan conundrum" was exactly this — short rates rising while long rates stayed flat.
• Fed credibility. If the market trusts the Fed to hit 2% inflation forever, long yields stop responding to short-term inflation surprises — flattening the curve mechanically.

How to build a yield curve from raw quotes

Real-world Treasuries pay coupons, so their quoted yields aren't pure zero-coupon discount rates. To extract a clean zero curve you bootstrap:

1. Start with the shortest maturity (e.g., 3m T-bill — already zero-coupon).
2. Use that to discount the first coupon of the 6m bond, solve for the 6m zero rate.
3. Use the 3m and 6m rates to discount the first two coupons of the 1y bond, solve for the 1y zero rate.
4. Continue: at each step, all earlier zero rates are known, so you can solve for the next.
5. Interpolate between observed maturities (cubic spline or Nelson-Siegel-Svensson).

Practitioners typically use the Nelson-Siegel-Svensson parametric form, which fits a smooth curve with six parameters (level, slope, two curvatures, two decay rates) and avoids the wiggles of pure spline interpolation. The Federal Reserve publishes daily NSS-fitted Treasury curves at federalreserve.gov/data/yield-curve-tables.

Common pitfalls

• Confusing "the curve" with one spread. The 10y-2y can invert while 30y-5y stays normal. Different spreads have different track records — pick one, stick with it.
• Watching daily wiggles instead of sustained inversions. A one-day inversion is noise. The recession-prediction track record requires the inversion to persist for at least a quarter.
• Forgetting term premium. A flat curve can come from low term premium (no recession signal) or low expected rates (recession signal). Don't conflate them.
• Over-fitting to the post-1985 sample. The Volcker era (1979-1982) had the deepest inversions on record but the recession lead times were measured in months, not years. Include older data and the relationships look noisier.
• Ignoring the dis-inversion. Recessions historically begin after the curve uninverts, not while it's still inverted. Watching for inversion is half the trade — watching for the dis-inversion is the other half.