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# Come together: Statistical arbitrage

Statistical arbitrageurs use high-tech tools to identify and capture fleeting pricing anomalies caused by technical rather than fundamental factors. But consistently executing a strategy to exploit those anomalies is a rare talent.

But consistently executing a strategy to exploit those anomalies is a rare talent.

Stock prices tend to revert to the mean. That basic assumption defines the portfolio strategies of most statistical arbitrage traders. They usually do well when markets make small moves of relatively short duration, and they get into trouble when markets lurch unexpectedly - and keep at it for a long time. For that reason, even before September 11, many statistical arbitrage hedge funds were struggling last year. Despite relatively low institutional trading volumes, "U.S. equity markets experienced two major directional moves with little change in market leadership in the year's first nine months," explains Neil Ramsey, president of Ramsey Quantitative Systems. (The Standard & Poor's 500 index dropped 15 percent between February and March and suffered an additional 21 percent decline between late August and mid-September.) Such extended moves are a prescription for pain for many statistical arbitrage traders, who make bets on small, short-term market moves.

No one knows exactly how much money is invested in statistical arbitrage strategies. The biggest players in the business, including the proprietary trading desks of major investment banks like Morgan Stanley and BNP Paribas, as well as such firms as D.E. Shaw & Co. (total assets: $2.7 billion) and Citadel Investment Group (total assets: $6 billion), don't report their returns or asset flows to monitoring services like Chicago-based Hedge Fund Research. Based on the 60-odd statistical arbitrage hedge funds it follows, HFR estimates that $4.8 billion was invested in the category at the end of the third quarter of 2001, but the actual total is likely much higher.

Statistical arbitrage traders are typically long underperforming stocks and short overperformers. They make numerous high-volume bets on anticipated small market moves, profiting as both groups of stocks (the longs and the shorts) revert to normal price levels. But sometimes the reversion to the mean is delayed. So for the eight months ended August 31, the average statistical arbitrage fund monitored by HFR declined 1.96 percent. The events of September 11 exacerbated those declines, but thanks to gains in October and November, the average fund was up 2.3 percent for the first 11 months of 2001.

The term "statistical arbitrage" is something of a misnomer. "Arbitrage implies that we are locking in a risk-free profit, but that isn't what we're doing," says David Shaw, chairman and founder of D.E. Shaw, one of the oldest statistical arb shops, founded in 1988. A more accurate label, in his view: algorithmic trading. Essentially, statistical arbitrage strategies are driven by computer algorithms that are designed to recognize stock price patterns and to identify deviations that can be expected to quickly revert to the norm. "Statistical arbitrageurs use high-tech tools to identify and capture fleeting pricing anomalies caused by technical rather than fundamental factors," says Christopher Dean, CEO of Vector Capital Management. A technical anomaly might reflect a supply-demand imbalance or another nonfundamental causal factor.

The strategy carries its risks, of course. A major one is the possibility that a price anomaly believed to be random actually has a fundamental cause. Another potential threat: The strategy is well conceived but poorly executed.

According to Shaw, virtually all statistical arbitrage strategies can be broken down into three principal processes. The first relies heavily on sophisticated quantitative methods and software to cull through historical market data to recognize price patterns. The second process involves risk management. Statistical arbitrageurs aim to run a portfolio that is purely market neutral.

But the final step - execution - is the linchpin of any statistical arb strategy, according to most practitioners. As more and more novices set up hedge funds, veterans cite an ability to execute as a key skill. "We can all use computers to find pricing anomalies," Dean says. "But what really separates the good from the mediocre players in this arena is the quality of execution. We are high-frequency traders, so any slippage or implementation cost is magnified."

The challenges they faced in 2001 were very different from the market conditions that prevailed in 2000, which was an exceptionally sweet environment for the statistical arb strategy. "2000 was as good a year as we can imagine," says Ramsey. Both volatility and liquidity were high, and stock prices tended to move in normal patterns. The average statistical arb hedge fund in HFR's database gained 8.9 percent in 2000.

Many individual funds, including some that do not appear in HFR's index, did considerably better. D.E. Shaw's equity and equity-linked strategies gained 60.3 percent; Vector's Vector Capital Fund gained 56.19 percent; Ramsey's unleveraged D. Quant Fund gained 41 percent; and Sabre Fund Management's Sabre Market Neutral Fund gained 39.53 percent. In contrast, the S&P 500 declined 9.1 percent.

Hedge Fund Research estimates that its statistical arbitrage fund universe experienced modest asset inflows of about $540 million in the first three quarters of 2001, but a number of statistical arbitrage managers insist that they saw more substantial cash inflows during the period. "Our asset base doubled in the first six months of this year," says Ramsey. As of November 30 the firm had assets of $500 million.

In good markets and bad, most statistical arbitrage players like to keep a low profile. "This is a very hush-hush arena," says Ramsey. Shaw explains, "We are attempting to profit from very small price effects that we are able to uncover mathematically." It's only by trading in very high volume, and by painstakingly managing risk and minimizing trading costs, he says, that statistical arbitrageurs are able to generate attractive returns.

Vector Capital Management uses a purely quantitative approach to building its portfolio. The firm's computer models analyze stocks not in isolation, but relative to their industry groups. Vector will buy an underperformer and take an equal offsetting position in a basket of stocks that represent its peer group.

Taking contrary positions in the belief that the market overreacts in the short run, Vector Capital Fund had sizable long positions in economically sensitive stocks for most of this year. "During June, July and August, the market was reacting to dramatically changing perceptions about the strength of the U.S. economy, and it was anticipating a downturn," he adds. Thus "going into September 11, [the fund] was experiencing a down period with losses of normal magnitude," Dean explains. During the three months ended August 31, the fund lost about 5.5 percent.

In the wake of the terrorist attacks, it suffered a 10 percent loss in September. But despite its June-to-September losses, the fund is up 2 percent year to date through November 30. Since its October 1998 inception, it has returned an average annual 30.1 percent, with a standard deviation of 15 percent and a correlation to the S&P 500 of 0.29.

D.E. Shaw also sailed serenely through a difficult year. Shaw's equity and equity-linked strategies (a combination of statistical arbitrage and a convertible-bond strategy) gained 27.4 percent through November 30. "Apart from a transient increase in volatility during the period immediately following the attacks," says Shaw, "we have observed no significant change in market conditions for market-neutral, statistical arbitrage strategies since September 11."

Shaw utilizes a complex combination of 24 predictive models to identify small pricing anomalies for his market-neutral portfolio. Since its July 1988 start, and despite the firm's highly publicized 1998 difficulties in the wake of the Russian debt default, Shaw's strategy has generated an average annual return of 24.9 percent with an annualized standard deviation of 9.8 percent and a correlation to the S&P 500 of 0.01.

"It's still been a good year," says Ramsey. "Volatility is still historically high, and there haven't been a lot of mergers or earnings surprises or other events which interfere with stocks' tendency to move in predictable patterns." Despite losing about 6 percent in September, Ramsey's D. Quant Fund is up 10.5 percent for the ten months ended October 31 and boasts an average annual return of 18 percent since its 1998 inception.

Like most statistical arbitrage managers, Ramsey deploys a combination of pairs and basket trades. (A pairs trade consists of offsetting long and short positions in two highly correlated stocks; a basket trade consists of offsetting positions in theoretically equivalent baskets of stocks.) During the D. Quant Fund's first two and a half years, Ramsey applied his statistical arbitrage strategy only in the U.S. equity markets. But this year he expanded the fund's reach to Europe and Japan.

Sabre Fund Management utilizes a pairs strategy to run its Sabre Market Neutral Fund, which typically consists of about 500 pairs of stocks. For each pair, the fund sells the overperformer short and buys a dollar equivalent position in the underperformer with the expectation that the stocks' prices will revert to the mean within a short time period. Sabre's average holding period is about five days. The fund recently liquidated a successful pairs trade that consisted of a short position in Lloyds TSB Group and a long position in HSBC Holdings.

For the first few years after its May 1997 launch, the Sabre Market Neutral Fund invested exclusively in the U.K. But now about 85 percent of its assets are spread over six European markets, with the remaining 15 percent in the U.S. Since its launch, the fund has generated an average annual return of 23 percent with a standard deviation of about 11 percent. That's impressive in any language.