Discourse Processes
ISSN: 0163-853X (Print) 1532-6950 (Online) Journal homepage: https://www.tandfonline.com/loi/hdsp20
Using story‐based causal diagrams to analyze
disagreements about complex events
Brian P. Shapiro , Paul van den Broek & Charles R. Fletcher
To cite this article: Brian P. Shapiro , Paul van den Broek & Charles R. Fletcher (1995) Using
story‐based causal diagrams to analyze disagreements about complex events, Discourse
Processes, 20:1, 51-77, DOI: 10.1080/01638539509544931
To link to this article: https://doi.org/10.1080/01638539509544931
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DISCOURSE PROCESSES 20,51-77 (1995)
Using Story-Based Causal Diagrams
to Analyze Disagreements About
Complex Events
BRIAN P. SHAPIRO
University of Arizona
PAUL VAN DEN BROEK
CHARLES R. FLETCHER
University of Minnesota
People often disagree about the causes of complex events. Previous research has
shown that disagreement often results from cognitive and pragmatic constraints
that govern people's tendency to attribute outcomes to partial rather than complete causes. This article applies the Trabasso, van den Broek, and Suh (1989)
story-based procedures to a narrative of the 1987 stock market crash. The content
and structure of the resulting causal diagrams are then used to analyze some
opposing causal explanations that were offered by different investigative commissions. The diagrams reveal that some major disagreements involved conflicting
interpretations of the crash's multiple indirect and psychological causes. The diagrams also show that some causal explanations were incomplete and implausible
because they ignored or contradicted relevant events and causal relations. Implications for discourse comprehension research are discussed, and the advantages of
using causal diagrams to mitigate constraints on causal comprehension and explanation are explored.
People often disagree about the causes of complex events. The debate over
the 1987 stock market crash is a good example. Different investigators had
the knowledge and time to interpret the evidence, but they still reached
opposing conclusions. For example, some investigators attributed the crash
to changes in investors' long-term expectations, others attributed it to a
general market panic, and yet others attributed it to a small number of
large institutions which sold millions of dollars of securities in a matter of
seconds. The 1987 crash is typical of causally complex events: Its outcomes
were caused by multiple antecedent conditions, its causal relations were of
various types, and many of its antecedent conditions directly caused each
other but only indirectly caused the outcomes.
We are grateful to Art Graesser, Susan Ranney, and three anonymous reviewers for their
comments on an earlier version of this article.
Correspondence and requests for reprints should be sent to Brian P. Shapiro, University
of Arizona, Karl Eller School of Management, 301 McClelland Hall, Tucson, AZ 85721.
51
52
SHAPIRO, VAN DEN BROEK, AND FLETCHER
Research in the philosophy and psychology of causal reasoning has
identified many reasons for people's failure to understand and agree about
an event's causes. A scenario's complexity and the lack of a universal
definition of causality often leave the analysis of causal relations open to
multiple interpretations (Hart & Honore, 1985; Mackie, 1974). In addition,
several cognitive and pragmatic constraints govern the tendency to attribute outcomes to partial rather than complete causes. Among these constraints are knowledge and memory limitations (Bloom, Fletcher, van den
Broek, Reitz, & Shapiro, 1990; Chiesi, Spilich, & Voss, 1979; Spilich,
Vesonder, Chiesi, & Voss, 1979), conversational constraints (Collingwood,
1940; Graesser & Franklin, 1990; Hilton, 1990; Mackie, 1974), and motivational biases (see Kunda, 1990, for a review). These constraints can lead
different people to attribute the same event to different causes.
This article demonstrates how the explicit representation of events as
causal diagrams of nodes and causal relations can be used to analyze causal
disagreements. It also explores how causal diagrams may reduce the cognitive and pragmatic constraints that make people unable or unwilling to
communicate to others a complete event representation. Our approach is
based on two common assumptions in cognitive psychology that link individuals' mental representations with their causal judgments and decisions.
The first assumption is that an individual's mental representation of a
scenario reflects his or her understanding of that scenario (Kintsch, 1988).
Discourse comprehension research has provided extensive psychological
evidence that readers construct causal network representations of stories
in long-term memory (see van den Broek, 1990b, for a review). The second
assumption is that judgment and decision making are mediated by an
individual's mental representation (e.g., Newell & Simon, 1972). Pennington and Hastie (1986, 1988, 1992) have provided experimental evidence for both assumptions by demonstrating that jurors use story-like
mental representations of trial evidence to reach their verdicts.
Drawing on these psychologically validated assumptions, we propose
that many disagreements can be traced to individuals' causal network
representations of the disputed events. To illustrate this idea, we apply the
Trabasso, van den Broek, and Suh (1989) procedures to a narrative of the
1987 stock market crash. We then use the resulting diagrams to analyze the
opposing causal explanations offered by different investigative commissions. Unlike other procedures for constructing causal diagrams (e.g., see
Axelrod, 1976; Hogarth, Michaud, & Mery, 1980; Maruyama, 1963; Sev6n,
1984), the Trabasso et al. procedures assign a story category to each event
and causal relation. Our analysis demonstrates that the story categories are
especially useful for analyzing opposing interpretations of the crash's multiple indirect and psychological causes. We also find that some investigative commissions' explanations were incomplete or implausible because
CAUSAL DIAGRAMS
53
they omitted or contradicted some of the relevant events and causal relations.
Our work extends previous research on the analysis of causal diagrams
in several ways. First, whereas others have suggested that the analysis of
causal diagrams could have implications for understanding disagreement
about causal relations (e.g., see Einhorn & Hogarth, 1986; Hilton, 1990),
we make explicit some of those implications. Second, discourse comprehension research has used causal diagrams to represent simple story
events. We demonstrate that the story-based procedures generalize to a
more naturalistic and complex narrative. The crash narrative is complex in
part because its recursive event chains blur the distinction between cause
and effect and between direct and indirect causes. Without those distinctions, existing discourse models might have difficulty finding good explanations for complex events (e.g., see Graesser & Franklin, 1990; Graesser,
Lang, & Roberts, 1991). Finally, discourse models typically assume that
most respondents will sincerely try to provide high-quality explanations. In
contrast, we discuss the pragmatic constraints that can make people unwilling to reveal their complete event representations.
This article is organized as follows: We first describe the Trabasso et al.
(1989) procedures for constructing story-based causal diagrams. We then
discuss the cognitive and pragmatic constraints that govern the tendency
to attribute events to incomplete causes. Next, we use causal diagrams to
analyze major disagreements about the 1987 crash. Finally, we compare
our work with Graesser and Franklin's (1990) QUEST model of question
answering, and we explore how causal diagrams may mitigate the constraints on causal comprehension and explanation.
STORY-BASED CAUSAL NETWORK REPRESENTATIONS
Researchers have noted that causal diagrams allow the causal role of each
event to be defined in terms of its causal relations to other events in the
diagram (cf. Danto, 1985; Graesser, 1981; Graesser & Clark, 1985; Pennington & Hastie, 1986; Trabasso et al., 1989). This article uses causal
diagrams to evaluate the quality of opposing explanations for the 1987
stock market crash. A complete explanation for the crash should account
for all known events and causal relations, and a plausible explanation
should not contradict them (cf. Pennington & Hastie, 1993). We recognize
that individuals who do not share the same causal model may reasonably
disagree about the causal roles of hypothetical or future events (e.g., see
Axelrod, 1976; Hogarth et al., 1980; Sev6n, 1984). However, the 1987 crash
involved actual events whose occurrence was verified by several investigative commissions. This allows us to evaluate the relative completeness and
plausibility of opposing causal explanations for the crash.
SHAPIRO, VAN DEN BROEK, AND FLETCHER
54
Our approach is based on extensively used and psychologically validated systems for representing the causal structure of narrative events
(e.g., see Graesser & Franklin, 1990; Trabasso et al., 1989). Under this
approach, the construction of a causal diagram involves three steps: (a)
identification of nodes that correspond to the scenario's events, (b) identification of causal relations, and (c) assembly of the diagram. Each event
and causal relation is also assigned to one of several story categories. This
section summarizes the Trabasso et al. procedures for assigning the categories and describes the psychological properties of causal diagrams.
Trabasso et al.'s Causal Network Model
Story Events. Trabasso et al.'s (1989) causal network model is a representation of how people reason about story events. The model assigns each
story event to one of five categories, represented as labeled nodes in
Figure 1. Setting information (S) introduces story characters in time and
space. Goals (G) are a protagonist's desired outcomes. Attempts (A) are
a protagonist's goal-directed actions. Outcomes (O) are events and conditions that may or may not satisfy a protagonist's goals. Reactions (R) are
a protagonist's mental states or internal reactions. These categories resemble event classifications developed by others (e.g., see Graesser & Clark,
1985; Graesser & Franklin, 1990; Mandler & Johnson, 1977; Schank &
Abelson, 1977).
The causal network model implies that a complete story or explanation
of human behavior must include each event category. For example, a story
is incomplete if it fails to describe the reasons for a protagonist's behavior.
S
0)
—
Figure 1. Causal network model story events and causal relations (adapted from Trabasso,
van den Broek, and Suh, 1989). The event categories are S (setting information), G (goals),
A (attempts), O (outcomes), and R (reactions). The causal relation categories are M
(motivational, "9 (psychological), <E> (physical), and E (enablement).
CAUSAL DIAGRAMS
55
Mandler and Johnson (1977) also reported evidence that incomplete stories are more difficult to comprehend and recall.
Causal Relations. The labeled arcs in Figure 1 represent causal relations among the event categories. Trabasso et al. (1989) and van den Broek
(1990a) described four criteria that have enabled researchers to reliably
identify causal relations among pairs of events. These criteria have been
discussed at length in philosophy (e.g., Hume, 1739/1964; Lewis, 1976;
Mackie, 1974), law (Hart & Honore, 1985), and psychology (e.g., Bindra,
Clarke, & Shultz, 1980; Downing, Sternberg, & Ross, 1985; Einhorn &
Hogarth, 1986; van den Broek, 1988).
Temporal priority stipulates that a cause cannot occur after its effect.
Temporal sequence is an important structural feature of scripts (e.g., see
Schank & Abelson, 1977). Ohtsuka and Brewer (1992) have also reported
that it is often easier to comprehend discourse when its structure corresponds to the temporal structure of the underlying events. Operativity
further stipulates that in order for a direct causal relation to exist between
cause and effect, the cause must be active (have causal force) when the
effect occurs. For candidate causal pairs that satisfy both temporal priority
and operativity, causal relations are identified by judging whether the
antecedent is necessary or sufficient in the circumstances for the consequent (van den Broek, 1990a, 1990b). An antecedent is considered necessary in the circumstances for a consequent if it satisfies the counterfactual
criterion "If the antecedent had not occurred in the circumstances, then
the consequent would not have occurred" (Hart & Honore, 1985; Lewis,
1976; Mackie, 1974). An antecedent is considered sufficient in the circumstances for a consequent if it satisfies the criterion "If the antecedent occurs
in the circumstances and the usual events are allowed to run on from there,
then the consequent will occur" (Hart & Honore, 1985; Mackie, 1974). The
phrase in the circumstances recognizes that causal judgments also depend
on the investigator's knowledge or assumptions about the circumstances
surrounding the alleged cause (cf. Einhorn & Hogarth, 1986; Hart &
Honore, 1985; Mackie, 1974).
In Figure 1, all of the causal relations assume that both temporal priority
and operativity are satisfied. The categories of causal relations that can
exist among each pair of events are determined as follows. A causal relation is motivational (M) if the antecedent describes goal information and
if necessity in the circumstances is satisfied. The causal relation is psychological (^) if the antecedent describes an internal state or reaction (R) and
if necessity in the circumstances is satisfied. The causal relation is physical
(<I>) if it is neither motivational nor psychological and if sufficiency in the
circumstances is satisfied. All other causal relations are enablement (E).
56
SHAPIRO, VAN DEN BROEK, AND FLETCHER
Psychological Properties of Causal Diagrams
These procedures produce a branching network of categorized events and
causal relations with many psychologically valid properties. For example,
events with many causal connections to other events are recalled or summarized more often (Black & Bower, 1980; Fletcher & Bloom, 1988;
Graesser & Clark, 1985; Trabasso, Secco, & van den Broek, 1984; Trabasso
& van den Broek, 1985), recalled more quickly (O'Brien & Myers, 1987),
and rated as more important (O'Brien & Myers, 1987; Trabasso & Sperry,
1985; Trabasso & van den Broek, 1985; van den Broek, 1988) than otherwise similar events with fewer causal connections. The content and structural properties of causal diagrams also successfully predict people's goodness-of-answer judgment latencies and their answers to causal questions
(Graesser & Franklin, 1990; Graesser et al, 1991). However, people's
mental representations of stories tend to have fewer causal relations than
networks constructed with the Trabasso et al. (1989) procedures (e.g., see
Bloom et al., 1990; Fletcher & Bloom, 1988; McKoon & Ratcliff, 1992).
Moreover, when people give causal explanations, they often attribute
outcomes to partial, rather than complete, causes (Einhorn & Hogarth,
1986; Hart & Honore, 1985; Hilton, 1990; Mackie, 1974; Mill, 1872/1973).
Thus, in reality, individuals tend to be unable or unwilling to acquire and
communicate to others a complete event representation. Cognitive and
pragmatic constraints can explain this tendency.
CONSTRAINTS ON CAUSAL COMPREHENSION
AND EXPLANATION
In this section, we first describe partial causes and their relation to the
events in a causal diagram. We then discuss the cognitive and pragmatic
constraints that govern the tendency to attribute events to partial rather
than complete causes.
Partial Causes and Their Relation to Events in a Causal Diagram
The Trabasso et al. (1989) criteria for evaluating causal necessity and
causal sufficiency in the circumstances recognize that each single event in
a causal diagram is only a partial cause. For example, a protagonist's
behavior is only partly caused by the goal because other events and circumstances are also required to produce the behavior. As such, a protagonist's goal may be considered necessary but not sufficient for his or her
behavior. More formally, Mackie (1974) used the term INUS condition to
denote an insufficient and necessary part of an unnecessary but sufficient
set of conditions for an outcome in the assumed causal field. Mackie also
used the term minimal sufficient condition to denote a sufficient set of
INUS conditions for an outcome. Using these terms, a protagonist's goal
CAUSAL DIAGRAMS
57
is an INUS condition and hence only part of a minimal sufficient condition
for his or her behavior.
In this article, we consider a causal diagram or explanation to be complete if it describes a minimal sufficient condition for each known event.
We also consider a causal diagram or explanation to be plausible if it does
not contradict the known facts (cf. Pennington & Hastie, 1993). In a
subsequent section, we show how a causal diagram can be used to evaluate
the completeness and plausibility of opposing causal explanations, but first
we discuss the cognitive and pragmatic constraints that govern people's
tendency to attribute events to incomplete and implausible causes.
Cognitive Constraints
Memory and knowledge limitations are among the most influential cognitive constraints on causal attribution. These constraints can prevent people
from encoding and retrieving relatively complete event representations.
Memory Limitations. Working memory limitations are known to constrain the number of direct causal relations that readers can encode among
pairs of events (Bloom et al., 1990; Fletcher & Bloom, 1988; Gernsbacher,
Varner, & Faust, 1990; Just & Carpenter, 1992; Keenan, Baillet, & Brown,
1984; McKoon & Ratcliff, 1992; Myers, Shinjo, & Duffy, 1987; Trabasso &
Suh, 1993). Although long-term memory retrieval may supply missing
information, it requires additional processing effort (Bloom et al., 1990;
O'Brien, 1987; O'Brien & Myers, 1987) and may displace other information from working memory (see Just & Carpenter, 1992, for a review).
Some readers tend to search long-term memory only when they cannot
identify a sufficient (or "adequate") causal relation among clauses that are
already activated in working memory. Many readers also tend to avoid
extensive retrieval in the absence of specific processing goals that encourage more elaborative encoding (Bloom et al., 1990; Fletcher & Bloom,
1988; van den Broek, Risden, & Husebye-Hartmann, 1995; see McKoon &
Ratcliff, 1992, for a review). In summary, memory limitations can prevent
people from encoding and retrieving causal relations.
Knowledge Limitations. Psychologists have long recognized that prior
knowledge provides an efficient and effective structure for encoding and
retrieving domain-related information (e.g., Bartlett, 1932; Chiesi et al.,
1979; Graesser & Clark, 1985; Rumelhart, 1980; Schank & Abelson, 1977;
Spilich et al., 1979). However, a relevant schema must be activated in order
to influence encoding and retrieval (Bransford & Johnson, 1972; Smith &
Swinney, 1992). If more than one schema is available, only the activated
schema strongly influences comprehension (e.g., Pichert & Anderson,
1977). Along these lines, an individual's perspective may selectively acti-
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SHAPIRO, VAN DEN BROEK, AND FLETCHER
vate a particular schema and, thus, make some events appear more salient
than others. For example, research on actor-observer differences has demonstrated that observers tend to attribute the causes of an actor's negative
behavior to the actor's enduring traits, whereas actors tend to attribute
their own negative behavior to situational variables (see Watson, 1982, for
a review). Jones and Nisbett (1972) suggested that actor-observer differences may result from the actors perceiving situational variables as standing out in relation to their predispositional traits (the causal field). In
contrast, observers may perceive the actor's traits as figural against the
background of other situational variables. An implication is that individuals who do not share the same knowledge or perspective may disagree
about an event's causes.
In summary, an individual's ability to identify causal relations depends
on cognitive constraints such as limited attentional capacity and available
background knowledge.
Pragmatic Constraints
Pragmatic intentions can also make an individual's causal explanations
incomplete. Conversational constraints and motivational biases are among
the most influential pragmatic constraints.
Conversational Constraints. Mackie (1974) observed that the purpose
of a conversational exchange often dictates which of several candidate
causes are most relevant to an explanation. Hilton (1990) used Grice's
(1975) conversational maxims to further characterize how people's causal
explanations are governed by such interpersonal factors as who does the
explaining, to whom the explanation is given, and why the explanation is
needed. For example, the maxim of relevance enjoins speakers to stick to
the point and not give irrelevant answers, and the maxim of quantity
enjoins speakers to provide no more information than is necessary in the
exchange. To follow these maxims, a cooperative explainer must either
know or assume what the explainee already knows and then try to fill the
gap in the explainee's knowledge.
Similarly, Graesser and Franklin's (1990) QUEST model of question
answering predicts that good answers to causal questions will vary depending on the question category (e.g., why, how, enable, when, and what-isthe-consequent questions). QUEST also predicts that different questions
will lead people to access their event representations in different ways. An
implication is that a cooperative individual who overtly attributes an event
to a partial cause may nevertheless covertly understand its complete cause.
Thus, some disagreements may occur simply because conversational constraints lead different individuals to attribute the same event to different
parts of the same implicitly agreed-upon minimal sufficient condition.
CAUSAL DIAGRAMS
59
Motivational Biases. Most theories of discourse comprehension and
question answering assume that individuals will sincerely try to follow
Grice's (1975) maxim of quality. That maxim directs speakers to say something they know not to be false and to avoid saying something for which
they lack sufficient evidence (see also Hilton, 1990). However, causal
attributions are also known to be highly selective and directionally biased,
especially when people attempt to justify their beliefs or try to persuade
others to reach a particular conclusion (e.g., Bettman & Weitz, 1983; Staw,
1980; Tetlock, 1983, 1985; Tetlock & Boettger, 1989). An explanation is
selective if it reports only some of an event's relevant antecedent conditions, and it is biased if an alternative explanation may also be supported
by the available evidence (Kunda, 1990). A biased explanation can mislead
people who are unable to evaluate the explanation's quality.
In summary, cognitive and pragmatic constraints can lead different
individuals to attribute the same events to different partial causes. The
next section uses causal diagrams to analyze opposing causal explanations
for the 1987 crash. A subsequent section explores how causal diagrams
may mitigate the cognitive and pragmatic constraints on causal attribution.
CAUSAL ANALYSIS OF THE 1987 CRASH
Several investigative commissions reconstructed the same 1987 stock market crash events but they disagreed about its causes. In this section, we first
describe a causal network model of how computerized trading strategies
can cause a crash. We then apply the model to a narrative of crash events
and use the resulting diagrams to analyze some major disagreements.
Cascade Theory: A Causal Model of Program Trading in Stocks
and Futures
Most popular theories of stock market psychology attribute large stock
price declines to a fundamental change in investors' rational expectations
or to a general market panic wherein large numbers of individuals collectively drive prices downward. In contrast, the cascade theory attributes
severe market declines to a small number of large institutions whose
computerized trading strategies can sell millions of dollars of securities in
a matter of seconds (see the Appendix for a brief summary of computerized trading strategies). The October 1987 crash provided investigators
with a unique opportunity to investigate the validity of the cascade theory
claims. As described in a subsequent section, some people disagreed with
the cascade theory.
Table 1 and Figure 2 use a causal network model to describe the cascade
theory, as summarized by the Commodity Futures Trading Commission
(CFTC; 1988b, p. 2). As in the causal model of Figure 1, the cascade theory
60
SHAPIRO, VAN DEN BROEK, AND FLETCHER
TABLE 1
Events in the Cascade Theory of Program Trading's Role During a Stock Market Crash
O^ Stock prices begin to decline
S2: as a result of fundamentally negative economic news.
G3: Portfolio hedgers want to hedge their stock portfolios against falling stock prices,
A4: so they sell futures,
O5: and this causes index futures prices to decline.
O6: Stock index futures trade at a significant discount to the underlying stock index.
G7: Index arbitrageurs want to profit from the price disparity in the stock and futures indices,
A8: so they buy the relatively underpriced futures
A,: and they sell the relatively overpriced basket of stocks.
O10: Stock prices decline further.
Note. Based on Commodity Futures Trading Commission (1988b, p. 2).
uses psychological categories to explain how program trading transforms
initial stock price declines into steeper declines. In addition to the Trabasso et al. (1989) categories, we use a ^PGM category to link nodes where
a protagonist's goals and internal reactions are not explicitly mentioned.
Schank and Abelson (1977) observed that, when people explain behavior,
they often leave out intervening mental states, particularly when the mental states are easily inferred. ^ G M is shorthand for the psychological
causation (^) [sometimes also an unstated antecedent internal reaction,
R]) of an unstated goal (G) which motivates subsequent events (M).
The cascade theory begins with an initiating event. This is represented
in Figure 2 as fundamentally negative economic news (S2). This initiating
event (S2) psychologically motivates some traders to sell stocks (not explicitly shown in Figure 2), which then causes initial stock price declines (Oj).
Computerized trading practices then amplify the initial declines as follows:
Portfolio insurers who want to hedge their stock portfolios against falling
stock prices (G3) sell futures (A4). This causes a decline in the futures
index (O5). These events cause the futures index to trade at a significant
discount to the underlying stock index (O6). Index arbitrageurs then want
Figure 2. The cascade theory of program trading's role during a stock market crash (events
based on Commodity Futures Trading Commission, 1988b, p. 2).
CAUSAL DIAGRAMS
61
to profit from the price disparity in the stock and futures indices (G7).
Therefore, they buy the relatively underpriced futures index (A8) and sell
the relatively overpriced stock index (A9). These trades cause stock prices
to decline further (O10). The feedback loops show that if the process
continues, stock prices will continue to cascade downward.
In the following, we apply the cascade theory to two major event sequences of the crash.
Causal Diagrams of Crash Events
The events in our causal diagrams are based on excerpts from the Presidential Task Force on Market Mechanisms' (1988, pp. 29-34) narrative of crash
events. The Task Force's conclusions are widely regarded as the most objective and complete of the various investigative reports (Waldman, 1988). Table 2 and Figure 3 describe the week before the crash. It begins with two
causal chains of events (Sx-A6) that precipitated the initial stock price declines (O7). It then describes how computerized program trading strategies
amplified those declines. During that time, the Dow Jones Industrial Average fell more than 250 points. Over the weekend, it was widely publicized
that many portfolio insurers and mutual funds had fallen significantly beTABLE 2
Events of the Week Before the 1987 Stock Market Crash
St:
O2:
O3:
A4:
R5:
A6:
O7:
A8:
O9:
A 10 :
Su:
O I2 :
A 13 :
O, 4 :
R15:
R I6 :
Rw:
R18:
A,,:
A 20 :
In response to disappointingly poor merchandise trade figures,
the dollar declined in currency markets.
Long-term interest rates rose.
In addition, congressional filing of antitakeover tax legislation
made takeover stocks appear less attractive,
prompting risk arbitrageurs to sell stocks of takeover candidates.
Stock prices declined.
Investors in mutual funds called to redeem their shares.
Mutual funds fell far behind in their selling programs.
Mutual funds sold large volumes of stock.
During this time, $60 to $90 billion of equity assets (e.g., stocks) were under portfolio
insurance administration.
Portfolio insurers fell behind in selling programs,
so they actively sold large volumes of futures.
Futures index prices declined.
Index arbitrageurs understood the selling strategies of portfolio insurers and mutual
funds
and saw them fall behind in their selling programs.
The index arbitrageurs anticipated the huge forced selling by portfolio insurers and
mutual funds,
and they anticipated repurchasing stock at lower prices.
The index arbitrageurs therefore sold more stock than they bought,
and they bought only some futures.
Note. Based on Presidential Task Force on Market Mechanisms (1988, pp. 29-30).
62
SHAPIRO, VAN DEN BROEK, AND FLETCHER
Figure 3. The week before the 1987 stock market crash (events
based on Presidential Task Force on Market Mechanisms, 1988,
pp. 29-30).
hind in their selling programs. Consequently, by the time the New York
Stock Exchange opened for trading on the following Monday, index arbitrageurs (among others) were already poised to sell large volumes of stocks in
anticipation of the other institutions' huge forced selling.
Table 3 and Figure 4 describe the morning of October 19,1987—the day
of the crash. This scenario begins with the selling pressure that accumulated over the weekend. It then describes how interactive and reactive
program trading in stocks and futures amplified the declines. These events
set the stage for steeper declines during the afternoon of the crash.
Analysis of Causal Relations
Causal diagrams can be used to analyze the causal roles of their events
along four dimensions: direct causes, indirect causes, sufficiency in the
CAUSAL DIAGRAMS
63
TABLE 3
Events of the Morning of the 1987 Stock Market Crash
S,: A large selling pressure accumulated over the weekend.
S2: Sell orders rapidly accumulated when the New York Stock Exchange opened at 9:00 a.m.
Monday,
S3: and there were few buyers.
O4: Consequently, most of the Dow Jones Industrial Average stocks did not open until after
much delay.
O5: Until 11:00 a.m., the Dow Jones Industrial Average was based in part on Friday's closing
prices.
O6: From 9:00 a.m. to 11:00 a.m., the Dow Jones Industrial Average declined sharply,
A7: as large numbers of shares were sold by mutual funds
A8: and large numbers of shares were sold by index arbitrageurs.
S9: Meanwhile, the Chicago Mercantile Exchange opened on time.
O10: Portfolio insurers who fell behind in their selling programs on Friday
A u : sold large numbers of futures contracts throughout the morning.
O]2: Futures contract prices declined more than the stock index prices.
O13: A large but illusory discount existed between the futures and stock indices.
R14: The size of the discount made selling stocks rather than futures relatively more attractive.
S15: One portfolio insurer who had the authority to sell stocks
A]6: sold 13 baskets of stocks worth $100 million each.
R17: Index arbitrageurs believed that the large but illusory discount was real,
R,8: and saw a tremendous profit opportunity.
A19: Many index arbitrageurs sold the stock index and,
R20: thinking that the prices of futures contracts would decline even further,
A21: delayed buying the futures contracts.
R22: The discount of futures relative to stocks made the stock market appear weak and
overpriced to investors
Ku: who were discouraged from buying stocks.
Note. Based on Presidential Task Force on Market Mechanisms (1988, pp. 30-34).
circumstances, and necessity in the circumstances. This analysis provides a
basis for evaluating the quality of opposing causal explanations.
Direct Causes. Discourse comprehension research has shown that an
event's perceived causal centrality and importance generally increase with
the number of direct causal relations with other events. We can use direct
causal relations as an index of causal centrality and importance in our
diagrams. The most central node in Figure 3 has seven direct causal relations (see O7). The two most central nodes in Figure 4 have eight and five
direct causal relations (O6 and O13, respectively). These highly central
nodes all refer to securities prices. The significant discount (O13) is especially noteworthy because it shows that an abnormally large price disparity
existed between the stock and futures indices. Its causal centrality shows
that it had an important and pervasive influence on subsequent market
behavior.
64
SHAPIRO, VAN DEN BROEK, AND FLETCHER
(8)
Figure 4. The morning of the 1987 stock market crash (events based on
Presidential Task Force on Market Mechanisms, 1988, pp. 3C*-34).
Indirect Causes. An event's indirect causal relations also define its
causal role. Consider, for example, the Securities and Exchange Commission's (SEC's) conclusion about the indirect role of market psychology:
In addition to direct effects, the existence of futures trading and the use of
derivative products in index-related trading strategies, in our view, had a
significant indirect [italics added] impact on the markets—particularly on
October 19—in the form of negative market psychology. The knowledge by
market participants of the existence of active portfolio insurance strategies
created, in our view, a market "overhang" effect in both the futures and
stock markets. (SEC, 1988, p. xiii)
CAUSAL DIAGRAMS
65
Our diagrams show that indirect causes are necessary to adequately
explain the steep stock price declines. In Figure 3, the causal role of O 7
(stock price declines) is more clearly evident if one traces beyond its direct
consequences through intervening psychological events (R15, R17, and R18)
to its more distant and indirect consequences (A10, A13, A19, and A20).
These indirect consequences of O 7 are also its direct or indirect causal
antecedents. In Figure 4, the causal role of O13 (the discount of futures
relative to stocks) is more clearly evident if one traces through its direct
psychological consequences (R14, R17, and R22) to its more distant and
indirect consequences (A16, A19, A21, and R23). These indirect consequences of O 13 in turn directly caused further stock price declines (O6) and
indirectly caused additional futures price declines (O12). These events
ultimately caused the discount (O13) to widen further. Notably, Figure 4
also shows only indirect causal relations between futures sales and stock
sales (e.g., see A u and A19). As discussed later, the absence of a direct
causal relation between those events led some investigators to disagree
about the causes of the crash.
Causal Sufficiency. The criterion of sufficiency in the circumstances
recognizes that no single event by itself is sufficient for an outcome. Consistent with the cascade theory, Figures 3 and 4 show that the stock price
declines were caused by a complex web of interactive and reactive program trading. Because each trading strategy was necessary but not sufficient for the crash, an explanation is incomplete if it attributes the crash to
only one trading strategy. An explanation is also incomplete if it ignores
the psychological determinants of trading behavior. For example, a complete explanation for why index arbitrageurs sold more stocks than they
bought (A19 in Figure 3) must include the arbitrageurs' beliefs about
others' imminent trades (R1S-R18 in Figure 3). An explanation would be
incomplete if it considered only the prevailing securities prices (O 7 and
O14) and the portfolio insurers' actual sales of futures (A13).
Counter)'actual Necessity. A single event may also be considered causally important if its counterfactual removal would have significantly altered the course of subsequent events. The criterion of necessity in the
circumstances discussed earlier allows the investigator to consider the
counterfactual consequences of removing specific events. For example,
Figure 4 shows that if stocks had opened on time (contrary to O4), the
posted stock prices would have declined more sharply (contrary to O6).
This in turn would have reduced the size of the discount (contrary to O13).
Similarly, if futures trading on the Chicago Mercantile Exchange had not
begun until most stocks had opened (contrary to S9), portfolio insurers
would not have sold futures contracts (contrary to A n ) . Again, this would
66
SHAPIRO, VAN DEN BROEK, AND FLETCHER
have resulted in a smaller discount. Some investigators' recommendations
regarding how to prevent future crashes reveal that the investigators considered these counterfactual implications.
In summary, the analysis of direct causes, indirect causes, causal sufficiency, and causal necessity can provide a more complete understanding
of an event's causal role. The causal analysis also provides a basis for
evaluating the quality of opposing causal explanations.
Analysis of Disagreements
Some investigators attributed the crash to all of the major program trading
strategies, others attributed the crash to only a few of those strategies, and
yet others attributed the crash to fundamental changes in investors' perceptions. In this section, we use our causal diagrams to analyze two kinds
of causal disagreement. In the first case, different people attributed the
crash to different parts of the same implicitly agreed-upon minimal sufficient condition. In the second case, different people attributed the crash to
different minimal sufficient conditions.
Different Parts of the Same Minimal Sufficient Condition. Two investigative commissions who offered relatively complete causal explanations
agreed that both the portfolio insurers and the index arbitrageurs played a
significant role during the crash:
While index arbitrageurs may not have accounted for a substantial part of
total daily volume, they were particularly active during the day at times of
substantial price movements. They were not, however, the primary cause of
the movements; rather, they were the transmission mechanism for the pressures initiated by other institutions. (Presidential Task Force on Market
Mechanisms, 1988, p. 42)
Futures trading and strategies involving the use of futures were not the "sole
cause" of the market break. Nevertheless, the existence of futures on stock
indexes and the use of the various strategies involving "program trading"
were a significant factor in accelerating and exacerbating the declines. (SEC,
1988, p. xiii)
Both conclusions are consistent with the cascade theory's claim that each
trading strategy contributes to a crash.
In contrast, some portfolio insurers who actively sold futures denied their
role in the crash. When told that portfolio insurance influenced 20% of
stock selling during the crash, one portfolio insurance manager asked
"What about the other 80%?" (Wallace, 1988, p. Dl). His question implicitly argues that portfolio insurance alone was not a sufficient cause. Other
portfolio insurance managers argued that the real damage was done by
CAUSAL DIAGRAMS
67
index arbitrageurs who traded in anticipation of the portfolio insurers'
trades. Those managers placed more explanatory weight on index arbitrage
than on their own portfolio insurance trading behavior. By not fully acknowledging their own role in the crash, the managers' explanations were
less complete than those of the aforementioned investigative commissions.
Node density, causal distance, and actor-observer differences might
explain why the portfolio insurers were more willing to blame the index
arbitrageurs than themselves. The portfolio insurers' actions (A13 of Figure
3; An and A16 of Figure 4) have an average of 3.33 causal relations. That
is slightly more than the 2.8 average causal relations for the index arbitrageurs' actions (A19 and A20 of Figure 3; A8, A19, and A2i of Figure 4). In
addition, three nodes representing index arbitrageurs' actions have direct
causal relations with declining stock prices. In contrast, only one node
representing portfolio insurers' actions has a direct causal relation with
declining stock prices. These differences in node densities and causal distance might have made it more difficult for the money managers to understand their own role in the crash. The portfolio insurers' conclusions may
also be attributed to actor-observer differences. From the portfolio insurers' perspective, their own actions may have appeared to them as standing
conditions, whereas the index arbitrageurs' actions may have stood out as
events in relation to the causal field.
Whatever the specific reasons for disagreement, all of the portfolio insurers managers did attribute the crash to at least part of the same minimal sufficient condition that was identified by the SEC (1988) and the Presidential
Task Force on Market Mechanisms (1988). When pressed further, one manager conceded this point: "I'm not saying that portfolio insurance was not
part of the fabric of the decline. But that fabric has many more threads than
portfolio insurance" (Wallace, 1988, p. D8). Thus, the manager's initial disagreement with the investigative commissions was more apparent than real.
His later comments reveal that he at least implicitly agreed with the minimal
sufficient condition described by the cascade theory. We now turn to a more
fundamental disagreement about the cascade theory.
Different Minimal Sufficient Conditions. Two investigative commissions agreed that the minimal sufficient condition described in the cascade
theory is a valid description of the crash. Although those commissions
placed more explanatory weight on program trading practices, they also
acknowledged the role of precipitating conditions:
Whatever the causes of the original downward pressure on the equity market, the mandate of the Task Force was to focus on those factors which
transformed this downward pressure into the alarming events of the stock
market decline. (Presidential Task Force on Market Mechanisms, 1988, pp.
1-2)
68
SHAPIRO, VAN DEN BROEK, AND FLETCHER
We may never know what precise combination of investor psychology, economic developments and trading technologies caused the events of October.
Instead, the Report attempts to reconstruct the trading activity during the
October market break and analyze how the trading systems for stock and its
derivatives (i.e., options and futures) may have contributed to the rapidity
and depth of the market decline. (SEC, 1988, p. xi)
In contrast, the CFTC concluded that the massive selling of stocks and
futures "was precipitated by an unprecedented change in investors' perceptions and was not initiated by technical trading strategies which interacted with each other and the stock market" (CFTC, 1988b, p. 1). By
denying program trading's role, the CFTC implicitly argued that the precipitating conditions alone were a sufficient cause. To support its conclusion, the CFTC analyzed stock and futures trades in 5- and 10-min intervals
in the days surrounding the crash. It found that portfolio insurance sales of
futures was neither particularly heavy when stock prices fell the most, nor
particularly light when stock prices began to recover. The CFTC argued
that its findings "cast substantial doubt upon both the cascade theory and
the supposition that futures prices were leading the stock market as reasonable representations of what occurred during the morning of October
19" (CFTC, 1988a, p. vi).
The CFTC's disagreement with the other commissions is fundamental.
It is not merely an example of attributing the same event to different parts
of the same implicitly agreed-upon minimal sufficient condition. Unlike
the other investigative commissions, the CFTC argued that the minimal
sufficient condition for the crash did not include program trading. When
taken at its face value, the CFTC's conclusion appears to discredit the
cascade theory. Some people might further argue that the opposing conclusions about program trading's role are supported by different yet
equally valid causal models. However, our diagrams clearly show that the
commission's conclusion is neither complete nor plausible. For example,
by analyzing the time series of only actual stock and futures trades, the
CFTC's explanation is incomplete because it failed to consider the pervasive psychological causes that were widely known to have influenced trading during the crash (see also Gamill & Marsh, 1988). Even a layperson can
see from our diagrams that the interactions among different program
traders must be explained at least in part by those psychological causes.
The CFTC's explanation is also implausible because it assumes a direct
causal relation between portfolio insurance and index arbitrage trading
behavior. Our diagrams explicitly show that only indirect causal relations
existed between sales of futures and sales of stocks (e.g., see nodes A n and
A19 in Figure 4). The absence of a direct causal relation between those
events argues against finding a direct correlation between the trading
volumes of stocks and futures.
CAUSAL DIAGRAMS
69
Why, then, did the CFTC offer its implausible explanation? One possibility is that the CFTC's staff members simply did not know about the
indirect and psychological causes before it published its own report. Such
knowledge limitations are not tenable, for several reasons. First, the CFTC
officially restated its conclusions in a press release after the other investigative reports had been published. It is difficult to conceive how knowledge limitations could explain why the CFTC's experienced staff would
have overlooked or misunderstood the other reports. Second, the CFTC's
explanation can account for all of the setting information (Sj-Ag in Figure
3; all other S nodes in Figures 3 and 4), all of the actual buying and selling
behavior in both the stock and futures markets (A), and all of the actual
stock and futures price outcomes (O). In contrast, its explanation fails to
account for 10 out of 43 nodes (approximately 23%), all of which are
psychological responses (R). This observed frequency of omitted psychological responses is significantly greater than the approximately 2.6 psychological responses that would be expected if the 10 nodes were randomly
omitted, X*(l) = 27.58, p < .001. Finally, the 10 omitted events do not have
more direct causal relations than the price outcomes' other causal antecedents and consequences, Mann-Whitney U = 146.0,p > .5, one-tailed. This
argues against an interaction between causal density and the CFTC staff
members' cognitive ability to understand the causal relations.
Another possibility is that the CFTC's opposition to the cascade theory
can be attributed to pragmatic factors, such as the desire to dissuade
decision makers from imposing costly regulations on the futures markets.
Although we do not have direct empirical evidence to implicate the role of
pragmatic factors, many market observers believed that the CFTC's conclusions were biased and self-serving (e.g., see Waldman, 1988).
In summary, we have used story-based causal diagrams to analyze opposing explanations for the 1987 crash. The diagrams reveal that the portfolio
insurers' and CFTC's explanations were incomplete because they failed to
account for all known events and causal relations and that the CFTC's
explanation was implausible because it asserted the existence of direct
causal relations between events whose causal relations were only indirect.
Our analysis of the diagrams' content and structural properties suggests that
cognitive constraints may plausibly account for some of the portfolio insurers' incomplete explanations. In contrast, the CFTC's selective explanation
was likely driven by motivational rather than cognitive factors.
DISCUSSION
Stock market crashes, oil spills, and civil wars are examples of complex and
undesirable events that affect many lives. In order to effectively control
such events, it is useful to understand their causes. However, the causes of
70
SHAPIRO, VAN DEN BROEK, AND FLETCHER
a complex event can be a source of major disagreement. Our objective has
been to illustrate how story-based causal diagrams can facilitate the analysis of such disagreements. We applied the Trabasso et al. (1989) procedures to a narrative of 1987 crash events, and then used the resulting
story-based diagrams to analyze some major disagreements about the
causes of the crash. Our analyses yielded four main findings. First, some
explanations for the crash were incomplete because they omitted known
events and causal relations. The story categories in our diagrams further
highlighted that one incomplete explanation selectively omitted almost the
entire category of psychological events. Second, one investigative commission's explanation was implausible because it asserted the existence of
direct causal relations between events whose causal relations were in fact
only indirect. Third, the diagrams distinguished between two kinds of
causal disagreement. One disagreement involved attribution to different
parts of the same implicitly agreed-upon set of conditions, whereas the
other disagreement involved attribution to different sets of conditions.
Fourth, an analysis of the diagrams' content and structural properties
revealed that cognitive factors can plausibly account for some but not all
of the incomplete explanations for the crash.
In summary, story-based causal diagrams can facilitate the analysis of
causal relations in complex settings. In the following, we compare our
approach to Graesser and Franklin's (1990) QUEST model of question
answering. We then explore the possible advantages of using causal diagrams to aid causal comprehension and explanation.
Components of Good Causal Explanations
Our objective has been to use causal diagrams to identify the components
of a complete and plausible explanation for complex events. Following
Pennington and Hastie (1993), we have argued that a complete explanation should account for all known events and causal relations and that a
plausible explanation should not contradict them. In contrast, the objective of Graesser and Franklin's (1990) QUEST model is to incorporate
known cognitive constraints on people's ability to find good answers to
question about an event's causal role in a knowledge structure. Accordingly, QUEST uses three psychologically validated search criteria that
simulate people's tendency to give incomplete answers. An arc search
procedure selects candidate nodes in the knowledge structure that are on
legal paths connected to the queried node and prunes out nodes that are
on illegal paths. For example, a good answer to a why-event question
should include the event's antecedents but not its consequences. Constraint satisfaction avoids irrelevant and implausible answers by pruning
out answers that are inconsistent with the content of the queried node.
Finally, a structural distance constraint selects nodes that are structurally
CAUSAL DIAGRAMS
71
close to the queried node, such that the quality of an answer is negatively
correlated with the number of arcs between the answer node and the
queried node.
QUEST'S search criteria may be unable to identify a complete causal
explanation for a complex event, for two reasons. First, recursive event
chains in complex settings such as the 1987 crash blur the distinction
between cause and effect, and they diminish the usefulness of the distinction between direct and indirect causes. Without those distinctions,
QUEST would have difficulty finding good explanations for complex
events. Second, QUEST'S search criteria may sometimes give high quality
ratings to incomplete answers. For example, many of the incomplete explanations for the 1987 crash correctly attributed the stock price declines
to some of their direct causal antecedents and thereby would satisfy
QUEST'S search criteria. This suggests that a more global search criterion
is needed to identify the components of a more complete explanation.
Such a criterion might, for example, identify all of an event's direct and
indirect causal antecedents in a causal diagram. The more complete set of
nodes could then be used to evaluate the relative completeness of different
causal explanations for the event, as we have done in our analysis of the
1987 crash. A global search criterion would be useful to decision makers,
inasmuch as complete causal explanations provide a better basis for making good decisions about how to control events.
Although a global search criterion might enable QUEST to identify the
components of a complete causal explanation, in reality cognitive and
pragmatic constraints lead most individuals to attribute events to incomplete rather than complete causes. In the following, we briefly describe
how causal diagrams may reduce those constraints.
Advantages of Causal Diagrams
Earlier we reviewed evidence that knowledge and memory limitations can
prevent individuals from fully understanding all of an event's causal relations. Generalizing from prior research on the use of external memory aids
to facilitate judgment and decision making (e.g., see Fischhoff, 1982), an
explicit causal diagram may reduce the memory constraints on a person's
ability to encode and retrieve causal relations. For example, a causal
diagram may allow an investigator to more fully consider the causal roles
of already identified events before gathering additional evidence, to consider one part of the event representation without losing sight of the other
parts, and to counterfactually trace the consequences of adding or removing events without having to rely on limited memory.
Discourse comprehension research has demonstrated that schematic
knowledge greatly facilitates the encoding and retrieval of event relations
(e.g., see Bransford & Johnson, 1972; Chiesi et al., 1979; Pichert & Ander-
72
SHAPIRO, VAN DEN BROEK, AND FLETCHER
son, 1977; Smith & Swinney, 1992; Spilich et al, 1979). Although the
Trabasso et al. (1989) causal network model is not a complete substitute
for domain-specific knowledge, its story categories identify the basic components of a complete and plausible event explanation. As such, the categories can help identify incomplete explanations and can guide the search
for missing information. For example, if physical events alone do not
sufficiently explain a protagonist's behavior, the causal network model
model would direct attention to the protagonist's goals and internal reactions.
Finally, pragmatic constraints can also lead people to.attribute outcomes to incomplete causes. For example, it is probably not a coincidence
that the investigative commissions with close ties to the stock market
tended to blame the crash on the futures markets, and vice versa. Other
studies have shown that people tend to be less willing to offer incomplete
or implausible explanations when they expect that their explanations will
be scrutinized by others (e.g., Kunda, 1990; Tetlock, 1983, 1985). Those
studies suggest that if the causal structure of a scenario is made available
to all interested parties through an explicit causal diagram, biased explanations will be offered less often, and those that are offered will less likely
survive others' careful scrutiny.
Nonetheless, it should also be recognized that an explicit causal diagram
may sometimes hinder rather than help comprehension. Just as some readers tend to process information passively and conduct little elaborative or
reconstructive processing unless they are explicitly instructed to do so (e.g.,
McKoon & Ratcliff, 1992), individuals may engage in less elaborative processing when they are given a preconstructed causal diagram. Research on
availability biases has demonstrated that individuals are often misled by
problem representations and may have difficulty retrieving other relevant
but unspecified information from memory (e.g., see Fischhoff, Slovic, &
Lichtenstein, 1978; Mehle, Gettys, Manning, Baca, & Fisher, 1981; Tversky
& Kahneman, 1973; see also Pennington & Hastie, 1988). Along these lines,
a causal diagram might make individuals less likely to spontaneously generate other relevant causes that they might identify without the diagram. A
causal diagram may also induce a hindsight bias whereby individuals assign
a higher probability to a past outcome than they would have estimated in
foresight (see Hawkins & Hastie, 1990, for a review). Such hindsight and
availability biases might make the causal relations in a causal diagram appear more plausible than is warranted. These potential disadvantages highlight the importance of carefully constructing causal diagrams that are objectively complete and unbiased.
Altogether, the representation of complex events as networks of causally related nodes can provide a powerful tool for analyzing a scenario's
causal structure and for understanding why people misunderstand or dis-
CAUSAL DIAGRAMS
73
agree about causal relations. The methods described in this article, if
carefully applied, can provide such a tool. That such a tool is needed is
illustrated by the description of a triple-murder trial case in 1994 in Russia's first jury trial since the Bolsheviks banned juries in 1917:
There was no verbatim transcript of the trial. Neither the defense nor the
prosecution thought to make diagrams or maps to help jurors visualize an
extremely complicated web of events that may or may not have occurred
during the night in question. "It's our first experience with juries," said
Yevgeny Ciderenko, deputy justice minister for reform. "Later, we'll have
such things" (Stead, 1994, p. 4).
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APPENDIX
Summary of Computerized Program Trading in Stocks and Futures
Various computerized program trading strategies bought and sold large
volumes of stocks and futures during the crash. Stocks represent corporate
ownership claims. Normally, stock prices depend primarily on corporations' current and future earnings. Stock prices generally fall when more
shares of stock are waiting to be sold than bought (supply exceeds demand). Conversely, stock prices generally rise when more shares are waiting to be bought than sold (demand exceeds supply). Futures contracts
represent promises to deliver stocks (or a specified equivalent cash settlement) at a specified time. Futures contract prices depend primarily on the
price of the underlying stock (or portfolio of stocks) and, thus, normally
CAUSAL DIAGRAMS
77
rise and fall with stock prices. Many stocks and futures are traded in
"baskets" or portfolios of securities, each with its own price index. For
example, the Standard and Poor's (S&P) 500 stock index is a weighted
average of the prices of 500 underlying stocks, and the price of the corresponding S&P 500 futures contract is normally based on the price of the
underlying S&P 500 stock index. During the crash, futures traded at an
abnormally large discount relative to stocks.
The trading strategies of index arbitrageurs, portfolio insurers, and
mutual funds received much of the blame for the abnormal discount between futures and stocks. Their computerized strategies used the stock and
futures indices to buy and sell millions of dollars of securities in a matter
of seconds. Index arbitrageurs attempted to profit from price disparities
between stocks and futures by selling the higher priced stock index and
buying the lower priced futures index. In addition, many pension and
endowment funds used portfolio insurance strategies to mechanically compute optimal stock-to-cash ratios for stock portfolios. During the crash,
these strategies automatically generated buy and sell orders based on the
prevailing trends in stock prices. Because trading of futures contracts
usually could be accomplished more quickly and at lower cost than trading
of stocks, most portfolio insurers attempted to adjust their stock-to-cash
ratios by selling futures contracts rather than by selling the stocks directly.
The cash raised by selling futures contracts was expected to provide an
effective hedge against falling stock prices. Finally, many mutual funds
allowed their customers to redeem their shares on demand. During the
crash, those mutual funds received many customer redemption requests
and therefore had to sell large blocks of shares.