Value at Risk

Value at Risk, almost always shortened to VaR, answers one plain question: how much could this position lose, most of the time, over the next few days?

It is not a guess. It is built from how much the underlying has actually moved in the past — its volatility — combined with a confidence level the risk manager chooses, commonly 95% or 99%.

Say a position has a one-day VaR of Rs 2 lakh at 99% confidence. That means the loss on that position over the next day should not exceed Rs 2 lakh on 99 days out of 100. It does not mean the loss can never be more than Rs 2 lakh — the remaining 1% is exactly the days it can, and VaR says nothing about how much worse those days could be.

The XXI-A workbook introduces VaR twice, both times as the reason a number exists rather than as a method to compute it.

In the chapter on securities markets, initial margin — the money a clearing corporation collects from both parties to a trade before it lets the trade settle — is described as "a percentage of transaction value arrived at based on concept of Value At Risk philosophy" (Chapter 2). In the derivatives chapter, VaR is defined directly as "a statistical measure of loss for the contract value within a defined confidence interval," and the workbook says the margin the clearing house charges depends on both the price volatility of the underlying and the value-at-risk for the contract (Chapter 5).

Neither chapter gives a confidence level or holding period of its own — XXI-A explains the concept margin rests on, not the arithmetic behind a specific figure. What it does establish is the chain a portfolio manager has to plan around: higher volatility raises VaR, which raises initial margin, which ties up more of the client's capital as margin rather than as investment.

One-day VaR (illustrative) = Position value × daily volatility × confidence multiplier (2.33 for 99% confidence, 1.65 for 95%)

The XXI-A workbook does not publish a VaR calculation, so the figures below are illustrative only, built to show how the concept it describes would work in practice.

Portfolio manager Rohan Mehta holds a position worth Rs 40,00,000 in Nifty futures for a client. The index has shown daily volatility of roughly 1.5%, and the clearing corporation is assumed to set margin off a 99% confidence one-day VaR.

One-day VaR = Rs 40,00,000 × 1.5% × 2.33 = Rs 1,39,800

On 99 days out of 100, the position should not lose more than roughly Rs 1,39,800 in a single day. If the clearing corporation sets initial margin at, say, 1.5 times this VaR figure as a buffer, the client's initial margin on this one position becomes roughly Rs 2,09,700 — capital that sits with the clearing corporation instead of being deployed elsewhere in the portfolio.

On the 1 day in 100 that the loss exceeds Rs 1,39,800 — an overnight policy shock that gaps the index down 4%, say — the mark-to-market loss can run to several lakh more. VaR gave no warning of how much further it could go; it only estimated the threshold, not the worst case.

Chapter 2 (Introduction to Securities Markets) uses VaR to explain why initial margin exists at all, and Chapter 5 (Derivatives) defines the term directly while explaining why margin depends on both volatility and VaR. The XXI-A question is conceptual, not computational: why does a derivatives position tie up more margin than an equity position of the same value, and what single concept explains it. The term recurs across several other NISM papers wherever margining or portfolio risk is taught; answer an XXI-A question from what this workbook actually says — a confidence-interval loss measure driving margin — rather than a fuller VaR model seen elsewhere.

• VaR is a threshold, not a ceiling. A 99% one-day VaR of Rs 1.4 lakh does not cap the loss at Rs 1.4 lakh — it means losses beyond that happen on roughly 1 day in 100, with no limit stated on how large they can be.
• A higher confidence level produces a bigger VaR number, not a smaller one. Moving from 95% to 99% confidence widens the estimated loss; it is not extra safety on top of a fixed number.
• Initial margin and mark-to-market margin are different tools. The workbook distinguishes initial margin — collected upfront and VaR-based — from MTM margin, the notional loss an open position has already suffered over a period from price movement. VaR feeds the first, not the second.
• XXI-A gives no confidence level or holding period of its own. Treat any specific number in a question as information given in that question, not as a workbook fact to recall.