Value at Risk (VaR)

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.

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.

Purpose

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

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

Value at Risk vs Conditional VaR (Expected Shortfall)

Practical example

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 it 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 mistakes

• 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

Professional usage

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.

Frequently asked questions

Voice search & related questions

Natural-language questions people ask about Value at Risk (VaR).

Sources & references

Last reviewed 12 July 2026. Educational content only — not investment advice. Markets and rules change; verify current conventions with SEBI, NSE/BSE and your broker.