Toward Maximum Diversification: Maximising the Diversification Ratio
Does maximum diversification improve the portfolio when correlations are estimated poorly?
Compute the diversification ratio from a dated volatility and covariance estimate, then compare out-of-sample allocations with a simple benchmark under the same constraints and costs. Estimation error can change the selected weights and erase an apparent advantage.
Maximum-diversification properties depend on covariance and volatility assumptions in the model.
Evidence map
| Aspect | Finding |
|---|---|
| What it is | An allocation rule that needs no expected returns. |
| Key result / formula | The diversification ratio is the weighted average of the constituents' volatilities divided by the volatility of the portfolio. |
| Why it matters for backtesting | For a user of Stochastly the ratio is more useful as a diagnostic than as an objective. |
What it is
Choueifaty and Coignard define a ratio measuring how much a portfolio's volatility falls below the weighted average volatility of its constituents, and propose holding the portfolio that maximises it.
Key result / formula
It equals one for a single asset or for perfectly correlated assets and grows as correlations fall, so maximising it is a direct instruction to exploit whatever independence exists among the holdings. The authors show that the maximising portfolio has a distinctive property: under their assumptions every constituent has the same correlation with the resulting portfolio, which is an appealing definition of neutrality, and that the portfolio is the one an investor would hold if they believed expected returns were proportional to volatility, an assumption weaker and more defensible than estimating each return separately. Empirically they report that the construction outperformed both capitalisation weighting and equal weighting over their sample, and it sits in the same family as risk parity and minimum variance, differing in the objective rather than in the machinery.
Why it matters for backtesting
Computed on their existing allocation it shows immediately whether the holdings are doing any diversifying work, and computed through time it shows the ratio collapsing in stressed periods, which is the realistic picture of what diversification delivers when it is needed. Used as an objective it inherits the weakness shared by constructions built on an estimated covariance matrix: the maximiser will concentrate on whichever pair appears least correlated in the sample, and that pair is often the one whose correlation is most badly estimated, which is why the constraint literature matters here (see [Why Imposing the Wrong Constraints Helps]). Comparing this allocation against risk parity and equal weighting on the user's own data, out of sample, is the practical basis for the choice.
Source
Choueifaty & Coignard, "Toward Maximum Diversification", Journal of Portfolio Management 35(1), 2008, 40-51. Primary source