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Mean Reversion

Mean reversion is the empirical tendency of interest rates to return to a long-run equilibrium level over time. Periods of unusually high or low rates are followed by movements back toward the historical average, though the speed of reversion and the equilibrium level itself may shift over time.

Mean reversion in interest rates is supported by economic logic:

  • High rates slow borrowing and economic activity, eventually leading to easing
  • Low rates stimulate activity and inflation, eventually leading to tightening
  • The central bank's mandate creates an anchor: the Fed targets inflation and employment, implicitly constraining how far rates can deviate from equilibrium

Mean reversion is a core assumption in most term structure models:

  • Vasicek model: rates follow a mean-reverting process with normally distributed shocks
  • Cox-Ingersoll-Ross (CIR) model: similar but with volatility proportional to the rate level, preventing negative rates
  • ACM model: uses mean-reverting factors to generate yield curve dynamics

The speed of mean reversion matters:

  • Fast mean reversion → short-term rate fluctuations are temporary, long-term yields are stable, the curve is flat
  • Slow mean reversion → rate changes are persistent, long-term yields are volatile, the curve can sustain steep or inverted shapes

The z-score shown on the morning dashboard reflects mean reversion logic: yields far from their historical mean (high absolute z-scores) are statistically likely to revert, though the timing is uncertain. The Salomon Brothers yield curve primer (Part 7) provides the mathematical framework for mean-reverting rate models.

Why Rates Revert and Prices Do Not

Mean reversion is a reasonable assumption for interest rates and a poor one for most asset prices. The difference explains why term structure models are built the way they are.

An equity index has no natural ceiling. Earnings can grow without limit, so the price can too, and a price far above its ten year average tells you little about the next move.

An interest rate is bounded by economics on both sides. Rates far above the growth rate of the economy suppress borrowing until activity slows and policy eases. Rates far below it stimulate borrowing until inflation forces policy to tighten. Neither extreme is stable, and both create the forces that undo them.

A central bank makes the boundary explicit. An inflation target is a public commitment to push back against sustained deviation. That commitment gives the process an anchor that no equity index has.

The anchor is real and it is loose. Rates have spent years far from any plausible long run level, which is enough time to ruin a position built on the expectation that they would not.

The Two Unknowns

Every mean reverting model needs two inputs, and neither can be observed.

The level. Reversion is toward something, and that something is not the historical average. The long run neutral rate depends on productivity growth, demographics, and the global demand for safe assets. All three drift. A mean estimated from thirty years of data can describe a regime that no longer exists.

The speed. A model with fast reversion treats every deviation as temporary, which produces a flat curve and low long yields. A model with slow reversion treats deviations as persistent, which allows steep or inverted shapes to survive. The same observed curve is consistent with both, so the speed has to be estimated, and estimates of it are unstable.

The consequence is that a mean reversion signal is a statement about a model, not about the market. Two analysts applying the same method to the same data with different windows will disagree about whether a yield is extreme, and neither is making an error.

Believing In It Is Not the Same as Trading It

The empirical case for reversion is stronger than the case for any particular trade built on it.

A position that profits from reversion is short the deviation. It gains slowly while the deviation narrows and loses quickly while it widens. That payoff shape has two practical consequences.

The first is that the trade can be right and still fail. A yield two standard deviations from its mean can go to four before it returns. The position is closed out on the way there, so the eventual reversion arrives after the trader has left.

The second is that the signal is strongest exactly when it is least reliable. Extreme readings cluster during regime changes, which are the times when the historical mean is most likely to be the wrong reference. A z-score of three is as likely to mean the distribution has shifted as it is to mean the yield is stretched.

The usual discipline is to pair the statistical signal with an economic reason. A yield that is high relative to history and high relative to the policy path implied by the curve is a different case from one that is high because the policy path has genuinely moved.

FAQ

Do interest rates really mean revert?

The long run evidence supports it, in the sense that rates have repeatedly returned toward a central level over decades rather than trending indefinitely. The evidence over shorter horizons is much weaker. Deviations can last for years, and formal tests often fail to reject the hypothesis that rates follow a random walk over a few years of data.

What is the mean that rates revert to?

There is no agreed answer. Candidates include the historical average over some window, the neutral policy rate implied by the Federal Reserve's own projections, and the long run rate implied by the forward curve. Each gives a different reference and therefore a different signal. Stating which one is being used is part of stating the signal.

How does mean reversion affect the shape of the curve?

Through the expected path. If short rates are above the long run level and are expected to revert, the average expected rate over ten years is below the current short rate, which pushes the long yield down and can invert the curve. Fast assumed reversion flattens the curve, and slow reversion allows it to stay steep.

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Related Terms

  • ACM Term Premium Model — The Adrian, Crump, and Moench model that decomposes Treasury yields into rate expectations and term premium components.
  • Expectations Hypothesis — The theory that long-term yields equal the market's expectation of future short-term rates, with no risk premium.
  • Z-Score — The number of standard deviations a value lies from its historical mean, used to identify extreme readings.
  • Yield Volatility — The standard deviation of yield changes, measuring how much interest rates fluctuate over a given period.

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