Yield Curve

A yield curve is a line showing the yields available on one issuer's debt across a range of maturities at a single moment. The SEC's investor glossary describes it as "a line graph that shows the relative yields on debt over a range of maturities from three months to 30 years," adding that investors, analysts and economists use yield curves to evaluate bond markets and interest rate expectations.

When the phrase is used without qualification it means the US Treasury curve, because Treasury securities share one borrower and one credit standing across every maturity, so the differences along the curve are about time rather than about who is borrowing. That is what makes it a reference point for everything else: corporate and municipal borrowing costs are commonly described as a spread above the Treasury curve at the same maturity.

The reference curve is a published construct with a stated method, not an observation of trades. Treasury describes its official curve as a par yield curve derived using a monotone convex method. Its inputs are indicative, bid-side market price quotations, expressly "not actual transactions," for the most recently auctioned securities, obtained by the Federal Reserve Bank of New York at or near 3:30 PM each trading day. The current input set is the most recently auctioned 4-, 6-, 8-, 13-, 17-, 26- and 52-week bills, the 2-, 3-, 5-, 7- and 10-year notes, and the 20- and 30-year bonds. Because bills pay no interest along the way, their inputs are bid discount rates corresponding to their bond equivalent yields, so they arrive on the same footing as the rest. The finished rates are usually posted by about 6:00 PM Eastern each trading day.

Two consequences follow from that method and are worth carrying. The published points between the input maturities are interpolated rather than observed, so a "7-year rate" on a day when no 7-year security is the most recent issue is a computed value. And the method itself has changed: monotone convex replaced a quasi-cubic hermite spline in December 2021, and Treasury reserves the right to change inputs or method again. A curve is a measurement with a methodology, and comparisons across long spans of history cross at least one methodological break.

Shapes, and the vocabulary attached to them. An upward-sloping curve, where longer maturities yield more than shorter ones, is the common case and is called normal. A curve is steep when the gap between short and long is unusually wide and flat when short and long yields converge. When longer yields fall below shorter ones the curve is inverted, which is a distinct subject with a research literature of its own and is covered under the inverted yield curve.

Why the normal shape is upward-sloping has two standard accounts, and they are not alternatives. One is about expectations: a long rate embeds what the market expects short rates to do over the intervening years, so a curve sloping upward is consistent with an expectation that short rates will be higher later. The other is about compensation: committing money for thirty years exposes a lender to more that can go wrong than committing it for three months, and the extra yield is payment for accepting that. Both forces are present in any observed curve, and no reading of a curve can separate them.

The second curve. Alongside the ordinary series, Treasury publishes Daily Treasury Par Real Yield Curve Rates, built from inflation-protected securities. Reading the two together separates the part of a nominal yield that compensates for expected inflation from the part that does not, which is a different question from the shape of either curve on its own.

Read the maturities along the horizontal axis and the yields up the vertical one, then compare two points. The difference between two yields on the same curve is called a spread and is usually quoted in basis points. Because every point belongs to the same issuer, the spread describes the price of time rather than the price of credit.

A hypothetical example of reading one. On a given day the published rates are 4.10% at three months, 4.30% at two years, 4.70% at ten years and 4.95% at thirty years.

The curve slopes upward across its whole length, which is the normal shape. The gap between the ten-year and the three-month is 4.70% − 4.10% = 0.60 percentage points, or 60 basis points. The gap between the thirty-year and the ten-year is only 0.25 percentage points, so the curve is steeper at the short end than at the long end, which is typical.

What the numbers do not say is where rates go next. They are the prices quoted for lending to one borrower for various lengths of time on that day, and reading them as a published forecast attributes to the curve an intention nobody had.

Pros

• Published daily by the issuer, free, and consistent across every maturity, so it is the cleanest available picture of the price of time.
• Uses one borrower throughout, which strips out differences in credit and leaves maturity as the only variable.
• Provides the reference against which other borrowing costs are quoted, from corporate bonds to mortgages.
• The real curve alongside it allows the inflation component of yields to be examined separately.

Cons

• It is built from indicative quotes rather than completed trades, so it is an estimate of where the market is, not a record of where it traded.
• Points between the input maturities are interpolated, so not every published rate corresponds to a security anyone can buy.
• The derivation method has changed over time, which complicates long historical comparisons.
• It describes today's prices only. Reading a shape as a forecast imports a claim the data does not make.