Estimate 99% Confidence Interval Downside Risk

This guide explains the main ways to calculate VaR, worked examples, how to scale VaR to longer periods, expected shortfall, and the important limits of VaR.

Three ways to calculate VaR

Parametric VaR

Assume returns follow a normal distribution and use the portfolio's standard deviation:

VaR = portfolio value × z × daily standard deviation

where z is 1.645 for 95% confidence and 2.326 for 99% confidence. For short periods, the average return is usually small enough to ignore.

Historical VaR

Take the portfolio's actual daily returns over a past period, such as the last 500 days, sort them from worst to best, and read off the loss at the chosen percentile. For 99% VaR with 500 days, that is the fifth-worst day. Historical VaR makes no assumption about the shape of returns.

Monte Carlo VaR

Simulate thousands of possible outcomes using a model of how the portfolio's prices move, then read the percentile from the simulated results. This method handles options and complex positions better than the parametric method.

A worked example

A portfolio is worth ₹10 lakh, and its daily returns have a standard deviation of 1.2%.

• 95% one-day VaR: ₹10,00,000 × 1.645 × 1.2% = ₹19,740
• 99% one-day VaR: ₹10,00,000 × 2.326 × 1.2% = ₹27,912

So on about 1 day in 100, the portfolio could be expected to lose more than about ₹27,900, if returns behave as the normal distribution assumes.

Scaling VaR to longer periods

Under the same assumptions, VaR scales with the square root of time:

10-day VaR = 1-day VaR × √10

The 10-day 99% VaR in the example is about ₹27,912 × 3.16 = ₹88,265. This shortcut assumes returns are independent from day to day and that the portfolio does not change, which is rarely exactly true.

Expected shortfall

VaR tells you the threshold, not how bad losses are beyond it. Expected shortfall, also called conditional VaR, is the average loss on the days that are worse than VaR. If the 99% VaR is ₹27,912, the expected shortfall might be ₹35,000 or more, depending on how heavy the tail of losses is. Many regulators now prefer expected shortfall because it captures the size of extreme losses.

VaR for options positions

Parametric VaR works poorly for options because option values do not change linearly with the underlying. A short straddle may lose little on most days and a great deal on a large move, a pattern a standard deviation does not capture. For options, use historical or Monte Carlo methods that reprice the positions at each simulated level, or look at the full payoff in the option profit calculator.

The limits of VaR

• Fat tails. Market returns have more extreme days than the normal distribution predicts. Parametric VaR underestimates the frequency of large losses.
• It says nothing beyond the threshold. A 99% VaR does not describe the worst 1% of days.
• History may not repeat. Historical VaR only knows the period it was calculated on. A calm period produces a low VaR just before a volatile one.
• Correlations change. In a crisis, assets that normally move independently often fall together.
• Liquidity. VaR assumes positions can be closed at market prices, which may not hold in a crash.

VaR is a useful summary of normal risk, not a guarantee against extreme loss. Use it alongside stress tests and drawdown limits.

Using VaR in trading

• Set a daily risk budget, such as keeping 99% one-day VaR below 2% of capital.
• Compare strategies on the same basis.
• Watch changes. A rising VaR shows the portfolio's risk is growing, whether from larger positions or higher volatility.
• Combine with hard limits. An MTM stop loss caps actual daily losses, which VaR only estimates.

For other risk measures, see the maximum drawdown calculator and the Sharpe ratio calculator.

Frequently asked questions

Sources

• Jorion, P. (2006). Value at Risk: The New Benchmark for Managing Financial Risk. McGraw-Hill
• Artzner, P., Delbaen, F., Eber, J.-M. and Heath, D. (1999). Coherent Measures of Risk. Mathematical Finance, 9(3), 203–228