CVaR — What It Says About Tail Risk That VaR Won't

VaR tells you that in 95 percent of months you will not lose more than eight percent of your capital, and that sounds reassuring. The question VaR refuses to ask concerns the remaining five percent: once the threshold actually breaks, how deep is the average loss. CVaR answers it. Conditional Value-at-Risk, also called Expected Shortfall, is the measure the Basel Committee on Banking Supervision adopted for bank capital in 2019 in place of VaR. Here is how a retail trader can use this number without dressing it up as false precision.

How CVaR differs from VaR and why that difference is not cosmetic

VaR at the 95 percent confidence level is the loss threshold you will not exceed with 95 percent probability over a chosen horizon. If twelve months of account history show that the loss did not exceed 8 percent of equity in 95 percent of months, the monthly VaR₉₅ is minus 8 percent. The catch is that VaR says nothing about the remaining five percent of months. The loss inside them could be minus 10 percent or minus 35 percent, and VaR will report the same number.

CVaR is the conditional average loss inside those tail months. Formally it is the expected value of the loss given that the loss is worse than the VaR threshold — in shorthand E[L | L < VaR_α]. For a historical sample this means: sort the monthly returns from worst to best, take the ones worse than the VaR threshold, and average them. That is the entire recipe. CVaR will always be at least as bad as VaR, because it averages the worst slice of the distribution rather than its edge.

Why the Basel Committee swapped VaR for Expected Shortfall in 2019

The 2008 crisis exposed VaR. Banks holding credit-product positions could lose multiples of their daily VaR₉₉ in a single session. The Basel Committee, in its 2013 consultation paper Fundamental review of the trading book (BCBS 265), proposed replacing VaR with Expected Shortfall, and the January 2019 standard (BCBS 457) made the change binding. In the European Union, FRTB has applied in full since 1 January 2023.

"A key element of the revisions is the move from value-at-risk to an expected shortfall measure of risk under stress." — Basel Committee on Banking Supervision, Minimum capital requirements for market risk, BIS, 2019

The reasoning rests on three independent legs. First, ES is a coherent risk measure in the sense of Artzner, Delbaen, Eber and Heath — in particular it is subadditive, so portfolio risk can never exceed the sum of position risks. VaR lacks that property, which produces paradoxes where diversification appears to raise VaR. Second, ES has no jumps: a small change in confidence level produces a smooth change in value. Third, ES weighs the shape of the tail rather than its starting point, so it punishes portfolios with fat tails more than portfolios with thin ones.

How to compute CVaR on a retail account — an illustrative example

Picture an account that starts at 50,000 PLN and runs for twelve months. The equity curve produces the following monthly returns (hypothetical, illustrative example):

Three caveats deserve to be on the table. Twelve months is a small sample — a CVaR computed as the average of two values is unstable, and a single bounce will move it by tens of percent. Second, historical CVaR assumes that the future resembles the past, and Black Swans break that assumption by definition (COVID in March 2020, the Swiss franc in January 2015, the 2008 crisis). Third, CVaR computed from monthly returns ignores weekend gaps and intraday spikes, which on the forex market often dominate the monthly average.

Why a retail trader needs CVaR if the 1 percent rule already exists

The 1 percent rule (or the 0.5 percent conservative variant) governs sizing on a single trade. CVaR governs the portfolio at the monthly scale. The two tools are not in competition — they complement each other. You apply the 1 percent rule before you have any equity curve. You run CVaR after a few months of trading to see whether your fixed-fractional sizing is producing a quiet tail you cannot see in the mean.

In practice it looks like this: a trader with a monthly CVaR₉₅ of minus 11.5 percent is told that the exposure held simultaneously on three USD-correlated pairs will likely produce a deeper loss in a dollar-shock scenario than the 1 percent rule per trade would suggest. We do not change the 1 percent rule. We lower the number of simultaneously open correlated positions or cut leverage. The decision is qualitative; the metric only points the direction.

The most common misreadings of CVaR

• Confusing the confidence level with the probability of loss. CVaR₉₅ does not mean you will lose 11.5 percent in 95 percent of months. It means the average loss inside the 5 percent of months where VaR broke.
• Computing CVaR from daily returns and rescaling to a month. Scaling risk from days to months requires caution — multiplying by the square root of the number of days only holds under the normal-distribution assumption, which the forex market rarely satisfies.
• Treating CVaR as a guarantee. The number describes what already happened. The next tail can be deeper, especially when the regime changes (central-bank interventions, liquidity crises).
• Skipping the Sharpe and Sortino context. CVaR on its own will not tell you whether a strategy is sound. Pair it with the Sharpe ratio and the Sortino ratio so you see the return-to-risk relationship rather than only the size of the tail.

What to do tomorrow to make CVaR work for you

1. Pull the monthly returns from at least the last twelve months out of your trading platform or journal, sort them from worst to best and compute CVaR₉₅ as the average of the worst five percent of observations — with twelve months that is the average of the two worst readings, with twenty four months one to two.
2. Compare the CVaR number against the maximum drawdown you can tolerate emotionally and financially, then write that figure into your risk-management plan next to the 1 percent rule per trade, so both measures are visible when you decide on position sizing.
3. Check whether your positions are correlated: if you simultaneously hold several pairs sharing the same base currency, a CVaR built from isolated positions will understate portfolio risk — when in doubt, cut leverage or reduce the count of simultaneously open correlated trades.
4. Recompute CVaR after every quarter and watch the trend; a rising CVaR while the 1 percent rule stays constant signals either rising market volatility or implicit exposure creep — in both cases it is worth pausing and reading the trade journal carefully.
5. If your portfolio covers many instruments, consider a Monte Carlo simulation seeded with historical returns so you obtain CVaR from many more paths than twelve months — the methodology is described in the article on Monte Carlo strategy simulation.

For more on the regulatory context of the measure, see the ForexMechanics risk management section.