What Is the Yield Curve?

Shape, inversion, and what it signals — the yield curve explained from normal to inverted and why it is the discounting backbone of every fixed-income instrument.

The yield curve is the starting point for almost everything in fixed income. It plots the yield to maturity of a set of bonds — typically U.S. Treasuries — against their time to maturity, from the overnight rate out to 30 years. The shape of that curve at any moment summarises the market's collective view on growth, inflation, and monetary policy, which is why economists, traders, and central bankers track it obsessively. If you are trying to understand rates and bond prices, or you are building a discounting model for any fixed-income instrument, the yield curve is where the analysis begins. The bond pricing calculator on this site uses Treasury yields as its default discount rates — this post explains what those rates represent and why their shape matters.

The three shapes of the yield curve explained

Most of the time the yield curve slopes upward: longer maturities carry higher yields than shorter ones. A 2-year Treasury might yield 4.3 % while a 10-year yields 4.8 %. That premium for longer maturities reflects two things: the uncertainty of lending money for a longer period, and the extra compensation investors demand for tying up capital when the future is unknown. This is the normal shape.

When short and long yields converge the curve is described as flat. A flat curve signals that the market sees little difference in risk between lending for two years and lending for ten — typically because it expects rates to fall at some point in the medium term, offsetting the maturity premium.

An inverted curve flips the relationship: short yields exceed long yields. The canonical measure is the 2s10s spread — the 10-year yield minus the 2-year yield. When that number is negative the curve is inverted. In 2023 the 2s10s reached roughly −100 basis points, the deepest inversion since the early 1980s. Inversions like that carry a particular significance discussed below.

What drives the shape

Three forces interact to set yields at each maturity:

• Rate expectations. If the market expects the Fed to cut rates over the next two years, investors will accept a lower yield on a 2-year note today, because rolling over short-term bills will be less attractive once cuts arrive. This mechanism — formalised in the pure expectations hypothesis — means the long end of the curve embeds the market's expected path of short rates.
• Term premium. Beyond pure expectations, longer bonds carry extra risk: inflation could surprise, supply could surge, or the issuer could deteriorate. Investors demand additional compensation for bearing that uncertainty. The term premium is positive in normal times, which is why normal curves slope up even when the market expects rates to stay flat.
• Supply and demand. Central bank asset purchase programmes (quantitative easing) buy long-duration bonds, pushing their prices up and yields down, compressing the curve. Heavy Treasury issuance has the opposite effect, steepening the back end when supply floods the market.

Inversion and the recession signal

Every U.S. recession since 1955 has been preceded by an inversion of the 2s10s spread, typically with a lag of six to eighteen months. The intuition is straightforward: if the Fed has raised short-term rates sharply to fight inflation, the front end of the curve rises above the back end, which is anchored by subdued long-run growth expectations. High short rates tighten financial conditions, compress bank lending margins, and slow credit creation — the transmission mechanism to recession.

The signal is not perfect. The curve inverted briefly in 1966 without a subsequent recession, and the lag between inversion and contraction can be long enough to create false urgency. Still, as a single indicator it has the best track record of any widely watched macro signal, which is why fixed-income traders watch the 2s10s spread daily and treat a persistent inversion as a structural warning, not noise.

Spot, forward, and par curves

The curve that appears on financial terminals — Treasury yields plotted against maturity — is the par curve: the yield at which bonds priced at par (face value) would trade. It is the most observable, but not the most useful for pricing.

The spot curve (also called the zero curve) strips out the coupon effect and gives the yield on a single cash flow at each maturity. Zero-coupon bonds sit directly on the spot curve by construction; coupon bonds must be decomposed to extract it. Each coupon-bearing bond is essentially a portfolio of zero-coupon cash flows, and the spot curve prices each flow at its own maturity-specific rate rather than a single blended yield.

The forward curve is derived from the spot curve and gives the implied rate between two future dates. The 1-year rate, 2 years forward, answers the question: what rate does the market imply for a one-year investment starting two years from today? Forward rates are critical for pricing floating-rate instruments and interest rate derivatives.

Bootstrapping the curve from market instruments

Market participants do not observe the spot curve directly — they observe prices on Treasury bills, notes, and bonds. Bootstrapping is the iterative process of extracting spot rates from those prices, starting at the short end and working outward.

The mechanics: a 6-month T-bill trades at a discount and delivers a single cash flow, so its spot rate is read off directly. A 1-year coupon note pays a coupon at 6 months and principal plus coupon at 12 months. The 6-month spot rate is already known, so the 12-month spot is backed out as the only unknown that makes the present value of the note equal to its market price. The process continues maturity by maturity. A simple two-step example:

Maturity	Instrument yield	Bootstrapped spot rate
0.5 yr	4.80 %	4.80 %
1.0 yr	4.65 % (semi-annual coupon bond)	4.64 %
2.0 yr	4.50 % (semi-annual coupon bond)	4.48 %

The small differences between the par yield and the bootstrapped spot rate grow at longer maturities, especially when the curve is steeply sloped, because the coupon payments arriving before maturity are discounted at earlier — and different — spot rates. Once the full spot curve is constructed, forward rates follow algebraically: if the 1-year spot is r₁ and the 2-year spot is r₂, the implied 1-year forward rate one year from now is f = [(1 + r₂)² / (1 + r₁)] − 1.

The yield curve as a discounting framework

The reason every fixed-income practitioner needs to understand the yield curve is that it is the raw material for discounting. Bond prices, mortgage-backed security valuations, swap pricing, and liability discounting in pension funds all reduce to the same operation: project cash flows, assign a discount rate at each maturity, and sum present values. The yield curve supplies those discount rates. A parallel shift of 100 basis points moves the price of a 10-year bond by roughly 8–9 %, while leaving a 2-year bond down only about 2 % — precisely because longer maturities compound the discounting effect across more periods.

That sensitivity to the curve shape is why duration, convexity, and key-rate durations exist: they measure a portfolio's exposure not just to the level of rates but to where on the curve a move occurs. Whether you are pricing a single bond or stress-testing a fixed-income portfolio, the yield curve is not background context — it is the model.