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Minimum CVaR

UPDATED 2026-09-24

Minimum CVaR is an allocation method that chooses the weights whose average loss on the worst days is as small as possible. It looks only at the bad tail of the returns — the worst 5% of days by default — and ignores how the portfolio behaves on ordinary or good days, so it tells apart two instruments that variance would treat as equally risky when one of them has rare, deep falls. The method picker labels it "Minimum CVaR" and describes it as "Reduces the average loss on the worst days". Its variant Scenario CVaR applies the same objective to generated possible futures instead of past days.

Also seen as: mean-CVaR optimisation, minimum expected shortfall, CVaR minimisation

What does Minimum CVaR minimise?

It minimises the conditional value at risk (CVaR, also called expected shortfall): the average loss across the worst share of outcomes, where that share is the Tail share you set.

CVaRα=E[ L∣L≥VaRα ]\text{CVaR}_\alpha = \mathbb{E}\left[\,L \mid L \ge \text{VaR}_\alpha\,\right]

where: LL is the portfolio's loss on one day, α\alpha is the tail share, and VaRα\text{VaR}_\alpha is the loss that only the worst α\alpha of days reach. In words: line up every day of the calculation window from worst to best, keep the worst 5%, and average them — that average is what the method pushes down.

Variance counts a +3% day and a −3% day as the same amount of risk. CVaR only ever counts losses, which is why two instruments with the same volatility can come out very differently.

What is the tail share?

The Tail share is the one setting Minimum CVaR has: "The worst share of days or scenarios over which the method measures the average loss." It runs from 1% to 25% and starts at 5%. A small share looks at the few most extreme days only, which makes the estimate noisy; a larger share averages over more days and is steadier, but looks less deep into the tail.

What happens when the window is too short for the tail share?

When the in-sample window times the tail share comes to less than one day, the average of the worst days becomes the single worst day, and the method quietly turns into a worst-day minimiser. The app warns before you run, with the message "Too little data for this tail share" and the arithmetic behind it — for a 1-month window at 4%: about 21 days × 4% = less than one day. The warning offers two fixes: lengthen the in-sample period, or switch to Entropic Value at Risk, which has no such limit because every day contributes to it ("Switch to EVaR").

What is Scenario CVaR?

Scenario CVaR minimises the same average loss, but over generated possible futures instead of the days in the window. At each rebalance it builds a set of scenarios, each one a possible next period assembled from real days of the window, and minimises the average loss of the worst share of those scenarios. The picker describes it as "Generates possible futures and reduces the worst losses across them".

Two things change as a result. The loss it looks at is the loss over a whole next period rather than a single day, and the scenarios can combine days that never followed each other in history — two instruments that never fell on the same day can still fall in the same scenario. The limit is the other side of the same coin: a kind of market the window never contained cannot appear in any scenario.

Two settings describe the scenarios, 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, about one month.

Because Scenario CVaR measures its tail over the scenarios rather than over the window's days, a short window does not trigger the low-data warning for it. The same check runs against the number of scenarios instead, and within the ranges the app accepts — at least 100 scenarios, a tail share of at least 1% — its tail always keeps at least one scenario.

What does the robustness radius do?

The Robustness radius makes Scenario CVaR also guard against scenario sets slightly different from the one it generated: "Also protects against scenarios slightly different from the generated ones. The higher it is, the more evenly the weights spread." It is off by default; switched on, it runs from 0.001 to 0.1 and starts at 0.01.

In theory terms it is distributionally robust optimisation: the method assumes an adversary may shift the scenarios a small distance — the radius — before the loss is measured, and minimises the worst loss that could result. The effect you see is that concentration is penalised, so a larger radius spreads the weights more evenly. From a radius of about 0.02 upward the weights become almost equal and every other setting stops mattering; with joint-crash scenarios also on, the app says so: "At this radius the weights become almost equal", with an action to reduce the radius to 0.01.

What are joint-crash scenarios?

Joint-crash scenarios change how Scenario CVaR generates its futures: instead of reusing whole days from the window, each instrument keeps its own history of daily moves while the link between instruments is drawn so that they tend to crash together more often than the window alone shows — a Student-t copula, in textbook terms. The app puts the trade-off plainly: "t copula: instruments tend to crash together. It is a different way to generate scenarios, not necessarily a better one." What it gives up is the way calm and stormy days cluster in real history.

Switched on, it adds Tail heaviness, from 3 to 30 and 5 by default: "Lower = more extreme joint crashes."

How does Fincanva handle it?

  • Minimum CVaR and Scenario CVaR are offered at both levels: across the instruments of a strategy, and across the strategies of a Combined.
  • Both read the calculation window (In-sample, 12 months by default). Neither reads the Risk estimation choice: they work on the returns themselves, not on a volatility-and-correlation estimate.
  • The Tail share starts at 5% and accepts 1% to 25%; a value outside that range shows an error on the field, and the backtest does not run until it is corrected.
  • Both are marked "slow to compute" in the picker: each rebalance solves an optimisation over every day or scenario.

Which plan includes Minimum CVaR and Scenario CVaR?

Both depend on your plan, at each level where they are offered. The robustness radius and joint-crash scenarios come with Scenario CVaR itself.

Minimum CVaR inside a strategy

Included from Ultimate upwards. See what each plan includes.

Minimum CVaR inside a Combined

Included from Ultimate upwards. See what each plan includes.

Scenario CVaR inside a strategy

Included from Ultimate upwards. See what each plan includes.

Scenario CVaR inside a Combined

Included from Ultimate upwards. See what each plan includes.

What does it look like in practice?

Two instruments both have 15% annual volatility over a 12-month window of about 252 days. Instrument A moves in even steps every day, about ±0.95% on a typical day. Instrument B is calmer most days, about ±0.57%, but had four days of −6% — and those four days alone supply almost two-thirds of its variance, which is how its annual volatility still comes out at 15%.

  • At a 5% tail share the method averages the worst 252 × 5% ≈ 12–13 days.
  • A's worst 5% of days average about −1.95%. B's worst 5% are its four −6% days plus its eight or nine worst ordinary days, about −1.25% each, and average about −2.8%.
  • Variance sees two equally risky instruments; Minimum CVaR sees one with about 40% more tail loss, and leans toward A — holding some B only where B's bad days fall on days when A did well, which lowers the mix's own tail.

Shrink the window to 1 month (about 21 days) at the same 5% and 21 × 5% ≈ 1.05 day remains — right at the edge. At 4% it drops below one day, and the app shows the low-data warning described above.

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Fincanva is for education and illustration only. It is not personalised financial advice, and past or simulated results do not predict future ones. Read the Terms Addendum

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