What does the interest rate model measure?

It asks whether the S&P 500 looks expensive given where the 10-year Treasury yield sits. Low rates normally support higher stock prices; the model flags periods when stocks are high relative to their trend while rates are also low (or not high enough) relative to history.

How is the composite calculated?

Inflation-adjust the S&P 500 with CPI, express it as a z-score versus its own exponential trend, express the 10-year Treasury yield as a z-score versus its historical mean, then subtract: composite = S&P z − rate z. A positive reading means stocks are high given the rate environment.

How is this different from the Excess CAPE Yield?

Both ask whether rates justify current equity prices, and both vote on the homepage YES/MAYBE and overvaluation probability. The Excess CAPE Yield is a single premium (earnings yield minus the real bond yield). This page shows the two-dimensional view — stocks vs rates in z-score space — and a time series of how far out of phase those two series are.

What do the verdicts mean?

Above +1σ is Overvalued; above +2σ is Strongly Overvalued — the same bands used elsewhere on this site. Fair Value is the middle ±1σ band. The composite can stay elevated for years; it describes valuation conditions, not near-term timing.

How often is it updated?

Every US market weekday, about an hour before the opening bell, from the same FRED and multpl series that feed the other gauges.

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Valuation

Interest rate model

S&P 500 position conditioned on the 10-year Treasury yield — a CMV-style composite plus the 2-D view of stocks vs rates.

+4.84σ

Strongly Overvalued

As of July 27, 2026

As of July 27, 2026, the real S&P 500 sits +4.48σ above its exponential trend while the 10-year Treasury yield (4.47%) is -0.37σ versus its historical mean. Combined, that is a strongly overvalued reading for stocks given the rate environment.

Complementary to the Excess CAPE Yield. This gauge votes on the homepage YES/MAYBE and the overvaluation probability.

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The purple composite is S&P z minus rate z. When it is above zero, stocks look high given where interest rates are. Above +1σ is Overvalued; above +2σ is Strongly Overvalued.

Historical crashes marked on this chart (6)

The dashed red lines flag major US market crashes. Note how the composite behaved in the run-up to each.

Kennedy Slide (1962): A rapid spring 1962 sell-off (the 'Flash Crash of 1962') wiped roughly 27% off the S&P 500 amid fears over the economy and a clash with steelmakers. Markets stabilized and recovered within about a year.
1973–74 oil crisis bear market (1973): The OPEC oil embargo, Watergate, and stagflation drove a roughly 48% decline over nearly two years — the worst bear market since the 1930s. Stocks took years to recover in real terms.
Black Monday (1987): On October 19, 1987 the Dow fell 22.6% in a single day — the worst one-day drop in history — driven partly by program trading. The economy avoided recession and markets recovered within two years.
Dot-com crash (2000): The tech bubble burst in March 2000; the Nasdaq lost about 78% by 2002 as internet valuations collapsed. A mild recession followed and tech stocks took roughly 15 years to reclaim their peak.
Global Financial Crisis (2008): The subprime mortgage meltdown and Lehman Brothers' collapse cut the S&P 500 about 57% into March 2009. It triggered the Great Recession, sweeping bailouts, and a decade of near-zero interest rates.
COVID crash (2020): Pandemic lockdowns caused the fastest bear market ever in February–March 2020, a roughly 34% plunge in weeks. Unprecedented Fed and fiscal stimulus sparked a rapid recovery to new highs.

Stocks vs rates (2-D view)

Each point is a month: the 10-year yield’s z-score on the x-axis and the real S&P 500’s z-score versus its exponential trend on the y-axis. The gray line is an ordinary least-squares fit (slope -0.356, R² 0.127). Today is marked in red.

Points in the upper-left (high stocks, low rates) are the expensive quadrant for this model. The scatter is the cross-section of the same rates-vs-stocks relationship that the Excess CAPE Yield summarizes as a single premium number.

Overview

Lower interest rates usually support higher equity prices: borrowing is cheaper for firms, and safer bond yields push investors toward stocks. The interesting cases are when that relationship breaks — stocks high and rates not especially low, or stocks high even when rates have already normalized. This model follows the Current Market Valuation approach: put both series in z-score units relative to their own trends, then combine them.

How to read it

A composite near zero means the S&P’s distance from trend is roughly matched by where rates sit versus their long-run average — a normal pairing. Readings above +1σ mean stocks look rich given the rate backdrop; readings below −1σ mean the opposite. The peak of the sample is typically the late-1990s internet bubble, when equities ran far ahead of trend while bond yields were near normal.

How it’s calculated

Take the monthly S&P 500 index level (via multpl / Shiller) and divide by CPI to get a real (inflation-adjusted) price series.
Fit an exponential trend to that real series (log-linear least squares) and convert each residual into a z-score using the standard deviation of residuals.
Take the monthly 10-year constant-maturity Treasury yield (FRED GS10) and express it as a z-score versus its flat historical mean.
Form the composite as S&P z minus rate z. Low rates (negative rate z) and high stocks (positive S&P z) both push the composite up — the expensive side.
For the scatter, plot every month’s rate z against its S&P z and fit an ordinary least-squares line. A negative slope is the usual inverse relationship between rates and equity position.

Versus the Excess CAPE Yield

The Excess CAPE Yield (ECY) answers the same economic question — do rates justify equity prices? — as one number: cyclically adjusted earnings yield minus the real 10-year Treasury yield. This page instead shows the two raw ingredients in z-score space and their difference over time. Use ECY when you want Shiller’s earnings-based premium; use this model when you want the price-vs-rate geometry. Neither replaces the other — both vote on the homepage headline and the overvaluation probability.

Criticisms

A flat historical mean for the 10-year yield ignores the decades-long decline in rates; some of what looks like “low rates” may be a new regime rather than a temporary deviation.
The S&P exponential trend is fit over the full sample, so the historical z-scores are a descriptive, hindsight view — not a fully point-in-time signal.
Combining two z-scores with equal weight is a modeling choice. Earnings-based alternatives (like ECY) can disagree when margins or payout policy shift.
This is not a market-timing tool and is not financial advice. High readings describe stretched conditions, not a scheduled decline.

Frequently asked questions

What does the interest rate model measure?: It asks whether the S&P 500 looks expensive given where the 10-year Treasury yield sits. Low rates normally support higher stock prices; the model flags periods when stocks are high relative to their trend while rates are also low (or not high enough) relative to history.
How is the composite calculated?: Inflation-adjust the S&P 500 with CPI, express it as a z-score versus its own exponential trend, express the 10-year Treasury yield as a z-score versus its historical mean, then subtract: composite = S&P z − rate z. A positive reading means stocks are high given the rate environment.
How is this different from the Excess CAPE Yield?: Both ask whether rates justify current equity prices, and both vote on the homepage YES/MAYBE and overvaluation probability. The Excess CAPE Yield is a single premium (earnings yield minus the real bond yield). This page shows the two-dimensional view — stocks vs rates in z-score space — and a time series of how far out of phase those two series are.
What do the verdicts mean?: Above +1σ is Overvalued; above +2σ is Strongly Overvalued — the same bands used elsewhere on this site. Fair Value is the middle ±1σ band. The composite can stay elevated for years; it describes valuation conditions, not near-term timing.
How often is it updated?: Every US market weekday, about an hour before the opening bell, from the same FRED and multpl series that feed the other gauges.

Composite history