Read the machinery
No black box
01What sigma means here
Each monthly real-wealth reading is compared with a straight trend fitted to the natural logarithm of the full series. Sigma measures the historical dispersion of those log residuals. It is a descriptive comparison score—not a probability, target or timing signal.
02Fit calculated from the data
The server computes ordinary least squares, residual sigma, R², CAGR and every fitted band from the bundled monthly observations, and the page draws what it returns. No slope, intercept or sigma constant is stored separately, so an updated series cannot silently retain an outdated fit.
03Series construction
December 1845–November 1871 uses Schwert monthly U.S. total returns deflated with historical CPI estimates. December 1871 onward uses Shiller's Real Total Return Price. The segments are normalized and joined at the declared splice month.
04Important limitations
Pre-1913 CPI values are estimates. Dollar levels depend on the deflator, source vintage and splice method. The full-sample fit includes the latest partial observation when one is declared, so a new month can slightly revise every historical sigma position.
05Distance from trend
The lower panel expresses the same deviation shown by the main valuation model in simple percentage terms. A reading of +40% means real total-return wealth is 40% above the fitted historical trend; −20% means it is 20% below it. It uses the same fitted trend as the main chart and is descriptive, not a return forecast or timing signal.
