Value at Risk (VaR)
Value at Risk (VaR) is the loss that a portfolio is not expected to exceed over a given horizon at a given confidence level, so a one-day 95 percent VaR of ₹20,000 means that on 95 percent of days the loss should be no worse than ₹20,000.
Quick Answer
Value at Risk (VaR) is the loss that a portfolio is not expected to exceed over a given horizon at a given confidence level, so a one-day 95 percent VaR of ₹20,000 means that on 95 percent of days the loss should be no worse than ₹20,000.
Definition of Value at Risk (VaR)
Value at Risk (VaR) measures the loss a portfolio should not exceed over a set horizon at a given confidence level, for example a 1-day 95% VaR.
Key takeaways on Value at Risk (VaR)
- VaR is the loss not expected to be exceeded at a set confidence over a set horizon
- Parametric VaR is z × σ × V; historical VaR reads a quantile of past losses
- It always needs a confidence level and a horizon to be meaningful
- Its blind spot is the tail: it never tells you how bad the losses beyond it are
Value at Risk (VaR) at a glance
| Family | Tail-risk metric |
|---|---|
| Formula | Parametric 1-day VaR = z × σ × V (z ≈ 1.645 at 95%, 2.33 at 99%) |
| Measures | Loss not exceeded at a confidence level over a horizon |
| Typical read | Quote horizon and confidence together, e.g. 1-day 95% |
| Blind spot | Says nothing about how bad the tail beyond it is — pair with CVaR |
Value at Risk (VaR) in simple words
Value at Risk answers a specific question: over the next day or week, how bad could a normal-but-bad loss be, and how often would it be exceeded. A one-day 95 percent VaR of ₹20,000 says that on about 19 of every 20 days the loss stays within ₹20,000, and on roughly one day it is worse. It is a single, comparable risk number, but its most dangerous feature is what it hides: it tells you the threshold you rarely breach, not how catastrophic the loss is on the days you do breach it.
Why Value at Risk (VaR) matters
This page defines Value at Risk, shows how the parametric and historical methods compute it, ties it to confidence level and horizon, and stresses its central blind spot: it says nothing about the size of losses beyond the quantile.
Visual explanation
Value at Risk (VaR)
Value at Risk (VaR) — professional explanation
What VaR is, precisely
Value at Risk is a quantile of the loss distribution: the loss level that will not be exceeded with a stated probability over a stated horizon. It always has three parts, a confidence level (say 95 or 99 percent), a horizon (say one day or ten days), and an amount (in rupees or as a percentage). A one-day 99 percent VaR of ₹35,000 means that on 99 percent of days the loss should be no more than ₹35,000, and on the remaining 1 percent it is worse by an unspecified amount. VaR is therefore a statement about a threshold and a frequency, not about the worst case, and quoting a VaR without its confidence level and horizon is meaningless.
Parametric VaR and its normality assumption
The parametric or variance-covariance method assumes returns are normally distributed and computes VaR as z × σ × V, where σ is the portfolio's volatility over the horizon, V is the portfolio value and z is the z-score for the confidence level, about 1.645 at 95 percent and 2.33 at 99 percent. It is fast and needs only a volatility and, for a portfolio, a correlation matrix, but it inherits the normal distribution's thin tails. Real market returns have fatter tails, so parametric VaR systematically understates the probability and size of extreme losses, and the understatement is worst exactly in the tail events it is meant to warn about.
Historical and Monte Carlo VaR
Historical VaR makes no distributional assumption: it takes the actual distribution of past returns, sorts the losses, and reads off the loss at the chosen quantile, for example the fifth-worst day in a hundred for a 95 percent one-day VaR. It captures the fat tails present in the sample but assumes the future resembles that sample and is blind to any shock larger than anything in the window. Monte Carlo VaR simulates many possible return paths from an assumed model and reads the quantile from the simulated losses, offering flexibility at the cost of depending on the model chosen. All three methods answer the same question and can give materially different numbers.
Scaling across horizons and confidence levels
VaR grows with both the horizon and the confidence level. Under the common square-root-of-time rule, a ten-day VaR is about √10 times the one-day VaR, a scaling that assumes returns are independent and identically distributed and that breaks down when volatility clusters or autocorrelation is present. Raising the confidence from 95 to 99 percent raises the z-score from 1.645 to 2.33, so the VaR figure rises even though the underlying portfolio is unchanged. Because these choices move the number so much, two VaR figures are only comparable if they share the same horizon and confidence level.
The tail blind spot and regulatory context
The defining weakness of VaR is that it is silent about the severity of losses beyond the threshold. A 99 percent VaR of ₹35,000 is consistent with an actual bad-day loss of ₹40,000 or of ₹4,00,000; VaR does not distinguish them, because it only marks where the tail begins, not how deep it goes. This is why Conditional VaR, the average loss beyond the VaR, was developed as a complement, and why regulators and the Basel framework moved toward Expected Shortfall. A further subtlety is that VaR is not sub-additive in general, so the VaR of a combined portfolio can exceed the sum of the parts, an awkward property for a risk measure.
Using VaR without being lulled by it
VaR is genuinely useful as a common yardstick for comparing the risk of different books, setting exposure limits and communicating a normal bad-day loss to non-specialists. The failure mode is treating the VaR number as the worst case, sizing to it, and being surprised when a tail event delivers a multiple of it. Sound practice reads VaR alongside Conditional VaR, stress tests and maximum drawdown, backtests how often the VaR was actually breached, and remembers that the days that ruin accounts live in the tail VaR deliberately ignores.
Formula for Value at Risk (VaR)
Parametric 1-day VaR = z × σ × V; z ≈ 1.645 at 95%, 2.33 at 99%. Historical VaR = the loss at the chosen quantile of the sorted loss distribution.
z = the z-score for the chosen confidence level (about 1.645 for 95 percent, 2.33 for 99 percent), assuming a normal distribution. σ = the portfolio's return volatility (standard deviation) over the horizon, e.g. daily volatility for a one-day VaR. V = the portfolio value in ₹. Confidence level = the probability that the loss stays within the VaR (95 or 99 percent). Horizon = the time period over which the loss is measured (one day, ten days). Historical VaR instead reads the loss at the matching percentile of actual past losses, making no normality assumption.
How professionals apply Value at Risk (VaR)
Risk desks use VaR as one lens among several, never as the worst case. They compute it by more than one method, backtest how often actual losses exceeded the VaR to validate the model, and always pair it with Conditional VaR and explicit stress tests that impose historical and hypothetical shocks. Regulators moved the Basel market-risk framework from VaR toward Expected Shortfall precisely because VaR ignores tail severity, and disciplined practitioners size for the tail beyond the VaR, not for the VaR itself.
Practical example: Value at Risk (VaR)
Illustrative example (Indian market)
A trader holds a ₹5,00,000 equity-index portfolio with a daily volatility of 1.5 percent, so the one-day standard deviation in rupees is 0.015 × ₹5,00,000 = ₹7,500. The parametric one-day 95 percent VaR is 1.645 × ₹7,500 ≈ ₹12,340, and the one-day 99 percent VaR is 2.33 × ₹7,500 ≈ ₹17,475. So on about 95 percent of days the loss should stay within roughly ₹12,300, and on about 99 percent within ₹17,500, if returns were normal. The trap is that on the worst 1 percent of days, the loss is not ₹17,500 but some larger, unstated amount, and because equity-index returns have fatter tails than the normal model assumes, both figures understate how bad those rare days actually get. Scaling to a ten-day horizon multiplies by about √10, giving a ten-day 99 percent VaR near ₹55,000, under the independence assumption.
Around events such as a Union Budget, RBI policy or index expiry, Indian index returns can gap far beyond a normal-distribution estimate, so a parametric VaR calibrated on calm days will understate the loss on those days. A trader who treats the 99 percent VaR as the worst case can face a single-session loss several times the VaR when a fat-tailed event lands.
Value at Risk vs Conditional VaR (Expected Shortfall)
| Aspect | Value at Risk (VaR) | Conditional VaR (CVaR) |
|---|---|---|
| Question answered | How bad is the threshold I rarely breach | How bad is the average loss when I do breach it |
| Reads the tail? | No; only marks where the tail begins | Yes; averages the losses beyond VaR |
| Sensitive to extreme losses | Insensitive once past the quantile | Fully sensitive to tail severity |
| Sub-additive | Not in general | Yes; a coherent risk measure |
| Regulatory trend | Historically dominant | Basel shift toward Expected Shortfall |
Advantages
- Summarises portfolio risk in one comparable, communicable number
- Ties an explicit probability and horizon to a rupee loss threshold
- Works across asset classes and aggregates to the portfolio level
- Useful for setting exposure limits and comparing books
- Multiple methods (parametric, historical, Monte Carlo) allow cross-checking
Limitations
- Blind spot: VaR says nothing about the size of losses beyond the quantile, so it is silent on how deep the tail goes
- Parametric VaR assumes normality and understates real fat tails
- Historical VaR is blind to any shock larger than its sample window
- Not sub-additive in general, so it can misrepresent diversification
- Square-root-of-time scaling assumes independent returns, which fails when volatility clusters
Why Value at Risk (VaR) matters in practice
- Frames a normal bad-day loss for limits and communication
- Its blind spot is why tail events routinely exceed the quoted figure
Common misconceptions about Value at Risk (VaR)
Misconception: VaR tells you your worst-case loss.
Reality: No, and treating it as the worst case is a serious error. VaR is a threshold rarely breached, not a maximum. On the days the loss exceeds VaR, it can be a small or a very large multiple of the VaR figure, and VaR gives no information about which.
Common mistakes with Value at Risk (VaR)
- Treating VaR as the maximum or worst-case loss rather than a threshold
- Quoting a VaR without stating its confidence level and horizon
- Relying on parametric VaR while ignoring its thin-tail assumption
- Sizing positions to the VaR figure as if the tail beyond it were harmless
- Assuming a 95 percent VaR breach is rare rather than expected on 1 in 20 days
- Scaling to longer horizons with the square-root rule despite volatility clustering
Frequently asked questions about Value at Risk (VaR)
How is VaR calculated?
The parametric method computes VaR as z × σ × V, where z is the confidence z-score, σ the portfolio volatility over the horizon and V the portfolio value. The historical method instead reads the loss at the chosen percentile of actual past returns, and Monte Carlo simulates paths to read the quantile.
What does a 95 percent VaR mean?
It means that with 95 percent probability the loss over the horizon will not exceed the VaR amount, so the loss is expected to be worse on about 5 percent of periods, roughly one day in twenty. The 5 percent breach is expected, not a rare failure.
What is the z-score for 95 and 99 percent VaR?
Under the normal assumption, the one-tailed z-score is about 1.645 for 95 percent confidence and about 2.33 for 99 percent. Raising the confidence level raises the z-score, so a 99 percent VaR is larger than a 95 percent VaR on the same portfolio.
What is the difference between parametric and historical VaR?
Parametric VaR assumes returns are normally distributed and uses volatility and a z-score, which is fast but understates fat tails. Historical VaR makes no distributional assumption and reads a quantile from actual past losses, capturing observed tails but remaining blind to any shock bigger than its sample.
How do I scale VaR to a longer horizon?
A common rule multiplies the one-day VaR by the square root of the number of days, so a ten-day VaR is about √10 times the one-day figure. This assumes returns are independent and identically distributed and breaks down when volatility clusters, so it is an approximation.
Why does VaR understate risk in India around events?
Because parametric VaR assumes normal returns while Indian index returns gap sharply around events like the Budget, RBI policy and expiry. Those fat-tailed moves are more frequent and larger than the normal model predicts, so a VaR calibrated on calm days underestimates the loss on event days.
Is VaR additive across positions?
Not in general. VaR is not sub-additive, meaning the VaR of a combined portfolio can exceed the sum of the individual VaRs, which is an undesirable property for a risk measure. Conditional VaR is sub-additive and therefore coherent, another reason it is preferred for aggregation.
Voice search questions about Value at Risk (VaR)
Natural-language questions people ask about Value at Risk (VaR).
Does VaR tell me my worst possible loss?
No, and that is the trap. It only tells you a level you rarely go past. On the bad days you do go past it, the loss can be much larger.
Which is more conservative, ninety-five or ninety-nine percent VaR?
Ninety-nine percent. It looks further into the tail, so the number is bigger for the same portfolio, but it also leans harder on the model being right.
Why can a real loss beat my VaR by so much?
Because markets have fat tails, especially around big events. VaR based on a normal bell curve underestimates how often and how far those rare moves go.
People also ask
Related questions answered in dedicated explainers.
Sources & references
- Jorion, P. (2007). Value at Risk: The New Benchmark for Managing Financial Risk (3rd ed.). McGraw-Hill.
- Dowd, K. (2005). Measuring Market Risk (2nd ed.). John Wiley & Sons.
Published 13 July 2026. Educational content only — not investment advice. Markets and rules change; verify current conventions with SEBI, NSE/BSE and your broker.