Value at Risk (VaR)

The intuition

Daily returns cluster around zero with a spread that volatility measures. If you know the spread, you can say how large a loss would be unusual: a two-standard-deviation move happens on roughly one day in forty, a 2.33-standard-deviation move on one day in a hundred. VaR takes that threshold and expresses it in rupees on your position. It does not say how bad the worst day could be, only where the ordinary bad days end. Exchanges therefore pair it with an extreme loss margin, which exists precisely for the days beyond VaR.

Formula

Parametric one-day VaR at confidence c = z_c × σ_daily × position value, where z_c is 2.33 at 99% and 1.65 at 95%

Multi-day VaR ≈ one-day VaR × √(days), under the assumption that daily returns are independent

Daily volatility is usually estimated with an exponentially weighted moving average so that recent days matter more, which is the method SEBI’s risk framework specifies for the cash segment.

Worked example (illustrative prices)

Suppose NIFTY is at 24,000 and its estimated daily volatility is 0.9%. One lot of NIFTY futures (65 units) has a notional of ₹15,60,000.

Measure	Calculation	Amount
One-day 99% VaR	2.33 × 0.9% × 15,60,000	about ₹32,700
One-day 95% VaR	1.65 × 0.9% × 15,60,000	about ₹23,200
Five-day 99% VaR	32,700 × √5	about ₹73,100
Six-sigma margin rate (cash-segment style)	6 × 0.9%	5.4%, so the 9% floor would apply

The last row shows why exchange margins are far above a one-day VaR: the cash-segment rule uses six standard deviations and a floor, and the derivatives segment uses SPAN scan ranges set from volatility, so that the margin covers moves well past the 99% point. A trader who sizes a position so that the one-day 99% VaR is 1% of capital would, on this example, hold about half a lot per ₹65 lakh of capital, which is a useful reality check on leverage.

Why it matters

• It is the basis of cash-segment margins. Every delivery and intraday trade in a stock is margined at VaR plus ELM, and those same rates drive the delivery margin on stock F&O in expiry week.
• It is the right unit for position sizing. Fixing a VaR budget per trade keeps exposure consistent across a quiet market and a volatile one, because the rupee limit shrinks automatically as volatility rises.
• Portfolio VaR rewards diversification. Positions that do not move together have a combined VaR below the sum of their parts, which is the same logic SPAN applies within an underlying.
• It is blind to the tail. VaR says nothing about losses beyond the threshold, so a short option book with small VaR can still carry a large loss on a gap day. Stress tests and the exposure margin fill that gap.

Common mistakes

• Reading VaR as the worst case. It is the boundary of ordinary losses; on one day in a hundred the loss is larger, sometimes much larger.
• Scaling by time without thought. The square-root rule assumes independent returns and breaks down around events such as results, policy days and expiry.
• Using a long, equally weighted history during a volatility shift. The exchange uses exponentially weighted volatility for a reason: last month’s calm understates today’s risk.
• Applying linear VaR to options. An option’s loss is not proportional to the move, so VaR on an option book should be computed by repricing across scenarios, as SPAN does.

Indian specifics

SEBI’s cash-segment risk framework, restated in its 2020 circular, classifies stocks by liquidity. Group I stocks, which traded on at least 80% of days over the previous eighteen months with a mean impact cost of 1% or less, carry a VaR margin of six sigma with a 9% floor; Group II stocks, liquid but with higher impact cost, six sigma with a 21.5% floor; Group III, illiquid stocks, 50% if traded at least once a week and 75% otherwise. Broad-market index ETFs have a 6% floor. An extreme loss margin, generally 3.5% for Group I, is charged on top. A SEBI working group recommended in early 2026 that cash-segment margins be rationalised with a 12.5% floor; that proposal had not been notified as a circular when this page was written. In the derivatives segment the equivalent of VaR is the SPAN price scan range, and the ELM is the exposure margin.

FAQ

What does Value at Risk mean?

The loss a position should not exceed over a set horizon at a set confidence, such as 99% over one day; larger losses occur about one day in a hundred.

How is VaR margin calculated on NSE for stocks?

Six sigma of daily volatility with floors of 9% (Group I) and 21.5% (Group II); Group III at 50% or 75%; plus extreme loss margin.

What is the difference between VaR and SPAN margin?

VaR is a loss threshold used for cash-segment margins; SPAN is a scenario-based system for F&O portfolios that handles options' non-linear payoffs.

Why is VaR plus ELM charged instead of VaR alone?

VaR covers ordinary bad days; ELM covers the tail beyond it.

How can a trader use VaR?

Set a VaR budget per trade (say 1% of capital at 99% one-day) so position size shrinks when volatility rises.

Related terms

• Historical volatility, the sigma in the formula
• SPAN margin, the derivatives-segment counterpart
• Exposure margin, the tail cushion
• Delivery margin, where cash-segment VaR reaches F&O
• Realized volatility, measured from past returns
• Risk management rules, turning VaR into limits