Methodology — Diversification Ratio & Effective Number of Bets

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

Three complementary lenses on the same question — "how diversified is this portfolio, really?" One is a volatility ratio; the other two express diversification as an effective number of independent bets, a count that is usually smaller than the raw number of holdings. All three take a set of portfolio weights (which must be fully invested, summing to the whole book) and, where noted, the return covariance among the holdings.

Diversification ratio

This is the Choueifaty–Coignard ratio: the weighted average of each holding's standalone volatility, divided by the actual volatility of the portfolio as a whole. When holdings move together, the portfolio's own volatility is close to that weighted average and the ratio sits near its floor; when holdings offset one another, portfolio volatility falls below the average and the ratio rises. It is always one or greater, and equals exactly one only when there is no diversification benefit at all — a single position, or holdings that move in perfect lockstep. Because it compares volatility to volatility, it carries no units and needs no annualization: the answer is the same whatever return frequency the covariance was built from.

Effective number of bets (weight space)

This lens looks at the weights alone and asks how concentrated the book is, returning the count of positions the portfolio effectively holds. It is the reciprocal of a standard concentration measure (the Herfindahl–Hirschman index). For an equal-weight book it equals the actual number of holdings; as weight piles into a single name it collapses toward one. The result always lands between one and the number of holdings. Covariance plays no part here — this is purely about how the money is spread.

Effective number of bets (PCA space, Meucci)

Meucci's version counts independent sources of risk rather than positions. It works from the covariance structure: it identifies the underlying principal components (the independent directions of variance), measures how evenly total risk is spread across them, and turns that spread into a bet count using the entropy of the variance spectrum. When risk is shared equally across all the components — as with uncorrelated, equal-variance holdings — it equals the number of components; as risk concentrates into a single dominant factor (holdings converging toward perfect correlation), it falls toward one. Like the weight-space count it ranges between one and the number of holdings, but it depends only on the covariance, not on the weights. Tiny negative values that can arise as numerical noise on a degenerate covariance are discarded before the spread is measured.

Honest limits

• All three describe realized, historical diversification — a description of the book as measured, not a forecast of how it will behave.
• Each needs a fully-invested set of weights; a book whose weights do not sum to the whole is rejected rather than rescaled silently.
• The two covariance-based lenses require a well-formed covariance aligned to the holdings, and are undefined when there is no volatility to speak of — a portfolio (or matrix) with zero variance has nothing to divide by, so no ratio is reported rather than a meaningless one.
• The two "number of bets" counts measure different things — position spread versus independent risk sources — and can disagree; that gap is itself informative.