Robust worst case

Also seen as: worst-case optimisation, maximin allocation

What does Robust worst case optimise?

It maximises the return of the worst scenario — a maximin rule:

where: $w$ is the set of weights, $s$ runs over the generated scenarios, and $r_s(w)$ is the portfolio's return in scenario $s$ at those weights. In words: for each candidate mix, find its worst scenario; then keep the mix whose worst scenario is the best of all those worsts.

Compare Scenario CVaR, which looks at the same kind of scenarios but averages the worst share of them. Robust worst case looks at one scenario only, which makes it the cleanest "protect the floor" objective and also the most sensitive to that one extreme scenario.

Where do the scenarios come from?

Each scenario is a possible next period assembled from real days of the calculation window, the same way Scenario CVaR builds its scenarios. Two settings describe them, under Advanced settings:

• Number of scenarios — "How many possible futures are generated at each rebalance." From 100 to 2,000; 500 by default.
• Horizon of each scenario — "How many trading days each generated future covers." From 5 to 63 days; 21 by default.

A kind of market the window never contained cannot appear in any scenario, so the floor it protects is the worst the window's own days can be recombined into.

How does Fincanva handle it?

• Robust worst case is offered at both levels: across the instruments of a strategy, and across the strategies of a Combined.
• It has no tail share and no other setting beyond the two scenario settings above. It reads the calculation window (In-sample, 12 months by default) and does not read the Risk estimation choice.
• With a single instrument there is nothing to choose: it receives the whole weight.
• The picker marks it "slow to compute": each rebalance generates the scenarios and solves an optimisation over them.

Which plan includes Robust worst case?

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?

Across 500 generated one-month scenarios, three candidate mixes behave like this:

In prose: A has the best average and the deepest floor, C the weakest average and the shallowest floor, and B sits between them on both. Robust worst case chooses C, because −4.1% is the least severe worst case — the averages play no part in the choice. A method that weighed the average, such as Stochastic programming with a low risk aversion, could choose differently.