18

G. J. Santoni

0.J Sarifoni is a senior economist at the Federal Reserve Bankof St. Louis. Thomas A. Pollmann provided research assistance.

The October Crash: SomeEvidence on the Cascade Theory

“It’s the nearesl thing to a meltdown that lever want to see.”John J. Phelan, Jr., Chairman of the New York Stock Exchange

HE record one-day decline in stock prices on

October- 19, 1987, stripped roughly 22 pet-cent fromstock values. More disconcerting, however, wet-cthe speed of the adjustment, the tumultuous ti-ad-ing activity in financial markets and the uncer-tainty that prevailed during the week of October19. These aspects of the crash bore a surprisingresemblance to previous financial panics thatmany thought were historical artifacts outmodedby modern regulatory and surveillance systems aswell as by advances in the financial sophisticationof mar’ket participants. The crash shocked thiscomplacency and reawakened considerable inter’-est in financial panics and their causes.

As with its 1929 predecessor, the list of popularexplanations for- the panic of 1987 runs the gamutfr-om the purely economic and financial to thefrailties inherent in human nature see oppositepagel. Recently, a number- of more-or-less official

investigating agencies have released reports about

the October panic.’ Generally speaking, these re-ports do not attempt to identify the reason for thedecline in stock prices. Rather, the)’ focus on the

factors that characterized it as a panic: the sharp-ness of the decline on October 19 and the tumultu-ous trading activity that occurred on this day andduring the following week.

Virtually all of the reports agr-ee that the inabilityof the New York and other cash market exchangesto process the unpr-ecedented volume of tradesquickly contributed impor-tantly to the marketturmoil. They disagree widely, however-, about thereasons for- the sharpness of the decline.

The Brady Commission Repor-t attributes thedownward ‘cascade’’ in stock prices to pro-grammed trading — more specifically, to the ti-ad-ing strategies known as index ar-bits-age arid por’tfb-

‘See, for example, the Report of the Presidential Task Force onMarket Mechanisms (1988): U.S. General Accounting Office(1988): U.S. Commodity Futures Trading Commission (1988):and the report of Miller, Hawke, Malkiel and Scholes (1987).

Some Poptilai’ Njotioiis Regarding the Crash of ‘87

‘t~,’llStrcl has .at1ipiantcd I.as~rrg.is .~thin (In \lcildrn ()rtr’bti Ii). flail stn’c-t,— lt’rzru ( t~ \irurte (ii Ic and l)isiie~land .t~-lire ericlan heici lclstitrc 1” iirr~c-iiihr—ddeii in digital

~ii,cce ~ icr p chv;tcrr—, air’ Oracle tdi ttec &,iie,, coop airci ~Iri11,IiIictlI~lirriicli,-ds ul rclIiil)ult~sappeac ii’ the Clinic6 I! lAils l’i Inc ehios Plea— ttt’l~rc’clliii’’ a ,c11 till ilitti a J);Iriir

sLire ist,tiicl ¼\lidIUcIiilciic’ir attn Iheachilts l)a~trlI .‘ai’,r~c’c-.\rni ~cik limes\\lliNv hcnihes liP’ ri’th,thitt’cl. cIJLIUI do tim -

‘I )r’c’ciiil,er’ 1.5 1987lra~c’ t~hatr~re ilrp~n anti-c I. v~hncle\ UI I he’;~~arric—dlit,

- i’uittild•-, air(I rrl)liclils al-c’ hke irarnarlc—s 1)11 auiirl tl0~\it., fllOl1IIiI~iIticiure bcuge ,eenrs In

ship llic’~tal~etin-ti ItIr turin 11w pIll lug ciiire iac’r \‘•ir’i~ tt~t\c lr:rc1go~i’rs \t,iii~ ii;c~

- - ‘,tirc’k,, .11111 ticrciil, t\ liii) lInt inriiiarlr ‘,~\o;-sp I 1w zirkasse~an’ deans tcleiitrtialilv.

‘—ti—pours the stILl) \ III get Iictc) Ii otittit as\nici tire ‘it,t oi us. \\hr) irreteirded riot to iroluci’ -

- . . .. ‘atti tasi i.’,ed9_lelt it Ii tire Ii iii ul c Ii ‘airing op Ilic’ ne

- ~i~ti’~h,iil riot C hri~tian,Sneirre \JunilcnRobert I’. hleirir \uri ~ni~l fj~p,

- . ,_ ‘Or-rohej- 30 P387..Ortulic’i 22 III.’,,

lit_cijrin_ ii p hrc-girniiiirg It, sc-i’ that rhc— ti~e—veicrnil! rriii’kcl cit the i-.i~hItir~\~,rsa ni’v~(,,rh.b~ ( )ne railers gair is ,uiiill)c’i siciss .rncl 11w

age, ccltII}lIet(’ ~~illi tic- iii itc’il,liisrir and cii Costs CII lc-c’dtng c:citrrptltris and broken, c a

pilol it PXiessi’S ol all sirt-~tdhttitoi’i’.ts. I -ike tic- in! t\dsIela/./ \ge cr1 I Smut t-itigc-ialcls tire ~eais incus Lu~’eir,,Iietr .\nn ink limitsc-iiciihitic’d liii’ cornairri’ iii ~v,-aiIhacicfvcjiith ‘\hc~11. 1988\~illlliii’ sIigiltl~sirristi I anra ci! sci-let nuder—

sleuic lttrg-~U pi-ob;rhh- uc;old ira~r hail unl~a till)—

flulliani Glabr’isccn .~eulurk I iiricss 130-polo! chop II it macmt been cli- crciiptitcrs

ii Jereinther Ii 1387.Vn’clerick Ruupp C Jur,,slian Sr/errrr

‘\\‘c’’ti’ ri-en thi-crogh c1

ttltc t Ie\% ‘. ear-s ri thuulur ‘Or-Wiper rn 19871

~ hicir up lets We hail i’achi’ci rh~tiiiliiii~iitiinn hit-h uas high rc’uaicls cod no risk Wc’ aretlc)~%tcirdc’i-staiictiirg that lh,tt is no! the i-asp .1 his iVstflrtiI,fliS Oil pr’ogiailriiiiti teaching’

~~ilI make it a rrrarkel ~~here tIli- inch~idual in-Price 1.. Pcwt-suii .\en lurk -i i!IIV.S ~c-stur Cflfl tread wirhrcicit tern ut lire mcfln1)iitersI )ecembei I:; I 987’

- I ch\at’d .\ Ge-pile .\nr ink lr,rp,’.sI Itintatc’h ‘‘jc- wIll viev~(iris period as nut- ill •\c,~cirjh,ei 3. 19871.

~t rich ue until,’ a \ (fl unpin taint nlist,iki’. t\ hat~tt’dici \~asilRcrrt’c’ cliii ii Ut?icial svstttfli linintreahtv lii III~ 11Usd. Wi.’ sI toirici stan In liatniiii rr4

- . - index I rpticm ar’hitntge and I un-n Irr’occ eti With\lartin t.tlrtcnr \ms I rr,-k I cures -

olirci r’loi tins ~~hich ‘a ii! restore ptihiiic’ cciii—)ec ‘crinnhiri- II 198,’ . . . -

hdpon: rn tire hntnntl markels I bc tutrirhc- has‘hir~eslor’~koew that stocks flc9it ovec-pricrd c\ c-ri Icnrson tin belies cr that tin’ tn’ctsenl L4.tclldt i’~

In any tracilticinat t-aiuation rIic’astlle such as rigged It is. \lan~-ucnilcl Ire bctitc~ciii ill a ca -

pr’ic-e’c-altnicigs nulirrs arId piicc’ 0 book value ,,iclcr strict Urcu-e inctotile inpert to lose lrLrt haveThe~also knew that tint c:c,inihri ration ~i i~’o a gricici nital and it gciod time s~.hitc’the~etc dci—giant leading and portloho insor’aorcc c’ould lug it.smirch [IC cc’s plonimcctrn~ - . - -

I )cmaicl lic’gin, t S. ~renate I lcczu’ing.,\nisc! C. t\ aflame, \‘eni lurk I runes (‘crnunhitce cur Ranking. ttCnLlsi ig arid

‘Xoycnnher 3 1987’ I ‘than .Uiairs ‘\iav 21, 1088 1q. 7i; 77:.

The TradIng Strategiesd- in tin t cia try u-admgin t rid fUtures because

bitt a turn portfo e ansatio sit Iarg Ice eta Cida at I mIst i itt, adam at

ant ~ p uutuumtttrn ~ In arMs g Isa drug ira gyba eden

lape n th portia TnaOa~mmi1 ant the r ~iin~tb to to tntb 12rod rae 12 otb rtfbho 1dmbonds ci win are ha Id in This adni vat gyatr impS profit

turn ~ ft tomiypi 11 ancish thrdpneethpertiho Idi igbn- eMut Ms band r ~ ~ of! karithe

12 p mate at’ ci 12 dSure tbeaxne atok ci be of latyprc iii

the at alp th 12 Itsfronitbe fa I it in. at ad

~ I cia t a tadeps dono S an a

- a cia at anill alpine be

cant! Invb at isa - UtIiU Tb.

* ad 12 t t

tO IS*e tOt it $EIOf> frafl~ atev pit I U GeneSMcatdrng Offtc~e p

Mimpdtt~nt* panic

assetlan one teatieS tie ~S 50G about

ho insui ance (see ahot for a discussion o - thes’ the evid nc advanced h the Br adv Commis ion

strategies) -‘ I his conclusion however, is qircs in support of the cascadc theory.tioned 5cr iou iv in i’epor ts filed by thc C ommoditv , - - -

- - - -. . Ihrs paper examines minute by-minute priceI ututes trading Commission ((FlU and Chicago da a gather ed from th’ cash and futur s mar kctMercantile Exchangc MEt, these reports attub- - . -.

- - - fos stocks h oni Octobcr lo 23 to determine ii theutc the swift decline in - tock prices to a massn c

- . - - data are best explained by thc cascade theory orvision in investors perceptions of tim funda -

- the different ti-ading rules in the two mas-kets.mental determinants of sto k prices.4 Fuither

more since difler ens rules govern tradng in the Re olving tin is ue is important hecau e of thecash and futures ma kets a careful analysis of thc leg slats e and regulators’ proposals spawned byeffect of these different rules ii ay better explain the October pa c. Fos example the regulatow

See the Report of the Presidenhal Task Force on Market Mecha- See U.S. Commodity Futures Trading Commission (1988), pnisms (1988) pp. v 15, 21, 29 30 and 34—36 mx and Miller Hawke, Malkiel and Scholes (1987), p. 6See U.S. Commodity Futures Trading Commission (1988) pp See Miller, Hawke Malkiel and Scholes (1987), pp 21—23,25iv v vim and 38—138 (especially p 137)- and Miller Hawke 37 and 49—50Malkiel and Scholes(1987). pp 6 8 10—11 41—43 and 55—56

21

proposals advanced by the Brady Commissioninclude:

(1( One agency to coordinate regulatory issuesthat have an impact across all financialmarkets;

(2( Unified clearing systems aci-oss relatedfinancial markets;

(31 Consistent margin requirements in the cash

and futures markets;(41 Circuit breaker mechanisms (such as price

limits and coordinated trading halts(; and(SI Integrated information systems across re-

lated financial markets,’

Proposals 3 and 4 clearly reflect the Commission’sbelief that progi-ammed trading contr-ibuted sig-nificantly to the panic. Furthermore, the actiontaken by the New York Stock Exchange (NYSE( torestrict use of its Designated Order Turnaround(DOTI system by progi-am ti-aders suggests that theofficials of this exchange also subscribe to theBrady Commission’s explanation! ‘I’his belief wasreaffirmed more recently, Beginning Fehruaiy 4,1988, the NYSE has denied use of the DCII’ systemto program traders whenever the Dow Jones In-dustrial Average moves up or down by more than50 points from its previous day’s close,

THE’ cASGAIJE THEORY

The Brady Commission suggests that the stockmarket panic is best explained by the ‘cascadetheory.” This theory argues that “mechanical,price-insensitive selling” by institutions usingportfolio insurance strategies conti’ibuted signifi-

cantly to the break in stock pr-ices! In an effort toliquidate the equity exposure of their poi-tfoliosquickly, these institutions sold stock index futurescontracts in the Chicago market. Such sales low-ered the price of the futures contmacts relative tothe price of the equivalent basket of stocks in theNew York cash mar-ket. The decline in the futur’esprice relative to the cash price induced index ar-hi-trageurs to purchase futures contiacts in the Clii-cago mamtet (which, in their view, were under-valued( and sell (short( the underlying stocks in

the New York market (which, in their view, wereovervalued m’elative to futuresL Thus, index arbi-trage tr-ansmitted the selling pressur’e from theChicago fijtui-es mam-ket to the New Yom-k cash mar-ket causing cash p1-ices in New York to decline,

‘I’he stor does not end here. According to the

theory, the decline in cash prices triggered a fur--ther selling wave in the Chicago market by portfo-lio insur-ers that index arbitr’ageurs, again, trans-

mitted to the New York mar’ket. ‘i’his process wasr’epeated time after time causing a “downwardcascade’ in stock prices.”

‘i’he Brady Commission suggests that support

for’ the cascade theory can be found by examiningthe behavior of the spread (the hasist hetween theprice of stock index futur-es contracts and the cashprices of the shares undem-lying the contracts.”The basis is nos-mally positive. Stock index fi.rtui-espr-ices generally exceed cash pm’ices because the

net costs of car-rying stock forwar-d Iintei-est costless expected diviclends( am-c typically positive.”During the panic, however, the basis turned nega-tive. The Comnussion suggests that this obsen’a-tion is consistent with the cascade theory.

Chart 1 plots both the price of the DecemberStandard and Poor’s 500 futures contract and theStandard and Poor’s index of 500 common stocks.The latter- r’epr-esents the cash price of the stocksunderlying the futures contract. The data coverhalt-hour intervals during October 15—23, 1987,Chait 2 plots the basis — the difference betweenthe two prices shown in chart lAs one can see,the basis fell below zero in the late afternoon ofOctober 16 and, with a few exceptions, remainednegative for the rest of the week. In the BradyCommission’s view, this evidence provides impor-tant support for the cascade theory,

THERE IS LESS TO rFIIE: CASCAIJETHEORY THAN MEETS THE EYE

The Negative Basis

As mentioned, proponents of the cascade theorysuggest that their theory is supported by the nega-

‘Report of the Presidential Task Force on Market Mechanisms(1988), p. vii.

tThe DOT System is a high-speed, order-routing system thatprogram traders use to execute simultaneous trades in thecash and tutures markets.

‘Report of the Presidential Task Force on Market Mechanisms(1988), p.v.

‘Ibid.. pp. 15, 17, 21, 30—36 and 69. It is apparent that ourknowledge of stock marketpanics has advanced considerably

in the 58 years since the 1929 crash. “Black Tuesday” wascaused by adownward price “spiral.” “Bloody Monday” was a“cascade.”

“Report of thePresidential Task Force on Market Mechanisms(1988), pp. lII.1—1II,26, especially Il1,16—I11,22,

“See Figlewski (1984), pp. 658—60; Burns (1979), pp. 31—57;Cornell and French (1983), pp. 2—4; Modest and Sundaresan(1983), pp. 22—23; Santoni (1987), pp. 23—25; Schwarz, Hilland Schneeweis (1986), pp. 326—46; Working (1977); Kawal-ler, Koch and Koch (1987), p. 1311.

22

Chart 1Cash and December FuturesS&P 500 Index S&P 500 Index

300

275

250

225

200

175

15 16 19 20 21 22 23

October 1987*Euiures marker closed

Chart 2Basis = December Futures — Cash

10

0

—10

—20

—30

—40

—50

—60

IS 16 19 20 21 22 23October 1987

*Futures marker closed

T~lI~! eMnopl~!’~aqireqrsewnssealdwexaaqj,,‘~L—L9‘dd‘(egar)ASIRGJ93B5,

as1a2uttpklaz\aopqM‘iuaarad~njuaaiodgniorj

~ll~j‘~‘spuap~uputap?,rrp.&ior~lpaiaadx’aaqijeqiWuTwnssl?suorwinapiaJeptirtsswiopadp~aue~

‘dqaiqM01iunowenipsiaarrdpaiaaclxasiq,l,~4‘~ouuroajreajCauo>jao~samJonaiadpniand-xnnq~snwinaleavInund‘U0ifl~~PUI‘USO’—tt’l

=(os’MSSipoisnipJo‘aarrdIun.rananm‘suouduinssnnsntpanpu~5,’iunaandS~i~‘spunp

-!A~u~ninaqiMo.J~pniandxani.ppun~uncundiicraje,iisn.rniuittuni—Wi.io1nip1j5s~“~‘punp~A!p

pnMnsqoATpuarananqiimpiluiwnssn“d‘)faOiSP

jonar.rdrnn.ranaaprsniejnap.~aiJn(qPiJOVPu~d

‘lOS’LTS—9C~tS=

‘naiad1un~i.ina~punAiouuioajannAnuo~aoisapiJonatadpniandxnntpunnAunq

naunaajJipnqiSI~poisG~iJonaiadqseaiun~ranaapipunannKnuoulnaninw01pnrnpIanaluoasarni

nJonaiadapiunavunqsisnqapi‘MO(,CrnAnan

sisoauo~aus-unajimppunjnuoneanansannWn.riiqan‘&ionrpnpnasnanippoddnsAprnssnanir

jousnopsiseqnapnWnuP‘J~A~M01I‘GiJnqOiaOJojunou.insiqj,,-‘~‘~‘~j‘annAnipJopunnipinpniand~nn~nip~luunpsAepWuipeaiiunnhnsqnsuopun

-xnpunpt~ppnipSS~)(ainpnisnaulHMOaiIPIflOM91anqo~a~JouoouanlJnn~priopnAInsqosinqn/ui

£3

24

remains constant, Notice that this results in adecline in the curr-ent price of the stock from$17.50 to $1288, a reduction of about 30 percent.Fur1hermore, since the expected price of the stockone year from now falls to $13.27, the basis falls to

$391 = $1327— 812.881. Other things the same, adecline in the expected growth i-ate of dividendscauses a decline in the curr-ent price, the futuresprice and the basis. For reasons discussed later,futures prices typically respond to new informa-tion more rapidly than indexes of cash mas-ketpr’ices. This was particularly so during the crash.In terms of our example, if the futures pr-ice de-clines immediately to $13.27 but cash prices adjustless quickly, the observed basis may be negativeduring the adjustment period. In shor-t, there is noneed for a special theory, like the cascade theory,to explain the behavior of the basis during theweek of October 19,’~

.trrationai Price-Insensitive Traders

Stock prices declined throughout the day ofOctober 19, 1987. The decline was particularlysharp in the afternoon (see chart flAt about 1:30p.m. EST, the price of a December S&.P 500 futurescontract was about 15 points lower than the cashpi-ices of the stocks under-lying the contract (thatis, the basis was —15 points, see chart 2). Thismeans that liquidating the basket of stocks under-lying the S&P 500 through futures mar-ket saleswas about $7,500 niore costly (before transactioncostsl than liquidating the same basket in the cashmarket.” Yet, according to the cascade theory,

portfolio insurers continued to liquidate in thefutures mar’ket. In the words of the Brady Com-mission, this appar-ently anomalous behavior wasthe result of “mechanical price-insensitive selling.”

Put moie bluntly, the theory attributes the obser--vation to irrationality on the part of porttblio man-agers who, by most accounts — including those of

the Brady Commission — are credited with beinghighly sophisticated financial experts.

The Missing il.rhs

The cascade theory depends on index arbitr-ageactivity to transnut selling pressur-e from the fir-tures to the cash market. Yet, by all accounts, in-

dcx arbitrage virtually ceased about 1:30 p.m. ESTon october’ 19.6 Cash market prices, however, fellsharply between 1:30 and the market’s close. TheS&P 500 index lost about 30 points during thistime, while the Dow fell by more than 300 points.Furtherniore, index ai-bitrage was severely re-stricted in subsequent trading days because theNYSE limited use of its DOT system by arbitra-

geur-s. However, this did not pr’event a furthersharp decline in stock prices on October 26.

Foreign Markets and Previous Panics

The cascade theory fails to explain why stockmarket panics in for-eign markets occurred at thesame time as the US. panic. Programmed tradingis virtually nonexistent in overseas markets. Yetthese markets crashed as qirickly and by as muchas the U.S. market. Between October 16 and 23, forexample, the UK. stock market declined 22 per-cent, the German and Japanese markets fell 12percent, the French market fell 10 percent and theU.S. market declined 13 percent. What’s more,programmed trading dates back no further- than1982 when stock index futures contracts begantrading. U.S. stock market panics have a muchlonger history. Since the cascade theory does notexplain these other panics, there is some reason tobe skeptical about its usefulness in explaining thelatest U.S. panic.

AN ALTE’R.NATIVE EXPLANATION:EFFICIE.NT MARKETS

A long-standing proposition in both economicsand finance is that stock prices ai’e formed in ef-ficient mar’kets.” This means that all of the rele-~‘ant information currently known about interestr’ates, dividends and the future prospects for firms(the fundamentals) is contained in current stock

prices. Stock prices change only when new infor-mation regarding the fundamentals is obtained bysomeone. New information, by definition, cannotbe predicted ahead of its arrival; because the newsis just as likely to be good as it is to be bad, jumpsin stock pr-ices cannot be pi-edicted in advance.

If the efficient markets hypothesis is correct,past piice changes contain no useful information

“See, in addition, Malkiel (1988), pp. 5—B.

“Thevalue of a S&P 500 futures contract is $500 times the levelof the index, Consequently, it the cash market index is about255 and the futures market index is about 240 as they were at1:30 p.m. EST on October 19, the value of the basis: B$500(240) — $500(255) = —$7,500.

“See the Report of the Presidential Task Force on Market Mecha-nisms (1988), pp. vi, 32 and 40; U.S. General AccountingOffice (1988), pp.43 and 45—46; U.S. Commodity FuturesTrading Commission (1988), pp. vi and 46.

“See Brealey and Meyers (1984), pp. 266—81; Malkiel (1981),pp. 171—79; Brealey (1983), pp. 15—IS; Leroy (1982) andFama (1970).

25

about future price changes. With some addedassumptions, this can be translated into a usefulempirical proposition. If transaction costs are low,the expected return to holding stock is constantand the volatility of stock prices does not changeduring the time period examined, the efficientmarket hypothesis implies that observed changesin stock prices will be uncorr’elated. The sequenceof prce changes are unrelated; they behave as

random variables. This is sometimes called“weak form efficiency.”

This implication contiasts sharply with a cen-tral implication of the cascade theory. The cascadetheoiy suggests that price changes in both thecash and futures markets are positively corielatedwith their own past. This follows from the theory’scircularity which attributes sharp price declines toimmediately preceding sharp declines.

The behavior of U.S. stock prices generally con-forms to the efficient markets hypothesis in thesense that past changes in stock prices contain nouseful information about future changes.” How-ever, when data on stock price indexes are ob-served at very high frequency lintra-day but notday-to-day), changes in the level of cash niarketindexes ar-c correlated and appear to lag changesin futures prices.” This behavior appears to favorthe cascade theory. When difi’erences in the‘mar-ket-making” techniques employed in the

cash and futures markets are taken into account,however, intra-day data from both markets rejectthe cascade theoiy, while, on the whole, they areconsistent with the efficient markets hypothesis.”

Market-Making in the Gash Market

Trading on the NYSE is conducted by memberswho trade within an auction framework at postsmanned by specialists.” Specialists’ activities ar-cconcentrated on a par’ticular group of stocks thatare traded at a particular post. One of the mainfunctions of a specialist is to execute limit ordersfoi other members of the Exchange. A limit orderis an order to buy (sell) a specified number ofshares of a given stock when and if the price of thestock falls (rises) to some specified level. The spe-

cialist maintains a book in which these orders ar-crecorded and to which only lie has access. Theability to place a limit order’ with a specialist freesthe hr-oker who places the order’ tr-om having towait at the post for a pr-ice movement that maynever-occur.

For example, suppose the infor-mation con-tained in the specialist’s book for shar-es of XYZcot-poration is summarized in figure 1.” The de-mand curve aggregates the purchase ordei’s thathave been placed with the specialist. These in-

clude bids of $9’/s for’ 400 shares, $9¾for 300shares, etc. The supply curve aggregates the spe-cialist’s sell orders of 100 shares at $l0’/s, 200shares at $10’/4, etc. Broker’s, standing at the post,trade XYZ shares with each other’ and the special-ist. At any time, a brokei- may i-equest a quote fr’omthe specialist who, given the information in figure1, would respond “$B’/s for 400, 100 at $10‘/s,” Thisindicates that the specialist has buy or’der-s for 400shares at $97/s and sell orders for 100 shares atS10’/s. If the buy and sell orders of the other bro-kers at the post are in balance at the current price,trading in XYZ shares will occur within the pricerange of $9’/s bid and £10 i/~ ask.”

Suppose, however, that a broker has a marketbuy order for 300 shares that he is unable to crosswith a broker with sell orders for 300 shares at thequoted spr-ead (in this case, at an ask pr-ice of$10’/s or less). Since the specialist’s quote indi-cates that he will sell 100 shares at 510½,the bro-ker will respond “Take it.” The broker has pur-chased 100 shares from the specialist at $10’/s.Since the broker must buy another 200 shares, hewill ask for a further- quote. If nothing further hasoccur-red, the specialist will quote “$97s for 400,200 at 810¼.”The broker will respond “Take it.”The broker has satisfied the market buy order for300 shares of XYZ. He purchased 100 shares at$10’/s and 200 shares at $10’/4. Of course, the bro-ker could have acquired 300 shares immediatelyby offering to pay a price of $

10i/

4hut the cost

would have been gr-eater. Instead, it pays the bro-ker to try to “walk up” the supply curve by execut-ing a number of trades rather than jumping di-rectly to the pt-ice that will get him 300 shares in

“Malkiel (1981), Brealey (1983) and Fama (1970).

“See Perry (1985); Atchison, Butler and Simonds (1987) andHarris (1988).

“See Grossman and Miller (1988) for a discussion of why trad-ing rules many differ across the markets.

“Of course, the NYSE is not the only cash market for stocks, butit is a major market. Because of its relative size, the discussionfocuses on this market.

“For purposes of exposition, the figure anddiscussion ignorethe effect of “stops” and “stop loss orders” on the book.

“See Stoll (1985), Shultz (1946), pp. 119—44 and The New YorkStock Exchange Market (1979), pp. 14—21 and pp. 30—31 -

26

Figure 1An Illustration of Limit Order Supply and Demand

Quantity(in hundreds)

one trade.” Similar reasoning applies to situationsin which excess market sell orders exist at thequoted spread.

Notice that this process of “walking up” thesupply curve or’ “walking down” the demandcurve can generate a sequence of recorded trans-action pr ces that run in the same direction. The

larger the excess of market buy (or sell) orders isrelative to the size of the specialist’s limit order-s atvarious prices, the longer the sequence of re-

corded transaction prices that run in the samedirection and the greater the likelihood that re-

corded price changes over the time interval ar’e

correlated. This situation is particularly likely toarise during panics when large order imbalancesdevelop at quoted pr-ices.

Specialist Rule 104

Specialists are required by rule SR 104 to main-tain a “fair and otderly” market. More specifically,the rule states that

Itilie maintenance of a fair and orderly market im-plies the maintenance of price continuity with r-ea—

Price

101/2

101/4

109~/8

93/4

95/s

1 2 3 4 5 6 7 8 9

“Under NYSE rules, public orders have precedence overspe-cialists’orders at the same price. See Stoll (1985), p. 7.

27

sonablr depth, and the minimizing of the effects oftemporary disparity between supply and demand.

In connection with the maintenance of a fair andor’der’ly market, it is commonly desir’ahle that aspecialist engage to a reasonahle degree under exist-ing circumstances in dealings for his own accountwhen lack of price continuity, lack of depth. or clis—paritybetween supply and demand exists or’ is rea-sonably to be anticipated.”

For example, rule SR 104 requires the specialistto buy shares for his own account to assist themaintenance of an orderly mar-ket if~in his estima-tion, sell orders temporarily exceed buy orders atthe existing market price and conversely. If theseimbalances are truly temporary, the trades re-quir-ed by SR 104 will be profitable for- the special-ist; evidence indicates that specialists typically sellon up ticks in pr-ice and buy on down ticks.” Iflarge order imbalances develop that threaten theorderliness of the market, the specialist may insti-tute an opening delay or trading halt. The special-ist needs the approval of a floor official or- governorto do this and to establish a new opening price.”

The effect of SR 104 is to smooth what would

otherwise be abrupt movements in stock prices, atleast over shor4 periods of time a few minutes).

Rather than allowing the price to move directly tosor~renew level, specialist trading temporarilyretards the movement. This can generate a se-quence of cor-related pt-ice changes.

Mark.et~Making in the Futures Market

Trading in futures mar-kets is governed by CFTCr-ules that require all trades of futures contracts tobe executed openly arid competitively by “openoutcry.” In particular, the trading arena, or pit, has

no single auctioneer through whom all trades ar-cfunneled. Rather, the pit is composed of manytrader-s who call out their bids and offers to eachother. The traders are not required to stabilize themar-ket. They may at any time take any side of atransaction even though this might add to an im-balance of buy and sell orders at the quoted price,and they may leave the pit (r-efuse to trade) at anytime. At the time of the crash, there was no rule

regarding limit moves in the price of the Standar-dand Poor’s futures contract.

‘I’hese rules contain no r-equirement to smoothout movements in the price. Tr’aders ar-c free tomove the price immediately to a new level. Unlike

the cash market, there are no trading rules in fu-tures markets that are likely to result in correlatedprice changes. Furthermore, since there were norules that retarded price changes in the futuresmarket, futures prices were fl-ce to adjust morequickly than cash prices so changes in futur-esprices may lead changes in cash prices.

.Diflèrent instruments

It is important to note that different instrumentsare traded in the cash and futures markets. Stockindex futures contracts are agreements between aseller )short position) and a buyer (long position)to a cash settlement based on the change in astock index’s value between the date the contractis enter-ed by the two par-ties and some futuredate.” The instrument underlying the futures con-

tract is a large basket of different stocks, that is,the stocks contained in the Major- Market Index,the Value Line index, the S&.P 500 Index, etc. No

such instrument is traded in the cash market,where purchasing or- selling 500 different stocks,for example, requires as many different transac-tions arid can only be executed at significantlyhigher- costs.”

The different instruments traded in the cashand futures mar-kets have a further implication forrhe relationship between observed price changes

between the two n arkets. The cash market pricesshown in chart 1, as well as those examined by theBrady Commission, are measured by an index.The index is an average of the prices of all thestocks included in the index. When the index is

observed at a very high frequency (say, minute-by-minute), some of the stocks included in the indexmay riot have traded during the interval betweenobservations, if not, the level of cash prices mea-sured by the index includes some prices fromprevious observations. in other words, the index

“Report ot thePresidential Task Force on Market Mechanisms

(1988), p. vi—7, Rule 104 is taken seriously. See pp. vi—9.

“See Stoll (1985), pp. 35—36,

“It was the application of SR 104 that resulted in the openingdelays and trading halts that occurred during the week ofOctober 19. For stocks included in the S&P 500, these delaysand halts averaged 51 minutes on October19and 78 minuteson October20, See U.S. General Accounting Office (1988), p.

“See Schwarz, Hill and Schneeweis (1986), p.9.

“For example, the cost of trading one futurescontract based ontheStandard and Poor’s 500 is about $500 lower than tradingthe equivalent basket of stocks in the cash market. See Miller,Hawke, Malkiel and Scholes (1987), p. 11, and U.S. GeneralAccounting Office (1988), p. 20.

56.

28

includes some “stale” prices. The term used todescribe this phenomenon is “nonsynchronoustrading.”

Typically, nonsynchr’onous tr’ading does notcr-eate a serious measur-ement problem. Under-normal conditions, a buy or- sell order is executedin about two minutes on the NYSE. On October 16and during the week of October 19, however, the

time required to execirte orders rose markedly:”On those days, the index contained a considerablenumber of stale prices.” The subsequent piece-meal adjustment of these stale prices for indiiid-

ual stocks could explain correlated changes in thelevel of the cash market index. This is shown inthe table 2 example. The example assumes thatthe index is a simple average of the prices of threestocks (A, B and C) divided by the average price inperiod zem and multiplied by 100. The initialprices (in period zero) are equilibrium pr-ices (i.e.,they contain all currently available relevant infor-mation). Then, new information becomes availablein period I that eventually will cause a 10 percentdecline in all stock prices. if there is nonsynchro-nous trading, the revisions will occur- piecemealfor each of the stocks. One example of this isshown in the table: the price of stock A falls inperiod 1, the price of stock B falls in period 2, etc.If the index is repor-ted in each per-iod, it will dis-

play positively corr’eiated changes as shown in thetable.

The stale price pr-ohlem is not relevant for fu-tures mar’ket prices; futures prices are actualprices. As a result, changes in futures prices willappear to lead changes in the cash mar-ket index ifthe index contains a substantial number of stale

prices.

THE DIFFEHE’NT IMPLICATIONS

The centr-al feature of the cascade theory is thatdeclines in cash and futures prices reinforcedeach other and led to further declines in both

markets. The theory suggests that declines in thepr-ice of stock index futures contr-acts caused adecline in the cash prices of the underlying stocks,

and this dr’op caused a further decline in thepr-ices of index futures contracts. If the theory iscorrect, changes in cash prices will be positivelycorrelated with past changes in the price of indexfutures and conversely. The cascade theory fur-

ther- implies that price changes in cacti market arepositively correlated with their own past changes.This follows from the circularity of the theorywhich attr-ibutes sharp declines in stock prices toimmediately preceding sharp declines. Finally,since the cascade theory contends that this spe-cific behavior caused the panic, these correlationsshould be observed during the panic, but not atother times.

The efficient markets hypothesis suggests thatmarket-making in the cash market and nonsyn-chronous trading could produce intra-day cashmarket price changes that are correlated. Further-more, the hypothesis suggests that changes infutures prices may lead changes in cash prices.These implications are similar to the implicationsof the cascade theory. The two differ’, however, inthree important respects. Unlike the cascade the-ory, the efficient markets hypothesis suggests that:

(11 Changes in the price of stock index futurescontracts are uncorrelated,

(2) Changes in cash prices do not lead changesin futures prices, and

i3) Relationships that exist across the two mar-

kets are not unique to the panic.

“See U.S. General Accounting Office (1988), p. 73.

“See Harris (1988); Reportof the Presidential Task Force onMarket Mechanisms (1988), p. 30; Miller, Hawke, Malkiel andScholes (1987), pp. 21—22 and 34—35; U.S. CommodityFutures Trading Commission (1988), pp. v, IS and 8-1through 8-9.

29

TESTING THE TWO THE’ ORIESThese theories are tested using minute-by-

minute data on the level of the Standard andPoor’s 500 index (S&P 500) and the price of theDecember 1987 Standard and Poor’s 500 indexfutures contract (S&P 500 Futur-es). The level of theS&,P 500 index represents the cash price of thestocks underlying the S&P 500 futures contr-act. All

tests are conducted using first differ’ences of thenatural logs of the levels. This tr-ansformation of

the data approximates one-minute per-centagechanges (expressed in decimals) in cash and fu-tures market prices. The data cover’ the tradingdays immediately before, during and after thepanic: October 16, 19 and 20.”

A few comments about the data are important.The NYSE, on which the great bulk of the stocks

included in the S&P 500 index are traded, wasopen from 9:30 am. to 4:00 p.m. ES~’T’on the abovedays. The CME, which trades the S&P 500 futurescontract, was open from 9:30 am. to 4:15 p.m. ES’I’on October 16 and 19; on October 20, however,trading in the S&.P 500 futures contract was haltedfrom 12:15 p.m. to 1:05 p.m. EST. All tests reportedhere eyclude the period on October20 when trad-ing in the futures mar-ket was halted.

Were changes in Stock PricesCorrelated?

Table 3 presents the results of a test (called aBox-Pier-ce test) based on the estimated autocorre-lations of percentage changes in cash marketprices. This test is designed to determine whetherthe data ar-c significantly correlated, that is,whether current changes in cash market pricesar-c related to their- own past changes. Both theo-ries discussed in this paper suggest that intra-day,high-frequency cash market price changes will bepositively correlated, although the reasons for thepositive correlation are considerably different. As aresult, these data do not help discriminate be-

tween the two theories. if the data pr’ove inconsis-tent with this implication, however, neither- theory

performs well in explaining the behavior of cashmarket prices.

The data in table 3 indicate that minute-to-

minute changes in the S&P 500 Index ar-c signifi-cantly correlated. Furthermore, the correlationsar-c positive at least over the initial lag.”

tash~Miiwt,/ ‘~ / “‘ / N

nmer$eent~gsbtuW.N/Mtnü~bbth~APaOfttd~fl /

~p~S4~r1t ~-*pMsfl,,

7,,! ‘~‘4t~á~rsi,‘~ ~ /

~f,’ e,,/%S‘A / /7

Np / / N

7 / ~ N I / N// / ~ ,,A~ NA 7’’ ~

‘p //7!/// / //,,/

‘A’~2i/,~iàiSff

‘</~ /~N/’ N/f’, ,“~ “;f~p,,N A /!A/ Ai>,~ A/ ff’’,’

A /“,~/‘ Se~/ ‘f”~f” “~,‘7 ,,,,,, ,‘/~ 7/ /

A/A’ ~“/4/77 A “~~a~’A’ “P9

/ ‘A~ ‘, ~*‘A’ “~/\ ,p’’7’/7

/ A ~ 174 “ 4/

7 ,, A N A

/ 4~/ A’

‘1’ / ‘~,‘~p”,~,’”

A, ‘,~/‘‘P”~ ‘/77’,/7’A ~. ‘N’// // A /

d,/ pf’A/,,’~’ ‘ ~, A

/

*47” ~ c~ ~aS,I’’ “~~‘A’-’-~tA i~-~—C”~”,?ir’ ‘-7’~’AC4~

A

Table 4 presents the results of the same test for’the December S&.P 500 futures contract. Tin, ef-ficient markets hypothesis and the absence of

specialist traders suggest that these changes ar-cnot correlated. Conversely, the cascade theory

“Minute-by-minute price datawere also examined for OctoberIS and 21—23. In each case, the qualitative results were thesame as those presented here.

“These correlations are analyzed further below.

30

pr-edicts that percentage changes in the futuresprice will he positively correlated.

‘the data pr-esented in table 4 ar-c consistent

utursM*i~etN with the efficient mar-kets hypothesis, not the cas-coefficientsand cade theory. None of the test statistics for’ October

So Pl*ce~tstI~~r irst N 16 (panel A), October20 (panel D( and for the hulk

DIffmtn~s~gs~ft* of the trading day on October19 (panel C) indicate

Mfrn!*~by4*ut~Pn~e significant corr-elations at conventional signifi—~Rdu ~ntr*cfl cance levels~.’fheseprice changes are serially un-

cor-related.’~Data for- the first 90 minutes of tr’adingPs~t* Oøpbe~ ~ on October- 19 (panel B) are an exception. During

A$ret ~ this period, changes in the futures pr-ice wer-e sig-~cOeftk$%* ~statt nificantly correlated with the change the previous

ruinirte. This correlation, however’, is negative, nor

positive as the cascade theory implies.” Thus, theevrdence presented in table 4 is inconsistent with

420 8 the cascade theory, while, on the whole, it con-/ $0 forms to the efficient markets hypothesis.

S is the Cash Market Efficient?

S a ssaaS$U. The table 3 results indicate that intr’a-day

/ ‘A~ta~’n changes in cash market prices are cor-related. PutS another way, past price changes contain some

rnformatron about future changes for- the next fewminutes. Is this infor-mation useful in the sense

3 / that it can be pr-ofitabiv exploited by traders? Ifso,it would suggest that cash market trader’s do riot

1’ incorporate information efficiently. This, of course,would provide evidence against the effir:ient mar-kets hypothesis.

~sneIC ~1flWj ~aa 41 ~tSfl -

In par’t, the answer’ to this question depends onthe length of the time per-iod over- which the pr-ice

t~~tit , changes are r-elated. if the time period is short,

1 2 03 shorter- than the time required to execute a trans-S At? action, the infor-mation contained in past pr-ice

I changes cannot be exploited profitably and the

cash market is efflr-,ient,

‘l’ahle 5 helps answer this question. The tables

data ar-c estimates of the length of the lagged rela-

~ rionship between current and past cash marketprice changes for October 16, 19 arid 20. The esti-mates were obtained by r’egressing the contempo-

raneous minute-to-minute price change on the 15029 previous minute-to-minute pr-ice changes. Ini-

tially, this specification was identified as the unre-

e stricted model, To determine whether’ the esti-at is

S ‘~! “Thesame result was obtained when datafor October 15 and21—23 were examined.

vrltlcatvSjetor 4 lagsrsaS’ 4$oxPler *1’bcio “This puzzlingresult for the first 90 minutes of trading on Octo-ète$ ot syaWerrtdlealessi~tr,cante otorrelatron. ber 19 may be due to the fact that manystocks had not yetC ~ ~ ,~ .m opened for trading on the NYSE and the rumors at that time

that the SEC would calla trading halt. See Miller, Hawke,Malkiel and Scholes (1987), wire report summary.

31

N ‘ ‘, , , ,,, , ‘, ‘

tables1 / A A

SmSteginiietstt~amet N N ‘A A A N

~an~t4tfl3a4~OOf-S5S1~ A A

N ,“//A ‘‘“‘A /,,>,/,‘‘A’’ ~,\ ‘N’,,! / / / A,,’,,’’’ A’’7’A’ ,,,,//,

N’ /~ ~oat4 MM A N /

$ /‘A, AC’,, ,‘ A’ ‘,‘, N N

A’ ,‘M’,’ 7///,N 1’~~/~ 1 AN,/N, “, ‘A ‘A,NN

7~‘~/ ‘AA/ /AA’/’ ‘A’” ‘~‘ ‘ ‘N’~’ N

N OW SA A A A N

N / 7 ‘A A

Npaneto/OptoIsv* 1$87øtSOa*rt~~4~C*p$aS1)’N

S ‘A / / A N7N /A / N

7 N A’N N! , N ‘A’

N N ‘AN

A AN N N N N

N NaNc~ S ~ I ,LPtSA N 55 ‘A03 N

~N’’’A”, N~N~ç/,,A77,/7,771 ~ ,‘AAN’’Nl/,’/’< “,“,~‘,I IN N N , ‘A/ A /

,, N / / N 7

// ‘ / ‘ ,A’ /‘~/~,/// ‘ / //,,,//‘‘ A/ / 1’ A A N

mated coefficients am’e sensitive to the lag lengthand to identily statistically redundant lags, the lagstm-uctur-e was successively shor’tened by one lag.At each stage, the t-statistic for the coefficient ofthe most distant lag was examined. Ifthe test indi-cated the coefficient was statistically insignificant,that lag was dropped and the equation was r’eesti-mated with one less lag. ‘l’his process was r’e-peated until the test r-ejected the hypothesis thatthe estimated coefficient of the most distant re—maining lag was zero!”

The estimates shown in table 5 indicate that thelags ranged from about two minutes on October’ 16to five minutes on October 20.” It r-equir-es about

two minutes to execute a trade on the NYSE undernormal trading conditions. During the panic, exe-cution times ranged from about 10 to 75 minutesat tirues.” in view of this, the lags estimated intable 5 do not appear’ to be long enough to r-eject

the efficient muar-kets hypothesis; also, since theyvaried over the period, it is doubtfnl that pastpr-ice changes contained information that couldbe exploited by traders.

Did Stock Price Changes ReinforceEach Other Across Markets?

The central feature of the cascade theory can betested by deternunirig whether- past pr-ice changesin the futur-es market help explain cur-rent pricechanges in the cash market and conversely. This isdone by regr-essing the change in cash prices onpast changes in cash prices; then, past changes infutures pr-ices ar-c added to the estimated r-egres-sion equation to see if they imnpr-ove the equation’sexplanatory power. An F-test is conducted to de-termine whether- the addition of the futures mar-ket data significantly increases the cash priceequation’s coefficient of determination (H’). The

“See Anderson (1971), pp. 223 and 275—76. It is possible thatthis test may reject some lags that are, in fact, significant iftaken as a group. To control for this, F-tests were run with thelag length in the unrestricted model setat 15. Thenumber oflags in the restricted model was set at 12 to determine if thethree omitted lags were significant. The lags in the restrictedmodel was then reduced to nine and the test repeated, etc.

problem that the probability of rejecting the null hypothesis (theestimated coefficient is zero) when it is true rises as the laglength is reduced. Consequently, the true lag lengths may beshorter than those estimated in tableS. See Batten and Thorn-ton (1983), pp. 22—23, and Anderson (1971), pp. 30—43.

“U.S. Government Accounting Office (1988), p. 73.

“The lag had declined to about three minutes by October 23.The method used in this paper to estimate lag length has the

32

N

~ ‘~J’ C

/ — a/

I

/

test is then revcrsed, with the change in ftrturesprices as the dependent variahle.

The r-esults of this test are presented in table 6for each of the trading days examined in this pa-per-. The lag length employed on each day is theone identified by the table 5 test.” The results forcash market prices show that the addition of pastchanges in futures prices improve the regressionestimates; this suggests that price changes in thefutures mar-ket preceded those in the cash market.‘I’his r-esult is consistent with both the cascadetheory and the efficient mar’kets hypothesis. Fur’-them-more, it is not unique to the panic; it has beenobserved for intm-a-day price data during other

periods as well.4’

Other table 6 results, however-, are inconsistentwith the cascade theory. The inclusion of pastchanges in cash prices in the regressions thatestimate the change in futures pr-ices does not sig-nificantly impr-ove the estimates, This rejects thenotion that past changes in cash prices help ex-

plain changes in ftrtures prices. ‘I’his finding isinconsistent with the centr-al featur-e of the cas-cade theory, which suggests the panic was causedby declines in cash and futures prices that becamelar-ger as they tumbled over’ each other on the waydown,

CONCLUSION

This paper has examined the cascade theory,which has been advanced as an explanation of theOctober 1987 stock market panic. The theory relieson the notion that stock traders behave “mechani-cally,” are “insensitive to price,” and execute

“Hsiao(1981) uses asimilar method. These lag lengths apply tothe cash market, Analysis of the futures market suggests thatthe appropriate lagfor this market is zero.

“See Kawaller, Koch and Koch (1987).

tr-ansactions in markets without regard to transac-

tion costs, ‘these assertions are inconsistent withthe behavior of wealth-maximizing individuals.Not only ar-c the theoretical underpinnings of the

cascade theory weak, the data do not support thetheory. tnstead, the observed relationships that doexist between the markets are not unique to thecr-ash and can be explained by a theory that relieson wealth maximizing behavior-.

Almost 60 years later’, the cause of the ‘GreatCr-ash” in October 1929 is still being debated.Those with even longer memories know that them-cis little agm’eement about what caused the stockmarket panic in 1907. Although financial reformsfollowed each of these panics, history indicatesthat the refomms have done little to r-educe thefrequency or- severity of panics. Without a reliabletheoretical guide to the mechanics of a panic, anyr-eform is no more than a “shot in the dark.” Theevidence presented in this paper suggests that thereform,s advanced by proponents of the cascade

theory are unlikely to alter- this historical pattern.

REFERENCES

Anderson, Theodore W. The Statistical Analysis of Time Series(John Wiley and Sons, Inc., 1971).

Atchison, Michael D., Kirt C. Butler, and Richard R. Simonds,“Nonsynchronous Security Trading and Market Index Auto-correlation,” Journalof Finance (March 1987), pp. 111—18.

Batten, Dallas S., and Daniel L. Thornton, “Polynomial Distrib-uted Lags and the Estimation of theSt. Louis Equation,” thisReview (April1983), pp. 13—25.

Brealey, R. A. An Introduction to Risk and Return from CommonStocks (The MIT Press, 1983).

Brealey, Richard, and Stewart Meyers. Principles of CorporateFinance (McGraw-Hill, 1984).

Burns, Joseph M. A Treatise on Markets: Spot, Futures, andOptions (American Enterprise Institute, 1979), pp. 31—55.

Cornell, Bradford, and Kenneth R. French, “The Pricing ofStock Index Futures,” Journal of Futures Markets (Spring1983), pp. 1—14.

Fama, Eugene F. “Efficient Capital Markets:A Review ofTheory and Empirical Work,” Journal of Finance, Papers andProceedings (May 1970), pp. 383—417.

Figlewski, Stephen. “Hedging Performance and Basis Risk inStock Index Futures,” Journal of Finance (July 1984), pp.857-69.

Grossman, Sanford J., andMerton H. Miller. “Liquidity andMarket Structure,” Princeton University Financial ResearchCenterMemorandum No.88 (March 1988).

33

Harris, Lawrence. “Nonsynchronous Trading and the S&P 500Stock-Futures Basis in October 1987” (University of SouthernCalifornia Working Paper, processed January 11, 1988).

Hsiao, Cheng. “Autoregressive Modelling and Money-IncomeCausality Detection,” Journal of Monetary Economics (Janu-ary 1981), pp. 85—106.

Kawaller, Ira G., Paul D. Koch, and Timothy W. Koch, “TheTemporal Price Relationship Between S&P 500 Futures andthe S&P 500 Index,” Journal of Finance (December 1987), pp.1309—29.

Leroy, Stephen F. “Expectations Models ot Asset Prices: ASurvey of Theory,” Journalof Finance (March 1982), pp. 185—217.

Malkiel, Burton G. “The Brady Commission Report,” PrincetonUniversity Financial Research Center Memorandum No, 92(May 1988).

________- A Random Walk Down Wall Street (W. W. Nortonand Company, 1981).

Miller, Merton H., John D. Hawke, Jr., Burton Malkiel, and MyronScholes. Preliminary Report of theCommittee of InquiryAppointed by the Chicago Mercantile Exchange to Examinethe Events Surrounding October 19, 1987 (December22,1987).

Modest, David M., and Mahadevan Sundaresan, “The Rela-tionship Between Spot and Futures Prices in Stock IndexFutures Markets: Some Preliminary Evidence,” JournalofFutures Markets (Spring 1983), pp. 15—41 -

Perry, Philip R. “Portfolio Serial Correlation and Nonsynchro-nous Trading,” Journal of Financial and Quantitative Analysis(December 1985), pp. 51 7—23.

Report of the Presidential Task Force on MarketMechanisms(U.S. GovernmentPrinting Office, January 1988).

Santoni, G. J. “Has Programmed Trading Made Stock PricesMore Volatile?” this Review (May 1987), pp. 18—29,

Schwarz, Edward W., Joanne M. Hill, and ThomasSchneeweis, Financial Futures (Dow Jones-Irwin, 1986).

Shultz, Birl E, The Securities Marketand How It Works (Harperand Brothers, 1946).

Stoll, Hans R, The Stock Exchange Specialist System: AnEconomic Analysis. Monograph Series in Finance and Eco-nomics (Salomon Brothers Center for the Study of FinancialInstitutions, New York University, 1985).

The New York Stock Exchange Market (New York Stock Ex-change, June 1979).

U.S. Commodity Futures Trading Commission, Final Report onStock Index Futures and Cash Market Activity During October1987 (U.S. Commodity Futures Trading Commission, January1988).

U.S. General Accounting Office, Financial Markets: PreliminaryObservations on the October 1987 Crash (U.S. General Ac-counting Office, January 1988).

Working, Holbrook, Selected Writings of Holbrook Working(Chicago Board of Trade, 1977).