The rest of this page is the long version: the picture, the mechanics and the research record.
The benchmark everyone trusts is structurally skewed.
The $50 trillion passive industry runs on one idea: market-capitalisation weighting, traceable to Laspeyres' price index of 1871. It was adopted for calculational convenience — and it carries an intrinsic positive bias. As a stock rises, it earns a bigger weight, so the index buys more of it.
That is a rich-get-richer machine — it mistakes momentum for merit and quietly concentrates risk in a handful of names. A 150-year-old convention, not a law of markets. E&R treats it as only half the story.
E&R™ was designed — over fifteen years.
Each layer of the framework traces to peer-visible work, published openly on SSRN since 2010. The methodology is the accumulation of that record.
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The E&R framework
One idea — that markets are neither purely Normal nor purely Non-Normal — turned into a probabilistic engine. Underneath E&R™ sits a three-state Markov framework, published as 3N (Normal, Non-Normal, Non-Linear). Here it is explained two ways: the plain picture first, then the mechanics underneath. Both are driven by the same control.
Two jars, five hundred balls
Picture the market as a jar of 500 balls — one per stock. In one jar only a handful, about seven, actually move: they swell and shrink while the other 493 sit still. In the other there’s no fixed set — all 500 are always breathing, a different scatter growing and fading every moment. Real markets look far more like the first jar — so E&R reads all 500 at once to find the few that carry it at a given moment, rather than assuming in advance which they are.
THE METHOD → Diversifying blindly across all 500 grows at the market average; concentrating on a fixed few misses the rotation. Smart diversification is the edge — estimate each stock’s chance of growing and you can tilt a broad basket toward the balls about to swell, away from those that aren’t. That’s what E&R measures: each stock as odds, not a verdict — how likely it is to persist, revert, or sit in transition. The chain below shows how those odds are measured. Diversify toward the balls with better odds of growing — and capture the rotation.
Take a real five-threshold model of the market — five return states a stock moves between, each in its own colour. It’s a Markov chain: for every state, the odds of staying put plus the odds of leaving sum to 100%. Links run both ways, and the two directions need not match. Over a single day each state holds 100% of itself — five disconnected circles. Lengthen the horizon and each state leaks into its neighbours, tying the circles into a chain; then probability jumps two states at a time, folding the chain into a shape; until, over long horizons, every state reaches every other and self-persistence falls near 50% — a fully-connected polygon, far less predictable.
This is where portfolio construction comes from. At each rebalance E&R reads every stock’s transition odds, overweighting the states most likely to persist or improve over the target horizon and underweighting those likely to decay — sizing by measured edge, not market value. These are conviction holdings, not short-term trades: held while the odds stay in their favour, turned over only as the probabilities shift.
Ring thickness = self-persistence · each link carries two directional odds, coloured by the state they leave. After Pal, “The [3N] Model of Life” (SSRN 3830047).
Order, disorder & the state between
Markets modelled as a Markov chain across multiple probabilistic states — every asset carries measurable odds of persistence, reversion or transition.
Balancing Normal & Non-Normal
Value bets on reversion; cap-weighting bets on persistence. E&R measures the prevailing regime and normalises across both — correcting for recency, anchoring and confirmation bias.
The market's fingerprint
Every stock has a fingerprint — the pattern in how it really moves. Machine Beta rebuilds the index from these probability weights rather than market value, learning the structure of returns directly, at lower tracking error.
A better basket, measured against the S&P 500
The Exceptional & Rich basket ranks the market on relative cap growth rather than size. We didn't back-test for winners: since January 2014 a portfolio was launched every single month-end — 324 in all — and run on one-, two- and three-year clocks. Every start date, every cadence, no discretion. When a design wins from any starting point, it isn't luck — it's structure.
The outcome: a rules-based basket active managers can run as an index-replacement strategy — broad enough to track the market, tilted enough to beat it.
Reconstruction of the book’s Figures 5–12; excess-return and drawdown magnitudes read from the published charts, growth compounds the stated annual excess over the S&P 500. Illustrative of the case study, not a live composite. Source: Pal, End of Passive Investing (2025), ch. 11.
Researched, attributed, forward-tested — every strategy earns its way live.
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The full research record
Every paper below is publicly available on SSRN. Together they trace the derivation of E&R from first principles — time, probability, mean reversion, value, and finally machine-learned factors. Filter by research theme:
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