It’s become practically cliché to note that the 2008 market crash was a stark reminder that hedge funds too can suffer at the hands of a series of highly improbably and unanticipated events – even after looking at their strategy, their diversification and the mean and variance of their past returns.

Yet a recent research study (free registration required) by TrimTabs and BarclayHedge entitled “Do Hedge Fund Investors Care About ‘Fat-Tails’ Risk” caught our attention for a theory put to test: Can hedge fund investors hedge themselves from unforeseen risk events – kurtosis, in economic-speak – that the hedge funds they’re writing checks to might be taking?

We  pride ourselves on being somewhat schooled in the nuances of economic and financial market phraseology, thanks in large part to the resources of CAIA and others at our disposal (shameless plug, but CAIA has this study on building a hedge fund portfolio with kurtosis and skewness available on its Web site). But we’re also grateful when someone else defines an academic term for us, which the TrimTabs study thankfully does:

“Kurtosis measures the risk of a highly implausible event coming to pass more frequently than one would expect from a normally distributed variable.”

TrimTabs and BarclayHedge analyze how the kurtosis of hedge fund returns is measured; how, if at all, it impacts hedge fund flows; and if kurtosis is in fact priced in to hedge fund returns, or if non-normal returns offer arbitrage opportunities for sophisticated investors.

The study finds that in contrast to returns on individual securities and contracts like stocks, gold, oil or bonds, individual hedge fund returns display significant excess kurtosis, for the most part thanks to hedge funds’ ability to utilize leverage. (See illustration below.)

Source: TrimTabs Hedge Fund Flow Report

Indeed, the study’s results show that hedge fund returns display high levels of kurtosis. At the fund level, kurtosis averaged 33.1 in the past 10 years. Kurtosis is also extremely volatile, with peaks of 127.8 in 2003 (a stock market bottom) and 91.8 in 2007 (likely due to the sharp and simultaneous sell-off of quantitative strategies in the summer).

In fact, the results of the study show even higher levels of kurtosis than most academic studies because it focuses on individual fund returns rather than a composite hedge fund index.

Source: TrimTabs Hedge Fund Flow Report

So is that a good thing or a bad thing? At first blush, its not a good thing. All else equal, investors should avoid high kurtosis. A 90% loss means near ruin for investors, and a 90% gain does not offset it, the report notes. The fact that hedge fund returns display much more kurtosis than the assets in which they invest suggests that kurtosis is the result of leverage, which magnifies the likelihood of extreme outcomes, as the chart below shows.

The level of kurtosis also highly depends on the hedge fund strategy being employed. According to the study, fixed income and convertible arbitrage strategies show the most kurtosis, while equity market neutral is the only strategy for which the presence of kurtosis is not certain.

“This too, we ascribe to leverage,” the study notes. “It is not uncommon for fixed income and convertible arbitrage funds to use leverage ratios of 20:1, but strategy constraints and the volatility of stocks force much more caution from equity market neutral funds.”

Source: TrimTabs Hedge Fund Flow Report

On deeper reflection, however, the study notes that since most hedge fund investors do not seem to care about “fat-tails” risk, sophisticated investors with the ability to diversify their hedge fund portfolios should be able to diversify away kurtosis without any cost in terms of returns or variance – good news.

Conclusion: Kurtosis within hedge funds remains one of the last free lunches for sophisticated investors. Translation: If the buffet has enough different kinds of food to sample, and you know the right way to mix them, your chances of getting an unforeseen wallop of indigestion will be less.

Critics of hedge funds often charge that they simply sell insurance (“volatility”) for a premium and cross their fingers that they never have to pay up.  Hedge funds, they say, are “short vol.”  When volatility goes up, they go down, and vice versa.

But there may be a little more to the story than meets the eye.

Studies have shown that, in theory, active management thrives during periods of time when stocks are less correlated – when the so-called “cross-sectional dispersion” between stock returns is highest (i.e. their average correlation is lowest).

Back in late 2008, we covered a presentation by Steve Sapra of Analytic Investors that contained the following chart showing the average stock-by-stock correlation of US equities (blue line).

Note that correlations were low around the turn of the century.  This makes intuitive sense for anyone investing around then.  Stocks seemed to have a mind of their own as some sectors bubbled, then blow-up while others held the line.  Indeed, as the orange line shows, average stock volatility peaked in the Halcyon days of March 2000.  This combination provided unprecedented opportunities for those who could read the tea leaves at the time.

But does high volatility always lead to opportunities for the most active managers of all, hedge funds?  A report published by Moody’s recently contains an interesting appendix that seems to say “yes.”

The following chart from the report ranks monthly hedge fund industry returns from lowest to highest and shows the corresponding change in the VIX for that month. (Click to enlarge)

If anything, this chart shows that hedge funds have performed better in times of relative calm – that as a whole, they are “short vol.”  When the markets get wonky, hedge fund managers apparently have just as much trouble as the next guy.  Explains Moody’s:

“…although it is true that risk exposures of funds can vary substantially, they are participants in the financial markets and a sudden re-pricing of risk across the board can catch managers off guard, in the same way as other market participants…”

Still, as Moody’s points out, hedge funds are quick learners and are able to adjust their positioning faster than traditional managers.  As a result, they don’t stumble as far and their cumulative performance tends to recover quicker (as the following chart from the report shows – click to enlarge).

So hedge funds may thrive in relative stability.  But they also seem to perform “less poorly” during market upheavals.  This seems to support the argument that active management beats passive management in times of chaos.

However, as Sapra points out, that chaos must be accompanied by cross-sectional dispersion in order for active management to fully realize its potential.

During the ‘99-’03 pop in average stock volatility, hedge funds did okay.  But during the 2008 jump in vol, hedge funds took a pie in the face.

The difference?  Average stock correlation was low in the ‘99-’03 time period and was astronomical in 2008.

So the bottom line seems to be that high volatility might only be bad for hedge funds when cross-sectional volatility is also high.  Unfortunately the Moody’s report did not account for this variable.

Since the dawn of hedge fund indexes, detractors have charged that it’s simply impossible to capture the aggregate performance of an industry using voluntarily-provided data.  The voluntary nature of hedge fund indexes has given birth to a litany of alleged “biases” and inaccuracies from survivorship and backfilling to selective reporting and outright BS.

The challenge for investors, academics and regulators has been that there is no objective way to measure this bias.  There is no “compulsory” database against which to compare the bevy of voluntary ones in existence today. More…

Academics and researchers who study the hedge fund industry sometimes say that the best way to gauge the average performance of hedge funds is to look at an index of funds of funds (FoFs), not an index of hedge funds themselves.  The funds of funds, the argument goes, contain many funds that do not report to any databases – and would therefore be missed by indexes of single hedge funds.  In addition, an index of  funds of  funds is more diversified and is therefore a better representation of so-called “hedge fund beta.”

The HFRI Composite routinely shellacked the FoF Index in the 1990s.  But since the turn of the century, the FoF index has generally exhibited performance that resembled the broader indexes – with lower volatility…

While it may not look like it due to the absolute  performance disparity between the two indexes, the FoF Index actually has a high correlation to the Composite Index…

You can see this tight relationship in spades if you simply multiple each FoF Index monthly return by 1.4…

So in a sense, the HFRI FoF is a deleveraged version of the Composite Index.  Or, put another way: a portfolio containing roughly 66% Composite Index and 33% cash.

This tight relationship held up until last year when the HFRI FoF underperformed the HFRI Composite Index by a whopping 8.5%, even higher than 2003’s 7.9% under-performance (note that 2003, like 2009, was another barn-burner for the Composite Index.)

So what happened?  Theories abound.  Author and industry commentator Cathleen Rittereiser recently told Dow Jones:

“Arguably, funds of funds, could and should have reinvested their cash in hedge funds a lot earlier, especially if anecdotes are true that every fund in creation was open.”

Rittereiser is reflecting a common view of last year’s FoF under-performance – that funds of funds were sitting on mattresses full of cash they hoarded in case of massive withdrawals.  This cash cushion apparently came back to haunt them.

A new study from Fitch Ratings backs up this hypothesis.  The following chart from the firm’s recent Q1, 2010 Quarterly Hedge Fund Report shows that funds of funds actually performed in line with single hedge funds on a risk-adjusted basis.  (If you draw a Capital Market Line between the HFRI Composite (green triangle) and, say, a 2% risk free rate, the FoF index isn’t really that far below it). (Click to enlarge chart)

Some say it wasn’t the mattresses full of cash that were the problems for FoFs, it was their return-chasing (or “safety-chasing”) behaviour.  After watching global macro stay afloat in a stormy 2008, funds may have sought refuge in the strategy.  Kristoffer Houlihan, Director of Risk Management at PAAMCO told the FT as much recently.  According to the FT:

“…some managers sought refuge in global macro, a generally conservative, steady strategy. In 2008, global macro funds were off only fractionally, beating the industry average by more than 20 percentage points. This year, as of November, global macro has registered gains just north of 8 per cent, trailing the industry by 13.5 percentage points. The strategy delivered absolute returns, but in the context of the 2009 bull market its performance looked sluggish.”

Whatever the reason for last year’s anomaly, it will be very interesting to see if fund of funds indexes come back in line in 2010.  Things are off to a good start.  The difference between the HFRI Composite and the HFRI FoF Index in January: 1 bp.

We are accustomed to judging the value-added of investment funds in somewhat of a vacuum.  That is to say, we do so without regard to our own judgments about where markets will go in the future.   All that seems to really matter is the risk adjusted performance of a fund vs. its benchmark.  If that benchmark goes up by, say, 10%, we hope our managers beat it by, say, 3%.  If it goes down by 10%, we still hope to beat it by 3%.  Despite the “absolute return” moniker conferred upon hedge funds, they too aim to simply beat their appropriate index, whether it be the HFRI convert arb index in the short term or the S&P 500 over the long run. More…

The voluntary nature of hedge fund reporting has made many commentators see hedge fund indices and, by extension, hedge fund industry performance, with a somewhat jaundiced eye.  Since hedge fund databases are designed as surreptitious marketing vehicles for hedge funds, the worst performing funds are likely to be absent from the indices.

But others counter that the best performing funds are also likely to abstain from voluntary reporting since they believe it might be viewed as kind of tacky by its rarefied clientele. More…

We review a lot of academic research here at AllAboutAlpha.com.  Some of it can be a little dense and we’re the first to admit that we often can’t follow the mathematical nuance or arcane calculus contained in some of it.  Still, we try to distill these papers down to a simple lesson or two that can be communicated in the 5 minutes or so that you have to read our daily posts.

But occasionally, we come across academic-style articles written by practitioners.  Not surprisingly, these tend to be a little more, well, practical.  Here’s a great example… More…