Value at Risk & CVaR
Trading Intelligence
10 min read
var95cvar95
Understand VaR and Conditional Value at Risk (Expected Shortfall) for measuring tail risk in your trade distribution.
Loading
10 min read
Understand VaR and Conditional Value at Risk (Expected Shortfall) for measuring tail risk in your trade distribution.
VaR tells you the door to the danger zone. CVaR tells you what happens once you walk through it.
Value at Risk is a statistical measure that quantifies the maximum expected loss over a given time period at a specific confidence level. It answers the question: "What is the worst loss I can expect under normal market conditions?"
For example, a daily VaR of $500 at 95% confidence means:
VaR is defined by the percentile of the loss distribution. At 95% confidence, VaR is the 5th percentile of your return distribution. At 99% confidence, it is the 1st percentile.
The concept originated in institutional finance -- banks and hedge funds use it to set capital reserves. But for discretionary and systematic traders, VaR provides a concrete, intuitive risk boundary that connects directly to position sizing and drawdown management.
There are three primary approaches:
The simplest method. Take your actual trade returns (or daily PnL), sort them from worst to best, and find the value at the desired percentile.
For 95% VaR with 100 trades:
Advantages: No assumptions about distribution shape. Uses your actual data. Disadvantages: Requires sufficient historical data. Past distribution may not represent future conditions.
Assumes returns follow a normal distribution and calculates VaR using the mean and standard deviation:
VaR = Mean - (Z-score * Standard Deviation)
For 95% confidence, the Z-score is 1.645. For 99%, it is 2.326.
Advantages: Simple formula, easy to compute. Disadvantages: Assumes normality. Trading returns are almost never normally distributed -- they have fat tails and skewness, which means parametric VaR systematically underestimates extreme losses.
Simulates thousands of possible return paths based on your strategy's statistical properties, then extracts the VaR percentile from the simulated distribution.
Advantages: Can model complex, non-normal distributions. Flexible. Disadvantages: Computationally intensive. Quality depends on the accuracy of input assumptions.
For most active traders, Historical VaR is the most practical and reliable method. It requires no distributional assumptions and directly reflects your actual trading outcomes.
VaR has a critical limitation: it tells you nothing about the severity of losses beyond the threshold.
A 95% VaR of $500 says losses will exceed $500 on 5% of days. But will those bad days produce losses of $510 or $5,000? VaR is silent on this question.
This is known as the "VaR break" problem. Two strategies can have identical VaR but completely different tail risk profiles:
| Strategy | 95% VaR | Worst 5% Losses |
|---|---|---|
| A | -$500 | -$510, -$520, -$530, -$540, -$550 |
| B | -$500 | -$600, -$900, -$1,500, -$2,800, -$5,000 |
Both have the same VaR. But Strategy B has catastrophic tail risk that VaR completely hides. This is why VaR alone is dangerous as a risk metric.
Conditional Value at Risk (CVaR), also called Expected Shortfall (ES), addresses VaR's blind spot. It measures the average loss in the worst-case scenarios -- specifically, the mean of all losses beyond the VaR threshold.
For 95% CVaR:
Using the example above:
Now the difference is stark. Strategy B's CVaR is four times worse than Strategy A's, revealing the hidden tail risk that VaR missed entirely.
CVaR is a strictly more informative metric than VaR for several reasons:
It looks inside the tail. VaR draws a line in the sand. CVaR explores what lies beyond that line. For traders who care about survival, what happens in the worst 5% of outcomes matters more than where the boundary sits.
It is coherent. In mathematical risk theory, CVaR satisfies all properties of a "coherent risk measure" -- including subadditivity, which means diversifying a portfolio always reduces or maintains CVaR. VaR does not have this property, which can lead to paradoxical results where adding a hedging position appears to increase risk.
It penalizes fat tails. Trading returns are fat-tailed. Extreme losses occur more frequently than a normal distribution predicts. CVaR naturally captures this because it averages the actual extreme outcomes, however severe they may be.
It drives better decisions. When you optimize a strategy to minimize CVaR rather than VaR, you are directly reducing the expected damage of worst-case scenarios, not just the probability of crossing a threshold.
Using your last 200 trades at 95% confidence:
Suppose your results show:
This means:
1.2R or less2.1RIf your CVaR is significantly larger than your VaR, you have fat-tailed downside risk. This is common in strategies that occasionally experience gap moves, slippage beyond stops, or correlated drawdowns.
You can use CVaR to set maximum position sizes:
Max Position Size = Acceptable Loss / CVaR per unit
If your account can tolerate a maximum single-trade loss of $1,000 and your 95% CVaR is $200 per contract, you should trade no more than 5 contracts. This ensures that even in worst-case scenarios, your loss stays within acceptable bounds.
Sample size matters. With fewer than 50 trades, the 5th percentile is based on 2-3 data points. The estimate will be noisy and unreliable. Aim for at least 100 trades, ideally 200+.
Stationarity assumption. Both VaR and CVaR assume the past distribution is representative of the future. Regime changes, liquidity shifts, and market structure evolution can invalidate historical estimates.
Confidence level choice. 95% is standard but somewhat arbitrary. For capital preservation, 99% may be more appropriate. The tradeoff: higher confidence requires more tail data and produces noisier estimates.
Not a worst case. CVaR is the average of tail losses, not the absolute worst outcome. Your actual worst loss will exceed CVaR by definition.
| Dimension | VaR | CVaR |
|---|---|---|
| Definition | Loss at a specific percentile | Average loss beyond that percentile |
| Tail sensitivity | None (ignores losses beyond threshold) | High (averages all tail losses) |
| Coherent risk measure | No | Yes |
| Ease of calculation | Simple | Simple (requires one extra step) |
| Conservative | Less | More |
| Fat-tail awareness | Poor | Strong |
Adjust the skewness to see how the distribution shape changes. With negative skew, the left tail (losses) extends further — this is where VaR and CVaR become critical risk measures.