Why risk is so hard to measure

The accuracy and reliability of standard techniques for risk analysis used by the financial industry as well as in regulations.

Financial risk is usually forecasted with sophisticated statistical methods. However, in spite of their prevalence in industry applications and financial regulations, the performance of such methods is poorly understood. This is a concern since minor variations in model assumptions can lead to vastly different risk forecasts for the same portfolio, forecasts that are all equally plausible ex–ante. These results have problematic implications for many practical applications, especially where the cost of type I and type II error is not trivial.

Our aim in this paper is to analyze the most common practices in market risk modeling, identify under what conditions they deliver reliable answers, when and how they fail to live up to expectations and ultimately make recom- mendations to practitioners and regulators on their proper use. In particular, we focus on the three main challenges arise in the forecasting of financial risk: the choice of risk measure, data sample and statistical method. 

A large number of statistical methods for forecasting risk have been pro- posed, but as a practical matter, only a handful have found significant trac- tion, as discussed in Danielsson et al. (2015). Of these, all but one depend on some parametric model, while one, historical simulation (HS), is model independent. Our objective in this paper is not to compare and contrast the various risk forecast methods: after all, a large number of high–quality papers exist on this very topic. Instead, we want to see how a representa- tive risk forecast method performs, identifying results that are related to the technical choice on the other two key issues: risk measure and data. 

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