# How Value at Risk works and is calculated

If you invest online or hold a stock portfolio, you have probably already heard of the term "value at risk". It was invented in the 80's by Bankers Trust for the US financial markets and democratized in the 90's by JP Morgan with its RiskMetrics system. Before this period, it was impossible to compare the different risk measures of market activities with the methods used. Over time, however, derivatives have multiplied and the volatility of financial markets has increased significantly, leading to successive stock market crashes. This led financial institutions to develop a common risk indicator model. This is how the indicator we will talk about in this article was born and has become, since the Basel agreements in 1995, one of the essential indicators for the evaluation of financial risk.

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## Value at Risk: What is it?

Let us first take a moment to define Value at Risk more precisely. This term refers to the maximum potential loss for an investor on a given asset or portfolio of assets that can be achieved with a specific probability and a given time horizon. It is therefore the worst possible scenario over a given period and associated with a confidence index.

The Value at Risk can thus be interpreted as an indicator of the distribution of profits and losses for an asset or group of assets for a specific period.

### How is the Value at Risk assessed?

In defining this risk measure, three distinct elements are considered here with :

• The distribution of the profits and losses of the portfolio or asset concerned over a given holding period which is based on different types of calculations.
• The confidence level, which is expressed here as a numerical value between 0 and 1, is used to determine the probability of obtaining a return greater than or equal to the Value at Risk. For example, in the case of a normal distribution of profits and losses over a period with a VaR whose confidence level is 95% and an amount of 1 million euros means that the loss associated with this asset has a 95% chance of not exceeding this amount.
• The holding period of the asset or portfolio of assets is used to adjust the calculation of Value at Risk by taking into account the composition of returns. It is important to note that although the holding period of an asset varies from one investor to another, financial market regulators require common time horizons as part of the VAR calculation procedures.

In order to evaluate the Value at Risk, it is also necessary to make three main assumptions. The first concerns the normality of the profit and loss distributions, incorporating the fact that the evolution of the price of a financial instrument is considered to follow a lognormal distribution. A second assumption concerns the relationship between an N-day Value at Risk and a 1-day Value at Risk, since it is considered here that the N-day VaR is equivalent to the square root of N multiplied by the 1-day VaR. The last assumption concerns the average return on a financial asset, which is considered to be zero for the period in question.

### The most common methods of calculating Value at Risk :

As mentioned above, the calculation of the VaR depends largely on the estimation of the loss distribution. There are two methods for doing this. The oldest method is to use only the value of the position in the past. In the case of a portfolio of assets, the past value of the portfolio will be reconstructed from the different prices of the assets in its current composition. Once the risk factors have been determined, the historical data will be used to deduce a loss amount. In this method, little calculation and technique is used. Furthermore, this method of assessing VaR does not require any prior assumptions about the shape of the distribution. However, the fact that this method is so simple also has some disadvantages. Indeed, it is necessary here that the history is sufficiently large compared to the horizon of the VAR and its confidence level, but that it is not too large either, in order to ensure that the probability distribution has not changed too much over this period. Another drawback of this method is that it does not work for derivatives.

However, there is another common method of calculating VaR, which is the analytical or parametric method. This is based on statistical calculations and consists of defining a formula representing the profits and losses. This second method is based on various assumptions, including the fact that variations in risk factors follow a normal distribution, that the relationship between variations in portfolio values and variations in market values is linear, and that derivatives are linear and bonds can be reduced to linear payoffs.

### What is the interest of knowing the Value at Risk and for whom is this indicator intended?

Let's now look at the concrete use of the Value at Risk indicator and the people or institutions for whom it is intended. In reality, VAR is mainly used by banks and is intended for market professionals such as market operators, private fund managers or institutional fund managers, risk managers who are responsible for risk management and risk control, as well as accountants and institutional clients.

## Limitations and disadvantages of Value at Risk as an indicator :

As we have just seen in this article, the Value at Risk represents the maximum potential loss of an asset over a given period. But we have also seen that its evaluation is often based on imprecise elements that can have a direct influence on the result obtained.

• Thus, the first drawback of this risk assessment method concerns the assumption of the normality of variations in the prices of the various assets. We know that large market variations are often underestimated by the normal distribution.
• Another major disadvantage of the Value at Risk as an indicator is that the result obtained to anticipate the evolution of the price of an asset in the more or less near future is defined by an analysis of its past. This makes the result unreliable.
• We also know that Value at Risk necessarily requires a fixed horizon. This means that we should consider that the market is liquid and that it is possible to cut our positions at this precise horizon which is not always the case.
• Finally, another major drawback of Value at Risk is that its estimation is based on a large number of approximations and simulations. Although the technology has evolved considerably and the algorithms used are increasingly efficient, these elements remain approximations and are therefore by no means concrete and stable data.

The limitations of the Value at Risk mentioned above have led to the introduction of additional control methods such as backtesting and stress testing, which are now mandatory in order to verify the results of this indicator. Backtesting is used to determine the number of times the actual loss exceeded the VaR estimate. If this number is large, it is necessary to review the calculation method used. Stress testing is another method of validating VaR introduced by the Basel Committee. These mandatory tests work by subjecting asset portfolios to extreme market conditions in order to observe their behaviour in the face of extremely negative scenarios.

However, although Value at Risk has some shortcomings that we have just explained to you, it remains an interesting evaluation tool for risk management by providing a quantitative measure of this risk. You should therefore take this indicator into account when speculating on an asset or a portfolio of assets, but you should also use other risk assessment methods in parallel and place your stop orders at the right levels.

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