Conditional VaR (CVaR 95%)

What is Conditional VaR (CVaR 95%)?

Conditional VaR, also called expected shortfall or average tail loss, answers the question that plain Value at Risk leaves open. VaR 95% tells you the threshold worse than only 5% of periods, but it goes silent about what happens past that line. CVaR 95% steps over the line and averages everything beyond it. It is the mean return of the worst 5% of periods, so it always sits deeper (more negative) than the VaR it is paired with. If a strategy's VaR 95% is negative 7 percent and its CVaR 95% is negative 12 percent, that reads as: 1 month in 20 was worse than a 7 percent loss, and across those worst months the average loss was about 12 percent.

The metric exists because two strategies can share an identical VaR and behave completely differently in the tail. One might cap its bad months close to the VaR level, while the other occasionally plunges far below it. VaR cannot tell them apart; CVaR can, because it is sensitive to the depth of every loss in the tail, not just the location of the cutoff. That sensitivity is also why regulators and risk committees have steadily migrated toward expected shortfall. The Basel framework, in its post-crisis revisions, replaced VaR with expected shortfall as the headline market-risk measure precisely because VaR was blind to the severity of tail events.

CVaR also has a quieter mathematical virtue: it is a coherent risk measure, meaning it behaves sensibly when you combine positions. Diversifying two holdings can, under VaR, occasionally appear to increase risk, an artifact of VaR ignoring tail shape. CVaR does not suffer that paradox, so it adds up across a portfolio the way intuition says risk should. For a backtest reader the practical takeaway is simpler: CVaR is the number that tells you how much it hurts when it hurts.

Formula

The historical computation is direct. Sort every periodic return from worst to best, take the bottom 5% of the observations, and average them. That average is the CVaR. There is no distributional assumption: the worst months are whatever the data actually delivered, so the number reflects real fat tails rather than a bell-curve approximation. A parametric version exists for normally distributed returns, in which CVaR equals the mean minus sigma times the normal density at the 95th percentile divided by 0.05 (about 2.063 standard deviations below the mean), but that form understates tail severity for real return series, which lose more often and more deeply than a normal distribution predicts.

SledgeKey reports CVaR 95% using the historical method on the strategy's monthly returns over the test window. It identifies the worst 5% of monthly returns (the same tail that defines VaR 95%) and averages them, reporting the result as a monthly figure. Because the worst 5% of a monthly series is a small set, the convention matters at the boundary: when 5% of the sample is not a whole number of months, the calculation averages the clearly-in-tail observations. The reported number is always at least as deep as the VaR, by construction, since it is the mean of values that are all at or below the VaR threshold.

Why CVaR 95% Matters in Backtesting

CVaR informs the part of risk planning that VaR cannot reach: how much capital a bad stretch actually consumes. Knowing the boundary of the worst 5% is useful, but sizing a position to survive only the boundary leaves you exposed to everything deeper in the tail. CVaR gives you the expected severity of those tail months, which is the realistic input for deciding how much you can allocate without an ordinary bad patch becoming an account-ending one. It converts the vague worry of "what if the tail hits" into a number quoted in the same units as your returns.

The failure mode of ignoring CVaR is the one that recurs across financial history: a reassuring VaR figure masking a brutal tail. The 2008 crisis is the canonical example. Institutions reported VaR numbers that looked survivable, yet the losses that actually broke balance sheets came from the region past the VaR cutoff, exactly the region CVaR measures and VaR ignores by design. A strategy can advertise a comfortable VaR 95% and still have a CVaR 95% twice as deep, a signal that its rare bad months are far worse than the boundary suggests.

CVaR is most informative read as a pair with VaR. The gap between them is itself a diagnostic. A small gap means the tail is well-behaved, with the worst months clustered near the cutoff. A large gap means the tail is dangerous, with occasional losses far beyond the line. Read alongside Maximum Drawdown, which captures the worst compounded peak-to-trough event, CVaR rounds out the downside picture: VaR locates the tail, CVaR measures its average depth, and drawdown captures its worst compounded realization.

How SledgeKey Implements CVaR 95%

CVaR 95% appears on the backtest results page as a single monthly figure within the risk metrics, sitting next to VaR 95% so the two can be read together. It is computed from the same monthly returns the rest of the results use: the worst 5% of months are identified, and their average return is reported. Because it is empirical rather than parametric, it reflects the true depth of the strategy's worst months instead of assuming a normal distribution that would flatter the tail.

The benchmark's CVaR 95% is computed the same way over the identical window, so the comparison is the useful reading. A strategy with a shallower (less negative) CVaR than the benchmark delivered milder average losses in its worst months; a deeper CVaR means the tail months hurt more than the index did. Because the figure averages only a handful of observations, it is most stable over long windows and noisy over short ones, where a single extreme month can move it substantially. As a tail measure it always reads at least as deep as the VaR, and the distance between the two tells you how fat the left tail is.

Common Pitfalls

The first pitfall is treating CVaR as a worst-case number. It is an average, not a maximum. CVaR 95% is the mean of the worst 5% of periods, which means roughly half of those tail months were worse than the CVaR itself. A strategy with a CVaR 95% of negative 12 percent can still have suffered an individual month of negative 25 percent, because that single month is one of the observations being averaged. For the genuine worst case, read the worst single month and the maximum drawdown, not the CVaR.

The second pitfall is comparing a CVaR against a VaR as though they measured the same thing. CVaR is always deeper than VaR for the same data, by definition, so a CVaR that looks alarmingly worse than someone else's VaR may simply be the more honest of two measures. The useful comparison is CVaR against CVaR, on the same horizon and the same method. Comparing across methods or measures invites a false conclusion that one strategy is riskier when the difference is purely definitional.

The third pitfall is over-reading a CVaR estimated from too few observations. The worst 5% of a short monthly series may be only one or two months, and an average of one or two numbers is fragile. A single unusual month can dominate the estimate, making the CVaR swing widely if the window shifts by a few months. Treat CVaR from a short backtest as a rough indication of tail severity rather than a precise figure, and lean on longer windows when the number is going to drive a sizing decision.

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