Barbican Consulting Limited

# Value at Risk

**Market Risk**

Traders buy and sell financial products. As a result they often have positions or exposures. These exposures can arise because they are speculating or they have taken the other side of a client trade. Whatever the reason as prices move the market value of these positions will change.

This means that movements in foreign exchange rates, interest rates, credit spreads and commodity prices lead to profits and losses. This is called market risk. One of the most popular methods of measuring market risk is value at risk, (VAR). It has been used by banks for over a decade.

**What does it show?**

Value at Risk tells you how much money you can lose over a given time period and for a given level of confidence from the positions you hold. But it is not a guaranteed maximum loss figure. Your positions could lose you a lot more than VAR indicates.

Sometimes markets move by huge amounts in very short space of time. As a consequence your dealing positions can give you losses much greater than the VAR you have calculated.

It is this point that senior managers should be aware of. VAR is not a guaranteed maximum loss figure. Giving your dealers a VAR limit will not mean they cannot lose more.

**What affects Value at Risk?**

Four main factors influence your VAR number, they are:

Exposure: In general the larger the position you have the greater the risk. Therefore large positions create greater VAR.

Time: The longer you intend to hold the position the greater the VAR. As you may expect 10 day VAR is greater than 1 day VAR. (But not by a factor of 10, only the square root of 10).

Confidence: If you want a VAR that is very unlikely to be exceeded you will need to apply more stringent parameters. All things remaining constant this will increase your VAR and make it less likely to be exceeded.

Volatility: If you deal in risky things that have a history of going up and down in price, or if market conditions alter to make your positions move up and down in price your VAR will tend to increase.

It is important to put any VAR number you see into context. This means that if you are provided with a VAR number you should also know:

What is the probability that it will be exceeded?

What is the holding period?

Without this information you will be unaware of the parameters that have been used in the calculation of the VAR that you are working with.

**What are the advantages?**

Value at Risk has several advantages, they are:

VAR is just one number and in that sense becomes a lot easier to understand and monitor.

VAR provides you with a statistical measure of the probability of loss. Risk measures like duration and basis point value, (DV01), do not provide a statistical measure of the likelihood of loss. They just give you an absolute risk figure rather than a probability of such a loss arising. Therefore VAR is an improvement on these techniques.

VAR can be calculated for all types of assets. This means you can calculate VAR for interest rate risk, foreign exchange risk, credit risk and commodity price risk. Some firms add these individual VARs together to arrive at an overall VAR. You cannot do this with other risk measures.

**What are the disadvantages of Value at Risk?**

There are some weaknesses you should know about, they are:

VAR is not a maximum loss figure. From time-to-time you may find that the actual amount of money lost exceeds the VAR.

If you experience a loss greater than your VAR there is no guarantee that you will not experience another loss that exceeds your VAR the following day as well.

Many IT systems find the calculation of VAR challenging. Sometimes banks rely on spreadsheets to do this. Calculation errors and stale data can lead to inaccurate VAR reports.

Inaccuracy and doubts in the validity of VAR can also lead to it being used as a "soft limit". The breaking of a risk limit based on VAR is then treated with less seriousness than would otherwise have been the case.

Banks using VAR for the first time may be tempted to set a VAR limit much higher than the risk they have. The limit is so far from being breached that no one pays attention to VAR as a risk measure.

VAR does not deal with option positions very well. It also does not measure operational risks. This means that you can have losses that arise from poor controls and fraud.

**Is there anything we can do to improve the situation?**

Yes. Many firms do not solely rely on VAR to manage market risk. They use a variety of measures that may include traditional techniques like basis point value and stress testing. Stress testing shows what can happen when extreme market moves arise. It focuses attention to what can happen when markets move abnormally. You can see what a bad day could really cost you. By using several measures banks are looking for consistency in the reporting of risk. It is like having a second, third and fourth check on VAR.

**VAR and diversification**

In financial markets diversified asset portfolios are generally considered to be less risky than undiversified portfolios. If you have three traders one trading foreign exchange, another interest rates and the third credit, on most days you should get some diversification benefits. When one trader has a bad day another one will have a good day. The volatility of your profit and loss should be reduced.

When risk managers calculate VAR they can take into account this diversification effect. They can provide you with both undiversified and diversified value at risk.

The undiversified VAR figure tells you what might happen on a bad day. Undiversified VAR is a summation of the individual product VARs. This is when your foreign exchange trader, interest rate trader and credit trader all lose money together.

Diversified VAR takes into account the portfolio effect. This is important. It means in theory that adding trades or products can lead to changes in the VAR that are not as great as you may anticipate. (A theory that is anecdotally supported by some managers who use VAR).

Many banks therefore use the diversified VAR as an indication of what can happen in normal market conditions.

**VAR & regulators**

Regulators will not tell you how to calculate your VAR. But they are known to probe the methodology that is being used, question how appropriate it is and also assess senior manager's understanding of the risk measures the firm is using.

In general regulators are supportive of firms using VAR. Many firms have agreed with the regulator the use of VAR in order to calculate market risk and therefore the amount of regulatory capital required to support it.

If you agree to use VAR then the VAR model needs to be an accurate assessment of the risks you run. Therefore if you expect your VAR to be exceeded only 1 day in 100 days your regulator will not appreciate a frequency that exceeds this. It would indicate that your VAR model is inaccurate and your regulator may decide to increase the amount of regulatory capital you are holding.

**Finally a few numbers**

By way of illustration the following provides a simplified VAR calculation. Suppose you own a bond that has a price of 100% and you have calculated that the daily price volatility is 0.5%*.

Using statistics, (standard deviation, SD), there is an 84.1%, (1 SD), chance, that the price tomorrow will not fall below 100%-0.5%= 99.50%, a 97.7%, (2 SD), chance that the price tomorrow will not fall below 100%-1%= 99.00% and a 99.8%, (3 SD), chance that the price tomorrow will not fall below 100%-1.5%= 98.50%.

Put another way you are 99.8% certain that in normal market conditions your loss on holding this asset for one day will not exceed 1.5%, ($150,000 on a $10m position), this is the VAR**.

If you pick a more risky security, say one with a daily volatility of 1% your one day VAR for a 99.8% confidence interval is 3%, $300,000 on a $10m position. Increased volatility increases VAR.

This also means that if volatility changes your VAR can increase or decrease even when you positions remain unchanged.

What confidence interval and holding period should be used? That is entirely up to you. In determining the time horizon you may wish to consider how long it could take to liquidate positions. Many banks use between 5 and 10 days with a 2 or 3 standard deviation confidence interval. It just depends on how conservative you want your risk measure to be. ***

*Value at Risk uses standard deviation; this is sometimes referred to by traders as volatility. A standard statistical text book will explain standard deviation; it can also be calculated using spreadsheet add-in functions. It is a measure of the historic or implied price fluctuation of dealing positions and requires observing and collecting daily asset prices. Put simply the more an asset goes up and down in price the more volatile it is and the greater the perceived market risk. High price volatility equals high risk.

**Because financial markets do not strictly conform to normal or lognormal distribution the probability of a loss exceeding the VAR is greater than would be indicated. In real life the "tail" under the distribution curve is fatter than expected.

***As a rule of thumb, VAR increases with the square root of time. So if you want to calculate the VAR with a 99.8% confidence interval for a 10 day holding period for the asset with a 0.5% daily volatility the 10 day VAR will be 3.16 (square root 10) x 1.5 = 4.74% or $474,000 for a $10,000,000 position.

*First Published by Barbican Consulting Limited 2007*