Maximum Diversification

Also seen as: most diversified portfolio, MDP

What is the diversification ratio?

The diversification ratio compares what the portfolio's risk would be if its instruments moved in perfect lockstep with what it actually is:

where: $w_i$ is instrument i's weight, $\sigma_i$ its own volatility, and $\sigma_p(w)$ the volatility of the whole portfolio at those weights. The numerator is the risk of a mix with no diversification benefit at all; the denominator is the risk you really carry. A ratio of 1 means the instruments move together completely; the further above 1, the more diversification the mix is harvesting.

It is a third answer next to two others: MPT aims at the best risk-and-return trade-off, and Risk Parity equalises each instrument's share of the risk. Maximum Diversification asks only how much of the parts' risk disappears in the whole.

How is it different from Min Correlation?

Both reward instruments that move differently, but they aim at different targets: Min Correlation aims at the lowest overall correlation of the portfolio, while Maximum Diversification aims at the highest diversification ratio, in which each instrument's volatility sits directly. That makes it sensitive to how volatility is measured, which is why it also reads the Risk estimation choice.

How does Fincanva handle it?

• Maximum Diversification is offered at both levels: across the instruments of a strategy, and across the strategies of a Combined.
• It has no settings of its own. It reads the calculation window (In-sample, 12 months by default) and the Risk estimation choice — see Risk estimation.
• Weights are never negative.
• With most risk estimates — including the recommended Ledoit-Wolf · constant correlation — every instrument must have moved in price at some point inside the window: an instrument whose price stayed flat for the whole window, such as a suspended listing, stops the backtest rather than receiving a weight. Two estimates are the exception; Risk estimation names them.
• The picker marks it "slow to compute": it solves an optimisation at every rebalance.

Which plan includes Maximum Diversification?

It depends on your plan, at each level where the method is offered.

Inside a strategy

Included from Ultimate upwards. See what each plan includes.

Inside a Combined

Included from Ultimate upwards. See what each plan includes.

What does it look like in practice?

Three instruments all have 20% volatility. Two of them are near-twins, with a correlation of 0.9; the third moves independently of both.

• At Equal Weights (33.3% each) the portfolio's volatility is 20% × √(0.533) ≈ 14.6%, so the diversification ratio is 20% ÷ 14.6% ≈ 1.37.
• Maximum Diversification instead holds about 25.6% / 25.6% / 48.7%: the independent instrument gets nearly half, and the twins share the rest almost as if they were one instrument. The portfolio's volatility falls to about 14.0%, and the ratio rises to about 1.43.

The method did not look at returns at all — only at how much risk the mix sheds by combining instruments that do not move together.