Risk 2.0: Extreme Value Theory
Reviewing the Best of CIR in 2010.
BY Caroline Cakebread | December 14, 2010
2010 was a big year for Canadian Investment Review as we launched our brand new format as a 100% online publication able to bring readers the best and the brightest ideas in investment research in an instant. As the year draws to a close, we’ll be looking back at the top articles from the year, starting with this, our series by Ana Cascon and William F. Shadwick whose articles on Risk 2.0 turn the whole notion of risk management on its head and tackles the subject in a new and very different way. Read on below….
One of us recently gave a presentation entitled “The Right Answers to the Wrong Questions”, which was subsequently the subject of aCanadian Investment Review blog post by Tris Lett. The presentation, and the book we are writing with the same title, traces the emergence of the branch of probability and statistics called Extreme Value Theory in parallel with models of prices in mathematical finance over the course of the 20th Century. This history reveals a number of missed opportunities which, if taken, would have changed the course of finance and in particular the course of financial crises.
One of the most crucial of these was (and still is) the failure of the finance industry to make use of Expected Shortfall and Extreme Value Theory to manage the risk of large losses–something the insurance industry has been doing for several decades.
Here’s how it would have affected a manager with $10 million invested in Citigroup shares at the end of January 2007. In the previous 250 days, the worst one day loss on the Citigroup position was 2.47% or $247,000. How much worse could a 1-day loss be? While it is impossible to put a bound on this (aside from the knowledge that a stock price can go to zero), there is a useful answer, on average. Expected Shortfall, conditional on a loss of more than 2.47%, is the average of all returns below -2.47%.
By our calculations such an event could have been expected once in 136 days and the average of such losses would be 3.73%. In other words, our analysis said that a worse result was quite likely and that on average it would be about half again as great as the previous low, exposing the manager to a loss of $373,000. Armed with this information, he could have managed the risk by re-sizing the position if necessary. Find the full post and series here.