Policy implications if we use Power Law distribution

I have been working on my first paper with the title "Can Power Law help us avoid highly improbable tail events?" the premise of the argument is that if some economic variables fall in the Power Law distribution then policies associated with those economic variables need to be handled differently. For example, I am taking the problem of the Icelandic Krona, I have written about the Icelandic Krona before and I am convinced that it follows a Power Law distribution.

If we know that ISK follows a power law distribution and future fluctuations in ISK are going to follow the Power Law distribution should the Icelandic state still use the currency in its current form? or should it switch over to a more stable currency say the Euro? this debate is on-going in Iceland and I am afraid people are viewing this decision with their political lense and not the economic lense.

Just a simple switch in the probability distribution of the ISK has some serious policy implications. Lets do a simple thought experiment: The Financial Supervisory Authority of Iceland used a 20% devaluation of the ISK as a basis to stress test the banks in Iceland, why did they choose 20% because they thought ISK followed a Gaussian Normal Distribution and a 20% devaluation is a 2 or 3 sigma event or a very low probability of occurance, however if we change the distribution to Power Law a 20% devaluation of the ISK has a much higher probability therefore they would have chosen a much higher deviation for the stress test say 50% this would have shown the true color of the Icelandic banks capital adequacy and vulnerability to wholesale funding. The question is if the stress test had been done in 2006 when Iceland had a mini crisis, the FSA could have put a stop to the aggressive borrowing by the Icelandic banks which in turn would have reduced the leverage of the companies in Iceland and the citizens.

So choosing the right probability distribution matters! atleast that is the basis for my PhD thesis lets hope the thesis could influence some policy choices.

Icelandic Krona vs US Dollar - A Power Law Distribution

Image via Wikipedia

The Icelandic Krona currency exchange index follows the Power Law, it can be seen in the most rudimentary of analysis...

Here is the analysis of ISK-USD exchange rate data for however long I could get, a simple histogram shows visually that the exchange rate is distributed by a power law. In addition, I was able to do a Log plot of the observations and it clearly follows a path that should give us

enough indication that the ISK exchange does not follow a Normal "Bell" curve distribution.

However, last week I was talking to a currency trader and he told me that before the crash of the Icelandic Krona last year, they calculated the proabability of ISK crashing and they found it to be a 8 sigma (read highly unlikely! or A Black Swan) event... the fact that it happened proves atleast to me that the methods and theory used to analyze the ISK is not correct. I am writing a paper with Dr.Helgi Tomasson with University of Iceland with the title "Can Power Law help us avoid the highly improbable tail events?" hopefully we will be able to answer the above question.

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