Methodology — The Diversification Ladder

Transparency is a feature. This page explains what the Diversification Ladder is and why we compute it — in plain terms. The precise formulas and numeric conventions are documented in our internal methodology; the summary here is deliberate, not an omission.

"Am I diversified?" has no single honest number, so we answer it with a ladder: the same book restated five ways, each rung using more information, each rung a number of names.

The five rungs

1. Names — how many positions you hold. A count, not an estimate.
2. Effective names — weights — how many names your weights spread like (the 1-over-HHI count). An equal-weight book of N names reads exactly N; concentration pulls the reading down. Exact arithmetic — no estimation.
3. Effective names — risk — the same count applied to each name's share of portfolio risk rather than its weight. A book whose risk is dominated by two volatile names reads close to 2 here however many lines it holds.
4. Independent bets — a weight-aware count of genuinely uncorrelated bets (minimum-torsion effective number of bets). Ten names that all move together are closer to one bet than ten.
5. Worst-decile restatement — on the benchmark's worst one-in-ten days of your window, how many names did the book behave like? We measure the average pairwise correlation on exactly those days and restate it as the equivalent number of equally-correlated names.

The rungs are different readings, not a worsening sequence — a book whose risk is spread more evenly than its weights will read rung 3 above rung 2, and that is information about the book, not an error.

The honest parts

• Every estimated rung is gated. The bets rung needs a long enough window for a spectral estimate; the stress rung needs at least 50 stress days spanning at least 2 distinct market episodes (per the shared conditioning day sets). Below a gate, the rung shows why it is missing — and stress days that fail the gate are still reported as dated fact.
• The stress rung is never a full re-estimation on a handful of days — that would be noise dressed as structure. It is a pooled average of pair correlations, restated through exact arithmetic.
• A mechanical baseline sits beside the stress reading. Selecting days by the benchmark's own behavior mechanically shifts measured correlations even when nothing about the book changed (Boyer, Gibson & Loretan, 1997, Pitfalls in Tests for Changes in Correlations, Federal Reserve Board IFDP 597). We show what a constant-correlation book with your betas would have measured on the same days — only the gap beyond that baseline is information.
• Long-only. A book with short positions suppresses the ladder rather than reinterpreting it: "number of names" counts have no honest meaning over signed weights.
• Estimated rungs render coarse ("~6", never "6.34") — they are estimates, not measurements.

Sources

• Attilio Meucci, "Managing Diversification", Risk, May 2009; Meucci, Santangelo & Deguest, "Risk Budgeting and Diversification Based on Optimized Uncorrelated Factors" (minimum-torsion bets).
• Boyer, Gibson & Loretan (1997), "Pitfalls in Tests for Changes in Correlations", Federal Reserve Board IFDP 597.