Investing in some stocks should have qualified as an “extreme sport” says leading quant
Jul 9th, 2009 | Filed under: Performance, Analytics & Metrics, Today's PostToday, 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.
In each case the probability estimates indicated that further losses would likely be observed within a few months at most. Each time the previous worst loss was breached, the probability of a recurrence steadily increased until the next event in the cascade of severe losses that Citigroup’s share price suffered.
Extracting critical risk estimates from Citigroup share price returns distribution is possible because of the high degree of information which the price movements contain. The same approach can be applied to hedge fund returns.
Daily returns for hedge fund indices are not as rich in information as share prices from major markets however the EVT CVaR estimates also gave clear warnings ahead of the flurry of losses in strategies such as Convertible Arbitrage in September and October of 2008.
Financial data distributions have fat tails. Extreme events are both inevitable and of critical importance EVT CVaR estimates provided ample warning of both the increasing likelihood and increasing severity of those losses before they occurred.





(By Ranjan Bhaduri, PhD, CFA, CAIA, Member, 
A lot of funds of hedge funds focus almost exclusively on smaller, newer hedge funds. Whether its due to the backfill bias that gives young funds apparent superpowers or simply because their managers are hungrier, newer hedge funds seem to outperform their older compatriots. Similarly, smaller funds (regardless of age) have generally performed better than larger ones.
It is often argued that aggregate hedge fund performance data suffers from a near-fatal flaw: since it is voluntarily reported by the manager, hedge fund indices only include funds that the managers have deemed marketable. In 2002, David Hsieh of Duke University and William Fung of London Business School wrote a seminal article on this issue called “
In August 2007, as quant hedge funds were swooning in an eerie precursor to the credit crunch, we reported on an academic study of “hedge fund contagion” (
Ever noticed that the term “decoupling” is almost always used to describe a situation where one asset tanks and the other manages to hold up okay? A couple of years ago, many assumed that Asian economies had decoupled from the US economy - in other words, that a downdraft or stagnation in the US economy would not be commensurately felt in Asia.
When conducting due diligence on a hedge fund, it’s appropriate to ask a manager for their AUM history along with their return history. After all, studies (and intuition) say that assets start to flow into a fund only after it has put some solid numbers. Naturally, young hedge funds have fewer assets than more mature ones.
