JOURNAL OF INVESTMENT MANAGEMENT JOIM

JOIMwww.joim.com

JOURNAL OF INVESTMENT MANAGEMENT, Vol. 5, No. 4, (2007), pp. 5–54

© JOIM 2007

WHAT HAPPENED TO THE QUANTS IN AUGUST 2007?Amir E. Khandani a and Andrew W. Lo b

During the week of August 6, 2007, a number of quantitative long/short equity hedgefunds experienced unprecedented losses. Based on TASS hedge-fund data and simulationsof a specific long/short equity strategy, we hypothesize that the losses were initiated bythe rapid “unwind” of one or more sizable quantitative equity market-neutral portfolios.Given the speed and price impact with which this occurred, it was likely the result of aforced liquidation by a multi-strategy fund or proprietary-trading desk, possibly due to amargin call or a risk reduction. These initial losses then put pressure on a broader set oflong/short and long-only equity portfolios, causing further losses by triggering stop/loss andde-leveraging policies. A significant rebound of these strategies occurred on August 10th,which is also consistent with the unwind hypothesis. This dislocation was apparently causedby forces outside the long/short equity sector—in a completely unrelated set of markets andinstruments—suggesting that systemic risk in the hedge-fund industry may have increasedin recent years.

1 Introduction and summary

The months leading up to August 2007 were atumultuous period for global financial markets,with events in the US sub-prime mortgage marketcasting long shadows over many parts of the finan-cial industry. The blow-up of two Bear Stearns credit

aDepartment of Electrical Engineering and Computer Sci-ence, and Laboratory for Financial Engineering, MIT.bCorresponding author. MIT Sloan School of Management,50 Memorial Drive, E52-454, Cambridge MA 02142; direc-tor, MIT Laboratory for Financial Engineering; and ChiefScientific Officer, AlphaSimplex Group, LLC.

strategies funds in June, the sale of Sowood Capi-tal Management’s portfolio to Citadel after lossesexceeding 50% in July, and mounting problems atCountrywide Financial—the nation’s largest homelender—throughout the second and third quarterof 2007 set the stage for further turmoil in fixed-income and credit markets during the month ofAugust.

But during the week of August 6th, somethingremarkable occurred. Several prominent hedgefunds experienced unprecedented losses that week;however, unlike the Bear Stearns and Sowoodfunds, these hedge funds were invested primarily in

FOURTH QUARTER 2007 5

6 AMIR E. KHANDANI AND ANDREW W. LO

exchange-traded equities, not in sub-prime mort-gages or credit-related instruments. In fact, mostof the hardest-hit funds were employing long/shortequity market-neutral strategies—sometimes called“statistical arbitrage” strategies—that, by construc-tion, did not have significant “beta” exposure, andwhich were supposed to be immune to most marketgyrations. But the most remarkable aspect of thesehedge-fund losses was the fact that they were con-fined almost exclusively to funds using quantitativestrategies. With laser-like precision, model-drivenlong/short equity funds were hit hard on TuesdayAugust 7th and Wednesday August 8th, despite rel-atively little movement in fixed-income and equitymarkets during those two days and no major lossesreported in any other hedge-fund sectors. Then,on Thursday August 9th when the S&P 500 lostnearly 3%, most of these market-neutral fundscontinued their losses, calling into question theirmarket-neutral status.

By Friday, August 10th, the combination of move-ments in equity prices that caused the losses earlierin the week had reversed themselves, reboundingsignificantly, but not completely. However, facedwith mounting losses on the 7th, 8th, and 9th thatexceeded all the standard statistical thresholds forextreme returns, many of the affected funds hadcut their risk exposures along the way, which onlyserved to exacerbate their losses while causing themto miss out on a portion of the reversals on the 10th.And just as quickly as it descended upon the quants,the perfect financial storm was over. At least for themoment.

The following week, the financial press surveyed thecasualties and reported month-to-date losses rang-ing from −5% to −30% for some of the mostconsistently profitable quant funds in the historyof the industry.1 David Viniar, Chief FinancialOfficer of Goldman Sachs argued that “We were see-ing things that were 25-standard deviation moves,several days in a row…. There have been issues in

some of the other quantitative spaces. But nothinglike what we saw last week” (Thal Larsen, 2007).

What happened to the quants in August 2007?

In this paper, we attempt to shed some lighton this question by examining some indirect evi-dence about the profitability of long/short equitystrategies over the past decade and during August2007. We simulate the performance of a specificlong/short equity strategy to see if we can capturethe performance swings during the week of August6, 2007, and then use this strategy to compareand contrast the events of August 2007 with thoseof August 1998. We then turn to individual andaggregate hedge-fund data from the TASS databaseand the Credit Suisse/Tremont hedge-fund indexesto develop a broader understanding of the evolu-tion of long/short equity strategies over the pastdecade.

From these empirical results, we have developed thefollowing tentative hypotheses about August 2007:

1. The losses to quant funds during the secondweek of August 2007 were initiated by the tem-porary price impact resulting from a large andrapid “unwinding” of one or more quantitativeequity market-neutral portfolios. The speed andmagnitude of the price impact suggests that theunwind was likely the result of a sudden liqui-dation of a multi-strategy fund or proprietary-trading desk, perhaps in response to margin callsfrom a deteriorating credit portfolio, a decisionto cut risk in light of current market conditions,or a discrete change in business lines.

2. The price impact of the unwind on August 7–8caused a number of other types of equity funds—long/short, 130/30, and long-only—to cut theirrisk exposures or “de-leverage,” exacerbating thelosses of many of these funds on August 8thand 9th.

JOURNAL OF INVESTMENT MANAGEMENT FOURTH QUARTER 2007

WHAT HAPPENED TO THE QUANTS IN AUGUST 2007? 7

3. The majority of the unwind and de-leveragingoccurred on August 7–9, after which the lossesstopped and a significant—but not complete—reversal occurred on the 10th.

4. This price-impact pattern suggests that the losseswere the short-term side-effects of a sudden(and probably forced) liquidation on August7–8, not a fundamental or permanent break-down in the underlying economic drivers oflong/short equity strategies. However, the coor-dinated losses do imply a growing commoncomponent in this hedge-fund sector.

5. Likely factors contributing to the magnitude ofthe losses of this apparent unwind were: (a) theenormous growth in assets devoted to long/shortequity strategies over the past decade and, morerecently, to various 130/30 and other active-extension strategies; (b) the systematic declinein the profitability of quantitative equity market-neutral strategies, due to increasing competition,technological advances, and institutional andenvironmental changes such as decimalization,the decline in retail order flow, and the decline inequity-market volatility; (c) the increased lever-age needed to maintain the levels of expectedreturns required by hedge-fund investors in theface of lower profitability; (d) the historical liq-uidity of US equity markets and the general lackof awareness (at least prior to August 6, 2007)of just how crowded the long/short equity cat-egory had become; and (e) the unknown sizeand timing of new sub-prime-mortgage-relatedproblems in credit markets, which created a cli-mate of fear and panic, heightening the risksensitivities of managers and investors across allmarkets and style categories.

6. The fact that quantitative funds were singled outduring the week of August 6, 2007 had lessto do with a breakdown of any specific quan-titative algorithms than the apparent suddenliquidation of one or more large quantitativeequity market-neutral portfolios. Because suchportfolios consist primarily of exchanged-traded

instruments, the price impact of the rapidunwind was quickly transmitted to other funds,with the most severe losses experienced by port-folios with the largest overlap to the portfoliothat initiated the unwind. Not surprisingly, theportfolios with the largest overlap were thoseconstructed using similar methods, i.e., quan-titative equity market-neutral methods. But thefact that these portfolios are typically highlydiversified—involving several hundred positionson any given day—suggests that the impact ofthe unwind could be much broader, affectingmany other types of portfolios.

7. The differences between the behavior of our teststrategy in August 2007 and August 1998, theincrease in the number of funds and the averageassets under management per fund in the TASShedge-fund database, the increase in averageabsolute correlations among the CS/Tremonthedge-fund indexes, and the growth of credit-related strategies among hedge funds and pro-prietary trading desks suggest that systemic riskin the hedge-fund industry may have increasedin recent years.

8. The ongoing problems in the sub-prime mort-gage and credit sectors may trigger additionalliquidity shocks in the more liquid hedge-fundstyle categories such as long/short equity, globalmacro, and managed futures. However, theseverity of the impact to long/short equity strate-gies is likely to be muted in the near futuregiven that market participants now have moreinformation regarding the size of this sector andthe potential price-impact of another firesaleliquidation of a long/short equity portfolio.

We wish to emphasize at the outset that thesehypotheses are tentative, based solely on indirectevidence, and without the benefit of very muchhindsight given the recency of these events. Forthese reasons, this paper should be interpreted morelike an evolving case study, not formal academic

FOURTH QUARTER 2007 JOURNAL OF INVESTMENT MANAGEMENT


research. We are focusing on a rather timely topic,which does not afford the luxury of multiple roundsof critical review and revision through which moreenduring research findings are typically forged.

However, we wish to highlight another distinctionbetween academic research and this paper. Originalresearch typically offers novel answers to questionsthat have yet to be resolved. There is little point, andno credit given, to answering questions for whichthe answers are already known. But the answer tothe question of what happened to the quants inAugust 2007 is indeed known, at least to a numberof industry professionals who were directly involvedin these markets and strategies in August 2007.

Therefore, it is an odd task that we haveundertaken—to attempt to explain something that,at least to a subset of potential readers, needs noexplanation. And as a case study, our endeavor mayseem even more misguided because we do not haveready access to any of the primary sources: thehedge funds, proprietary trading desks, and theirprime brokers and major credit counterparties. Forobvious reasons, such sources are not at liberty todisclose any information about their strategies—indeed, any disclosure of proprietary informationis clearly not in the best interests of their investorsor shareholders. Therefore, it is unlikely we willever obtain the necessary information to conduct aconclusive study of the events of August 2007.

It is precisely this well-known lack of transparencyof hedge funds, coupled with genuine intellectualcuriosity and public-policy concerns regarding sys-temic risks in this dynamic industry, that led us toundertake this effort. Because the relevant hedge-fund managers and investors are not able to disclosetheir views on what happened in August 2007,we propose to construct a simple simulacrum ofa quantitative equity market-neutral strategy andstudy its performance, as well as to use otherpublicly available hedge-fund data to round out

our understanding of the long/short equity sec-tor during this challenging period. However, werecognize the difficulty for outsiders to truly under-stand such complex issues, and do not intend to beself-appointed spokesmen for the quants.

Accordingly, we acknowledge in advance that wemay be far off the mark given the limited datawe have to work with, and caution readers to beappropriately skeptical of our analysis, as we are.While some academics may have warned that sys-temic risk in the hedge-fund industry has beenon the rise (see, for example, Carey and Stulz(2007)), none of the academic literature has pro-duced any timely forecasts of when or how suchshocks might occur. Indeed, by definition, a true“shock” is unforecastable. Nevertheless, it is ourhope that the tentative hypotheses suggested byour empirical results, and the simple tools thatwe use to derive them, will stimulate additionalinvestigations—especially by those who do haveaccess to the data—that may lead to a deeperunderstanding of financial market dynamics understress.

We begin in Section 2 with a brief discussion of ter-minology, and in Section 3 we describe the specificquantitative test strategy that we plan to use as our“microscope” to study the effects of August 6–10,2007 on long/short equity strategies. We show inSection 4 that this test strategy does indeed cap-ture the losses that affected so many quants duringthat week. By comparing August 2007 to August1998, in Section 5 we observe that, despite themany similarities between the two periods, thereis one significant difference that may be cause forgreat concern regarding the current level of systemicrisk in the hedge-fund industry—our microscoperevealed not a single sign of stress in August 1998,but has shown systematic deterioration year byyear since then until the outsized losses in August2007. We attempt to trace the origins of this strik-ing difference to various sources. In particular, in



Section 6, we consider the near-exponential growthof assets and funds in the long/short equity category,the secular decline in the expected rate of return ofour test strategy over the years, and the increases inleverage that these two facts imply. With the appro-priate leverage assumptions in hand, we are ableto produce a more realistic simulation of the teststrategy’s performance in August 2007, and in Sec-tion 7 we lay out our “unwind hypothesis.” Thishypothesis relies on the assumption that long/shortequity strategies are less liquid than market partici-pants anticipated, and in Section 8 we estimate theilliquidity exposure of long/short equity funds inthe TASS database. We find evidence that over thepast two years, even this highly liquid sector of thehedge-fund industry has become less liquid. Andin Section 9, we investigate the changes in simplecorrelations across broad-based hedge-fund indexesover time and find that the hedge-fund industry isa more highly “connected” network now than everbefore. We conclude by discussing the broader issueof whether “quant” failed in August 2007 (Section10), some of the limitations of our analysis andpossible extensions (Section 11), and our currentoutlook for systemic risk in the hedge-fund industry(Section 12).

2 Terminology

Among experienced hedge-fund investors and man-agers, there is a clear distinction between the terms“statistical arbitrage,” “quantitative equity market-neutral,” and “long/short equity” strategies. Thefirst category refers to highly technical short-termmean-reversion strategies involving large numbersof securities (hundreds to thousands, depending onthe amount of risk capital), very short holding peri-ods (measured in days to seconds), and substantialcomputational, trading, and IT infrastructure. Thesecond category is more general, involving broadertypes of quantitative models, some with lowerturnover, fewer securities, and inputs other than

past prices such as accounting variables, earningsforecasts, and economic indicators. The third cate-gory is the broadest, including any equity portfoliosthat engage in shortselling, that may or may notbe market-neutral (many long/short equity fundsare long-biased), that may or may not be quantita-tive (fundamental stock-pickers sometimes engagein short positions to hedge their market exposureas well as to bet on poor-performing stocks), andwhere technology need not play an important role.In most hedge-fund databases, this is by far the sin-gle largest category, both in terms of assets and thenumber of funds.

More recently, a fourth category has emerged, the“130/30” or “active extension” strategies, in whicha fund or, more commonly, a managed account of,say $100MM, maintains $130MM of long posi-tions in one set of securities and $30MM of shortpositions in another set of securities. Such a strategyis a natural extension of a long-only fund where thelong-only constraint is relaxed to a limited extent.It is currently one of the fastest-growing areas inthe institutional money management business, andbecause the portfolio construction process is rathertechnical by design, the managers of such productsare primarily quantitative.

For the purposes of this paper, we sometimes referto all of these strategies as “long/short equity”for several reasons. First, these seemingly dis-parate approaches are beginning to overlap. Anumber of statistical arbitrage funds are nowpursuing lower-turnover sub-strategies to increasetheir funds’ capacities, while many long/shortequity funds have turned to higher-turnover sub-strategies as they develop more trading infrastruc-ture and seek more consistent returns. This naturalbusiness progression has blurred the distinctionbetween the long/short equity sub-specialties. Sec-ond, as long/short equity managers have grownin size, technology has naturally begun to playa more important role, even among fundamental



stock-pickers who find that they cannot expandtheir business unless they make more efficient useof their time and skills. Such managers have begunto rely on stock-screening software and portfolio-construction tools that allow them to leverage theirqualitative stock-selection skills, and automatedtrading platforms that allow them to execute theirstock picks more cost-effectively. These new toolshave made quants out of many fundamental stock-pickers. Indeed, even among the long-only equitymanagers, 130/30 strategies are transforming themulti-trillion-dollar equity enhanced-index busi-ness into a quantitative endeavor. We argue thatall four investment categories were impacted by theevents of August 6–10, 2007, largely because theirgrowth has pushed them into each other’s domains.Accordingly, in the event of a rapid unwind of anyequity portfolio, all four types of strategies are likelyto be affected in one way or another.

Therefore, throughout the remainder of thispaper, we shall use the broader term “long/short equity” to refer generically to all of thesedistinct activities, making finer distinctions whenappropriate.

3 Anatomy of a long/short equity strategy

To gauge the impact of the events of August 6–10,2007 on long/short equity portfolios, we con-sider a specific strategy—first proposed by Lehmann(1990) and Lo and MacKinlay (1990)—that wecan analyze directly using individual US equitiesreturns. Given a collection of N securities, considera long/short market-neutral equity strategy consist-ing of an equal dollar amount of long and shortpositions, where at each rebalancing interval, thelong positions consist of “losers” (underperform-ing stocks, relative to some market average) and theshort positions consist of “winners” (outperformingstocks, relative to the same market average). Specif-ically, if ωit is the portfolio weight of security i at

date t , then

ωit = − 1

N(Rit−k − Rmt−k),

Rmt−k ≡ 1

N

N∑i=1

Rit−k (1)

for some k > 0.

Note that the portfolio weights are the negative ofthe degree of outperformance k periods ago, soeach value of k yields a somewhat different strat-egy. For our purposes, we set k = 1 day. By buyingyesterday’s losers and selling yesterday’s winners ateach date, such a strategy actively bets on meanreversion across all N stocks, profiting from rever-sals that occur within the rebalancing interval. Forthis reason, (1) has been called a “contrarian” trad-ing strategy that benefits from market overreaction,i.e., when underperformance is followed by posi-tive returns and vice-versa for outperformance (seeAppendix A.1 for further details).

However, another source of profitability of contrar-ian trading strategies is the fact that they provideliquidity to the marketplace. By definition, losersare stocks that have underperformed relative tosome market average, implying a supply/demandimbalance, i.e., an excess supply that caused theprices of those securities to drop, and vice-versafor winners. By buying losers and selling winners,contrarians are adding to the demand for losersand increasing the supply of winners, thereby sta-bilizing supply/demand imbalances. Traditionally,designated marketmakers such as the NYSE/AMEXspecialists and NASDAQ dealers have played thisrole, for which they are compensated through thebid/offer spread. But over the last decade, hedgefunds and proprietary trading desks have begunto compete with traditional marketmakers, addingenormous amounts of liquidity to US stock mar-kets and earning attractive returns for themselvesand their investors in the process.



In providing liquidity to the market, contrariantrading strategies also have the effect of reducingmarket volatility because they attenuate the move-ment of prices by selling stocks for which there isexcess demand and buying stocks for which thereis excess supply. Therefore, an increasing amountof capital dedicated to market-making strategies isone potential explanation for the secular decline inUS equity-market volatility during the past 10 years.Once this market-making capital is withdrawn fromthe marketplace, volatility should pick up, as it hasover the past several months.

If mean reversion implies that contrarian trad-ing strategies will be profitable, then momentumimplies the reverse. In the presence of return per-sistence, i.e., positively autocorrelated returns, Loand MacKinlay (1990) show that the contrariantrading strategy (1) will exhibit negative profits. Aswith other market-making strategies, the contrar-ian strategy loses when prices exhibit trends, eitherbecause of private information, which the marketmicrostructure literature calls “adverse selection,” ora sustained liquidation in which the market-makerbears the losses by taking the other side and losingvalue as prices move in response to the liquida-tion. Therefore, whether or not (1) is an interestingstrategy in its own right, it can serve as a valu-able indicator of broad-based strategy liquidationsof long and/or short positions, and we will returnto this interpretation in Section 7.

Note that the weights (1) have the property thatthey sum to 0, hence (1) is an example of an “arbi-trage” or “market-neutral” portfolio where the longpositions are exactly offset by the short positions.2

As a result, the portfolio “return” cannot be com-puted in the standard way because there is no netinvestment. In practice, however, the return of sucha strategy over any finite interval is easily calculatedas the profit-and-loss of that strategy’s positions overthe interval divided by the initial capital required tosupport those positions. For example, suppose that

a portfolio consisting of $100MM of long positionsand $100MM of short positions generated prof-its of $2MM over a one-day interval. The returnof this strategy is simply $2MM divided by therequired amount of capital to support the $100MMlong/short positions. Under RegulationT, the mini-mum amount of capital required is $100MM (oftenstated as 2 : 1 leverage, or a 50% margin require-ment), hence the return to the strategy is 2%. If,however, the portfolio manager is a broker/dealer,then Regulation T does not apply (other regula-tions govern the capital adequacy of broker/dealers),and higher levels of leverage may be employed. Forexample, under certain conditions, it is possibleto support a $100MM long/short portfolio withonly $25MM of capital—leverage ratio of 8 : 1—which implies a portfolio return of $2/$25 = 8%.3

Accordingly, the gross dollar investment It of theportfolio (1) and its unleveraged (Reg T) portfolioreturn Rpt are given by

It ≡ 1

2

N∑i=1

|ωit |, Rpt ≡∑N

i=1 ωit Rit

It. (2)

To construct leveraged portfolio returns Lpt (θ) usinga regulatory leverage factor of θ : 1, we simplymultiply (2) by θ/2:4

Lpt (θ) ≡ (θ/2)∑N

i=1 ωit Rit

It. (3)

Lo and MacKinlay (1990) provide a detailed anal-ysis of the unleveraged returns (2) of the contrariantrading strategy, tracing its profitability to meanreversion in individual stock returns as well aspositive lead/lag effects and cross-autocorrelationsacross stocks and across time. However, for ourpurposes, such decompositions are of less relevancethan simply using (1) as an instrument to study theimpact of market events on long/short equity strate-gies during the second week of August 2007. Tothat end, we apply this strategy to the daily returnsof all stocks in the University of Chicago’s CRSP



Database, and to stocks within 10 market-capdeciles, from January 3, 1995 to August 31, 2007.5

Before turning to the performance of the contrar-ian strategy in August 2007, we summarize thestrategy’s historical performance to develop someintuition for its properties. Table 1 provides year-by-year average market capitalizations and share pricesof stocks in each decile from 1995 to 2007,6 andTable 2 reports the year-by-year average daily returnof (1) when applied to stocks within market-capdeciles, as well as for all stocks in our sample. Theresults are impressive. In the first year of our sam-ple, 1995, the strategy produced an average dailyreturn of 1.38% per day, or 345% per year assuminga 250-day year! Of course, this return is unrealis-tic because it ignores a number of market frictionssuch as transactions costs, price impact, shortsalesconstraints, and other institutional limitations. Inparticular, a daily rebalancing interval would implyextraordinarily high turnover across the set of 4,781individual stocks, which was simply not feasible in1995. However, we intend to use this strategy togauge the impact of market movements in August2007 relative to its typical performance, hence weare not as concerned about whether the results areachievable in practice.

The high turnover and the large number of stocksinvolved also highlight the importance that tech-nology plays in strategies like (1), and why fundsthat employ such strategies are predominantlyquantitative. It is nearly impossible for humanportfolio managers and traders to implement a strat-egy involving so many securities and trading sofrequently without making substantial use of quan-titative methods and technological tools such asautomated trading platforms, electronic communi-cations networks, and mathematical optimizationalgorithms. Indeed, part of the liquidity that suchstrategies seem to enjoy—the short holding periods,the rapid-fire implementation of trading signals,and the diversification of profitability across such

a large number of instruments—is directly relatedto technological advances in trading, portfolio con-struction, and risk management. It is no wonderthat the most successful funds in this disciplinehave been founded by computer scientists, math-ematicians, and engineers, not by economists orfundamental stock-pickers.

Table 2 confirms a pattern long recognized bylong/short equity managers—the relation betweenprofitability and market capitalization. Smaller-capstocks generally exhibit more significant ineffi-ciencies, hence the profitability of the contrarianstrategy in the smaller deciles is considerably higherthan in the larger-cap portfolios. For example, theaverage daily return of the strategy in the small-est decile in 1995 is 3.57% in contrast to 0.04% forthe largest decile. Of course, smaller-cap stocks typ-ically have much higher transactions costs and priceimpact, hence they may not be as attractive as thedata might suggest. The trade-off between appar-ent profitability and transactions costs implies thatthe intermediate deciles may be the most oppor-tune from a practical perspective, a conjecture thatwe shall revisit below.

Table 2 also exhibits a strong secular trend ofdeclining average daily returns, a feature that manylong/short equity managers and investors haveobserved. In 1995, the average daily return of thecontrarian strategy for all stocks in our sample is1.38%, but by 2000, the average daily return dropsto 0.44% and the year-to-date figure for 2007 (upto August 31) is 0.13%. Figure 1 illustrates the near-monotonic decline of the expected returns of thisstrategy, no doubt a reflection of increased compe-tition, changes in market structure, improvementsin trading technology and electronic connectivity,the growth in assets devoted to this type of strategy,and the corresponding decline in US equity-marketvolatility over the last decade.7 This secular declinein profitability has significant implications for theuse of leverage, which we will explore in Section 6.



Tab

le1

Year

-by-

year

aver

age

mar

ketc

apit

aliz

atio

nsan

dsh

are

pric

esof

US

com

mon

stoc

ks(C

RSP

shar

eco

des1

0an

d11

)wit

hsh

are

pric

esab

ove

$5an

dbe

low

$2,0

00w

ithi

nm

arke

t-ca

pita

lizat

ion

deci

les

from

Janu

ary

3,19

95to

Aug

ust3

1,20

07.

Dec

iles

bym

arke

tcap

ital

izat

ion

All

Year

Smal

lest

Dec

ile2

Dec

ile3

Dec

ile4

Dec

ile5

Dec

ile6

Dec

ile7

Dec

ile8

Dec

ile9

Larg

est

All

Cou

nt

Pane

lA:A

vera

gem

arke

tcap

italiz

atio

n($

MM

)19

9517

3457

8612

719

030

555

61,

269

8,25

01,

121

4,78

119

9618

3861

9214

021

033

459

11,

349

9,59

91,

293

5,27

319

9722

4774

109

164

248

407

708

1,53

912

,401

1,62

85,

393

1998

2449

7811

517

227

444

477

31,

735

16,0

112,

088

5,19

519

9923

5083

126

200

310

507

905

2,08

622

,002

2,76

44,

736

2000

2253

9214

824

939

864

71,

145

2,54

526

,050

3,36

14,

566

2001

2560

106

181

288

440

723

1,26

82,

863

26,0

073,

348

3,78

220

0227

6411

118

828

945

071

11,

235

2,69

623

,463

3,08

23,

486

2003

3173

130

213

327

498

795

1,37

12,

951

24,1

853,

146

3,37

620

0437

8614

924

436

356

987

51,

554

3,26

826

,093

3,42

53,

741

2005

4097

171

266

408

651

1,02

61,

772

3,81

128

,164

3,74

13,

721

2006

4410

518

729

845

271

71,

145

1,90

74,

073

30,1

543,

988

3,76

420

0747

109

195

313

472

739

1,18

82,

120

4,38

733

,152

4,36

33,

623

Pane

lB:A

vera

gepr

ice

($)

1995

11.0

711

.55

13.3

714

.84

16.9

618

.90

22.5

426

.49

32.4

545

.14

21.5

54,

781

1996

11.3

011

.92

13.0

614

.36

17.1

120

.12

23.4

728

.29

33.0

247

.95

22.4

05,

273

1997

12.3

913

.33

14.4

215

.88

18.5

222

.21

26.2

031

.07

36.5

252

.16

24.5

65,

393

1998

11.3

713

.15

14.3

415

.55

17.9

421

.76

25.4

029

.97

36.5

554

.06

24.5

35,

195

1999

10.3

111

.79

12.8

714

.14

16.5

821

.01

24.1

331

.62

36.9

954

.04

23.8

04,

736

2000

9.74

11.5

912

.31

13.8

517

.86

21.8

525

.89

34.0

340

.49

60.2

525

.39

4,56

620

0111

.34

13.1

013

.66

15.4

718

.47

20.7

025

.37

31.4

734

.96

42.7

123

.04

3,78

220

0212

.15

14.2

015

.02

16.1

618

.88

21.3

825

.35

28.4

333

.18

39.5

222

.73

3,48

620

0313

.65

15.5

616

.55

17.1

519

.89

21.2

526

.12

28.5

333

.86

41.8

323

.61

3,37

620

0413

.81

16.3

316

.88

17.8

420

.33

24.3

728

.21

32.5

438

.68

46.9

225

.84

3,74

120

0513

.48

16.4

016

.34

18.0

120

.84

25.0

129

.25

38.5

142

.50

51.1

427

.42

3,72

120

0613

.06

16.0

816

.28

19.3

321

.56

25.9

530

.44

40.0

845

.42

51.9

428

.24

3,76

420

0712

.61

15.1

816

.75

18.3

022

.32

27.3

230

.30

38.7

048

.70

56.5

628

.94

3,62

3



Tab

le2

Year

-by-

year

aver

age

daily

retu

rns,

stan

dard

devi

atio

nsof

daily

retu

rns,

and

annu

aliz

edSh

arpe

rati

os(√ 25

0×

(ave

rage

daily

retu

rn/st

anda

rdde

viat

ion)

)ofL

oan

dM

acK

inla

y’s(

1990

)con

trar

ian

trad

ing

stra

tegy

appl

ied

toal

lUS

com

mon

stoc

ks(C

RSP

shar

eco

des

10an

d11

)w

ith

shar

epr

ices

abov

e$5

and

less

than

$2,0

00,

and

mar

ket-

capi

taliz

atio

nde

cile

s,fr

omJa

nuar

y3,

1995

toA

ugus

t31,

2007

.

Mar

ketc

apit

aliz

atio

nde

cile

s

Year

Smal

lest

Dec

ile2

Dec

ile3

Dec

ile4

Dec

ile5

Dec

ile6

Dec

ile7

Dec

ile8

Dec

ile9

Larg

est

All

(%)

Aver

age

daily

retu

rns(

%)

1995

3.57

2.75

1.94

1.62

1.07

0.61

0.21

−0.0

1−0

.02

0.04

1.38

1996

3.58

2.47

1.82

1.34

0.84

0.52

0.19

−0.1

1−0

.04

0.02

1.17

1997

2.83

1.94

1.34

1.02

0.62

0.28

0.04

−0.1

20.

060.

140.

8819

982.

381.

451.

110.

620.

290.

03−0

.04

−0.1

20.

030.

100.

5719

992.

561.

410.

820.

38−0

.01

−0.1

1−0

.21

−0.3

5−0

.01

0.06

0.44

2000

2.58

1.59

0.92

0.14

0.03

−0.0

2−0

.14

0.16

0.00

0.03

0.44

2001

2.15

1.25

0.57

0.24

−0.0

10.

060.

13−0

.10

−0.1

1−0

.11

0.31

2002

1.67

0.85

0.53

0.29

0.28

0.26

0.28

0.20

0.11

0.09

0.45

2003

1.00

0.26

−0.0

70.

040.

110.

200.

180.

150.

040.

050.

2120

041.

170.

480.

310.

380.

250.

290.

220.

150.

05−0

.01

0.37

2005

1.05

0.39

0.13

0.11

0.09

0.11

0.05

0.08

0.01

0.02

0.26

2006

0.86

0.26

0.11

0.06

0.05

−0.0

2−0

.02

0.05

0.06

0.00

0.15

2007

0.57

0.09

0.08

0.18

0.16

−0.0

80.

04−0

.04

0.00

−0.0

40.

13

Stan

dard

devi

atio

nof

daily

retu

rns(

%)

1995

0.92

0.88

0.81

0.82

0.78

0.77

0.73

0.67

0.63

0.65

0.40

1996

1.07

1.00

0.79

0.81

0.88

0.84

0.90

0.90

0.83

0.73

0.48

1997

1.04

0.98

0.96

0.96

1.12

1.00

0.91

0.99

0.98

0.77

0.68

1998

1.59

1.67

1.23

1.22

1.57

1.25

1.29

1.43

1.08

1.00

0.84

1999

1.66

1.82

1.44

1.44

1.79

1.57

1.71

1.70

1.57

1.07

1.02

2000

1.57

1.69

2.06

1.89

1.76

2.15

2.18

2.29

2.44

2.56

1.68

2001

1.33

1.26

1.46

1.62

1.65

1.64

1.83

1.91

2.28

2.29

1.43



Tab

le2

(Con

tinue

d)

Mar

ketc

apit

aliz

atio

nde

cile

s

Year

Smal

lest

Dec

ile2

Dec

ile3

Dec

ile4

Dec

ile5

Dec

ile6

Dec

ile7

Dec

ile8

Dec

ile9

Larg

est

All

(%)

2002

1.17

0.89

1.14

1.07

1.25

1.11

1.30

1.42

1.50

1.50

0.98

2003

1.11

0.81

0.95

0.89

0.86

0.81

0.77

0.76

0.75

0.56

0.54

2004

1.35

1.01

0.87

0.76

0.76

0.78

0.80

0.74

0.69

0.57

0.53

2005

1.35

0.80

0.89

0.70

0.77

0.77

0.65

0.73

0.57

0.56

0.46

2006

1.07

0.90

0.83

0.84

0.70

1.07

0.68

0.68

0.64

0.61

0.52

2007

0.96

1.02

1.00

0.99

1.06

1.44

1.00

0.87

0.67

0.56

0.72

Ann

ualiz

edSh

arpe

ratio

(0%

risk

free

rate

)19

9561

.27

49.2

037

.79

31.2

621

.49

12.6

84.

62−0

.22

−0.5

40.

8753

.87

1996

53.0

839

.12

36.2

726

.10

15.1

79.

853.

38−1

.89

−0.6

90.

3638

.26

1997

43.1

531

.19

22.0

016

.66

8.67

4.45

0.74

−1.8

80.

952.

7920

.46

1998

23.6

113

.78

14.2

28.

092.

920.

39−0

.54

−1.3

20.

431.

5810

.62

1999

24.3

212

.25

9.05

4.22

−0.1

1−1

.08

−1.9

3−3

.23

−0.0

90.

826.

8120

0025

.96

14.9

17.

041.

180.

31−0

.18

−1.0

41.

140.

010.

214.

1720

0125

.56

15.6

86.

152.

30−0

.05

0.57

1.09

−0.7

9−0

.79

−0.7

33.

4620

0222

.54

15.1

07.

304.

283.

573.

683.

382.

241.

130.

987.

2520

0314

.32

5.19

−1.1

10.

631.

943.

913.

643.

090.

891.

335.

9620

0413

.76

7.55

5.60

7.96

5.11

5.90

4.27

3.20

1.12

−0.3

311

.07

2005

12.3

37.

722.

262.

421.

952.

291.

311.

740.

360.

628.

8520

0612

.72

4.49

2.08

1.18

1.14

−0.2

6−0

.56

1.08

1.60

−0.0

34.

4720

079.

401.

451.

332.

932.

40−0

.84

0.69

−0.7

4−0

.05

−1.0

32.

79



-1%

0%

1%

2%

3%

4%

5%

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Ave

rag

eD

aily

Ret

urn

s

Smallest Decile 2 Decile 3 Decile 4 Decile 5 Decile 6 Decile 7 Decile 8Decile 9 Largest All

Figure 1 Year-by-year average daily returns of Lo and MacKinlay’s (1990) contrarian trading strategyapplied to all US common stocks (CRSP share codes 10 and 11) with share prices above $5 and less than$2,000, and market-capitalization deciles, from January 3, 1995 to August 31, 2007.

The third panel of Table 2 reports the annualizedratio of the contrarian strategy’s daily mean returnto its daily standard deviation, where the annual-ization is performed by multiplying the ratio by√

250. This is the Sharpe ratio relative to a 0% risk-free rate, and is one simple measure of the strategy’sexpected return per unit risk. Although a Sharperatio of 53.87 in 1995 may seem absurdly high, itshould be kept in mind that in 1995, this strategycalls for the daily rebalancing of a portfolio with4,781 stocks on average (see Table 1). The trans-actions costs involved in such rebalancing wouldhave been formidable, but if one had the ability ortechnology to engage in such broad-based market-making, extraordinary Sharpe ratios may not be sounrealistic.8 Indeed, we expect the Sharpe ratios ofmore formal market-making activities such as spe-cialist profits on the New York Stock Exchange to

be quite high given the economics of price discov-ery. Therefore, the Sharpe ratios in Table 2 maybe somewhat inflated because we have not incorpo-rated transactions costs, but they are probably notoff by an order of magnitude, and their attractivelevels provide one explanation for the popularity ofstatistical arbitrage strategies among investors andhedge-fund managers.

4 What happened in August 2007?

Table 3 presents the unleveraged daily returns of thecontrarian strategy over the five-week period fromMonday, July 30 to Friday, August 31, 2007 appliedto our entire universe of stocks and to market-capdeciles. The three days in the second week—August7th, 8th, and 9th—are the outliers, with losses



Tab

le3

Dai

lyre

turn

sof

Loan

dM

acK

inla

y’s

(199

0)co

ntra

rian

trad

ing

stra

tegy

appl

ied

toal

lUS

com

mon

stoc

ks(C

RSP

shar

eco

des

10an

d11

)w

ith

shar

epr

ices

abov

e$5

and

less

than

$2,0

00,a

ndm

arke

t-ca

pita

lizat

ion

deci

les,

from

Mon

day

July

30,2

007

toFr

iday

Aug

ust3

1,20

07.



0.8

0.9

1.0

1.1

1.2

1.3

20070103 20070202 20070306 20070404 20070504 20070605 20070705 20070803

Cu

mu

lati

veR

etu

rn

0

2

4

6

8

10

Bill

ion

so

fS

har

esT

rad

ed

NYSE Daily Share Volume Contrarian CumReturn

Figure 2 Cumulative return of the contrarian trading strategy from January 3 to August 31, 2007, andthe NYSE daily share volume during this same period.

of −1.16%, −2.83%, and −2.86%, respectively,yielding a cumulative three-day loss of −6.85%.9

Although this three-day return may not seem thatsignificant—especially in the hedge-fund worldwhere volatility is a fact of life—note from Table 2that the contrarian strategy’s 2006 daily standarddeviation is 0.52%, so a −6.85% cumulative returnrepresents a loss of 7.6 standard deviations assum-ing independently and identically distributed dailyreturns!10 Moreover, many long/short equity man-agers were employing leverage (see Section 6 forfurther discussion), hence their realized returns weremagnified several-fold.

Curiously, a significant fraction of the losses wasreversed on Friday, August 10th, when the contrar-ian strategy yielded a return of 5.92%, which wasanother extreme outlier of 11.4 standard deviations.In fact, the strategy’s cumulative return for the entireweek of August 6th was −0.43%, not an unusual

weekly return in any respect. This reversal is a tell-tale sign of a liquidity trade. In fact, the plot inFigure 2 of the cumulative return of the contrarianstrategy from January 3 to August 31, 2007 showsa reasonably steady positive trend interrupted by aprominent dip during the second week of August,after which the trend seems to continue. The ele-vated levels of NYSE share volume during the latterpart of July and the first half of August, along with amini-dip in July in the contrarian cumulative returnseries, suggest the possibility that liquidations mayhave started several weeks prior to the August 7–10 event. We shall return to this interpretation inSection 7.

The decile returns in Table 3 show that the losses onAugust 7–9 were even more pronounced in some ofthe intermediate deciles, with cumulative three-dayreturns of −8.09% in decile 3, −9.33% in decile4, −8.95% in decile 5, and −8.81% in decile 8.



But as in the main strategy, these decile portfoliosexperienced sharp increases on Friday, August 10th,in most cases recouping a significant fraction of thelosses. We shall return to this empirical fact in Sec-tion 7 when we consider various interpretations forthe pattern of losses on August 7–9.

What makes this pattern of loss and gain so puz-zling is the fact that there were virtually no signsof market turmoil outside the world of quantitativeequity market-neutral funds on August 7th and 8th.For example, Table 4 reports the daily returns of9 major market indexes spanning a broad array ofasset classes (stocks, bonds, currencies, commodi-ties, and volatility) from July 30 to August 31, 2007,and nothing remarkable occurred on August 7thand 8th when the contrarian strategy first began tosuffer extreme losses. On August 9th, the S&P 500did lose 2.95% and the VIX jumped by 5.03, sig-nificant one-day moves for both indexes. But thesechanges cannot explain the losses earlier in the week,nor can they explain the outsized losses of manygenuinely market-neutral equity hedge funds, i.e.,funds that had virtually no beta exposure to the S&P500 and positive exposure to volatility.

The one remaining explanation for these extraordi-nary return patterns is that they were the result ofbroad-based momentum due to a large-scale strat-egy liquidation, as discussed in Section 3, and whenthe liquidation had run its course, the liquidation-driven momentum turned into a strong burst ofmean reversion that caused Friday’s reversal. Weshall return to this explanation in Section 7, afterwe explore the differences between August 1998and August 2007 and the implications for expectedreturns and leverage.

5 Comparing August 2007 with August 1998

The behavior of the contrarian strategy during thesecond week of August 2007 becomes even more

significant when compared to the performance ofthe same strategy during August 1998, aroundthe time of the Long Term Capital Management(LTCM) debacle. On August 17, 1998 Russiadefaulted on its GKO government bonds, causing aglobal flight to quality that widened credit spreadswhich, in turn, generated extreme losses in the daysthat followed for LTCM and other fixed-incomearbitrage hedge funds and proprietary trading desks.The specific mechanism that caused these losses—widening credit spreads that generated margin calls,which caused the unwinding of illiquid portfo-lios, generating further losses and additional margincalls, leading ultimately to a fund’s collapse—is vir-tually identical to the sub-prime mortgage problemsthat affected Bear Stearns and other credit-relatedhedge funds in 2007.

However, there is one significant difference betweenAugust 1998 and August 2007. Table 5 reportsthe daily returns of the contrarian strategy (1) dur-ing the months of August and September 1998,which show that the turmoil in fixed-income mar-kets had little or no effect on the profitabilityof our long/short equity strategy. In contrast toAugust 2007 where an apparent demand for liq-uidity caused a firesale liquidation that is easilyobserved in the contrarian strategy’s daily returns,the well-documented demand for liquidity in thefixed-income arbitrage space of August 1998 hadno discernible impact on the very same strategy.This is a significant difference that signals a greaterdegree of financial-market integration in 2007 thanin 1998. While this may be viewed positively as asign of progress in financial markets and technol-ogy, along with the many benefits of integrationis the cost that a financial crisis in one sector canhave dramatic repercussions in several others, i.e.,contagion.

There are several possible explanations for the dif-ference between August 1998 and August 2007.One interpretation is that in 1998, there were



Tab

le4

Dai

lyre

turn

sof

vari

ous

mar

ket

inde

xes

from

Mon

day

July

30,2

007

toFr

iday

Aug

ust

31,2

007.

Wit

hth

eex

cept

ion

ofth

eG

oldm

anSa

chs

Com

mod

itie

sIn

dex

and

the

Trad

eW

eigh

ted

USD

Inde

x,w

hich

are

obta

ined

from

the

Glo

balF

inan

cial

Dat

abas

e,al

lot

her

data

seri

esar

eob

tain

edfr

omD

atas

trea

m.

Inal

lcas

esth

eto

talr

etur

nsin

dex

isus

ed,

whi

chca

ptur

eth

eef

fect

sof

any

coup

ons

and/

ordi

vide

nds

that

wou

ldac

crue

toan

inve

stor

inth

eun

derl

ying

asse

tsof

thes

ein

dexe

s.



Tab

le5

Dai

lyre

turn

sof

Loan

dM

acK

inla

y’s

(199

0)co

ntra

rian

trad

ing

stra

tegy

appl

ied

toal

lUS

com

mon

stoc

ks(C

RSP

shar

eco

des

10an

d11

)w

ith

shar

epr

ices

abov

e$5

and

less

than

$2,0

00,

and

mar

ket-

capi

taliz

atio

nde

cile

s,fr

omM

onda

yA

ugus

t3,

1998

toFr

iday

Sept

embe

r30

,199

8.H

ighl

ight

edda

tes

are:

Aug

ust

17(d

efau

ltof

Rus

sian

GK

Obo

nds)

,Aug

ust

21(L

TC

Mlo

ses

$550

MM

inon

eda

y),S

epte

mbe

r3(fi

rstL

TC

Mle

tter

toin

vest

orsr

egar

ding

thei

rlos

ses)

,and

Sept

embe

r24

(new

sabo

utth

eba

ilout

byth

eco

nsor

tium

).



Tab

le5

(Con

tinue

d)



fewer multi-strategy funds and proprietary-tradingdesks engaged in both fixed-income arbitrage andlong/short equity, so the demand for liquid-ity caused by deteriorating fixed-income arbitragestrategies did not spill over as readily to long/shortequity portfolios. Another possible explanation isthat the amount of capital engaged in long/shortequity strategies, particularly statistical arbitragestrategies, was not large enough to cause any sig-nificant dislocation even if such strategies wereunwound quickly in August 1998. A third possi-bility is that in 1998, long/short equity funds didnot employ as much leverage as they were apparentlyusing in 2007.

We argue in the remaining sections that all three ofthese interpretations may be correct to some degree.

6 Total assets, expected returns, and leverage

To see how crowded the long/short equity cate-gory has become in recent years, we consider thegrowth in the number of funds and assets undermanagement (AUM) in the Long/Short EquityHedge and Equity Market Neutral categories of theTASS hedge-fund database.11 The TASS databaseis divided into two parts: “Live” and “Grave-yard” funds. Hedge funds are recorded in the Livedatabase if they are considered active as of thedate of the snapshot. Once a hedge fund decidesnot to report its performance, liquidates, closes tonew investment, restructures, or merges with otherhedge funds the fund is transferred into the Grave-yard database. A hedge fund can only be listed inthe Graveyard database after having been listed inthe Live database.12

Figure 3 shows that the Long/Short Equity Hedgefunds are the most numerous, with over 600funds in the Live database during the most recentmonths.13 However, the number of Equity Mar-ket Neutral funds has clearly grown rapidly over

the last two years, with just over 100 live fundsin the most recent months. Combining these twocategories and dividing the total assets under man-agement by the total number of funds in both Liveand Graveyard databases, we see from Figure 3that the average assets per fund has increased expo-nentially since 1994, starting out at $62MM inJanuary 1994 and ending at $229MM in July2007.

These assets do not reflect the inflows to activeextension strategies such as 130/30 funds, whichis one of the fastest growing products in the insti-tutional asset management industry. A recentlypublished research report estimates that $75 billionis currently devoted to such strategies, and in fiveyears this could grow to $1 trillion (see MerrillLynch, 2007). Although such strategies are netlong by construction, the fact that they hold shortpositions of up to 30% of their sizable asset basehas significant implications for long/short equityhedge funds. For example, because of the increasein shortselling due to 130/30 strategies, short-ing “hard-to-borrow” securities has become harder,more securities now fall into the hard-to-borrowcategory, short positions are less liquid, and “shortsqueezes” are more likely.

Of course, it is possible that the securities shortedby 130/30 strategies are held long by otherlong/short equity hedge funds and vice versa, whichwould enhance liquidity. But the factors causing130/30 strategies to short a security (e.g., finan-cial ratios, price patterns, bad news) are likely tobe the same factors causing hedge funds to shortthat security. Moreover, the naturally quantitativenature of 130/30 strategies creates an unavoid-able commonality between them and quantitativeequity market-neutral strategies. For example, theuse of commercially available factor-based port-folio optimizers such as those of MSCI/BARRA,Northfield Information Systems, and APT byboth 130/30 managers and equity market-neutral



0

200

400

600

800

1000

1200

Jan-94 Jan-96 Jan-98 Jan-00 Jan-02 Jan-04 Jan-06

Nu

mb

ero

fF

un

ds

0

50

100

150

200

250

AU

MP

erF

un

d($

MM

)

Graveyard Equity Market Neutral

Graveyard Long/Short Equity Hedge

Live Equity Market Neutral

Live Long/Short Equity Hedge

AUM Per Fund (Live and Graveyard)

Figure 3 Number of funds in the Long/Short Equity Hedge and Equity Market Neutral categories of theTASS database, and average assets under management per fund, from January 1994 to July 2007.

managers can create common factor exposuresbetween 130/30 and market-neutral portfolios.

The simultaneous increase in the number oflong/short equity funds, average assets per fund,and the growth of related strategies like 130/30,imply greater competition and, inevitably, reducedprofitability of the strategies employed by suchfunds. This implication is confirmed in the case ofthe contrarian trading strategy (1), as Figure 4 illus-trates. As the total assets in the Long/Short EquityHedge and Equity Market Neutral categories grow,the average daily return of the contrarian strategydeclines, reaching a low of 0.13% in 2007, andwhere the total assets in these two categories are at anall-time high of over $160 billion at the beginningof 2007.

It may seem counterintuitive that assets would flowinto hedge-fund strategies with declining expected

returns. However, recall that the average dailyreturns reported in Table 2 and plotted in Figure 4are based on unleveraged returns. As these strategiesbegin to decay, hedge-fund managers have typi-cally employed more leverage so as to maintain thelevel of expected returns that investors have cometo expect, particularly when the volatilities of theunderlying instruments have experienced the kindof secular decline in volatility that US equities haveduring this time period.14 And because many hedgefunds rely on leverage, the size of the positionsare often considerably larger than the amount ofcollateral posted to support those positions. Lever-age has the effect of a magnifying glass, expandingsmall profit opportunities into larger ones, but alsoexpanding small losses into larger losses. And whenadverse changes in market prices reduce the marketvalue of collateral, credit is withdrawn quickly, andthe subsequent sudden liquidation of large positionsover short periods of time can lead to widespread



0

20

40

60

80

100

120

140

160

180

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

AU

M($

Bill

ion

)

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

Ave

rag

eD

aily

Ret

urn

Equity Market Neutral

Long/Short Equity Hedge

Contrarian Avg Daily Return

Figure 4 Beginning-of-year assets under management for funds in Long/Short Equity Hedge and EquityMarket Neutral categories of the TASS database, from 1995 to 2007, and year-by-year average daily returnsof Lo and MacKinlay’s (1990) contrarian trading strategy applied to all US common stocks (CRSP sharecodes 10 and 11) with share prices above $5 and less than $2,000, from January 3, 1995 to August 31,2007.

financial panic, as in the aftermath of the default ofRussian government debt in August 1998.

To see how significant an effect this might be inthe long/short equity sector, we compute the neces-sary amount of leverage required in each year after1998 to yield an expected return for the contrar-ian strategy that is equal to 1998’s level. In otherwords, we seek values θ∗ for the leverage ratio suchthat:

E[Lpt ] ≡ θ∗

2E[Rpt ] = E[Rp,1998] (4a)

θ∗ = 2 E[Rp,1998]E[Rpt ] , t = 1999, . . . , 2007

(4b)

where (4) follows from the definition of leveragedreturns (3) and the factor of 2 follows from thedefinition of leverage as the sum of the gross longand short positions (which are equal in the caseof market-neutral portfolios) divided by the invest-ment capital. Table 6 shows that there has beensignificant “alpha decay” of the contrarian strategybetween 1998 and 2007, so much so that a leverageratio of almost 9:1 was needed in 2007 to yield anexpected return comparable to 1998 levels!

We can now simulate a more realistic version ofthe contrarian strategy in August 2007 using the2006 leverage ratio of approximately 8:1 as sug-gested by Table 6, simply by multiplying the entriesin Table 3 by 8/2 = 4, which we do in Table 7and Figure 5.15 These returns illustrate the potential



Table 6 Year-by-year average daily returns of Loand MacKinlay’s (1990) contrarian trading strategyapplied to all US common stocks (CRSP share codes10 and 11) with share prices above $5 and less than$2,000, from 1998 to 2007, and the return multi-pliers and leverage factors needed to yield the sameaverage return as in 1998.

Average Requireddaily Return leverage

Year return (%) multiplier ratio

1998 0.57 1.00 2.001999 0.44 1.28 2.572000 0.44 1.28 2.562001 0.31 1.81 3.632002 0.45 1.26 2.522003 0.21 2.77 5.532004 0.37 1.52 3.042005 0.26 2.20 4.402006 0.15 3.88 7.762007 0.13 4.48 8.96

losses that affected long/short equity managers dur-ing the week of August 6th. A naive statisticalarbitrage strategy like (1), with a leverage ratio of8:1, would have lost −4.64% on August 7th, fol-lowed by daily returns of −11.33% and −11.43%,respectively, on August 8th and 9th. By the closeof business on August 9th, the leveraged contrarianstrategy would have lost a little over a quarter of theassets it started with three days before!

The fact that the strategy recovered sharply onAugust 10th with a leveraged return of 23.67% issmall comfort for managers and investors who cuttheir risks on Wednesday and Thursday in responseto the unusual size and speed of the losses over thosetwo days. For those with the fortitude (and thecredit lines) to maintain their positions throughoutthe week, they would have experienced an arith-metically compounded weekly return of −1.72%,

which is not an unusual return in any respect.16

However, with cumulative losses of −25% betweenthe 6th and the 9th, many managers capitulated andwere forced to de-leverage prior to Friday’s reversal.

7 The unwind hypothesis

With the empirically more plausible results ofTable 7 in hand, we are now in a position to developsome additional hypotheses about the events ofAugust 2007, which we shall refer to collectivelyas the “unwind hypothesis.”

The fact that the leveraged contrarian strategylost −4.64% on Tuesday August 7th, and contin-ued to lose another −11.33% on the 8th, suggestsa sudden liquidation of one or more sizable market-neutral equity portfolios. Only a sudden liquidationwould cause the strategy to lose close to −5% inthe absence of any other significant market devel-opments. And the logic behind the inference thatmarket-neutral funds were being liquidated is thefact that both the S&P 500 and MSCI-ex-USindexes showed gains on August 7th and 8th, henceit is unlikely that sizable long-biased funds wereunwound on these two days.

The timing of these losses—shortly after month-end of a very challenging month for many hedge-fund strategies—is also suggestive. The formalprocess of marking portfolios to market typicallytakes several business days after month-end, andAugust 7–9 may well be the first time managers andinvestors were forced to confront the extraordinarycredit-related losses they suffered in July, which mayhave triggered the initial unwind of their more liq-uid investments, e.g., their equity portfolios, duringthis period.

The large losses on Tuesday and Wednesday—amounting to −15.98% for our leveraged con-trarian strategy—would almost surely have spilled



Tab

le7

Leve

rage

dda

ilyre

turn

sof

Loan

dM

acK

inla

y’s

(199

0)co

ntra

rian

trad

ing

stra

tegy

appl

ied

toal

lU

Sco

mm

onst

ocks

(CR

SPsh

are

code

s10

and

11)

wit

hsh

are

pric

esab

ove

$5an

dle

ssth

an$2

,000

,and

mar

ket-

capi

taliz

atio

nde

cile

s,fr

omM

onda

yJu

ly30

,200

7to

Frid

ayA

ugus

t31,

2007

,wit

h8:

1le

vera

geor

are

turn

mul

tipl

ier

of4.



-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

8/1/2007 8/6/2007 8/11/2007 8/16/2007 8/21/2007 8/26/2007 8/31/2007

Leveraged Contrarian Strategy S&P 500

S&P 600 (Small Cap) Lehman Corp-Gov

GSCI USD

Figure 5 Leveraged daily returns of Lo and MacKinlay’s (1990) contrarian trading strategy applied to allUS common stocks (CRSP share codes 10 and 11) with share prices above $5 and less than $2,000, andmiscellaneous indexes, for the month of August 2007, with 8 : 1 leverage or a return multiplier of 4.

over to long/short equity funds as well as to cer-tain quantitative long-only funds. In particular, ifour hypothesis is correct that the losses on August7th and 8th were caused by the unwinding of largeequity market-neutral portfolios, then any explicitfactors used to construct that portfolio would havegenerated a loss for other portfolios with the samefactor exposures. For example, if the portfoliosthat were unwound happened to be long low-P/E stocks and short low-dividend-yield stocks, theunwind will cause low-P/E stocks to decline andlow-dividend-yield stocks to rise (albeit temporarily,until the unwind is complete). All other portfolioswith these same factor exposures will suffer lossesduring the unwind process as well.

How likely is it that other funds would have thesame factor exposures? If they use similar quantita-tive portfolio construction techniques, then more

often than not, they will make the same kindof bets because these techniques are based on thesame historical data, which will point to the sameempirical anomalies to be exploited, e.g., the valuepremium, the size premium, the January effect, six-month momentum, one-month mean reversion,earnings surprise, etc. Moreover, the widespreaduse of standardized factor risk models such as thosefrom MSCI/BARRA, Northfield Information Sys-tems, and APT by many quantitative managers willalmost certainly create common exposures amongthose managers to the risk factors contained in suchplatforms.

But even more significant is the fact that manyof these empirical regularities have been incor-porated into non-quantitative equity investmentprocesses, including fundamental “bottom-up” val-uation approaches like value/growth characteristics,



earnings quality, and financial ratio analysis. There-fore, a sudden liquidation of a quantitative equitymarket-neutral portfolio could have far broaderrepercussions, depending on that portfolio’s specificfactor exposures.

Table 7 contains another interesting pattern that isconsistent with a statistical arbitrage unwind—thefact that the losses on August 7th and 8th were mostsevere for some of the intermediate-decile portfo-lios (deciles 3–5 and 8 each experienced cumulativelosses greater than the other deciles and the entireuniverse of securities). Given the pattern of aver-age daily returns of the contrarian strategy in decileportfolios (see Table 2), it is the intermediate-decileportfolios that should be most attractive to statisti-cal arbitrage funds. Securities in the larger deciles donot exhibit sufficient profitability, and securities inthe smaller deciles are too illiquid to trade in largevolume, hence they will not be of interest to thelarger funds.

In the face of the large losses of August 7–8,most of the affected funds—which includes market-neutral, long/short equity, 130/30, and certainlong-only funds—would likely have cut their riskprior toThursday’s open by reducing their exposuresor “de-leveraging,” either voluntarily or becausethey exceeded borrowing and risk limits set bytheir prime brokers and other creditors. This wasboth prudent and, unfortunately, disastrous. Theunintentionally coordinated efforts of so manyequity managers to cut their risks simultaneouslyled to additional losses on Thursday August 9th,−11.43% in the case of our leveraged contrar-ian strategy. But this time, the S&P 500 wasno longer immune, and dropped by −2.95% byThursday’s close, presumably partly a reflection ofthe risk reduction by long-biased and long-onlymanagers.17

ByThursday’s close, the economic forces behind theunwind were apparently balanced by countervailing

forces—either because the unwind and risk reduc-tions were complete, or because other marketparticipants identified significant mispricings dueto the rapid liquidations earlier in the week—and the losses stopped. Friday’s massive reversal,which generated a one-day return of 23.67% for theleveraged contrarian strategy, is the final piece of evi-dence that the losses of the previous three days weredue to a sudden liquidation, and not caused by anyfundamental change in the equilibrium returns oflong/short equity strategies, which would presum-ably have had a more permanent impact on pricelevels.

This pattern of short-term temporary price-impactfor purely liquidity-motivated trades is a classic con-sequence of market equilibrium with informationasymmetries between buyers and sellers. When largeblocks of securities are executed quickly, equilib-rium prices will exhibit greater moves to induce thecontra-parties to consummate the trades and bearthe risk that they are less informed about the secu-rities’ true values.18 If it is subsequently revealedthat the trades were not based on information, butmerely liquidity trades, prices move back to theirpre-block-trade equilibrium levels. And if thereis lingering uncertainty as to whether the tradeswere motivated by information or liquidity, pricesmay only partially revert back to their pre-block-trade levels. This partial-adjustment property of theprice-discovery process is one compelling reason for“sunshine” trades, the practice of pre-announcing alarge trade so as to identify oneself as a liquiditytrader with no proprietary information, so as toreduce the price impact of the trade (see Admatiand Pfleiderer (1991), and Gennotte and Leland(1990)).

The particular dynamics of the bounce-backon August 10th may have taken several forms.One possibility is that the unwind and subse-quent risk reductions were largely achieved byAugust 9th, and the resulting cumulative price



impact of the previous three days would havecreated even stronger trading signals for thoselong/short equity strategies that experienced themost significant losses.19 In the absence of furtherunwind-motivated price momentum, the naturalmean-reverting tendencies of equities that yield pos-itive expected returns for long/short equity strate-gies during “normal” times would return. Moreover,the price impact of the previous days’ unwindand risk-reduction trades would naturally revert tosome degree as the fraction of market participantsattributing such price movements to liquidity tradesincreases. However, only a partial reversal should beexpected because not everyone would come to thesame conclusion, and also because the de-leveragingof August 7–9 leaves a lower amount of capitalto be deployed by long/short equity strategies onthe 10th.

Another possibility is that the price impact ofAugust 7–9 was so severe that it drew the atten-tion of new investors who: (1) recognized that theclosing prices on August 9th were temporarily outof equilibrium due purely to a liquidity crunch;and (2) had access to significant sources of capi-tal to seize the opportunity to buy (sell) securities atartificially deflated (inflated) prices. This injectionof new capital—deployed in the opposite direc-tion of the unwind—could have turned the tide,supporting the strong reversal on August 10th.

These two possibilities are not mutually exclu-sive, but they both suggest that long/short equitystrategies are not as liquid as we thought. Alterna-tively, the common factors driving these strategieshave now become a significant source of risk,and the “phase-locking” behavior described in Lo(2001) apparently can cause as much dislocationin long/short equity strategies as in other parts ofthe hedge-fund industry. To verify this possibil-ity, we turn next to specific measures of illiquidityin long/short equity hedge funds in the TASSdatabase.

8 Illiquidity exposure

The rapid growth in the number of long/shortequity funds and assets per fund, coupled with thelikely increase in the amount of leverage each fundnow employs (see Section 6), suggest a significantdecrease in liquidity of long/short equity strategiesover the last decade. To explore this possibility, wepropose to measure the illiquidity exposure of fundsin the Long/Short Equity Hedge and Equity Mar-ket Neutral categories of the TASS database usingthe first-order autocorrelation coefficient of theirmonthly returns as suggested by Lo (1999) andGetmansky et al. (2004). Specifically, using themonthly returns of each fund in the TASS database,we compute:

ρ̂1i ≡ (T − 2)−1 ∑Tt=2 (Rit − µ̂i)(Rit−1 − µ̂i)

(T − 1)−1∑T

t=1 (Rit − µ̂i)2,

µ̂i ≡ T −1T∑

t=1

Rit (5)

which is simply the correlation between fund i’sreturn and its lagged return from the previousmonth. Getmansky et al. (2004) show that fundswith large positive values for ρ̂1i tend to be lessliquid,20 and using a rolling window to estimatethese autocorrelation coefficients for various assetreturn series allows us to capture changes in esti-mated illiquidity risk for those assets.

A striking example of the autocorrelation coeffi-cient as a proxy for illiquidity is given in Figure 6,which plots the 90-day rolling-window autocorrela-tions of the first-differences of daily spreads betweenthe March and April 2007 natural-gas futures con-tracts from August 9, 2004 through November 9,2006. The time series of first-differences of theMarch/April 2007 spreads is a proxy for the dailyreturns of one of the largest strategies that Ama-ranth Advisors was allegedly engaged in, and inwhich they were alleged to have built up a large and



-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

7/30

/200

4

8/30

/200

4

9/30

/200

4

10/3

0/20

04

11/3

0/20

04

12/3

0/20

04

1/30

/200

5

2/28

/200

5

3/30

/200

5

4/30

/200

5

5/30

/200

5

6/30

/200

5

7/30

/200

5

8/30

/200

5

9/30

/200

5

10/3

0/20

05

11/3

0/20

05

12/3

0/20

05

1/30

/200

6

2/28

/200

6

3/30

/200

6

4/30

/200

6

5/30

/200

6

6/30

/200

6

7/30

/200

6

8/30

/200

6

9/30

/200

6

10/3

0/20

06

Ch

ang

ein

Sp

read

-100%

-75%

-50%

-25%

0%

25%

50%

75%

100%

Au

toco

rrel

atio

n

2007 Spread Changes 90-Day Rolling Autocorrelation

Figure 6 First-differences of March/April 2007 natural-gas futures spreads (dots), and 90-day rolling-window first-order autocorrelations ρ̂1 (solid line) of those first-differences, from August 9, 2004 toNovember 9, 2006. Dotted lines indicate the two-standard-deviation confidence band for the rolling-window autocorrelations under the null hypothesis of zero autocorrelation.

illiquid position prior to their demise in September2006. Figure 6 shows that the rolling autocorre-lations began climbing throughout 2005, nearlybreached the 95% confidence interval in Septemberand October 2005, and did breach this threshold onApril 18, 2006, staying well above this level untilAugust 2006 when Amaranth and other similarlypositioned hedge funds were presumably forced tounwind this spread trade.

Using ρ̂1i as a measure of the illiquidity of eachfund i, we can construct three aggregate mea-sures of the illiquidity exposure of long/shortequity funds along the lines of Chan et al. (2006,2007), i.e., by computing the mean and medianof rolling-window ρ̂1i ’s over all funds i in theTASS Long/Short Equity Hedge and Equity Market

Neutral categories month by month:

ρ̂at ≡ 1

n

n∑i=1

ρ̂1it (equal-weighted mean) (6a)

ρ̂bt ≡n∑

i=1

AUMit∑j AUMjt

ρ̂1it (asset-weighted mean)

(6b)

ρ̂ct ≡ Median(ρ̂11t , . . . , ρ̂1nt ). (6c)

In Figure 7, the equal-weighted and asset-weightedmeans and the median of 60-month rolling-windowautocorrelations of individual hedge-fund returnsare plotted from December 1994 to June 2007using all funds in the two equity categories in bothLive and Graveyard databases that report assetsunder management in US dollars, and with at



-0.05

0

0.05

0.1

0.15

0.2

Dec-94 Dec-95 Dec-96 Dec-97 Dec-98 Dec-99 Dec-00 Dec-01 Dec-02 Dec-03 Dec-04 Dec-05 Dec-06

Au

toco

rrel

atio

n

0

300

600

900

1,200

1,500

Nu

mb

ero

fF

un

ds

Number of Funds Mean Median Asset-Wgted Mean

Figure 7 Mean, median, and asset-weighted mean 60-month rolling autocorrelations of funds in theTASSLive and Graveyard database in the Long/Short Equity Hedge and Equity Market Neutral categories, fromDecember 1994 to June 2007.

least 60 months of non-missing returns.21 Thesethree series tell the same story: except for a briefdecline in late 2004, the aggregate autocorrelationof Long/Short Equity Hedge and Equity MarketNeutral funds has been on the rise since 2000,implying a significant decline in the liquidity of thissector over the past 6 years.22

Of course, the absolute level of illiquidity expo-sure in these two categories is still considerablylower than in many other categories, e.g., Convert-ible Arbitrage or Emerging Markets (see Getmanskyet al. (2004) and Chan et al. (2006, 2007) for fur-ther details). But the fact that the autocorrelationshave increased at all in the most populous and, tra-ditionally, among the most liquid of all sectors inthe hedge-fund industry, is certainly noteworthy.

This is another indication that systemic risk in thehedge-fund industry has increased recently.

9 A network view of the hedge-fund industry

A common theme surrounding the “unwind”phenomenon in the hedge-fund industry iscredit and liquidity. Although they are separatesources of risk exposures for hedge funds andtheir investors—one type of risk can exist with-out the other—nevertheless, credit and liquidityhave been inextricably intertwined in the minds ofmost investors because of the problems encounteredby LTCM and many other fixed-income relative-value hedge funds in August 1998. There has beenmuch progress in the recent literature in modeling



credit and illiquidity risk,23 but the complex net-work of creditor/obligor relationships, revolvingcredit agreements, and other financial interconnec-tions is still largely unmapped. Perhaps some ofthe newly developed techniques in the mathemat-ical theory of networks will allow us to constructsystemic measures for liquidity and credit exposuresand the robustness of the global financial system toidiosyncratic shocks. The “small-world” networksconsidered by Watts and Strogatz (1998) and Watts(1999) seem to be particularly promising startingpoints. However, given the lack of transparency inthe hedge-fund industry, we have no direct way ofgathering the data required to estimate the “net-work topology” that is the starting point of thesetechniques.

One indirect and crude measure of the change inthe “degree of connectedness” in the hedge-fundindustry is to calculate the changes in the absolutevalues of correlations between hedge-fund indexesover time.24 Using 13 indexes from April 1994 toJune 2007 constructed by CS/Tremont,25 we com-pare their estimated pairwise correlations betweenthe first and second half of our total sample period:April 1994 to December 2000 versus January 2001to June 2007. If, for example, the absolute correla-tion between Multi-Strategy and Emerging Marketswas 7% over the first half of the sample and 52%over the second half, as it was, this might be a symp-tom of increased connectedness between those twocategories.

Figure 8 provides a graphical depiction of this net-work for the two sub-samples, where we have usedthick lines to represent absolute correlations greaterthan 50%, thinner lines to represent absolute cor-relations between 25% and 50%, and no lines forabsolute correlations below 25%. For the earliersub-sample, we estimate correlations with and with-out August 1998, and the difference is striking.Omitting August 1998 decreases the correlations

noticeably, which is no surprise given the ubiquityand magnitude of the LTCM event. But a com-parison of the two sub-periods shows a significantincrease in the absolute correlations in the morerecent sample. The hedge-fund industry has clearlybecome more closely connected.

Perhaps the most significant indicator of increasedconnectedness is the fact that the Multi-Strategycategory is now more highly correlated with almostevery other index, a symptom of the large influx ofassets into the hedge-fund industry. This increasedcorrelation is also consistent with the hypothesisthat forces outside the long/short equity sector mayhave caused an unwind of statistical arbitrage strate-gies in August 2007. In August 1998, multi-strategyfunds were certainly impacted by their deteriorat-ing fixed-income arbitrage positions, and no doubtmany of them liquidated their statistical arbitrageportfolios to meet fixed-income margin calls. Butbecause multi-strategy funds were not as significanta market force in 1998 as they evidently are now,their correlations to other strategies were not as largeas they are today.

Table 8 contains a more detailed comparison ofthe two correlation matrices. The absolute corre-lation matrix from the earlier sample is subtractedfrom that of the more recent sample, hence a pos-itive entry represents an increase in the absolutecorrelation in the more recent period, and is high-lighted in red if it exceeds 20% (negative entries lessthan −20% are highlighted in blue). Table 8 con-firms the patterns of Figure 8: absolute correlationsamong the various different hedge-fund categorieshave indeed increased in the more recent sam-ple, with considerably more positive entries thannegative ones.

To capture the dynamics of these changes in cor-relation structure among the CS/Tremont Indexes,in Figure 9 we plot the means and medians of the



Figure 8 Network diagrams of correlations among 13 CS/Tremont hedge-fund indexes over two sub-periods, April 1994 to December 2000 (with and without August 1998) and January 2001 to June2007. Thicker lines represent absolute correlations greater than 50%, thinner lines represent absolutecorrelations between 25% and 50%, and no connecting lines correspond to correlations less than 25%.CA: Convertible Arbitrage, DSB: Dedicated Short Bias, EM: Emerging Markets, EMN: Equity MarketNeutral, ED: Event Driven, FIA: Fixed Income Arbitrage, GM: Global Macro, LSEH: Long/Short EquityHedge, MF: Managed Futures, EDMS: Event Driven Multi-Strategy, DI: Distressed Index, RA: RiskArbitrage, and MS: Multi-Strategy.

absolute values of 36-month rolling-window corre-lations between the indexes, with and without themonth of August 1998.26 These graphs show thatthe mean and median absolute correlations amongthe indexes have been steadily increasing in recentyears, especially after 2004. The inordinate amountof influence that August 1998 has on these corre-lations underscores the potential for system-wideshocks in the hedge-fund industry.

The increase in correlations among hedge-fundreturns can be attributed to at least two potentialsources: increased exposure of hedge funds to stan-dard factors such as the S&P 500, the US 10-YearTreasury bond, and the US dollar index, andincreased linkages due to more complex channelssuch as liquidity and credit relationships throughmulti-strategy funds and proprietary trading desks.Unfortunately, without more detailed data from



Tab

le8

The

diff

eren

ceof

the

abso

lute

corr

elat

ion

mat

rice

sof

CS/

Trem

ont

Hed

ge-F

und

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xes

usin

gre

cent

data

(Jan

uary

2001

toJu

ne20

07)

and

earl

ier

data

(Apr

il19

94to

Dec

embe

r20

00),

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reth

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ith

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−18

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arbi

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le8

(Con

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tFi

xed

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Mar-97 Mar-98 Mar-99 Mar-00 Mar-01 Mar-02 Mar-03 Mar-04 Mar-05 Mar-06 Mar-07

Co

rrel

atio

nMean (w/o August 1998) Median (w/o August 1998)

Mean (with August 1998) Median (with August 1998)

Figure 9 Mean and median absolute 36-month rolling-window correlations among CS/Tremont hedge-fund indexes from March 1997 to June 2007, with and without August 1998.

hedge funds and their creditors and obligors, wehave no way of distinguishing between these twosources of commonality.

One subtlety in interpreting the time variationin correlations is the possibility that the changesare due to volatility shifts, not to changes in thecovariances of returns. This distinction may notbe particularly relevant from the perspective ofsystemic risk exposures because an increased corre-lation between variables X and Y does imply higherco-movement of two variables per unit of σxσy , irre-spective of whether that increase has come aboutfrom an increase in the numerator or a decrease inthe denominator. For example, suppose that thevolatility in X declines suddenly, but the covari-ance between X and Y remains unchanged, yieldingan increase in the absolute value of the correlationbetween X and Y . This increased absolute corre-lation is not spurious, but is the direct result of

the volatility of X declining while the covariancebetween X and Y remained unchanged, and thiscombination of facts does imply a more “signifi-cant” relation between X and Y , where significanceis measured in units of σxσy .27 Nevertheless, fromthe portfolio-construction perspective, increasesin correlation need not imply increased portfoliorisk, simply because the portfolio variance is theweighted sum of all the pairwise covariances ofthe constituent assets. Specifically, a decrease inthe volatilities of all assets while covariances areheld constant would imply a lower portfolio volatil-ity, despite the fact that all pairwise correlationshave increased in absolute value due to the lowerasset-volatility levels.

Figure 10 plots the 36-month rolling-window pair-wise covariances between the CS/Tremont Multi-Strategy Index and other CS/Tremont SectorIndexes from December 1996 to June 2007, where



-4

-3

-2

-1

0

1

2

3

Dec-96 Dec-97 Dec-98 Dec-99 Dec-00 Dec-01 Dec-02 Dec-03 Dec-04 Dec-05 Dec-06

Co

vari

ance

Convertible Arbitrage Dedicated Short Bias Emerging Markets Equity Market NeutralEvent Driven Fixed Income Arbitrage Global Macro Long/Short EquityManaged Futures Event Driven Multi-Strategy Distressed Risk Arbitrage

August 1998 August 2001

Figure 10 36-month rolling-window pairwise covariances between the CS/Tremont Multi-Strategy Indexand other CS/Tremont Sector Indexes from December 1996 to June 2007.

the rolling covariances to the Long–Short Equityand Equity Market Neutral Indexes are highlightedusing thicker lines. The 36-month window follow-ing August 1998 is also marked with dotted lines tohighlight the impact this period has on our rollingestimates. These plots show that in the 1990’s, pair-wise covariances between Multi-Strategy and othersectors were quite heterogeneous and noisy, but inthe last seven years, the covariances have clusteredtogether, with the exception of Dedicated Short Bias(as expected), and exhibit upward trends.

The fact that Multi-Strategy did not have a reli-ably negative covariance to Dedicated Short Biasin the 1990’s is notable, particularly in light ofthe strong negative covariance in the last half ofthe sample. One interpretation of this shift is thatMulti-Strategy did not have a significant equitycomponent in the 1990’s, but this has changed

over the past seven years, and is consistent with theincreased covariance between Multi-Strategy andthe two equity indexes since 1999.

Of course, volatility in US equity markets hasdeclined over the past seven years, so a significantportion of the increased correlations between Multi-Strategy and the two equity indexes is due to smallerdenominators, not just increased numerators. Butboth shifts have important implications for the sys-temic risk of the hedge-fund industry, and neithershould be ignored or dismissed.

Of course, pairwise correlations of indexes are verycrude measures of the connectedness of the hedge-fund industry. Moreover, the network map of theglobal financial system is considerably more com-plex, involving many different types of organiza-tions (banks, hedge funds, prime brokers, investors,



regulators, etc.), and different types of relationshipsbetween these organizations. Although a number ofrecent papers have applied the mathematical theoryof networks to financial markets,28 there is virtu-ally no data with which to calibrate such models.In an industry that protects its intellectual propertyprimarily through trade secrets, it may be impos-sible to collect the necessary information to mapthe network topology without additional regulatoryoversight.

10 Did “Quant” fail?

In light of Section 7’s unwind hypothesis, whatcan we conclude about whether or not quantitativeequity market-neutral strategies failed en masse inAugust 2007? We have a specific definition of fail-ure in mind: Do the losses of August 2007 signal abreakdown in the basic economic relationships thatyield attractive risk/reward profiles for such strate-gies, or is August 2007 an unavoidable and integralaspect of those risk/reward profiles?

An instructive thought experiment is to consider amarket-neutral portfolio strategy in which US equi-ties with odd-numbered CUSIP identifiers are heldlong and those with even-number CUSIPs are heldshort. Suppose such a portfolio strategy is quitepopular and a number of large hedge funds haveimplemented it. Now imagine that one of theselarge hedge funds decides to liquidate its holdingsbecause of some liquidity shock. Regardless of thisportfolio’s typical expected return during normaltimes, in the midst of a rapid and large unwind,all such portfolios will experience losses, with themagnitudes of those losses directly proportional tothe size and speed of the unwind. Moreover, itis easy to see how such an unwind can generatelosses for other types of portfolios, e.g., long-onlyportfolios of securities with prime-number CUSIPs,dedicated shortsellers that short only those securi-ties with CUSIPs divisible by 10, etc. If a portfolio

is of sufficient size, and it is based on a sufficientlypopular strategy that is broadly implemented, thenunwinding even a small fraction of it can cascadeinto a major market dislocation.

Therefore, it is tempting to conclude that the eventsof August 2007 are not particularly relevant to theefficacy of quantitative investing. The losses weremore likely the result of a firesale liquidation ofquantitatively constructed portfolios rather than thespecific shortcomings of quantitative methods. Inthis respect, the dislocation experienced by quan-titative equity market-neutral managers in August2007 resembles the dislocation experienced byUS equityholders in October 1987, fixed-incomearbitrage managers in August 1998, sub-primemortgage-related managers in 2007, Japanese real-estate investors in the 1990’s, internet-stockholdersin March 2000, and Dutch tulip-bulb investors inFebruary 1637.29 What played out in August 2007was not new at all, but may be an age-old dynamic ofrisk-taking opportunism punctuated by occasionalflights to safety and liquidity.

However, a successful investment strategy shouldinclude an assessment of the risk of ruin, and thatrisk should be managed appropriately. Moreover,the magnitude of tail risk should, in principle,be related to a strategy’s expected return given theinevitable trade-off between risk and reward. There-fore, it is disingenuous to assert that “a strategyis successful except in the face of 25-standard-deviation events.” Given the improbability of suchevents, we can only conclude that either the actualdistribution of returns is extraordinarily leptokur-tic, or the standard deviation is time-varying andexhibits occasional spikes.

In particular, as Montier (2007) observed, riskhas become “endogenous” in certain markets—particularly those that are recently flush with largeinflows of assets—which is one of the reasonsthat the largest players can no longer assume that



historical estimates of volatility and price impactare accurate measures of current risk exposures.Endogeneity is, in fact, an old economic conceptillustrated by the well-known theory of imperfectcompetition—if an economic entity, or group ofcoordinated entities, is so large that it can uni-laterally affect prices by its own actions, then thestandard predictions of microeconomics under per-fect competition no longer hold. Similarly, if acertain portfolio strategy is so popular that its liqui-dation can unilaterally affect the risks that it faces,then the standard tools of basic risk models such asValue-at-Risk and normal distributions no longerhold. In this respect, quantitative models may havefailed in August 2007 by not adequately captur-ing the endogeneity of their risk exposures. Giventhe size and interconnectedness of the hedge-fundindustry, we may require more sophisticated analyt-ics to model the feedback implicit in current marketdynamics.

For example, from a purely statistical perspective,the mere threat of a forced liquidation of a givenstrategy should increase the theoretical volatility ofthe entire class of such strategies, and the more illiq-uid the underlying assets and the larger the potentialliquidation, the larger the increase in volatility. Buttheoretical volatilities are not observable, and mustbe estimated, which is the crux of the problem: ifthe historical record contains no realizations of anextreme event, statistical estimators based on thatrecord alone cannot reflect the possibility of suchevents. Moreover, by definition tail events are rare,hence any statistical estimator of such events willbe based on very small samples and subject to largeestimation error.

Therefore, August 2007 offers a number of insightsfor improving the quantitative methods for measur-ing and managing risks. One of the most importantlessons is the need for measures of illiquidityrisk, and that volatility is an inadequate mea-sure of risk, especially for relative-value strategies

like quantitative equity-market neutral where themarket-making characteristics of the strategy tendto attenuate market fluctuations, yielding lowervolatility estimates that are used to justify higheramounts of leverage. In the case of August 2007,traditional risk measures could have been aug-mented with estimates of factor and illiquidityexposures in the Long/Short Equity and EquityMarket Neutral categories of the TASS databaseto yield a broader assessment of the risks facingmanagers in this sector. To the extent that we candevelop a better framework and a set of analyticsfor measuring illiquidity and other risk exposuresin financial markets—perhaps along the lines ofGennotte and Leland (1990), Lo (1999, 2001,2002), Getmansky et al. (2004), Getmansky et al.(2004), and Chan et al. (2006, 2007)—we maybe able to reduce the impact of future liquidityevents.

Another important issue is the role that invest-ment horizon played in the market reaction toAugust 2007. Short-term investors that reducedtheir risks intra-month suffered the most, whilemany long-term investors enjoyed positive returnsfor the month, and this difference bears furtherstudy. A related issue is the differences betweenstrategies employing exchange-traded securities thatare marked-to-market continuously, versus strate-gies with OTC contracts or highly illiquid securitieswhose valuations are not observed as frequently.This distinction may well explain why the after-math of August 2007 was so different than that ofAugust 1998. One possible explanation is that theinfrequent valuation of illiquid assets yields a cer-tain degree of flexibility for portfolio managers thatexchange-traded instruments do not allow. Thisflexibility comes from the fact that credit lines pro-vided by prime brokers and other creditors are oftencontingent on the valuation of the correspondingcollateral, and any material change in that valu-ation can trigger margin calls and, ultimately, areduction or withdrawal of credit. For portfolios of



continuously marked-to-market securities, margincalls can occur more frequently by definition thanfor portfolios with hard-to-value securities.30 Weconjecture that a major reason for the quick rever-sal of quantitative portfolios on August 10th isthe fact that the securities involved were mostlyexchange-traded equities, for which the price-discovery mechanism allowed market participantsto better understand the dynamics of the losses dur-ing August 7–9. Had the alleged unwind of August2007 involved illiquid OTC contracts, we suspectthat the losses would have been considerably largerand any reversal would have taken much longer tomaterialize.

While market participants will no doubt learn fromAugust 2007 and improve their strategies and riskmanagement protocols, it is unlikely that the pos-sibility of future dislocations can be completelyeliminated by such improvements. Events likeAugust 2007 may simply be unavoidable featuresof quantitative equity market-neutral strategies. Infact, the profit-and-loss patterns these strategiesin August 2007 are consistent with those of abroader set of market-making and relative-valuestrategies: small but steady positive returns mostof the time, coupled with occasional short-livedbursts of significant loss. Such risk/reward profilesare quite attractive to a certain set of investors—those that understand the nature of “tail risk”and can withstand the inevitable rare event. Forexample, which of the following two gambles isbest?:

G1 ={

$75,000 with probability 50%


G2 ={


−$1,000,000 with probability 2%

The first gamble entails less risk of loss (the worstcase is a gain of $25,000) but has an expected

return of $50,000, which is lower than the expectedreturn of $78,000 for the second gamble. The sec-ond gamble is almost sure to yield a higher payoffthan the first, but has a small probability of avery significant loss. There is no correct answerto which is best—the optimal choice dependsentirely on an individual’s risk preferences (see Lo(1999)).

A less contrived example is the catastrophe-insurance industry, in which insurers routinely betagainst tail events, and most of the time, they enjoysteady cashflows from their policyholders. However,on occasion, they suffer great losses when disas-ter strikes, but they are adequately capitalized sosuch events typically do not cause widespread dis-location in that industry. The one circumstancein which problems can arise in the catastrophe-insurance industry is when there is too much capital,causing so much downward pressure on insurancepremia that a number of insurers cannot covertheir costs, i.e., they become under-capitalized andcannot survive a tail event. In such cases, thedemand for catastrophe insurance cannot supportthe excess supply, and the occurrence of a tail eventcauses an industry shake-out where only the mostwell-capitalized insurers survive. In the aftermathof such a shake-out, premiums will rise, creat-ing great profit opportunities for the remainingplayers which, in turn, will attract new insur-ers to the industry, and the cycle begins again.The correspondence of this insurance cycle to thequantitative equity market-neutral business is noaccident.31

There is also a competitive and strategic element towhether a given manager or prime broker shouldreduce leverage given the actions of other man-agers and brokers. If we all agree to reduce leverageso as to decrease the likelihood of a major mar-ket dislocation due to forced liquidation, then eachmanager and prime broker has an incentive to devi-ate from this agreement and reap the benefits of



increasing leverage while everyone else cuts back.Without a mechanism for enforcing cooperation,such agreements are not stable, and unlikely toarise in practice.32 In fact, because of the lack oftransparency and coordination within the hedge-fund industry, and the strong relationship betweenperformance and business viability, competitivepressures will lead managers and prime brokers toincrease leverage in an “arms race” for generatingbetter returns.

This perspective provides further support for theAdaptive Markets Hypothesis of Farmer and Lo(1999) and Lo (2004, 2005), in which financialmarkets are not always and everywhere efficient,but where competition, mutation, adaptation, andnatural selection jointly determine the dynamics ofmarket prices and quantities. The growth in hedge-fund assets, the growth in the number of new hedgefunds, the apparent increase in leverage, and theproliferation of hedge-fund products and servicesare the most recent manifestations of the relentlesssearch for investment performance and economicgain, i.e., the survival instinct. As a particular type ofstrategy becomes “crowded”—meaning too muchcapital deployed relative to the returns generatedper unit risk—capital will leave this sector to seekout more attractive risk/reward profiles, therebyimproving the risk/reward profile for the remain-ing population, which then attracts new capital andrestarts the cycle.

Such cycles are commonplace in ecological modelsof population dynamics, and the Adaptive MarketsHypothesis is an application of this framework tothe population of investors, managers, and credi-tors. If August 2007 is to be viewed as a failure, itwas a failure to recognize the ineluctable cycle ofprofit and loss that all types of investment strategiesseem to exhibit over time. But to expect individ-ual market participants to identify and avoid suchcycles is not only unrealistic, it flies in the face ofbasic economics. In the absence of any reason for

coordination, market participants will seek to max-imize their own welfare, and doing so implies thateach will push the limits of his investments to thepoint at which the risk-adjusted expected returnsare equalized across all investment opportunities.With limited information regarding the nature andextent of other market participants’ investments,each participant must estimate the risk/reward pro-file of each strategy and determine the appropriatelevel of capital to deploy. Since such estimates aresubject to error, the natural feedback of losses andgains, i.e., action is spurred by losses and compla-cency is induced by gains, implies the waxing andwaning of strategies and the cyclical flow of capitaldescribed above.

A remaining open question is whether investorstruly understood and preferred the particular risksof quantitative equity market-neutral strategies inrecent years. While only “qualified investors” aremeant to have access to hedge funds, the ubiquityof delegated financial management suggests thatthe dislocation of August 2007 may well havespilled over to less sophisticated investors’ pensionfunds and other retirement assets. Whether thistype of spill-over effect is appropriate touches upona series of complex policy issues surrounding theimplicit paternalism of pension-fund managementby fiduciaries. Can a pension plan sponsor makeinvestment decisions that are in the “best interests”of all of the plan participants, even when those par-ticipants have widely varying risk preferences andfinancial objectives? Unfortunately, we have little toadd to this controversy, other than to acknowledgeits relevance for the question of whether quanti-tative equity market-neutral managers should orshould not have reduced their risk levels prior toAugust 2007. If all three sets of stakeholders—managers, investors, and creditors—were aware ofthe risks and willing to bear them, then August 2007is merely the cost of doing business. If not, thenAugust 2007 signalled another kind of failure inthis industry.



11 Qualifications and extensions

Although the unwind hypothesis of Section 7 seemsto be consistent with our empirical results, weemphasize the caveat of Section 1: all of our infer-ences are indirect, tentative, and without the benefitof much hindsight given the recency of these events.We have no inside information about the work-ings of the many hedge funds that were affectedin August 2007, nor do we have any proprietaryaccess to prime brokerage records, trading histories,or industry leverage data. Therefore, our academicperspective of the events during the week of August6–10 should be interpreted with some caution anda healthy dose of skepticism.

In particular, our empirical findings are based ononly one very simple strategy applied to US stocks,which may be representative of certain short-termmarket-neutral mean-reversion strategies, but is notlikely to be as good a proxy for the broader set ofquantitative long/short equity products that involveboth United States and international equities, andother securities. For example, we apply our naivestrategy indiscriminately to an undistinguished uni-verse of US securities, using no other factors besidespast returns, and with no consideration of exe-cution costs or risk-adjusted return contributions.This test strategy is clearly missing many other fea-tures of long/short equity funds. To continue themicroscope analogy, we have used just one lensof rather limited magnification to look at August2007. A more refined analysis using multiple lenseswith different resolutions will no doubt yield amore complex and accurate picture of the very sameevents. For example, the contrarian strategy doesnot contain any factor-based selection algorithms,hence its performance may not reflect as clearly theunwind of factor-based portfolios.

More importantly, even if our hypothesis is correctthat an unwind initiated the losses on August 7th,we cannot say much about the ultimate causes of

such an unwind. It is tempting to conclude that amulti-strategy proprietary trading desk’s increasedexposure to sub-prime mortgage portfolios causedit to reduce leverage by liquidating a portion ofits most liquid positions, e.g., a statistical arbitrageportfolio, thereby initiating the losses on August 7ththat cascaded into the subsequent rout. However,another possible scenario is that several quantita-tive equity market-neutral managers decided at thebeginning of August that it would be prudent toreduce leverage in the wake of so many problemsfacing credit-related portfolios. They de-leveragedaccordingly, not realizing that this strategy was socrowded and that the price impact of their liqui-dation would be so severe. Once this price impacthad been realized, other funds employing similarstrategies may have decided to cut their risks inresponse to their losses, which then led to the kind of“death spiral” that we witnessed in August 1998 asmanagers attempted to unwind their fixed-incomearbitrage positions to meet margin calls.

Whether or not the initial losses on August 7th werecaused by a forced liquidation or a voluntary reduc-tion in risk is impossible to determine from ouroutsider’s perspective. But the fact that an entirecategory of strategies as liquid as Long/Short Equitycould suffer such significant losses in the absenceof any real market news suggests that the currentlevel of liquidity is less than we thought. Alter-natively, we learned in August 2007 that there ismore commonality among long/short equity strate-gies than we anticipated. This commonality may beeven broader, as suggested by the fact that all theCS/Tremont Hedge-Fund Indexes yielded losses inAugust 2007 (see Table 9).

Our use of the TASS hedge-fund database alsorequires some qualification. The TASS databaseconsists entirely of funds that have voluntarilyagreed to be included, with no legal obligations toreport either regularly or accurately. In fact, manyof the high-profile managers that made headlines in



Table 9 CS/Tremont hedge-fund index returns forthe month of August 2007.

AugustIndex/sub strategies 2007 (%)

Credit suisse/tremont −1.53hedge-fund indexConvertible arbitrage −1.08Dedicated short bias −1.14Emerging markets −2.37Equity market neutral −0.39Event driven −1.88

Distressed −1.73Multi-strategy −2.03Risk arbitrage −0.65

Fixed income arbitrage −0.87Global macro −0.62Long/short equity −1.38Managed futures −4.61Multi-strategy −1.40

Source: www.hedgeindex.com

August 2007 are not included in TASS, and whilewe hope that this database contains an unbiasedcross-section of funds in the industry, we have noway to ensure that it is representative.33 And allof our inferences are indirect since we are unable toobtain direct information from hedge funds or theirprime brokers. Accordingly, we cannot be any moredefinitive in our conclusions than to say that, for themoment, the empirical facts seem to be consistentwith our hypotheses.

Finally, we conjecture that liquidations of variousstrategies and asset classes may have started earlier.For example, Figure 2 shows that the contrarianstrategy exhibited a smaller dip during the secondhalf of July, with NYSE daily volume at elevatedlevels during this period and into the first half ofAugust. Other liquid investment categories suchas global macro, managed futures, and currencystrategies may have experienced similar unwinds

during July and August as problems in the sub-prime mortgage markets became more prominentin the minds of managers and investors. For exam-ple, the so-called “carry trade” among currencieswas supposedly unwound to some extent in Julyand August 2007, generating losses for a numberof global macro and currency-trading funds. Obvi-ously, our long/short equity microscope is incapableof detecting dislocation among currency strategies,but a simple carry-trade simulation—similar toour simulation of the contrarian trading strategy—could shed considerable light on the dynamics ofthe foreign exchange markets in recent months.Indeed, a collection of simulated strategies acrossall of the hedge-fund categories can serve as akind of multi-resolution microscope, one withmany lenses and magnifications, with which toexamine the full range of financial-market activ-ity. We plan to explore such extensions in futureresearch.

12 The current outlook

In this paper, we have argued through indirectmeans that the events of August 6–10, 2007 mayhave been the result of a rapid unwinding of oneor more large long/short equity portfolios, mostlikely initially a quantitative equity market-neutralportfolio. This unwind created a cascade effect thatultimately spread more broadly to long/short equityportfolios, 130/30 and other active-extensionstrategies, and certain long-only portfolios (thosebased primarily on quantitative stock-selection andsystematic portfolio-construction methods). ByAugust 9th, this unwind and de-leveraging processwas over, and the affected portfolios and strategiesexperienced a significant but not complete reboundon the 10th.

With the caveats of Section 11 in mind, wedraw three broad conclusions from our indirectinferences.



The first is that the contrast between August 1998and August 2007 has important ramifications forthe connectedness of the global financial system. InAugust 1998, default of Russian government debtcaused a flight to quality that ultimately resulted inthe demise of LTCM and many other fixed-incomearbitrage funds. This series of events caught eventhe most experienced traders by surprise because ofthe unrelated nature of Russian government debtand the broadly diversified portfolios of some ofthe most successful fixed-income arbitrage funds.Similarly, the events of August 2007 caught someof the most experienced quantitative equity market-neutral managers by surprise. But August 2007 maybe far more significant because it provides the firstpiece of evidence that problems in one corner ofthe financial system—possibly the sub-prime mort-gage sector and related credit markets—can spillover so directly to a completely unrelated corner:long/short equity strategies. This is precisely thekind of “shortcut” described in the theory of math-ematical networks that generates the “small-worldphenomenon” of Watts (1999) in which a small ran-dom shock in one part of the network can rapidlypropagate throughout the entire network.

The second implication of August 2007 is that thenotion of “hedge-fund beta” described in Hasan-hodzic and Lo (2007) is now a reality. The factthat the entire class of long/short equity strate-gies moved together so tightly during August 2007implies the existence of certain common factorswithin that class. Although more research is neededto identify those factors (e.g., liquidity, volatility,value/growth, etc.), there should be little doubtnow about their existence. This is reminiscent ofthe evolution of the long-only index-fund industry,which emerged organically through the realiza-tion by most institutional investors that they wereinvested in very similar portfolios, and that a sig-nificant fraction of the expected returns of suchportfolios could be achieved passively and, con-sequently, more cheaply. Of course, hedge-fund

beta replication technology is still in its infancyand largely untested, but the intellectual frame-work is well-developed and a few prominent bro-ker/dealers and asset-management firms are nowoffering the first generation of these products. Tothe extent that the demand for long/short equitystrategies continues to grow, the increasing amountsof assets devoted to such endeavors will createits own common factors that can be measured,benchmarked, managed, and, ultimately, passivelyreplicated.

Finally, the events of August 2007 have some impli-cations for regulatory reform in the hedge-fundsector. Recent debate among regulators and legisla-tors have centered around the registration of hedgefunds under the Investment Advisers Act of 1940.While there may be compelling arguments for reg-istering hedge funds, these arguments are generallyfocused on investor protection which is, indeed,the main impetus behind the ’40 Act. But investorprotection is not directly related to systemic risk,and the best ways to deal with the former maynot be optimal for the latter. In particular, reg-istration does not address the systemic risks thathedge funds pose to the global financial systemand currently, no regulatory body has a mandate tomonitor, much less manage, such risks in the hedge-fund sector.34 Given the role that hedge funds havebegun to play in financial markets—namely, signif-icant providers of liquidity and credit—they nowimpose externalities on the economy that are nolonger negligible.

In this respect, hedge funds are becoming morelike banks. The fact that the banking industry isso highly regulated is due to the enormous socialexternalities banks generate when they succeed, andwhen they fail. But unlike banks, hedge funds candecide to withdraw liquidity at a moment’s notice,and while this may be benign if it occurs rarelyand randomly, a coordinated withdrawal of liquid-ity among an entire sector of hedge funds could



have disastrous consequences for the viability of thefinancial system if it occurs at the wrong time andin the wrong sector.

This observation should not be taken as a criticismof the hedge-fund industry. On the contrary, hedgefunds have created tremendous economic and socialbenefits by supplying liquidity, engaging in pricediscovery, improving risk transfer, and uncover-ing non-traditional sources of expected return. Ifhedge funds have increased systemic risk, the rel-evant questions are “by how much?” and “do thebenefits outweigh the risks?” No one would arguethat the optimal level of systemic risk for the globalfinancial system is zero. But then what is optimal,or acceptable?

The first step to addressing this issue is to developa better understanding of the likelihood and prox-imate causes of systemic risk; one cannot managethat which one cannot measure. The proposal byGetmansky et al. (2004) to establish a NationalTransportation Safety Board-like organization forcapital markets is one possible starting point. Byestablishing a dedicated and experienced team offorensic accountants, lawyers, and financial engi-neers to monitor various aspects of systemic risk inthe financial sector, and by studying every financialblow-up and developing guidelines for improvingour methods and models, a Capital Markets SafetyBoard may be a more direct way to deal withthe systemic risks of the hedge-fund industry thanregistration.

In the aftermath of the Second World War, a groupof socially minded physicists joined to form the Bul-letin of Atomic Scientists to raise public awarenessof the potential for nuclear holocaust. To illustratetheir current assessment of the appropriate state ofalarm, they published a “Doomsday Clock” indi-cating how close we are to “midnight,” i.e., nuclearannihilation.35 Originally set at 7 min to midnightin 1947, the clock has changed from time to time

as we have moved closer to (2 min to midnight in1953) or farther from (17 min to midnight in 1993)the brink of nuclear disaster. If we were to developa Doomsday Clock for the hedge-fund industry’simpact on the global financial system, calibrated to5 min to midnight in August 1998, and 15 min tomidnight in January 1999, then our current out-look for the state of systemic risk in the hedge-fundindustry is about 11:51pm.

For the moment, markets seem to have stabilized,but the clock is ticking…

Acknowledgements

The views and opinions expressed in this arti-cle are those of the authors only, and do notnecessarily represent the views and opinions ofAlphaSimplex Group, MIT, any of their affiliatesand employees, or any of the individuals acknowl-edged below. The authors make no representationsor warranty, either expressed or implied, as tothe accuracy or completeness of the informationcontained in this article, nor are they recommend-ing that this article serve as the basis for anyinvestment decision—this article is for informa-tion purposes only. We thank Cliff Asness, MihirBhattacharya, Jerry Chafkin, Nicholas Chan, PeterCurley, Dave DeMers, Arnout Eikeboom, JacobGoldfield, Shane Haas, Jasmina Hasanhodzic, JoeHaubrich, Joanne Hill, Mike Hogan, Jay Kaufman,Hayne Leland, Bob Litterman, James Martielli,Harry Mamaysky, Steve Mobbs, Pankaj Patel, TonyPlate, Steve Sapra, Michael Rogers, David Shaw,Jonathan Spring, Andre Stern, Ingrid Tierens,Phil Vasan and seminar participants at the BostonSecurity Analysts Society, Citigroup AlternativeInvestments, the International Monetary Fund, theNBER Market Microstructure Fall 2007 Meeting,Pacific Investment Management Co., SAC Cap-ital, and the University of Chicago for helpfulcomments and discussion. Research support from



AlphaSimplex Group and the MIT Laboratory forFinancial Engineering is gratefully acknowledged.

A Appendix

Throughout the Appendix, the following conven-tions are maintained: (1) all vectors are columnvectors unless otherwise indicated; (2) vectors andmatrices are always typeset in boldface, i.e., X andµ are scalars and X and µ are vectors or matrices.In Section A.1 we provide a more detailed exposi-tion of the contrarian trading strategy in Lehmann(1990) and Lo and MacKinlay (1990). Section A.2contains a derivation of the asymptotic standarderrors of the aggregate autocorrelations of Section8. And in Section A.3 we include the definitionsof the various hedge-fund categories on which theCS/Tremont Indexes are based.

A.1 A contrarian trading strategy

Consider a collection of N securities and denoteby Rt the N × 1-vector of their period t returns[R1t · · · RNt ]′. For convenience, we maintain thefollowing assumption:

(A1) Rt is a jointly covariance-stationary stochas-tic process with expectation E[Rt ] = µ ≡[µ1 µ2 · · · µN ]′ and autocovariance matri-ces E[(Rt−k − µ)(Rt − µ)′] = �k where,with no loss of generality, we take k ≥ 0since �k = �′−k .36

In the spirit of virtually all contrarian strategies,consider buying at time t stocks that were “losers”at time t − k, and selling at time t stocks that were“winners” at time t − k, where winning and losingis determined with respect to the equal-weightedreturn on the market. More formally, if ωit (k)denotes the fraction of the portfolio devoted to

security i at time t , let:

ωit (k) = − 1

N(Rit−k − Rmt−k) i = 1, . . . , N ,

(A.1)

where Rmt−k ≡ ∑Ni=1 Rit−k/N is the equally-

weighted market index. By construction, ωt (k) ≡[ω1t (k) ω2t (k) · · · ωNt (k)]′ is a “dollar-neutral” or“arbitrage” portfolio since the weights sum to zero.Accordingly, the weights have no natural scale sinceany multiple of the weights will also sum to zero.Therefore, it is most convenient to define theweights to be the actual dollar positions in eachsecurity, in which case the total dollar investmentlong (or short) at time t is given by It (k) where:

It (k) ≡ 1

2

N∑i=1

|ωit (k)|. (A.2)

Since the portfolio weights are proportional tothe differences between the market index and thereturns, securities that deviate more positively fromthe market at time t − k will have greater nega-tive weight in the time t portfolio, and vice-versa.Such a strategy is designed to take advantage ofstock market overreaction, but Lo and MacKinlay(1990) show that this need not be the only rea-son that contrarian investment strategies are prof-itable. In particular, if returns are positively cross-autocorrelated, they show that a return-reversalstrategy will yield positive profits on average, evenif individual security returns are serially indepen-dent ! The presence of stock market overreaction,i.e., negatively autocorrelated individual returns,enhances the profitability of the return-reversalstrategy, but is not required for such a strategy toearn positive expected returns.

Because of the linear nature of the strategy, its sta-tistical properties are particularly easy to derive. Forexample, Lo and MacKinlay (1990) show that thestrategy’s profit-and-loss at date t is given by:

πt (k) = ω′t (k)Rt (A.3)



and re-arranging (A.3) and taking expectationsyields the following:

E[πt (k)] = ι′�kι

N 2− 1

Ntrace(�k)

− 1

N

N∑i=1

(µi − µm)2, (A.4)

which shows that the contrarian strategy’s expectedprofits are an explicit function of the means, vari-ances, and autocovariances of returns. See Lo andMacKinlay (1990, 1999) for further details ofthis strategy’s statistical properties and an empiricalanalysis of its historical returns.

A.2 Statistical significance of aggregateautocorrelations

To gauge the statistical significance of the aggre-gate autocorrelations in Section 8, recall that underthe null hypothesis of no autocorrelation, the auto-correlation coefficient ρ̂1i is asymptotically normalwith zero mean and variance σ2

ρ ≡ 1/T . Therefore,we can derive the asymptotic variance of the meanautocorrelation ρ̂ in the usual manner:

Var

[n−1

n∑i=1

ρ̂1i

]= n−2 ι′�ι, (A.5)

where � is the covariance matrix of the vec-tor of n first-order autocorrelation coefficients[ ρ̂11· · ·ρ̂1n ]′. If we assume that the ρ̂1i ’s are uncor-related, then � is a diagonal matrix with 1/T ’s onthe diagonal. Therefore, the asymptotic varianceand standard error of ρ̂ is given by

Var[ρ̂] ≈ 1

nT, SE[ρ̂] ≈ 1√

nT. (A.6)

For n = 400 and T = 60, the standard error forρ̂ is 0.65%, hence a two-standard-deviation confi-dence interval around the null hypothesis of zerocorrelation is the range [−1.3%, +1.3%] which is

clearly breached by the graphs in Figure 7 for mostof the sample.

A.3 CS/Tremont category descriptions

The following is a list of descriptions of the cat-egories for which CS/Tremont constructs indexes,taken directly from the CS/Tremont website (www.hedgeindex.com):

Convertible Arbitrage. This strategy is identifiedby investment in the convertible securities of acompany. A typical investment is to be long theconvertible bond and short the common stock ofthe same company. Positions are designed to gen-erate profits from the fixed income security as wellas the short sale of stock, while protecting principalfrom market moves.

Dedicated Short Bias. This strategy is to maintainnet short as opposed to pure short exposure. Shortbiased managers take short positions in mostly equi-ties and derivatives. The short bias of a manager’sportfolio must be constantly greater than zero to beclassified in this category.

Emerging Markets. This strategy involves equity orfixed income investing in emerging markets aroundthe world. Because many emerging markets do notallow short selling, nor offer viable futures or otherderivative products with which to hedge, emergingmarket investing often employs a long-only strategy.

Equity Market Neutral. This investment strategy isdesigned to exploit equity market inefficiencies andusually involvesbeing simultaneously longandshortmatched equity portfolios of the same size within acountry. Market neutral portfolios are designed tobe either beta or currency neutral, or both. Well-designed portfolios typically control for industry,sector, market capitalization, and other exposures.Leverage is often applied to enhance returns.



Event Driven. This strategy is defined as “specialsituations” investing designed to capture pricemovement generated by a significant pendingcorporate event such as a merger, corporate restruc-turing, liquidation, bankruptcy or reorganization.There are three popular sub-categories in event-driven strategies: risk arbitrage, distressed securities,and multi-strategy.

Risk Arbitrage. Specialists invest simultane-ously in long and short positions in bothcompanies involved in a merger or acquisition.Risk arbitrageurs are typically long the stockof the company being acquired and short thestock of the acquiring company. The princi-pal risk is deal risk, should the deal fail toclose.

Distressed. Hedge Fund managers invest inthe debt, equity or trade claims of companiesin financial distress and general bankruptcy.The securities of companies in need of legalaction or restructuring to revive financial sta-bility typically trade at substantial discounts topar value and thereby attract investments whenmanagers perceive a turn-around will material-ize. Managers may also take arbitrage positionswithin a company’s capital structure, typicallyby purchasing a senior debt tier and short-selling common stock, in the hopes of realizingreturns from shifts in the spread between thetwo tiers.

Multi-Strategy. This subset refers to HedgeFunds that draw upon multiple themes, includ-ing risk arbitrage, distressed securities, andoccasionally others such as investments inmicro and small capitalization public compa-nies that are raising money in private capitalmarkets. Hedge Fund managers often shiftassets between strategies in response to marketopportunities.

Fixed Income Arbitrage. The fixed income arbi-trageur aims to profit from price anomalies betweenrelated interest rate securities. Most managers tradeglobally with a goal of generating steady returnswith low volatility. This category includes inter-est rate swap arbitrage, the United States andnon-US government bond arbitrage, forward yieldcurve arbitrage, and mortgage-backed securitiesarbitrage. The mortgage-backed market is primar-ily US-based, over-the-counter and particularlycomplex.

Global Macro. Global macro managers carry longand short positions in any of the world’s major cap-ital or derivative markets. These positions reflecttheir views on overall market direction as influ-enced by major economic trends and or events. Theportfolios of these Hedge Funds can include stocks,bonds, currencies, and commodities in the form ofcash or derivatives instruments. Most Hedge Fundsinvest globally in both developed and emergingmarkets.

Long/Short Equity. This directional strategyinvolves equity-oriented investing on both the longand short sides of the market. The objective is not tobe market neutral. Managers have the ability to shiftfrom value to growth, from small to medium to largecapitalization stocks, and from a net long positionto a net short position. Managers may use futuresand options to hedge. The focus may be regional,such as long/short US or European equity, or sec-tor specific, such as long and short technology orhealthcare stocks. Long/short Equity Hedge Fundstend to build and hold portfolios that are substan-tially more concentrated than those of traditionalstock Hedge Funds.

Managed Futures. This strategy invests in listedfinancial and commodity futures markets and cur-rency markets around the world. The managers areusually referred to as Commodity Trading Advisors,



or CTAs. Trading disciplines are generally system-atic or discretionary. Systematic traders tend to useprice and market specific information (often techni-cal) to make trading decisions, while discretionarymanagers use a judgmental approach.

Multi-Strategy. Multi-Strategy Hedge Funds arecharacterized by their ability to dynamically allo-cate capital among strategies falling within severaltraditional Hedge Fund disciplines. The use ofmany strategies, and the ability to reallocate capitalbetween strategies in response to market oppor-tunities, means that such Hedge Funds are noteasily assigned to any traditional category. TheMulti-strategy category also includes Hedge Fundsemploying unique strategies that do not fall underany of the other descriptions.

Notes1 For example, the Wall Street Journal reported on August

10, 2007 that “After the close of trading, RenaissanceTechnologies Corp., a hedge-fund company with oneof the best records in recent years, told investors thata key fund has lost 8.7% so far in August and is down7.4% in 2007. Another big fund company, HighbridgeCapital Management, told investors its Highbridge Sta-tistical Opportunities Fund was down 18% as of the 8thof the month, and was down 16% for the year. The$1.8 billion publicly traded Highbridge Statistical Mar-ket Neutral Fund was down 5.2% for the month as ofWednesday…Tykhe Capital, LLC—a New York-basedquantitative, or computer-driven, hedge-fund firm thatmanages about $1.8 billion—has suffered losses of about20% in its largest hedge fund so far this month…” (seeZuckerman et al., 2007), and on August 14, the WallStreet Journal reported that the Goldman Sachs GlobalEquity Opportunities Fund “…lost more than 30% ofits value last week…” (Sender et al., 2007).

2 Such a strategy is more accurately described as a “dollar-neutral” portfolio since dollar-neutral does not necessarilyimply that a strategy is also market-neutral. For exam-ple, if a portfolio is long $100MM of high-beta stocksand short $100MM of low-beta stocks, it will be dollar-neutral but will have positive market-beta exposure. Inpractice, most dollar-neutral equity portfolios are also

constructed to be market-neutral, hence the two terms areused almost interchangeably, which is sloppy terminologybut usually correct.

3 The technical definition of leverage—and the one used bythe US Federal Reserve, which is responsible for settingleverage constraints for broker/dealers—is given by thesum of the absolute values of the long and short positionsdivided by the capital, so

|$100| + | − $100|$25

= 8.

4 Note that Reg-T leverage is, in fact, considered 2:1 whichis exactly (2), hence θ:1 leverage is equivalent to a multipleof θ/2.

5 Specifically, we use only US common stocks (CRSP sharecode 10 and 11), which eliminates REIT’s, ADR’s, andother types of securities, and we drop stocks with shareprices below $5 and above $2,000. To reduce unneces-sary turnover in our market-cap deciles, we form thesedeciles only twice a year (the first trading days of Januaryand July). Since the CRSP data are available only throughDecember 29, 2006, decile memberships for 2007 werebased on market capitalizations as of December 29, 2006.For 2007, we constructed daily close-to-close returns forthe stocks in our CRSP universe as of December 29, 2006using adjusted closing prices from finance.yahoo.com.We were unable to find prices for 135 stocks in ourCRSP universe, potentially due to ticker symbol changesor mismatches between CRSP and Yahoo. To avoid anyconflict, we also dropped 34 other securities that aremapped to more than one CRSP PERMNO identifieras of December 29, 2006. The remaining 3,724 stockswere then placed in deciles and used for the analysis in2007. Also, Yahoo’s adjusted prices do not incorporatedividends, hence our 2007 daily returns are price returns,not total returns. This difference is unlikely to have muchimpact on our analysis.

6 The market capitalizations reported in Table 1 for theyear 2007 are based on shares outstanding as of Decem-ber 29, 2006 and should be interpreted as estimates forthe average market cap in these deciles. The “All Count”column is the daily average number of stocks in our uni-verse in each year. As stocks go bankrupt, delist, changefrom CRSP share code 10 or 11 to any other share code(prior to 2007), or fall outside of the $5-to-$2,000 pricerange, they are taken out of our universe.

7 Equity market-making profits are usually positively cor-related with the level of volatility, and most quantita-tive equity market-neutral strategies have a significant



market-making component to their returns, especially athigher trading frequencies.

8 In particular, in 1995 the minimum price-variation onmost stock exchanges was 12.5 cents per share, and whilethis may seem like a very high hurdle for any high-turnover strategy to overcome, recall that the contrarianstrategy tends to be a supplier of liquidity, hence it will beearning the spread on average, not paying it.

9 For simplicity, we use arithmetic compounding to arriveat the three-day cumulative return, which is a reasonableapproximation to geometrically compounded returnswhen the return values are relatively small in magnitude,and is also consistent with the typical way that long/shortequity market-neutral portfolios are implemented inpractice.

10 We use the strategy’s standard deviation in 2006 instead of2007 as the unit of comparison to provide a cleaner com-parison between 2007 and previous years. In particular, if2007 is viewed as “unusual” because of the phenomena weare studying in this paper, it is presumably unusual relativeto some benchmark other than its 2007 performance.

11 We use the August 20, 2007 snapshot of the TASSdatabase, and consider only those funds reporting theirAUM in US dollars.

12 The voluntary nature of reporting to TASS and othercommercially available hedge-fund databases obviouslyimparts a selection bias, so our results should be inter-preted with this bias in mind. See the review papers byAgarwal and Naik (2005) and Fung and Hsieh (2006)for comprehensive discussions of the impact of this andother biases in hedge-fund databases.

13 The fact that the number of funds drops in the mostrecent month is a common feature of the TASS data thatis typically caused by reporting lags, not necessarily agenuine decline in the number of funds in the category,hence the most recent month or two of data should bediscounted.

14 In fact, one can argue that the growth of quantitativeequity market-neutral strategies played a role in the down-ward trend in US equity-market volatility because most ofthese strategies are mean-reversion based, hence they tendto attenuate market fluctuations rather than accentuatethem as momentum strategies might.

15 We use the leverage ratio of 8:1 instead of the 2007 level tocapture the expectations of investors at the end of 2006which, in turn, is taken into account by the portfoliomanagers. In particular, the average daily return of thestrategy in 2007 was not known to either the investors orthe managers at the start of 2007.

16 The corresponding geometrically compounded weeklyreturn is −5.52% for the week, which is so different fromthe arithmetic case because of the magnitude of returnson August 8–10. This is certainly a bad return but not aterrible one under the circumstances. Whether geomet-ric or arithmetic compounding is appropriate depends onhow the strategy is implemented—some portfolio man-agers rebalance their positions each day to a fixed notionallong/short exposure within the month, irrespective ofdaily profits-and-losses, in which case arithmetic com-pounding is the more appropriate method for aggregatingdaily returns.

17 On Friday August 10th, the Wall Street Journal also citedgrowing concern about the sub-prime mortgage market,the move by BNP Paribas to suspend redemptions tothree of its mortgage-related investment funds, and theinjection of cash into money markets by the European andUS central banks as major factors in Thursday’s marketdecline. See Zuckerman et al. (2007).

18 See, for example, Kyle (1985), Easley and O’Hara (1987),O’Hara (1995, Chapter 6), and Gennotte and Leland(1990) for theories of equilibrium price dynamics withasymmetric information, and Barclay and Litzenberger(1988), Barclay and Warner (1993), Chan and Lakon-ishok (1993, 1995), and Holthausen et al. (1987, 1990)for empirical evidence regarding the price impact of largetrades. Ironically, Gennotte and Leland (1990) showthat portfolio insurance and related hedging behavior—which includes mean-reversion trades like our contrarianstrategy—can increase the likelihood of market crashes.

19 For example, in the case of the contrarian strategy (1),consider the contribution of security i to the profits atdate t , ωit Rit = −Rit (Rit−1 − Rmt−1)/N . Suppose thisis an unusually large losing position for a given portfolioweight ωit , which implies either that Rit−1 is larger thanRmt−1 and Rit is large and positive, or Rit−1 is less thanRmt−1 and Rit is large and negative. In either case, the lossis due to persistence or momentum in security i’s price—the bigger the loss, the more significant the momentum.This, in turn, implies a much bigger position of the samesign for security i at date t + 1 on average since ωit+1 =−(Rit − Rmt )/N and Rmt has much lower volatility thanRit . Therefore, large losses will, on average, yield biggerbets for the contrarian strategy (1).

20 They provide several arguments, both theoretical andempirical, but the basic intuition is straightforward: largepositive autocorrelation in asset returns is usually a signof informational inefficiencies in frictionless markets, butgiven how efficient hedge-fund strategies tend to be, the



only remaining explanation for such autocorrelation issignificant market frictions, i.e., illiquidity. For example,it is well known that the historical returns of residen-tial real-estate investments are considerably more highlyautocorrelated than, say, the returns of the S&P 500 indexduring the same sample period. Similarly, the returns ofS&P 500 futures contracts exhibit less autocorrelationthan those of the index itself. In both examples, the moreliquid instrument exhibits less autocorrelation than theless liquid, and the economic rationale is a modified ver-sion of Samuelson’s (1965) argument—predictability inasset returns will be exploited and eliminated only to theextent allowed by market frictions. Despite the fact thatthe returns to residential real estate are highly predictable,it is impossible to take full advantage of such predictabilitybecause of the costs associated with real-estate transac-tions, the inability to shortsell real properties, and othermarket realities. These frictions have, in turn, led to thecreation of real-estate investment trusts, and the returns tothese securities—which are considerably more liquid thanthe underlying assets on which they are based—exhibitmuch less autocorrelation.

21 If a fund’s AUM is missing in any given month, we usethe fund’s most recent non-missing AUM instead.

22 In particular, the approximate standard error for theequal-weighted mean of 400 60-month rolling autocorre-lations is 0.65% under the assumption of cross-sectionallyindependently and identically distributed autocorrela-tions. Therefore, statistical significance of the recent levelsof autocorrelation in Figure 7 is quite high. See AppendixA.2 for details.

23 See, for example, Bookstaber (1999, 2000, 2007), Get-mansky et al. (2004), Lo (1999, 2001, 2002), Kao(2002), and their citations.

24 Because most hedge-fund strategies involve shortselling ofone type or another, the correlations between the returnsof various hedge funds can be positive or negative andare less constrained than, for example, those of long-only vehicles such as mutual funds. And because in ourcontext, “connectedness” can mean either large positiveor large negative correlation, we focus on the absolutevalues of correlations in this analysis.

25 Specifically, we use CS/Tremont’s Convertible Arbitrage,Dedicated Short Bias, Emerging Markets, Equity MarketNeutral, Event Driven, Fixed Income Arbitrage, GlobalMacro, Long/Short Equity, Managed Futures, EventDriven Multi-Strategy, Distressed Index, Risk Arbitrage,and Multi-Strategy indexes. See Appendix A.3 for thedefinitions of these categories, and www.hedgeindex.com

for more detailed information about their construction.All indexes start in January 1994 except Multi-Strategy,which starts in April 1994.

26 We use a shorter rolling window in this case becausethe index returns are less noisy than the individual fundreturns used to estimate the rolling autocorrelations inFigure 7.

27 In particular, recall that the numerator of the correlationcoefficient, the covariance, is given by the expectation ofthe cross product (Xt −µx )(Yt −µy). If σx were to decreasemerely through a change in units (e.g., raw return insteadof percentage return), then (Xt −µx ) would undergo thesame decrease, thereby leaving the correlation coefficientunchanged. Therefore, if σx were to decrease without acorresponding change in (Xt −µx ), then it can be arguedthat there has been a genuine change in the relationshipbetween X and Y .

28 See, for example, Allen and Gale (2000), Freixas et al.(2000), Furfine (2003), Boss et al. (2004), Degryse andNguyen (2004), Upper and Worms (2004), and Leitner(2005).

29 The differences in recovery times for these dislocationsseem to be related to the liquidity of the underlying instru-ments and the breadth of participation in the specificstrategies involved. This intriguing pattern bears furtherinvestigation, and is one of the directions of our ongoingresearch.

30 For example, suppose a margin call is triggered by adecline of 20% or more in the value of a given portfo-lio. If this portfolio contains exchange-traded instrumentsthat are continuously marked to market, the first instanceof a 20% decline will trigger a loss of credit even if theportfolio’s value improves dramatically immediately afterreaching this critical level. If, on the other hand, the port-folio contains OTC contracts that are valued only once amonth, margin calls will occur less frequently.

31 However, an important difference is that the risksof the catastrophe insurance business are exogenouslydetermined, hence the primary source of variability inthat business is the amount of risk capital available.In the case of hedge-fund strategies, both the risksand the risk capital are endogenous and jointly deter-mined, which significantly increases the complexity of thedynamics.

32 More formally, they are not Nash equilibria, and suf-fer from the “Prisoner’s Dilemma.” See Luce and Raiffa(1957). Moreover, the possibility of Brunnermeier andPedersen’s (2005) “predatory trading” becomes morelikely in periods of financial distress, as in August 1998



and 2007, and in these cases, risks become endogenousin the sense of Montier (2007).

33 See Agarwal and Naik (2005) and Fung and Hsieh (2006)for excellent overviews of the hedge-fund industry andsome of the pitfalls with various hedge-fund databases.

34 A number of organizations have been actively involvedin addressing systemic risk in the hedge-fund industryincluding the Federal Reserve System (especially the NewYork Fed and the Board of Governors), the Office of theComptroller of the Currency, the International Mone-tary Fund, the SEC, the Treasury Department, and thePresident’s Working Group. However, none of these orga-nizations have any regulatory authority over the largelyunregulated hedge-fund industry, and cannot even obtainthe necessary data from hedge funds or their credit coun-terparties to compute direct measures of systemic risk.Even the very influential New York Fed exercises itsinfluence primarily through moral suasion.

35 Specifically, “The Bulletin of the Atomic Scientists’Doomsday Clock conveys how close humanity is tocatastrophic destruction—the figurative midnight—andmonitors the means humankind could use to obliterateitself. First and foremost, these include nuclear weapons,but they also encompass climate-changing technologiesand new developments in the life sciences and nan-otechnology that could inflict irrevocable harm.” Seewww.thebulletin.org for further information.

36 Assumption (A1) is made for notational simplicity, sincejoint covariance-stationarity allows us to eliminate time-indexes from population moments such as µ and �k ;the qualitative features of our results will not changeunder the weaker assumptions of weakly dependent het-erogeneously distributed vectors Rt . This would merelyrequire replacing expectations with corresponding proba-bility limits of suitably defined time-averages. See Lo andMacKinlay (1990) for further discussion.

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Keywords: Hedge funds; quantitative market-neutral; long/short equities; August 2007


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