Ed ThorpA MATHEMATICIAN ON WALL STREETStatistical Arbitrage – Part INewport Bay:Statistical arbitrage can get you this farwonder if I’m making a 2000, after the 7 years and 5 months that weThe pioneer of statisticalAs I finish breakfast the sun is rising over thehave operated the current system, our level ofhills to the east behind me. It illuminates themarket neutrality as measured by what financialarbitrage guides us throughtops of three financial towers to the west in thetheorists call beta has averaged about on aenormous business and shopping complex ofpre-fee unlevered basis with zero being complete-a typical day at the officeFashion Island. By the time the buildings are inly market neutral and representing the mar-full sun I make the 3-mile drive to my office inket itself. Our alpha, which measures risk-adjust-one of them. ed excess return, the amount by which our annu-alized return has exceeded that from investments“Thorp, my advice is to buy low and sell high.”Statistical arbitrage in actionof comparable risk, has averaged about 20 perMathematician William F. DonaghueLogging onto our computer system, I learn thatcent per year. This means that our past annualwe have already traded more than a millionrate of return before fees of 26 per cent can bet’s the spring of 2000 and another warmshares electronically and are ahead $400,000 inthought of as the sum of three parts: 5 per centsunny day in Newport Beach. From 600 feetthe first hour of trading. We’re currently manag-from Treasury bills with no risk, about 1 per centhigh on the hill I look 30 miles over the Pacificing a temporary high of $340 million, with whichfrom our slight market bias of ( times at Wrigley’s 26-mile-long Catalina Island,we have established positions of $540 millionthe markets’ average annual return over the 7stretched across the horizon like a huge of stocks long, and an equal dollar amountyears and 5 months of our track record is roughlyITo the left, 60 miles away, the top of equallyshort, consistent with our policy of keeping our1 per cent) plus the difference, a risk adjustedlarge San Clemente Island is visible peepingportfolio dollar neutral. We know both fromexcess return of 20 per cent. We were essentiallyabove the horizon. The ocean ends two and a halfcomputer simulations and historical experiencemarket away, with a ribbon of white surf breakingthat our dollar neutral portfolio will also general-Using our proprietary prediction model, ouron wide sandy beaches. An early trickle of fishingly be close to market neutral. Market neutralcomputers continually calculate a “fair” price forand sail boats stream into the sea from Newportmeans that the fluctuations in the value of theeach of about one thousand of the largest, mostHarbor, one of the world’s largest small-boatportfolio have very little relationship with theheavily traded companies on the New York andmoorings, with more than 8,000 sail and powerprice changes in whatever benchmark is chosenAmerican Stock Exchanges. Stocks with largevessels, and some of the most expensive luxuryto represent the market. For example one mighttrading volume are called “liquid”; they are easi-homes in the world. Whenever I leave on vaca-choose as a benchmark for an equity portfolio theer to trade without inducing a large “markettion I look back over my shoulder and S&P 500 Index or the Wilshire 5,000 index. Inimpact” cost. The latest prices flow into the com-44Wilmottmagazine
puters in “real time” and when the deviationOur billion shares a year amounts tofrom our calculated price for a security is largeenough, we buy what we predict are the under-priced stocks and short the overpriced stocks. Toabout 6 million shares a day, over control risk, we limit each stock we own to cent of our long portfolio. If every long posi-per cent of the total NYSE volume. Ation were at per cent then we would have 40stocks long. But we are continually entering andreduction of ¢ on two thirds of ourexiting positions so at any one time we can havebetween 150 and 300 stocks on the long , or one billion of those shares, Even with this level of risk control, plus addition-al constraints that tend to limit industry or sec-tor concentration, we can have some nasty sur-saves us $ million a yearprises. These come in the form of unexpectedmajor company developments that we can’t pre-dict, such as a disappointing earnings announce-biggest losers on the long side, and the same forand sell $540 million of new shorts, for anotherment. If we were to suddenly lose 40 per cent of athe short side. By comparing the first few with$1,080 million. So one turnover means per cent position, the portfolio could drop 1the rest of the 12 in its group, I can see quickly if$2,160 million and 25 turnovers a year means weper cent. Fortunately we rarely get more than oneany winners or losers seem unusually trading at the rate of about $54 billion perof these “torpedoes” per month. We also getEverything looks normal. Then I walk down theyear. With an average price of $36 per share we’reabout as many favorable surprises, leading tohall to Steve Mizusawa’s office. Steve is watchingtrading billion shares a year. Famed hedgecomparable windfall Bloomberg terminal checking for unusualfund manager Michael Steinhardt, when heWe limit each short position to per cent ofevents that are not part of our prediction modelretired recently, astonished many by announcingthe portfolio so we would have 67 positions if allbut might have a big impact on one of the stockshe had traded a billion shares in one year. Thewere at full size. In practice we typically have 150we trade. When he sees one of these events, suchMedallion Fund, a hedge fund closed to newto 300 positions because we’re always in theas the announcement of a merger, takeover, spin-investors, run by mathematician James Simons,process of building new positions and taking offoff or reorganization, he tells the computer to putincludes a similar even larger trading operationold ones. Our limit on the size of short positions isthe stock on the restricted list: don’t initiate awith a higher rate of turnover and a greaterlower than for long positions because a suddennew position and close out any that we have. Theannual trading volume. adverse move in a short position can be greaterrestricted list also has those stocks which we areOur billion shares a year amounts to aboutthan for a long position. The worst outcome for aunable to sell short, due to our brokers’ inability6 million shares a day, over per cent loss on a stock held long is for the stock to sudden-to borrow the total NYSE volume. A reduction of ¢ only become worthless, leading to a loss of 100 pertwo thirds of our trades, or one billion of thosecent of the original value of the billion shares a yearshares, saves us $ million a year. At an averageSimilarly, if a stock sold short doubles in price,Steve tells me, with his characteristic soft spokentrade size of 1,500 shares, we’re making 4,000the seller loses 100 per cent of the original valuemodesty, that the broker where we do about twotrades a day or 1 million trades (tickets) a year. Atof the stock sold short. But the stock could triplethirds of our business has reduced our commis-an all inclusive average cost of about ¢ peror quadruple in price, or worse, leading to lossessions by about ¢ per share. Steve has beenshare, our billion shares a year generate $ 200 per cent, 300 per cent or more, of the origi-working to achieve this but, as usual, doesn’tmillion a year in commissions and ticket value of the stock sold to this another $ million per year profit Our caution and our risk control measuresTo appreciate the savings you need to realizewhich the brokers make from lending us $210seem to work. Our daily, weekly and monthlyhow much we trade. Our portfolio turns overmillion, and another $ million or more perresults are “positively skewed,” meaning that weabout once every ten days, and with about 253year in profits to them from lending us stock tohave substantially more large winning days,trading days per year, that’s about 25 times persell short, and our brokers currently collectweeks and months than losing ones, and the win-year. A turnover at current levels means we sellabout $ million per year from us. Our mainners tend to be bigger than the losers.$540 million of stocks held long and replacebroker was smart to stay competitive by I scan the computer screen, which is showingthem with $540 million of new stocks, for a totalreducing the day’s 48 most interesting positions,value traded of $1,080 million. We also cover (buyWincluding the 12 biggest gainers and the 12back) $540 million of stock previously sold short To be continued in the next issueWilmottmagazine45
