How the Opulence Alpha studies are measured: data and methods

The universe is 1,767 US-listed common stocks. It was fixed when the platform was built and has not been re-sampled since. It has two layers. The first is every company that belonged to the S&P 500 at any time since 1996 and whose price history could be recovered: 1,027 companies, 413 of which have since delisted. They enter with their full history, which largely removes survivorship bias from the large-company layer: on 30 June 1996 the universe held 76% of the index's members with prices, and from 2010 on at least 96%. The 137 historical members it lacks are mostly companies that left the index before 2010 (119 of them) and whose prices could not be recovered. The second layer is 740 companies outside the index, chosen at construction to follow the market's sector proportions, mid capitalisations included, subject to minimum price and trading-value screens.

Measured today, the universe reflects that design. By latest market capitalisation, 55% of the 1,338 active companies are large (at least $10bn), 38% mid ($2–10bn) and 6% small. Its sector mix is close to that of the S&P Composite 1500 (the S&P 500, MidCap 400 and SmallCap 600 together): 7.9% of companies would have to change sector for the two to match exactly (Table 1). Sectors follow each company's current GICS classification throughout its history.

Of the 422 companies that have delisted, 302 left through a merger or acquisition, 31 through bankruptcy, 38 continued under a successor ticker and 51 for other or unrecorded reasons, as classified from their SEC EDGAR filings. Because the non-index layer was chosen from companies listed at construction, only 9 of its 740 companies have delisted, against 413 of 1,027 in the index layer: smaller companies that failed or were acquired earlier are under-represented. Section 5 therefore repeats each lead result on the stocks that were S&P 500 members on each date, the subset free of that bias.

The studies observe the universe every Wednesday from Jan 4, 1995 to Aug 19, 2026: 1,634 Wednesdays spanning 7,959 trading sessions. Wednesday keeps one observation per week away from the start and the end of the trading week; weeks whose Wednesday was a market holiday (17 of 1,651) are left out. A stock enters a Wednesday's cross-section when it has the signal and a measured outcome. The cross-section grows from a median of 832 stocks in 1995 to 1,331 in 2026 (median 1,148, range 820 to 1,371; Figure 1). In all the sample holds 1,889,758 stock-weeks from 1,763 companies; 331,954 of them (17.6%) come from the 422 companies that have since delisted.

The formation studies observe the universe every Wednesday from Jan 4, 1995 to Aug 19, 2026: 1,550 Wednesdays spanning 7,959 trading sessions. They leave out the weeks the platform's regime model flags as a likely change of market regime, when a formation's window straddles two regimes; with market holidays, 101 of 1,651 Wednesdays are left out. They hold 1,361,444 formation detections, one per stock and Wednesday, from 1,764 companies; 217,945 of them (16%) come from the 420 companies that have since delisted. The median Wednesday has 906 stocks with a formation, from 452 in 1995 to 1,065 in 2026 (Figure 1).

The outcome is the stock's return from the close on the signal's Wednesday to the close 1, 5, 21 and 63 trading sessions later, roughly a day, a week, a month and a quarter. Closes are adjusted for splits and, where the source records them, for dividends. Sessions follow one market-wide calendar, which matches the NYSE's trading days exactly from 1980 to 2026 (11,755 sessions). Outcomes start in 1995 because adjusted closes before then are unreliable in the source data, and run through Aug 21, 2026.

Each return is compared with the same Wednesday's cross-section: with the median stock for hit rates, and with the equal-weighted average for average excess returns. Rank correlations are unaffected by either. Returns are not winsorised or capped. A return that would run across a price bar flagged as bad data is left out rather than filled, and no delisting return is added: a company's outcomes end at its last trading day.

The outcome is the stock's return from the close on the detection's Wednesday to the close 5, 21 and 63 trading sessions later, on split-adjusted closes, in excess of the S&P 500 (the SPY fund) over the same sessions, as recorded by the pattern detector and capped at plus or minus 100%. Each detection uses only price bars up to its own day: a turning point is recognised only once later bars have confirmed it, never with hindsight. A bullish detection counts as a hit when that excess return beat the same Wednesday's median stock; a bearish one when it trailed it. Half of all stocks beat the median by construction, so chance is 50 in 100 on every date.

The detector also records whether the price reached the formation's drawn target before its stop, on daily closes, within 21 sessions for bullish formations and 42 for bearish ones; a stop or a timeout counts as a miss. Outcomes run through Aug 21, 2026. No delisting return is added.