Value at risk (VaR): meaning, methods and a simple example

How much could a portfolio lose on a bad day? Value at risk, or VaR, gives a single number to answer that. This page explains what value at risk means, the three common methods and why it should not be the only risk check.

Quick answer

Value at risk (VaR) is a measure that estimates the maximum loss a portfolio is expected to face over a set time period, at a chosen confidence level. For example, a one-day 99 percent VaR of Rs 1 lakh means that on 99 out of 100 days, the loss should not exceed Rs 1 lakh. It says nothing about how large the loss could be on the remaining bad day.

Key takeaways

• VaR estimates a loss limit for a set period and confidence level.
• A common setting is one day at 99 percent confidence.
• Three main methods are historical, parametric and Monte Carlo.
• Indian exchanges use VaR to set part of the margin.
• VaR does not show how bad losses can get beyond the limit.

What is value at risk?

It is a way to sum up the downside risk of a portfolio in one figure. It needs three things: a time period, such as one day; a confidence level, such as 95 or 99 percent; and the loss amount that results.

The measure became widely used after JP Morgan published its RiskMetrics approach in 1994. Banks, fund houses and regulators use it to track and limit market risk.

A simple example

Suppose your portfolio is worth Rs 10 lakh, and its one-day 95 percent VaR is Rs 30,000. This means that on 95 out of 100 trading days, you expect to lose no more than Rs 30,000. On about 5 days out of 100, the loss could be larger.

The important word is 'larger'. VaR does not say how much larger. A rare bad day could bring a loss of Rs 50,000 or Rs 2 lakh, and the figure alone would not show that.

How is value at risk calculated?

The historical method lines up past returns from worst to best and picks the cut-off point. The parametric method uses a formula based on volatility. The Monte Carlo method runs many simulated scenarios.

Value at risk in Indian markets

Indian clearing corporations use VaR to work out part of the margin traders must pay in the cash market. This VaR margin is designed to cover the large majority of one-day price moves for each share, and it is charged along with other margins.

Banks in India also use VaR-type measures for their trading books, under rules set by the RBI in line with global Basel norms.

What are the limits of VaR?

The biggest limit is that it ignores the size of losses beyond the cut-off. This is why global rules for bank trading books have moved towards expected shortfall, which looks at the average loss in the worst cases.

VaR also relies on past data and assumptions that can break during a crisis. It works best alongside other tools like stress testing, which asks what happens in extreme but possible events.

Frequently Asked Questions