Ed ThorpA MATHEMATICIAN ON WALL STREETStatistical Arbitrage – Part IIIHow a STAR was born fromCPUs the size of refrigera-tors, and proved in practicehe Bamberger version of statisticalarbitrage was driven by two keyideas. The main source of alpha wasthe short term reversal effect we haddiscovered in 1979/80. The main toolTfor risk reduction was to divide theuniverse of stocks into industry groups of fromtwo to thirteen stocks and trade each group sepa-rately on a dollar-neutral basis. Thus the portfo-lio reduced risk from the market and variousindustry factors. To back test the system and tosimulate real-time trading, we drew uponchilled to a constant 60F by its own cooling sys-rent BOSS return of 15 per cent was not com-Princeton-Newport’s 1,100 square foot computertem and had sealed doors and dust filters to keeppelling. But I had developed another methodroom filled with two million dollars worth ofthe air clean. Since smokers strongly emit tinythat I thought would be a substantial improve-equipment, a domain ordered, organized andparticles for an hour or more afterwards, Gerryment. After BOSS closed we programmed it andoverseen by Steve Mizusawa. Inside were banks ofagreed, with a lot of good natured kidding, not toagain earned satisfactory returns when wegigabyte disk drives the size of washinggo in the computer in January of 1988. By chance, wemachines, plus tape drives and CPUs the size ofOur joint venture was funded by Princeton-missed the crash of ‘87. How would we haverefrigerators. All this sat on a raised floor consist-Newport Partners and run in New York bydone? In October of 1987, market volatilitying of removable panels, under which snaked anBamberger as a turn-key operation. We called itbegan to rise. On Friday, October 16, the Dow, atordered jungle of cables, wires and other connec-BOSS Partners, for “Bamberger (plus) Oakley2,300 or so, fell more than 100 points, over 4%.tors. The room had its own halogen system. InSutton Securities,” the latter a broker dealer serv-On Monday, October 19 it fell again from aboutcase of fire the room flooded with non-com-ing Princeton-Newport Partners and related enti-2,200 to about 1,700, an unthinkable 508 points,bustible “halogen” gas automatically within 80ties. On capital ranging from 30 to 60 millionor 23%, by far the greatest one day percentageseconds. Once this happened the room had toodollars, BOSS started earning in the 25 to 30 perdrop in history. Computer simulations showedlittle oxygen for fire to burn or for people tocent annualized range in 1985. This graduallyour new statistical arbitrage product would havebreathe. We drilled on how to get out in time anddeclined to around 15 per cent or so in a good day. And the violent volatile days thathow to trigger the halogen manually, if neces-Bamberger then elected to retire a produced excellent returns. This was asary. This was high tech in the mid ‘80s. It hasHe felt that in the booming market of the ‘80s, aship for riding out been obviated by the enormous increase in15 per cent return was not worthwhile, and heTo control risk we replaced the segregationcomputer miniaturization, speed, and cheap-wanted to simply enjoy industry groups by the statistical procedureness. Now, for instance, hard disks the size of aPrinceton-Newport was returning 25 per centcalled factor analysis. Factors are common ten-CD can hold several gigabytes. The room wasor so net of fees to investors in 1987 so the cur-dencies shared by several, many, or all compa-36Wilmottmagazine
nies. The most important is the market factor. Forprofits. Expenses of the partnership may affectTable 1. Rates of Return for STAReach stock, this measures the tendency of thatactual returns. 30 day T-Bill Annualized returnDateCapitalSTARSTARS&P 500stock to mimic or track the market. Using histori-was per cent.(millions)ReturnAfter Feesw/Dividendscal prices, the daily returns on any stock can beAlong with the decline of statistical arbitrageJan. %%%expressed as the part due to its tendency to fol-at Morgan Stanley, people began leaving theFeb. %%%low the market plus what’s left over, the systems group that was in charge ofMar. %%%Financial theorists and practitioners have identi-it. Among the departing was David E. Shaw, whoApr. %%%fied a large number of such factors that helpin the words of Timemagazine was “… a formerMay %%%explain securities prices, to a degree which variesprofessor of computer science at ColumbiaJun. %%%with the stock and the factor. Some factors, likeUniversity, [who] had been wooed to Wall StreetJul. %%%participation in a specified industry group orby Morgan Stanley, where he specialized in theAug. %%%sector (. oil, financial) mainly affect subgroupsarcane field of quantitative analysis - using com-Sep. %%%of stocks. Other macroeconomic factors like theputers to spot trends in the market.” Shaw wasOct. %%%market itself, short term interest rates, long termlooking for $10 million in start-up . %%%interest rates, and inflation, affect nearly allPrinceton-Newport Partners was interested. Dec. %%% the spring of 1988, Shaw and I spent theJan. %%%The beauty of a statistical arbitrage product isday in my Newport Beach office, along with someFeb. %%%that it can be designed to approximately neutral-of our key people. We discussed his plan toMar. %%%ize as many of these factors as one desires. Thelaunch an improved statistical arbitrage product,Apr. %%%portfolio becomes market neutral by zeroing outand expand from that base. Princeton-NewportMay %%%the market effect: constrain the relation betweenPartners was able to put up the $10 million heJun. %%%the long and short portfolios so that the totalwanted for start-up. We were very favorablyJul. %%%effect of the market factor on the long side is justimpressed by Shaw and his ideas but we decidedMonthly %%%offset by the total effect on the short side. The port-not to go ahead because we already had a goodAnnualized %%%folio becomes inflation neutral, oil price neutral,statistical arbitrage product. Shaw found otherAnnualized %%%etc., by doing the same thing with each of thosebacking and created one of the most successfulAnn. Sharpe . Of course, there is a trade-off: the reduc-analytic firms on Wall Street. Later Shaw wouldRatio (Approx.)tion in risk is accompanied by a limitation in thebecome a member of the president’s science advi-Correlation of STAR with S&P 500choice of possible portfolios (only ones which aresory committee. Using statistical arbitrage as amarket neutral, inflation neutral, oil price neu-“core” profit center, he expanded into relatedtral, etc., are now allowed) and, therefore, thewould bet on them instead of neutralizing themhedging and arbitrage areas (the Princeton-attempt to reduce risk tends to reduce the Partners business plan again), and hiredWe got help applying factor analysis to theIt was fortunate that we had evolved beyondlarge numbers of very smart well trained quanti-model from John Blin, a former professor of prob-the Bamberger model because, in simulation, itstative types from academia. One of his smartability and statistics, and Steve Bender, a formerreturns continued to fall. Moreover, after a goodhires was Jeff Bezos, who, while researching busi-physicist. Their business, APT, computed and sold1987, Tartaglia had reportedly expanded statisti-ness opportunities in 1994 for Shaw, got the ideatheir current factor analysis for many tradedcal arbitrage at Morgan Stanley in 1988 to somefor an online bookstore and left to startsecurities. We called the new method “STAR” for$900 million long and $900 million short, .“STatistical ARbitrage.” At the request of one ofhad to drive down overall returns for the August of 1988, it was clear that the gov-our investors we sent a trading history to BARRA,The rumor was that they lost between 6 per centernment’s investigation of Jay Regan and othersa world leader in researching and developingand 12 per cent, leading to the winding down ofin the Princeton office of Princeton-Newportfinancial products. They tested STAR with theirthe product. If true, this misfortune may havePartners was likely to be serious, protracted andfactor model E2, which had 55 industry factorscome in part from the decline in performance ofcostly. This led us to phase out our STAR ventureand 13 macroeconomic factors. They found thatthe original product and any modified versionwith Blin and Bender as well as joint venturesour returns were essentially factor neutral. Ourthey might have evolved to, and also to thewith others. It also probably would havereturns did not appear to come from lucky dis-increasing market impact costs of the much larg-destroyed a venture with . Shaw had we elect-guised bets on various trades. Compare the performance of our newed to proceed. In fact, one of our limited partners,If I could predict the performance of factorsapproach, shown in Table “fund of funds” Paloma Partners, picked upWlike the market, inflation, gold, etc., then IFees have been calculated as 20 per cent ofthe Shaw
