What is the market saying when the curve changes shape?

You met the yield curve in Markets Foundations as a line that slopes up, sometimes flips, and makes headlines. Now that you can measure duration, it is worth a second, more careful look — starting with the fact that "the curve" is really three curves.

Which curve are we talking about?

• The par curve. The yields to maturity of bonds priced at par at each maturity. When someone says "the 10-year is at 4.2%", this is usually it.
• The spot (zero) curve. The yield on a single payment at each maturity — the rate for one cash flow arriving in n years, with no coupons in between. It is derived from the par curve by bootstrapping: solve the 1-year spot from the 1-year bond, use it to strip the 2-year bond's first coupon and solve the 2-year spot, and so on. This is the curve you should discount cash flows with; using a single YTM for every flow is a convenient approximation, not the truth.
• The forward curve. The rates the spot curve implies for future periods. If the 1-year spot is 4.0% and the 2-year spot is 4.5%, the implied 1-year rate one year forward is 1.045² ÷ 1.04 − 1 ≈ 5.0%.

That forward rate deserves a warning label. It is not a forecast. It is the break-even rate — the rate at which rolling two one-year investments would exactly match locking in the two-year. It tells you what is already priced, never what will happen.

Four shapes

• Upward-sloping (normal). Long yields above short. The usual state.
• Flat. Little difference across maturities — often a transitional state.
• Inverted. Short yields above long.
• Humped. Yields rise into the belly (roughly 2–5 years) and fall away after it.

Three of those are worth looking at rather than picturing. Flat is the one that needs no diagram.

What a shape actually encodes

Any shape is a mixture of two things that cannot be cleanly separated:

1. Expected future short rates. If the market collectively expects policy rates to be lower in three years than today, long yields will be dragged down relative to short ones.
2. The term premium. The extra compensation lenders demand for locking money up — for inflation uncertainty, for the price risk you now know how to measure, for liquidity. The next-but-one lesson pulls this apart.

This is why every confident sentence beginning "the curve is telling us…" is an interpretation. An inversion can come from expected cuts, from a compressed or negative term premium, or from both at once, and the mix is not observable.

Stating the limits honestly

In the United States, an inverted curve has preceded recessions of the past half-century — a track record that keeps it in the headlines. The honest fine print, in the Academy's data-literacy spirit: among the inversions that were followed by a recession, lead times ranged from a few months to roughly two years; the sample of recessions is small; and "every time so far" is weaker evidence than it sounds. The 2022–24 episode makes the point plainly — the 2s10s curve inverted in July 2022 and stayed inverted for about 26 months, the longest run on record and the deepest since 1981, while the economy kept growing and no recession has been dated for that period. Every recession was preceded by an inversion; not every inversion has been followed by a recession. The curve is a pressure gauge, not a timer.

We describe shapes and the arithmetic behind them here. We do not forecast rates, and we never suggest positioning.

In the data

A curve is one date read across every maturity, and the set of maturities has changed over time. Today the US Treasury curve has fourteen points, from one month to thirty years. On 2 January 1990 it had nine, below: no one-month, no twenty-year, and none of the in-between bill maturities added since.

Compare a curve shape across decades and check which points each date actually has: a gap is a maturity nobody quoted that year, and filling it silently makes a curve look flatter or smoother than it was.

Try it now

1. The newest Treasury curve is below, fourteen points from one month to thirty years. Take the 3-month, 2-year, 10-year and 30-year yields, sketch them on paper and name the shape. Then look at the 20-year against the 30-year and say whether the four points told the whole story.

2. Using the 1-year and 2-year yields you found, compute the implied 1-year forward rate one year out: (1 + s₂)² ÷ (1 + s₁) − 1.
3. Write two sentences — one about what the shape reflects, and one about what it cannot tell you. Keep both; the second is the harder discipline.