A century and a half up, through seven brutal crashes.
The index went from about 4 to roughly 7,400. Every chart here uses a log scale, the only honest way to show percentage moves evenly across that range.
The long run is up. The crashes are savage and recurring — 1929 (−86%), 1937, 1973–74, 1987, 2000–02 (−49%), 2008–09 (−57%), 2020 (−34%). Both are permanent features. Neither cancels the other.
overview
Can anyone predict the index? No.
We tested every forecasting model the honest way: train on the past, predict the future it hadn’t seen, roll forward, repeat. The benchmark to beat is the dumbest forecast there is — “tomorrow’s level = today’s level.”
Almost nothing beats it. We put this first on purpose.
backtest_skill_heatmap
backtest_error_by_horizon
model_gbm_direction
forecast_foundation_ensemble
backtest_turns_scorecard
Where the long run points, honestly bounded.
Short-horizon prediction has no skill. The long run is different. For nearly a century the index has climbed one steady line — about 7% a year after you strip out the noise.
Independent methods agree on that central path. They also agree the spread around it is enormous, and the timing is unknowable. A direction is not a price target.
compare_all
forecast_bayes_powerlaw
montecarlo_v2
forecast_real_return
decomp_secular_cyclical
The market lives in moods, not patterns.
Price level is unforecastable. The state the market is in is not. It runs calm for years, then flips into crisis and stays there. Those moods are sticky, and crises cluster around the famous crashes.
There are faint calendar and cycle rhythms too. They are real and they are tiny, and several are fading. None is a clock you can set a trade by.
regime_hmm
regime_switching
wavelet_scalogram
seasonality
hurst
Risk is the one thing you can model.
Price is unforecastable. Volatility is not. It clusters: a wild stretch tends to be followed by more wild days, a calm one by more calm days. That makes the near-term risk level genuinely predictable, unlike anything in price.
And the risk that matters most — crash risk — is far worse than a normal bell curve admits.
garch
evt
model_drawdown
sim_jump_diffusion
Valuation is where the signal actually lives.
There is one place equities are genuinely forecastable, and it is not timing. It is valuation. Measure how expensive stocks are — price against the last ten years of earnings — and history has reliably pointed to the next decade’s real return.
Buy expensive and the next ten years have tended to be weak. Buy cheap and they have been strong. This is the report’s one forecast we can partly check against history — though these ten-year windows overlap, so there are far fewer truly independent decades than it looks. Read the tilt, not a precise law. And it is mute on timing.
valuation_cape_overlay
valuation_cape
valuation_conditional_dist
valuation_erp
The honest map.
This is not advice to buy or sell. It is a map of where prediction works and where it is wishful thinking. Observation, not advice.
Unforecastable. Today's level is the best guess of tomorrow's. The AI models did no better. Ignore confident price targets.
Up, at roughly 7% a year through history, but the spread around that is huge and the timing is unknowable. A direction, not a target.
A choppy market mood, near the high end of valuation. Flat decades are an ordinary part of the cycle, not a break.
The forecastable part. Volatility clusters; plan for a worse-than-10% down day in most decades and a multi-year drawdown when crashes hit.
The one genuine long-horizon signal. Long-run real returns have averaged about +7% a year, but today's level is near its most expensive ever — and from valuations this stretched, the next decade has historically run far weaker, with the closest analogs near flat-to-slightly-negative (around −3% a year after inflation).
- —One price series plus one valuation series (Robert Shiller's public data). No options, breadth, or sector data.
- —Return figures are real total returns — dividends reinvested, then adjusted for inflation — so they reflect what a holder actually earned, not just the index's price change. The index level charts elsewhere are price only.
- —The long-horizon forward cones can't be fully validated; with 155 years you have only a handful of independent multi-decade windows. Those cones are scenarios, not validated forecasts.
- —The valuation forecast is the one long-horizon claim we can partly check. It predicts the next decade's return, not its timing — valuation was 'expensive' for years before both the 2000 and 2007 tops.
- —The trend assumes the past pattern continues. Past growth doesn't guarantee future growth.
- —Descriptive, not predictive. These models describe what happened; they don't tell you what's next.
Descriptive research, not financial advice. The S&P 500 can fall by half in a downturn and stay underwater for years — as it has more than once in this dataset.
Appendix — every chart & model inventory →