LIVING WITH KURTOSIS

Fund-of-hedge-fund managers are paying homage to the quantitative creed of postmodern portfolio theory.

In the 18th century physicians forsook folk wisdom for physiology, establishing medical schools and doing research. Now another emerging profession is trying to establish that it, too, has experienced enlightenment by stressing a rigorous commitment to science: Fund-of-hedge-fund managers are paying homage to the quantitative creed of postmodern portfolio theory.

Yet they exhibit a curiously schizophrenic attitude toward investing by the numbers. Asked “Do you use quantitative techniques?” fund-of-funds managers will reel off the fashionable quant approaches, such as Markowitz mean-variance optimization, scenario testing, Monte Carlo simulation and factor modeling. However, when pressed about which techniques they employ to construct portfolios, many will confess, sotto voce, that they don’t rely on any of them -- although, to be sure, they find quant analyses profoundly illuminating.

A few fund-of-funds specialists are brave enough to poke their heads above the parapet. Nicholas Verwilghen, Zurich-based head of quantitative research at EIM, one of Europe’s largest fund-of-hedge-fund managers (assets: $3 billion), says candidly, “We put portfolios together from a bottom-up basis and take a mostly qualitative view of the risks and returns that are inherent in strategies and managers.” As for quantitative techniques, they come into play, says Verwilghen, in identifying sources of risk and return, in anticipating how managers will react to market changes and in modeling the impact on portfolios.

Complications abound for would-be quants among fund-of-funds managers. “Let the data speak,” cry quant purists. Trouble is, hedge fund data -- where it’s available -- is about as pure as Wall Street slush in February. To begin with, a built-in survivorship bias can distort commercial databases of hedge fund performance. Last year Gaurav Amin and Harry Kat of the U.K.'s ISMA Centre at the University of Reading showed that only 59.5 percent of the hedge funds that existed in 1996 were still around five years later.

Less well understood but also a data glitch for fund-of-funds managers is what Brian Singer, head of asset allocation and risk management at UBS Global Asset Management, calls “membership” bias. He outlines the problem: " A finance professor told me about one of his former students who had launched ten funds. One failed, three were good performers, and one of the three was an excellent performer but very risky. [The rest were mediocre.] So he closed all of the funds bar the two with the best risk-adjusted returns, and now the world thinks that this is his historical track record.” Concludes Singer, “Historical data associated with hedge funds is all but meaningless unless you’ve gathered it yourself and know it is clean.”

Another bit of data obfuscation is smoothing of results. Such hedge fund strategies as distressed securities, special situations, convertible arbitrage and the more esoteric fixed-income arbitrages involve investing in illiquid securities with widely varying bid prices. And in times of market dislocation, bids can disappear altogether.

Thus funds, which typically report performance every month, enjoy a fair degree of latitude to steady returns in between. “The presence of stale prices due to either illiquidity or managed pricing can artificially reduce estimates of volatility and correlation,” concludes managing principal Clifford Asness and principals Robert Krail and John Liew of New Yorkbased AQR Capital Management in a study for Institutional Investor’s Journal of Portfolio Management (“Do Hedge Funds Hedge?” Fall 2001). Given most hedge funds’ professed intention to produce consistent returns, it would be surprising if they didn’t use smoothing to try to eliminate erratic, loss-making months.

Thus hedge fund data can be so corrupted that many quantitative techniques become extremely difficult to execute. Traditional optimization has “no value whatsoever,” contends EIM’s Verwilghen. “The danger is that you put information into a mean-variance optimizer and what you get out at the end is far worse than following an intuitive process. It would tend to systematically overweight dangerous funds.”

Andrew Weisman, head of risk management at a newly launched New York based hedge fund, Strativarius Capital, asserts that certain hedge fund strategies, particularly volatility arbitrages, may be “informationless,” that is, they offer no clue as to the portfolio managers’ skill. Yet many classical arb funds are just the sort that tend to exhibit consistent returns with low volatility -- until they blow up -- so they are likely to be overweighted in an optimization process.

Weisman, who constructed hedge fund portfolios when he was CIO of Nikko Securities Co. International in New York, warns that feeding an optimizer poor data and interpreting the output uncritically can be disastrous (see “Dangerous Attractions: Informationless Investing and Hedge Fund Performance Measurement Bias,” Journal of Portfolio Management, Summer 2002).

Jaakko Karki, head of research at London-based fund-of-funds manager International Asset Management, still sees a role for optimization in assessing hedge funds, provided that there’s enough data to work with. But he goes beyond the traditional mean-variance approach. Rather than relying on the two inputs of return and a variance measure (such as standard deviation), Karki resorts to the so-called higher moments of return distribution: skewness and kurtosis. Mean-variance optimization assumes that returns take a classic bell-curve shape. Skewness is the extent to which the tails -- the portions left and right that flare off to the sides of the basic bell form -- shoot out to either side; kurtosis is the steepness of the curve before it shoots out.

Karki says that these two measures are critical because they capture absolute return -- the goal of fund-of-hedge-funds managers. The ideal distribution: a very short left tail with a large positive right-hand skew, indicating a marked tendency to produce positive returns. “We cannot make an assumption that [hedge fund] returns are normally distributed,” says Karki. “But more to the point, we shouldn’t make that assumption, because that is not the return distribution we are seeking.”

UBS’s Singer sees factor analysis as a more profitable avenue of quant research than optimization in whatever guise. In a UBS working paper (“The Appropriate Policy Allocation for Alternative Investments,” October 2002; available at us.ubs-globalam.com), he, Kevin Terhaar and Renato Staub, UBS’s executive director of asset allocation and strategy and director of asset allocation and strategy, respectively, set out to find a process for determining the optimal allocation to alternative assets. Starting out with the premise that similar assets should have the same fundamental economic drivers and risk factors, Singer ignores the historical performance of assets and instead calculates the risk and return characteristics of conventional versus alternative assets.

The result is a factor approach to apportioning assets among traditional and alternative investments that Singer says could be readily adapted to divvying up money among different types of hedge funds. Nevertheless, he emphasizes that even factor analysis should not be allowed to stand in for qualitative judgment: “If you relied solely on any quant approach, you would be torturing the data to conform to a spurious truth rather than getting to the reality of risks.”

IAM’s Karki performs a similar exercise in evaluating hedge funds. “In the absence of meaningful data,” he says, “we try to construct portfolios by understanding their risk and return characteristics and then seeking to diversify those idiosyncratic risks away.”

Ultimately, though, quantitative analysis of hedge funds is at the mercy of the data available, and Strativarius’ Weisman detects no desire on the part of the hedge fund industry to help aspiring quants by providing greater transparency. “Hedge funds are used to being secretive, and that culture won’t change,” he says. “God invented monthly data so hedge fund managers could hide things.”

Strativarius provides weekly performance data and detailed risk reporting, but Weisman acknowledges that this is easier for a macro fund like his that operates in highly liquid markets, such as foreign exchange, than it would be for a fund with sensitive, illiquid positions.

Even the most diligent quantitative research, moreover, can’t get around the fact that hedge fund managers can do pretty much whatever they want to generate returns. Although most stick to a broad strategy, funds may step out of their template when opportunity arises. For example, because there’s scant merger activity, some M&A arbitrage funds are venturing into other areas.

“Hedge fund managers may set sail into new waters every day if that is where the opportunity is,” says EIM quant research chief Verwilghen. “People allocating money to hedge fund managers should spend more time getting to know the managers and less time worrying about the performance record.”

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