What Is Value at Risk (VaR)? Methods & Calculations

Value at Risk is a measure of market risk on a group of assets. It measures the worst expected loss over a given horizon under normal market conditions at a given confidence level.

KEY TAKEAWAYS

• Extreme price movements are rare, however, they are important and dangerous for financial institutions. Value at Risk has become a widely used measure for market risk.
• Future losses are uncertain. Find a loss that you are 99% sure is worse than whatever will occur. This is the Value at Risk.

Methods of Calculating Value at Risk

There are three methods of calculating Value at Risk.

1. Historical Method

The historical method is the simplest method for calculating Value at Risk. It is based on historical data. Implicitly assumes that the markets will behave in the future as they behaved in the past.

Calculation Methodology of Historical VaR:

• Identify the parameters of the market that influence the value of the portfolio
• Calculate the daily returns of these market parameters (on a large sample of historical data – two or more years)
• Apply these returns from the past to today’s market data and recalculate the value of the portfolio
• For each scenario replayed, calculate the profit or loss

2. Parametric Method

The parametric method, also known as the variance-covariance method, is a method that relies on the two factors – an expected return and a standard deviation. This method assumes that returns are normally distributed.

Calculation Methodology of Parametric Method:

• Estimate the mean and covariance matrix of asset returns
• Determine the portfolio’s expected return and standard deviation
• Calculate the value at risk using the portfolio’s standard deviation

3. Monte Carlo Simulation

The Monte Carlo method is a method, which can generate lots of data & scenarios to estimate the return of an asset. This method of Value at Risk computation is suitable for a great range of risk measurement problems.

Calculation Methodology of Monte Carlo Simulation:

• Break the portfolio down into the elemental risk components
• Create a large number of potential future states of the world for each risk component
• Revalue the portfolio under each potential future state of the world
• Create a distribution from the resulting changes in value and select the desired confidence interval

SEE ALSO: Numerical Methods in Finance

The Bottom Line

Value at Risk play an important role in quantifying risk exposure. It is an estimate, with a predefined confidence interval, of how much one can lose from holding a position over a set horizon. Potential horizons may be one day for typical trading activities or a month or longer for portfolio management.

This has been a guide to what methods used to calculate value at risk. Here we explain the calculation methodology for each method. You may also check out these additional resources from Money and Financial Literacy:

• Interest Rate – Definition & Key Factors That Influence Interest Rate
• Stochastic Modeling – Definition, History, Applications
• Fixed-Income Securities – Definition & Types