Yield curve: what the term structure reveals and why an inverted curve is seen as a warning sign

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The yield curve (term structure of interest rates) shows the yields offered by government bonds with different maturities, from a few months to thirty years. Normally it slopes upwards: if you tie up your money for longer, you get more interest. If short-term rates are above long-term rates, the yield curve is inverted. That has rarely happened and in the past preceded many recessions in the US. For investors, the curve explains what bonds yield, how strongly they react to interest rate changes and what the market thinks about future rates.

Shapes of the yield curve

The usual metric for the shape is the slope: the difference between a long-term and a short-term yield, e.g. ten years minus three months or ten years minus two years, measured in percentage points. If it is negative, the curve is inverted.

Why the curve usually slopes upwards: three explanations

• Expectations theory: long-term rates are the average of expected future short-term rates. If the market expects rising policy rates, the curve rises; if it expects rate cuts, it falls.
• Term premium: long-term bonds fluctuate more in price (see duration). Investors demand a premium for this. That is why the curve also rises when no change in interest rates is expected.
• Market segments: different buyers prefer certain maturities (banks short, insurers and pension funds long). Supply and demand in a segment shift its rates.

The pure expectations theory does not stand up to the data. Campbell and Shiller (1991) examined post-war US interest rates for almost all combinations of maturities between one month and ten years: a large gap between long-term and short-term rates predicted rising short-term rates over the long run, but a falling long-term yield in the short run, i.e. the opposite of what the pure theory requires. So the curve does contain expectations, but distorted by fluctuating premia.

Forward rates: what the curve says about future interest rates

From two points on the curve, you can calculate a forward rate: the interest rate you could lock in today for an investment in the future. It follows from the condition that a two-year investment must return the same as a one-year investment plus the subsequent investment at the forward rate.

The inverted yield curve as a recession signal

Hardly any economic indicator is as well known as the inverted yield curve. Harvey (1988) linked the real term structure to future consumption growth. Estrella and Hardouvelis (1991) showed that a positive slope of the yield curve goes hand in hand with rising real economic activity (in consumption as well as investment), that the slope contains additional information over leading indicators, real interest rates and past growth, and that it beats survey forecasts, both in and out of sample.

Estrella and Mishkin (1998) compared many financial variables as out-of-sample predictors of US recessions, one to eight quarters ahead. Stock prices helped over horizons of one to three quarters; for anything beyond one quarter, the slope of the yield curve was clearly the best single indicator. On its own, it usually performed better than in combination with other variables.

The explanation: a central bank that wants to curb inflation raises short-term rates. If the market expects the brake to work and rates to have to fall again later, long-term rates lag behind and the curve inverts. At the same time, the inversion makes banks' maturity transformation more expensive and can dampen lending.

Limitations: the time between inversion and recession has varied widely, there have been false signals, and bond purchases by central banks can push down long-term rates and distort the signal. The evidence comes mainly from the US. As a timing signal for equities, the curve is of limited use.

For advanced readers: describing the curve with a few numbers

Central banks and data providers do not publish yields for every possible maturity; instead, they estimate a smooth curve from the yields of many bonds. A widely used model is that of Nelson and Siegel (1987): three parameters describe the level, slope and curvature, and a fourth the position of the hump.

Svensson (1994) extended the model with a second hump; many central banks use this variant for their official yield curves. Diebold and Li (2006) modelled the three factors as time series in order to forecast the whole curve. That level, slope and curvature really are the most important common movements in bond yields had been shown by Litterman and Scheinkman (1991). This is the basis for breaking down a portfolio's interest rate risk into a few metrics (see key rate durations in the article duration).

The yield curve in the euro area

In the euro area there is not one yield curve but many: each member state issues its own bonds. The usual reference is the curve for German government bonds (Bunds), because Germany is regarded as the safest borrower. The curves of other countries lie above it; the gap (spread), e.g. between Italian and German ten-year bonds, measures the additional credit risk that investors see for that state. There are also curves derived from interest rate swaps and curves that central banks estimate from bonds of the highest credit quality.

A peculiarity of recent years was negative interest rates: from 2014 to 2022, the European Central Bank's deposit rate was below zero, and at times German government bonds had negative yields even at long maturities. When central banks raised policy rates rapidly in 2022 and 2023 to curb high inflation, the curve became clearly inverted in the US as well as in the euro area. Such phases show that interest rates and their structure are not constants of nature and that long-duration bond portfolios can lose heavily in a short time.

Worked example: the roll-down effect

With a steep curve, a bond earns more than its coupon even if interest rates do not change: with each year, it gets shorter and is valued at the lower yield of the shorter maturity.

What the yield curve means for investors

• Bond yields: you read a bond's yield to maturity off the curve; a bond fund with a medium maturity earns roughly the yield of that point on the curve, as long as the curve does not move.
• Roll-down effect: with a steep curve, a bond's yield falls the closer it gets to maturity, and its price rises as a result. This return disappears with a flat or inverted curve.
• Money market or long-term bonds? If the curve is inverted, the money market delivers more current income than long-term bonds. Long-term bonds only come out ahead if interest rates actually fall later.
• Equities: historically, an inverted curve has often been a late-cycle signal. However, the time until the recession and the reaction of share prices varied too much to turn it into a fixed rule (see market timing).

How Portfolio Lab calculates it

The Macro dashboard shows the slope of the yield curve for each region as the ten-year government bond yield minus the money market rate, in percentage points. The regime analysis assigns each month to a state: inverted if the slope is below zero, flat if it is below 0.5 percentage points, otherwise normal. It shows how your portfolio performed in each state. How strongly bond funds react to movements in the curve is shown by the key rate durations in the Look-through. How many rate steps the curve is pricing in is shown there in the Market expectations tab (see market expectations). Details are in the macro methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.