Bull & bear regimes in 150+ years of S&P real total returns, detected with hidden-Markov models — with a monthly regime nowcast. Not a forecast, on purpose.
What this is: every month, U.S. equity returns are re-fit with Gaussian hidden-Markov regime models on Shiller's monthly series back to 1871. The two-state model identifies a calm regime (~10% annualized volatility, positive real drift, ~83% of months) and a stressed regime (~25% volatility, strongly negative real drift, typical duration ~7 months). A forward filter — using no future information — turns the latest month into a regime nowcast: the probability the market is currently in each regime.
Latest update (2026-06, refreshed monthly): the filtered two-state model reads the U.S. equity market at 96% calm / 4% stressed. The three-state model reads 91% calm bull, 8% correction, 1% crisis. Conditional on today's reading, the probability of being in the stressed regime 12 months out is 16%, converging toward its long-run base rate of 17% — a regime nowcast decays to base rates by design; it is not a market forecast.
Filtered probabilities P(regime | returns observed through the stated month). The three-state model separates ordinary corrections from full crises; it carries wider parameter uncertainty than the two-state model (see methodology).
Top: real (inflation-adjusted) growth of $1 invested in the S&P composite with dividends reinvested, log scale. Bottom: smoothed probability of the stressed regime (two-state model). Every major drawdown since 1871 — 1907, 1929–34, 1937, 1973–74, 1981–82, 1987, 2000–02, 2008–09, 2022 — appears as a red band.
Monthly transition probabilities, two-state model:
Read this curve as decaying information. The nowcast says something about the next few months because regimes persist; twelve or more months out, today's reading has almost fully washed out and the curve approaches the unconditional base rate. A regime model that claimed otherwise would be overfitting its own persistence — this convergence is the model behaving correctly, and it is the reason we publish a nowcast rather than a forecast.
Episodes where the two-state model's most likely path spends two or more consecutive months in the stressed regime. The 2020 pandemic crash is the notable single-month episode excluded by that filter: the model assigned it 100% stressed probability in March 2020 and saw it resolve within a month — the fastest bear regime in the sample.
Monthly S&P composite prices, dividends and CPI from Robert Shiller's long-run dataset (1871–present), refreshed monthly from the maintained source. Returns are real total returns: price change plus reinvested dividends, deflated by CPI. The series is checked against known episodes on every refresh (1929–32 real drawdown ≈ −76%, 2007–09 ≈ −50%, long-run real return ≈ 7%/yr) before anything on this page updates.
Gaussian hidden-Markov models (Hamilton-style regime switching) on monthly real log total returns. Models with 1–4 states are fit by maximum likelihood with 50 independent EM restarts. The single-state model is the null every regime claim must beat. States are labeled by volatility, lowest first.
The full simulation methodology behind the QuantCalc planner is documented on the methodology page. The data behind this page is available as JSON.
A persistent state of market behavior with its own typical return and volatility. U.S. equity history since 1871 is well described by a calm regime — ~10% annualized volatility with positive real returns, about five-sixths of all months — and a stressed regime with ~2.5× the volatility and strongly negative average real returns, lasting about 7 months at a time.
A nowcast estimates which regime the market is in right now, given returns observed so far — it looks backward at realized data. Projecting it forward only blends today's reading with historical base rates through the transition matrix; it contains no claim about what the market will do next. That is the difference, and it is why the projection curve on this page converges instead of diverging.
With a hidden-Markov model: each month the market occupies an unobserved state, each state generates returns from its own distribution, and states persist according to a transition matrix estimated from 150+ years of data. The current regime probability comes from a forward filter using no future information.
On the fitted two-state model: a stressed regime begins with ~3% probability in any calm month (about once every 32 months) and ends with ~15% probability per month (typical duration ~7 months). About 17% of all months since 1871 are stressed-regime months.
Sequence-of-returns risk. Stressed regimes pair elevated volatility with negative average real returns for months at a stretch — on 150 years of data the calm-to-stressed gap is ~33 percentage points of annualized real return. Simulations that switch only volatility between regimes, without the return gap, understate the damage a stressed stretch does to a portfolio under withdrawals.
One email a month when the nowcast refreshes — the current reading, any regime change, and what it means for planning assumptions. Free.