Today, we bring you Part 2 of Dr. William Shadwick’s proposal to use “extreme value theory” in calculating value at risk (VaR) and its close cousin conditional value at risk (CVaR). (see Part 1).

Shadwick is a highly-regarded mathematician who crossed over into finance a decade ago and has since made his mark on the field of investment performance analysis, developing Omega Metrics® and winning a prestigious award from the Investment Management Consultants Association along the way. He is also the founder of Omega Analysis Limited, a quantitative research firm in London.

Special to AllAboutAlpha.com by: Dr. William Shadwick, Omega Analysis Limited

As I wrote two weeks ago, Extreme Value Theory Conditional Value at Risk (EVT CVaR) can be a very useful measure in portfolio analysis.

In a volatile market, EVT CVaR with a variable Value at Risk threshold (for example the worst loss in the past 250 days) is a useful method for tracking the evolving exposure of a portfolio position.  In fact, it provided accurate estimates of the declining fortunes of shares in companies such as AIG, Bank of America, Barclays Bank, Citigroup, HBOS, Lehman Brothers, Lloyds Bank Group and UBS over the past two years.

In each of these cases, the share price movements prior to severe loss events showed extremely fat tails.  Our implementation of EVT provided warning of the likelihood and severity of subsequent losses well in advance. Thus, while the weakness of these institutions may have come as a shock to their regulators, the prospect of large losses was quite apparent from their share price histories, through our CVaR estimates.

Citigroup’s Share Price Decline 2007-2009

By the end of 2006 the daily returns on Citigroup shares had tails too fat to be consistent with a normal distribution. The Tail Risk Level as measured by the “C-S Character” had been high for several months by the beginning of 2007. Those who followed this indicator after the publication of Omega Analysis’ Primer on Tail Risk on AllAboutAlpha.com in May 2007 received warning of this heightened risk well in advance of the impact of the credit crisis in the equity markets.

At the beginning of January 2007, the worst loss in the previous 250 days was the return of -4.69% on 20 January 2006. According to the normal model, the probability of a return less than or equal to -4.69% was one day in 78,000 years. By contrast, our tail estimate of the probability of such an event was one day in 588.

Table 1 shows Risk Assessment Levels and subsequent breaches, if any, at a monthly frequency.  In this table, we show a Monthly Risk Assessment report on Citigroup. Prior to the first trading day of each month we report: worst loss in sample, estimated probability of exceeding the worst loss, Conditional Value at Risk beyond the worst loss (based on the previous 250 days). The table shows the date and magnitude of any excess losses in the subsequent month. More…