Value at Risk – Methods with Example

Value at Risk (VaR) can be calculated in several different ways, and the method you choose materially affects the answer. This guide walks through the three main methods of calculating VaR — with worked examples — so you can see not just what VaR is, but exactly how it's computed. For the underlying concept, see our guide to what Value at Risk is; here we focus on the methods. It's a core topic in risk qualifications like the FRM.

A quick recap of VaR

Value at Risk estimates the maximum loss a portfolio is not expected to exceed over a set period, at a given confidence level. A one-day 95% VaR of £1m means there's a 95% chance the loss won't exceed £1m in a day — or a 5% chance it will. Every VaR figure has three parts: a time horizon, a confidence level, and the loss amount. The three methods below are simply different ways of arriving at that loss amount.

Method 1: The parametric (variance–covariance) method

The parametric method assumes returns follow a known distribution — usually the normal distribution — and calculates VaR from just two figures: the portfolio's expected return (often taken as zero over a short horizon) and its standard deviation (volatility). You multiply the volatility by the "z-score" for your chosen confidence level (about 1.65 for 95%, or 2.33 for 99%).

Worked example: a £1,000,000 portfolio has a daily volatility of 2%. The one-day 95% VaR is 1.65 × 2% × £1,000,000 = £33,000. In words: on 95% of days the loss should not exceed about £33,000. The method is fast and simple, but its reliance on the normal distribution means it can understate the risk of extreme losses, because real returns have "fatter tails" than the bell curve.

Method 2: Historical simulation

Historical simulation makes no assumption about the shape of the distribution. Instead, it takes a set of actual past returns for the portfolio, ranks them from worst to best, and reads off the loss at the chosen percentile.

Worked example: suppose you have the last 100 daily returns for a portfolio. For a 95% VaR, you find the 5th-worst outcome (the 5th percentile of the 100 days). If that day's loss was £40,000, then the one-day 95% VaR is £40,000. The appeal is that it captures the real historical behaviour of the portfolio, including fat tails and unusual moves. The drawback is that it assumes the past is a good guide to the future — if the historical window didn't include a crisis, the VaR won't reflect one.

Method 3: Monte Carlo simulation

The Monte Carlo method uses a statistical model to generate a very large number of random possible outcomes for the portfolio — often tens of thousands of simulated scenarios — and then reads the VaR off the resulting distribution of outcomes, just as historical simulation does with real data.

Worked example: you run 10,000 simulated daily outcomes for the portfolio based on its modelled behaviour. You sort the 10,000 results, and for a 95% VaR you find the loss at the 5th percentile (the 500th-worst outcome). Whatever that loss is — say £38,000 — is the one-day 95% VaR. Monte Carlo is the most flexible method and handles complex portfolios and non-linear instruments (like options) well, but it's computationally intensive and only as good as the model and assumptions behind it.

Comparing the three methods

Each method trades off simplicity, accuracy and effort differently:

• Parametric — fastest and simplest, but can understate tail risk by assuming normality.
• Historical simulation — intuitive and assumption-light, but limited by the historical window chosen.
• Monte Carlo — most flexible and powerful, but complex and model-dependent.

In practice, the same portfolio can produce noticeably different VaR figures under each method, which is exactly why understanding how VaR is calculated — not just what it means — matters so much. A common further step is to look beyond the VaR threshold at the average size of losses in the tail, a measure known as expected shortfall.

Why it matters for finance professionals

For anyone in risk, knowing the three VaR methods and their trade-offs is essential. The choice of method shapes the risk figure that drives limits, capital and decisions, so understanding each one — and crucially, what each can miss — is fundamental to sound risk measurement and a heavily examined topic in professional risk qualifications.

Frequently asked questions

What are the three methods of calculating VaR?

The parametric (variance–covariance) method, historical simulation, and Monte Carlo simulation. Each estimates the same VaR figure differently, with its own trade-offs in simplicity, accuracy and effort.

How does the parametric method work?

It assumes returns are normally distributed and calculates VaR from the portfolio's volatility multiplied by a z-score for the confidence level. For example, 1.65 × 2% × £1m gives a 95% VaR of £33,000.

What's the difference between historical and Monte Carlo simulation?

Historical simulation reads VaR off actual past returns; Monte Carlo generates a large number of simulated returns from a model and reads VaR off those. Both then take the loss at the chosen percentile.

Which VaR method is best?

It depends. Parametric is fastest but can understate tail risk; historical is intuitive but limited by its data window; Monte Carlo is most flexible but complex. Many firms use more than one and compare.

Build your risk skills with Learnsignal

Calculating Value at Risk is a core risk-management skill. Learnsignal's tutor-led courses, including the FRM, develop the risk-measurement understanding that topics like this build on — with clear teaching that covers both the methods and their limits.