Value at Risk - definition and explanation

 Over the years, it has also become more widely used in other risk areas and industries. If you translate "value-at-risk" literally into English, you get "value-at-risk" or "risk-weighted assets". What is the significance of this figure? How useful is this number for accurately assessing a risk?

There are many statistical concepts for risk management that can be used to evaluate it. They range from simple checklists to neural networks to extreme value theory. Over the years, financial service providers have developed sophisticated mathematical and statistical methods to calculate risk-adequate premiums.

Many "financial experts" fall prey to the mistaken belief that complex economic worlds can be compared to machines that function according to clear cause-and-effect chains. They can also be modelled with interdependent behavioural equations. Despite all these misconceptions, the attractiveness of a risk statement with a clear time horizon, risk level and probability is great. In this context, value at risk has become the "standard" risk measure in recent years.

The Birth of Value-at-Risk

Dennis Weatherstone was the chairman of J.P. Morgan's American investment bank. He required a one-page risk report every day at 4:05 p.m. that would show the bank's total market exposure and potential loss over the next 24 hours. Weatherstone was tired of the different methods used to assess market risk for different financial instruments. His previous report included a variety of beta factors, volatilities and gearing factors, as well as deltas, gammas and thetas. He wanted a single measure for all financial instruments.

Report 4.15 was born. J.P. Morgan's RiskMetrics(tm), a risk measurement product, was released in October 1994 and made available free of charge to all interested parties. This product is essentially based on a methodology known as "Value at Risk".

Calculation and definition of Value at Risk

The Value at Risk is the total loss in value due to a risk position defined by the company, which will not be exceeded with a predetermined probability (confidence level) within a certain period of time (holding period).

There are certain requirements for the calculation of the risk value:

•     The risks must be divided into different categories and described by a suitable distribution function.
•     The interdependencies between the risks must be known or estimated.
•     The risks must be predictable and reasonably stable over time. Extreme scenarios cannot be considered.

There are two ways to measure the value of risk: an analytical approach and a simulation approach.

The two approaches differ in the way they model the risk factors and the sensitivity to the portfolios in exness and positions under consideration. The model of the analytical approach is based on known relationships and correlations between the individual variables using a distribution assumption. In the simulation approach, the value at risk is calculated on the basis of simulations of various state developments.