VaR is an estimate of an amount of money. It is based on probabilities, so cannot be relied on with certainty, but is rather a level of confidence which is selected by the user in advance. VaR measures the volatility of a company’s assets, and so the greater the volatility, the higher the probability of loss.

**Definition**

Essentially VaR is a measure of the volatility of a bank trading book. It is the characteristics of volatility that traders, risk managers and others wish to become acquainted with when assessing a bank’s risk exposure. The mathematics behind measuring and estimating vola- tility is a complex business, and we do not go into it here. However, by making use of a volatility estimate, a trader or senior manager can gain some idea of the risk exposure of the trading book, using the VaR measure.

VaR is defined as follows:

*VaR is a measure of market risk. It is the maximum loss which can occur with X% confidence over a holding period of t days.*

VaR is the expected loss of a portfolio over a specified time period for a set level of probability. So, for example, if a daily VaR is stated as £100,000 to a 95% level of confidence, this means that during the day there is a only a 5% chance that the loss will be greater than £100,000. VaR measures the potential loss in market value of a portfolio using estimated volatility and correlations. It is measured within a given confidence interval, typically 95% or 99%. The con- cept seeks to measure the possible losses from a position or portfolio under ‘normal’ circumstances. The definition of normality is critical to the estimation of VaR and is a statistical concept; its importance varies according to the VaR calculation methodology that is being used.

Broadly speaking, the calculation of a VaR estimate follows four steps:

- Determine the time horizon over which the firm wishes to estimate a potential loss – this horizon is set by the user. In practice, time horizons of 1 day to 1 year have been used. For instance, bank front-office traders are often interested in calculating the amount they might lose in a 1-day period. Regulators and participants in illiquid markets may want to estimate exposures to market risk over a longer period. In any case a time horizon must be specified by the decision-maker.
- Select the degree of certainty required, which is the confidence level that applies to the VaR estimate – knowing the largest likely loss a bank will suffer 95 times out of 100, or in fact on 1 day out of 20 (i.e., a 95% degree of confidence in this estimate, or confidence interval) may be sufficient. For regulatory require- ments a 99% confidence interval may be more appropriate. Senior management and shareholders are often interested in the potential loss arising from catastrophe situations, such as a stock market crash, so for them a 99% confidence level is more appropriate.
- Create a probability distribution of likely returns for the in- strument or portfolio under consideration – several methods may be used. The easiest to understand is a distribution of recent historical returns for the asset or portfolio which often looks like the curve associated with the normal distribution. After determining a time horizon and confidence interval for the estimate, and then collating the history of market price changes in a probability distribution, we can apply the laws of statistics to estimate VaR.
- Calculate the VaR estimate – this is done by observing the loss amount associated with that area beneath the normal curve at the critical confidence interval value that is statistically associated with the probability chosen for the VaR estimate in Step 2.

These four steps will in theory allow us to calculate a VaR estimate ‘longhand’, although in practice mathematical models exist that will do this for us. Bearing these steps in mind, we can arrive at a practical definition of VaR not much removed from our first one:

*VaR is the largest likely loss from market risk (expressed in currency units) that an asset or portfolio will suffer over a time interval and with a degree of certainty selected by the user.*

There are a number of methods for calculating VaR, all logically sustainable, and estimates prepared using the different method- ologies can vary dramatically. At this point it is worthwhile remind- ing ourselves what VaR is not. It is not a unified method for measuring risk, as the different calculation methodologies each produce different VaR values. In addition, as it is a quantitative statistical technique, VaR only captures risks that can be quantified. Therefore, it does not measure (and nor does it seek to measure) other risks that a bank or securities house will be exposed to, such as liquidity risk or operational risk. Most importantly, VaR is not ‘risk management’. This term refers to the complete range of duties and disciplines that are involved in minimising and managing bank risk exposure. VaR is but one ingredient of risk management, a measurement tool for market risk.

An introduction to Value-at-Risk – Moorad Choudry

ISBN-10 0-470-01757-0