Limitations of normal distribution in economic risk analysis
Heinäkoski, Lauri (2018-05-08)
L. Heinäkoski
08.05.2018
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Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-201805091662
https://urn.fi/URN:NBN:fi:oulu-201805091662
Tiivistelmä
Benoit Mandelbrot argued the presence of power law tails in sampling distributions of economic time series leads to emergence of non-Gaussian stable distributions in economics. This thesis studies the Mandelbrot-hypothesis by examining the statistical foundations behind Central Limit Theorems and analyzing empirical data of economic prices. Implications of the hypothesis are pondered from the perspective of banking regulation and some difficulties related to models of economic risk are discussed in general terms.
Empirical section of the thesis studies time series data on S&P500 stock market index, USD/JPY currency exchange rate, and the market price of copper. The time series are tested for normality and power law tails. The null hypothesis of normality is highly rejected for each series of data using several robust tests. Furthermore, a power law model is successfully fitted to each data set, supporting the Mandelbrot-hypothesis.
Value-at-Risk is a common measure of financial- and market risk used in bank risk management and banking regulation. Each time series is fitted to simple univariate VaR models using the so-called 250-day-rolling-method to assess the performance of different statistical distributions in predicting economic risks. Non-Gaussian stable distributions and Student’s t distribution are found to highly outperform the normal distribution. More precisely, the normal distribution is found to systematically underestimate economic tail variability or the occurrence of ‘Black Swan’ events.
The limitations of using statistical models in economic risk management is discussed in the final chapters. The notion of model risk is brought up along with some other problems specific to economic risk management. The chapters attempt to discuss what kinds of insights one can derive from statistical models and what the models cannot tell. Finally, the Financial Crisis is brought up as an example of what can happen when imperfect risk models with faulty distribution assumptions become widely used in banking regulation and risk management.
The results suggest the use normal distribution in economic risk analysis may lead to biased results and systematic underestimation of true economic risks. The results are of primary interest to banks and banking regulators who must manage their market exposures and financial risks on a daily basis. The results are of secondary interest to any large corporations utilizing financial derivatives in production-related risk management. For example, a company mining copper would benefit greatly from the ability to better model the market price variability of copper.
Empirical section of the thesis studies time series data on S&P500 stock market index, USD/JPY currency exchange rate, and the market price of copper. The time series are tested for normality and power law tails. The null hypothesis of normality is highly rejected for each series of data using several robust tests. Furthermore, a power law model is successfully fitted to each data set, supporting the Mandelbrot-hypothesis.
Value-at-Risk is a common measure of financial- and market risk used in bank risk management and banking regulation. Each time series is fitted to simple univariate VaR models using the so-called 250-day-rolling-method to assess the performance of different statistical distributions in predicting economic risks. Non-Gaussian stable distributions and Student’s t distribution are found to highly outperform the normal distribution. More precisely, the normal distribution is found to systematically underestimate economic tail variability or the occurrence of ‘Black Swan’ events.
The limitations of using statistical models in economic risk management is discussed in the final chapters. The notion of model risk is brought up along with some other problems specific to economic risk management. The chapters attempt to discuss what kinds of insights one can derive from statistical models and what the models cannot tell. Finally, the Financial Crisis is brought up as an example of what can happen when imperfect risk models with faulty distribution assumptions become widely used in banking regulation and risk management.
The results suggest the use normal distribution in economic risk analysis may lead to biased results and systematic underestimation of true economic risks. The results are of primary interest to banks and banking regulators who must manage their market exposures and financial risks on a daily basis. The results are of secondary interest to any large corporations utilizing financial derivatives in production-related risk management. For example, a company mining copper would benefit greatly from the ability to better model the market price variability of copper.
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