Maximum Diversification

The diversification ratio (DR) is defined as: the numerator is the average asset volatility taken at the portfolio weights, the denominator is the portfolio volatility itself. For an asset that is perfectly correlated with the rest of the universe DR collapses to 1; for a portfolio of uncorrelated assets DR can grow as large as where is an effective number of bets.

Choueifaty and Coignard (2008) introduced the "Most Diversified Portfolio" (MDP) as the long-only weight vector that maximises DR. Choueifaty, Froidure and Reynier (2013) proved a number of attractive properties for the MDP: it is volatility-invariant (rescaling any asset's volatility leaves the optimum unchanged), every asset it holds has the same correlation to it, and any asset it leaves out is at least as correlated to it as the ones it holds. The authors also report empirical comparisons against cap-weighted, minimum-variance and equal-weight portfolios; those results are specific to their samples.

FolioLab implements MDP via skfolio's MaximumDiversification estimator, with the sample covariance of daily returns. The optimisation is convex and solves quickly. Per-name weight bounds, asset exclusions, and group sum limits such as sector caps pass to the estimator and enter the same program.

Two details of the run differ from the textbook ratio. First, skfolio subtracts the daily risk-free rate from the numerator, so the program maximises , which equals DR only at a zero rate. Second, before it solves, the run checks that at least one asset's annualised mean return is above the risk-free rate. When none is, the run lowers the rate to just below the highest mean return and marks the result as degraded.