Can you explain the VaR value for the risk

Value at Risk

What is Value at Risk?

Value at Risk is a key figure used by banks, insurance companies and investment funds to estimate the risk of a loss in stock or loan portfolios.
The term is abbreviated as VaR. The key figure makes it possible to quantify the risk of an investment. Financial service providers can use this to determine how high a possible loss of an investment is within a certain period of time and under normal market conditions.

VaR is used by banks and insurance companies as a measure of risk for investment portfolios that consist of several financial resources or for individual financial stocks. Based on the value at risk the likelihood of a maximum loss on an investment can be determined within a certain period of time. On the other hand, this calculation can be used to determine the so-called residual probability, i.e. how often the loss is higher than the average.

Influencing variables on the value at risk

For the calculation of the possible loss and the determination of the VaR 3 parameters needed. These are the holding period of the positions in days, weeks or months, the reference period - for example one year - and the so-called confidence level, referred to as the confidence level, in percent. The Value at Risk is usually recalculated daily by banks and investment companies.

In addition, certain requirements must be met for a meaningful calculation of the Value at Risk. In particular, they must be concerned with an investment Risks are divided into individual categories and described. In addition, it must be possible to estimate the interdependencies of the risks or, ideally, be known. Another important prerequisite for a reliable calculation is that the properties of the risks are stable over time and can be forecast with a high degree of reliability.

An example: An investment fund holds 100,000 shares in a single AG. The share price at the time of purchase was 60 euros, resulting in a total investment value of 6 million euros. To determine the VaR for the next day, the previous stock market year with 220 trading days is used as a reference, for example. A price loss of at least EUR 300,000 was recorded for these shares on 11 or 5% of the trading days in the past. The rest of the time, the remaining 209 or 95% of the days, the price losses were smaller or the price of the shares rose.

This results in a VaR for the next day that, with a confidence level of 95%, the loss of the shares will not exceed EUR 300,000 or 5% of the portfolio value.

Analytical approach and simulation approach to determine the value at risk

An analytical approach or a simulation approach can be selected for calculating the VaR. In the analytical approach, the Opportunities and risks of an investment firmly defined. In practice, this is usually done using a so-called normal distribution. The value at risk can then be calculated using a simple mathematical formula. Two simulation models are available for the simulation approach. These are the historical simulation and the Monte Carlo simulation.

In the historical simulation, the historical distribution of risks and opportunities is used as representative for the calculation of the value at risk. In the Monte Carlo simulation, opportunities and risks are mapped on the basis of random numbers Based on a previously performed random distribution simulated.

Criticism of Value at Risk

One of the main criticisms of Value at Risk is that this metric is cannot make any statement about the periodicity of a damaging event. For the example above, this means that the 11 days with a high loss do not have to occur over the period. It can just as well happen that the losses exceed the risk estimate for several days in a row and then do not recur for a long period of time.