Manajemen | Fakultas Ekonomi Universitas Maritim Raja Ali Haji 08832320309599096
Journal of Education for Business
ISSN: 0883-2323 (Print) 1940-3356 (Online) Journal homepage: http://www.tandfonline.com/loi/vjeb20
A Note on the Treatment of Uncertainty in
Economics and Finance
Anthony M. Carilli & Gregory M. Dempster
To cite this article: Anthony M. Carilli & Gregory M. Dempster (2003) A Note on the Treatment
of Uncertainty in Economics and Finance, Journal of Education for Business, 79:2, 99-102, DOI:
10.1080/08832320309599096
To link to this article: http://dx.doi.org/10.1080/08832320309599096
Published online: 31 Mar 2010.
Submit your article to this journal
Article views: 12
View related articles
Citing articles: 1 View citing articles
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http://www.tandfonline.com/action/journalInformation?journalCode=vjeb20
Download by: [Universitas Maritim Raja Ali Haji]
Date: 12 January 2016, At: 23:00
A Note on theTreatment of
Uncertainty in Economics
and Finance
ANTHONY M. CARlLLl
GREGORY M. DEMPSTER
Hampden-Sydney College
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:00 12 January 2016
Hampden-Sydney, Virginia
E
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ver since John von Neumann and
Oskar Morganstern published their
groundbreaking work, The Theory of
Games and Economic Behavior (1944),
the treatment of uncertainty in the classrooms of economics and finance has
been dominated by the application of
risk theory to the utility-maximization
framework. In defending the advantages
of this approach, some economists have
gone so far as to deny the coherence of
any distinction between risk and uncertainty, whereas others have maintained
that, in situations where risk theory is
inapplicable, behavior “may not be
explainable in terms of economic theory” (Lucas, 1981, p. 223). The most
common defense of risk theory, however, is on instrumentalist grounds and is
supported by the undeniable value of
the expected utility model as a normative theory of decision making.
Nevertheless, the relevance of the
standard risk model as a positive description of economic decision making
increasingly is being called into question
in theoretical work. Persistent evidence
from experimental psychology and economics suggests that the principles of
actual decision making are often inconsistent with the axioms of the standard
theory.’ Our purpose in this article is to
provide a method of categorizing the
types of uncertainty as well as to summarize various approaches to the problem for the educated businessman.As the
ABSTRACT. The treatment of uncertainty in the business classroom has
been dominated by the application of
risk theory to the utility-maximization
framework. Nonetheless, the relevance
of the standard risk model as a positive
description of economic decision making often has been called into question
in theoretical work. ’ In this article, the
authors offer an instructional approach
that recognizes the reality of decision
making by agents who know that they
do not know enough to form complete
probability distributions describing all
possible outcomes of their actions.
Students must recognize the fundamental difference between risk and the
broader concept of uncertainty. This
realistic presentation of the uncertainty
problem will allow undergraduate students to better understand the assumptions involved in modeling and their
relevance to economic and financial
problems.
tations, which means that the agents (a)
have access to all the information necessary to approach the economic problem
with which they are faced and (b) make
use of the information in a manner consistent with the standard axioms of rational decision theory.2 In the terminology
of Bayesian probability theory, this situation implies convergence between the
objective probability distributions governing real-world outcomes and agents’
subjectively formed assessments of those
objective conditions. Therefore, agents
do not make systematic errors in the forecasting of potential outcomes. Agents
make decisions that lead to suboptimal
outcomes not because of any entrenched
bias in the decision-making process, but
only because the actual outcomes usually will be different from the ex ante
expected (average) value dictated by
their assessments. In other words, even
with full knowledge of all possible outcomes and their associated probabilities,
decisions are still risky because we do
not know which of the possible outcomes
will materialize.
We have characterized risk in this
way to contrast it with the more general
phenomenon of uncertainty. First and
foremost, uncertainty refers to the
inability of the agent to accurately predict future outcomes. The phenomenon
of risk described above is one manner in
which uncertainty may manifest itself in
decision making. Thus, we can label
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demands of a competitive marketplace
prompt business professionals to adopt
more and more complex methods of
forecasting and planning, a working
knowledge of these alternative approaches will be of great value. We conclude
with a discussion of the importance of
these approaches for economic and
financial analysis and an example of how
such alternatives might be introduced in
an undergraduate classroom setting.
Degrees of Uncertainty
Most modem economic and financial
models posit agents with rational expec-
zyxw
November/December 2003
99
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:00 12 January 2016
risk as one category, or type, of uncertainty and designate it as Type A. But
there are circumstances under which
risk analysis cannot fully explain the
deviation between expected and actual
outcomes. One such circumstance
involves the possibility that subjectively
formed distributions may be systematically biased; that is, there may be a lack
of convergence between those assessments and the objective distributions
that govern reality. We can call this situation Type B uncertainty. Another possibility is that economic agents may fail
to form complete probability distributions as part of their subjective assessments because either (a) they do not
believe an objective distribution exists
or (b) they do not believe that they have
enough information about objective
conditions to form a subjective distribution that would remotely describe those
conditions. We designate this uncertainty as Type C3
One might categorize these “degrees”
of additional uncertainty by the amount
of information available to the economic
agent. Type B involves a deviation from
rational expectations but not a departure
from the axioms of rational choice.
Agents still make decisions based on risk
analysis, but the expected values of their
subjectively formed distributions are
biased because they lack some important
information about objective conditions.
On the other hand, Type C does involve a
departure from the axioms of expected
utility. In this sense, it is somewhat more
fundamental than Type B uncertainty.
Type C agents possess some information
that they believe is relevant for decision
making, but they realize that they do not
possess enough to form a complete subjective distribution of outcomes that is
even moderately accurate in representing
the actual realm of possibilities.
Dempster (1999) argued that these
types of uncertainty also might be distinguished on the basis of their root causes.
For Type B, the cause of the additional
uncertainty is faulty perceptions of
potential outcomes and their probabilities, so that subjectively formed distributions fail to converge with their objective
counterparts. Type C uncertainty, on the
other hand, arises because of the uniqueness (or “specificity”) of the situation at
hand. Without either some a priori
knowledge of the probabilities associated
with potential outcomes (as in a game of
dice) or some experience in similar situations (as in the case of insurable contingencies), there is no foundation for subjective outcome distributions upon which
actions can be based.
What Caplan and other proponents of
risk theory ignore, however, is the fact
that its application to decision making
requires a complete probability distribution, listing all of the possible outcomes
of a random variable and their associated probabilities. The random variable
must be defined by a set of mutually
exclusive outcomes whose probabilities
sum to one. If either an outcome or a
probability is unknown, expected values
and variances cannot be calculated. And
if expected values and variances cannot
be calculated, there is no basis from
which to make a decision under risk theory. In other words, to treat situations of
uncertainty as risky, it is necessary to
define both columns of the probability
distribution.
It is quite obvious that agents are
unable to assign probabilities to events
about which they are completely unaware, and therefore they cannot calculate expected values or variances that
will converge toward any objective values. If an agent is at least aware that
such unknown events are likely to exist,
he or she will also realize that one cannot decide, for example, on the maximum price to pay for a known opportunity on the basis of risk theory. It would
be reasonable for such an agent to make
a decision on the basis of intuition or
simple heuristics. Thus, consistent findings of economic behavior that contradict the standard model of decision
making may be a result, in part, of an
awareness on the part of economic
agents that their information set is
incomplete with regard to possible outcomes of their actions.
But it is also true that agents might
not assign probabilities to all possible
events of which they are aware. Perhaps
an example will be helpful here. Let us
assume that an agent faces three possible outcomes of a decision: (a) winning
$100 with a probability of 50%, (b)
winning $25 with an unknown probability, or (c) losing $90 with an unknown
probability. We represent this probability distribution in Table 1.
It is easy to see that no variance or
expected value can be calculated.
Therefore, risk theory provides no basis
for an optimal decision. This does not
mean, however, that the agent completely lacks information upon which to base
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Alternative Approaches
to Uncertainty
Unfortunately, the distinction between
the various degrees of uncertainty has
been blurred in the standard classroom
treatment of decision making. There are
generally two reasons given for the abandonment of such distinctions: (a) the
belief that few real-world situations
involve true uncertainty, so that the distinction, although valid, may be usefully
ignored; and (b) the fact that risky, rather
than truly uncertain, situations make certain economic models tractable. The sum
of these two general attitudes is neatly
expressed by Robert Lucas, who has
done much to bring the application of
risk models into mainstream economics
via rational expectations. Lucas acknowledged the validity of the distinction when
he admitted that his treatment of expectations is not relevant to situations of true
uncertainty. He concluded, however, that
in such cases “economic reasoning will
be of no value” (1981, p. 224).
True uncertainty is difficult to model
because it “renders the theory of probability virtually inapplicable to real-world
decision making,” and thus it is generally
thought that the risk-uncertainty distinction is “unhelpful” (Morgan & Henrion,
1990, p. 49). A number of non- mainstream traditions in economics and
finance nevertheless continue to maintain
that many situations involve choice under
true uncertainty and that mainstream practitioners are assuming away an important
distinction for the sake of convenience?
Some recent research continues to reinforce this dichotomy in economic
approaches. For example, Caplan (1999)
acknowledged that the standard treatment
“sounds implausible at first” (p. 836), but
then he actually went further than most
mainstream counterparts by questioning
the very coherence of the distinction
between risk and uncertainty and suggesting that the risk model is an accurate and
sufficient model for decision making.
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Journal of Education for Business
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TABLE 1. Probability Distribution No. 1
Value
(value)
Value*p
(value)
$100
50%
$50
?
?
?
?
P
$25
($90)
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:00 12 January 2016
TABLE 2. Probability Distribution No. 2
Value
$100
Not $100
P
(value)
Value*p
(value)
50%
50%
$50
?
a decision, for he or she knows (or
believes that he or she knows) that there
is a 50% chance of winning $100. And
although the agent does not have
enough information to assign probabilities to the other outcomes, he nonetheless may be willing to act or not act in a
certain manner solely on the basis of
intuition, a hunch, or even a heuristic
that has proved useful in the past.
It may be argued that the agent subjectively will assign probabilities to all
outcomes despite the absence of any
basis for their values. But why would
an agent expend resources (mental
effort, etc.) to form a subjective probability distribution that he knows to have
no connection with any actual state of
affairs? Will the agent necessarily be
made better off by doing so? Is it not
much more likely that the agent will
use trusted heuristics as a basis for
decision making rather than act on a
probability distribution he or she knows
to be false? To assert that probability
calculus will be used in such a situation
is to make the heroic assumption that
some estimation of probabilities, no
matter how significantly they might
bias the subjectively determined
expected value from its actual value, is
always preferred to none. Note, for
example, what would happen if we
assume that agents “divide the world
into two events”-for example, earning
$100 and not earning $100 (Caplan,
1999, p. 832). Such a decision process
would lead to the distribution that we
represent in Table 2.
This decision process leaves us no
better off than we were before, with no
expected value or variance that can be
calculated, so risk analysis provides no
basis for decision making. And there is
no reason to believe that arbitrarily
assigning a value to the unknown parameter will make the agent better off.
Therefore, one approach we can take
to the problem of incomplete probability
distributions is to allow for Type B or
Type C uncertainty involving biased
subjective evaluations. In this approach,
we might assume that agents act according to some basic heuristics in making
decisions characterized by incomplete
probability distributions. What kinds of
heuristics might be used in such a situation? Experimental tests in psychology
and economics suggest a number of possibilities, ranging from the familiar representativeness and availability heuristics to more formal (but still less than
fully “rational” in the standard economic sense) decision-making rules.
Uncertainty and Financial
Analysis
Recognition of the broader uncertainty concept can have profound implications for economic and financial analysis and can be demonstrated fairly easily
in a classroom setting. Consider, for
example, a standard formulation of
stock price determination under risk:
where P, is the current price, D, is the current l -year cash flow, R, is the annualized
interest rate on the financial asset, and
E[G,I is the expected growth rate in cash
flows. Standard risk analysis implies that
E[GJ equals the sum of all possible outcomes for G, times their respective probabilities. The interest rate is often
expressed as a function of an underlying
risk-free rate and a risk premium:
context. If R(B) is a linear function of
market risk in the long run, then we
have the familiar Capital Asset Pricing
Model (CAPM) formulation of risk and
return.
CAPM is used widely as a tool for financial analysis. Corporate finance officers use it to determine the long-run rate
of return they should expect to pay on
common stock. Securities analysts use it
to make judgments about whether
stocks are over- or undervalued. Although some academics have identified
theoretical problems with CAPM, it
continues to be a standard part of the
finance toolkit and curriculum. Little
work has been done, however, in regard
to the effects of alternative forms of
uncertainty on CAPM.
For example, consider the case in
which growth rates are subject to Type B
uncertainty. In dealing with insufficient
information for estimating objective
probabilities, agents may rely on heuristics that make use of past and present
information in some systematic way. An
example of a formal heuristic is provided by Barsky and De Long (1990) in
their important work on long swings in
financial asset markets. Consider their
hypothesized forecasting rule for the
natural log of dividend growth in a given
year:
zyx
E[G,I= (1 - 0 ) C. 8’
(for i = O...
m,
0c8c I]
where
is the natural log of the proportional rate of dividend growth from
year t - i - 1 to year t - i. Note that GI is
formulated as an expectation based
solely on past and present dividends.
What is interesting about this forecasting rule is that it provides for a built-in
momentum in financial asset valuations
and can, as Barsky and De Long indicated, lead to wide swings in asset markets on the basis of predicted fundamental values rather than any sort of
“irrational” behavior. It is a perfectly
rational way to forecast when agents
realize that they simply are not able to
uncover the objective values that apply
to a given situation.
Finally, even short-term swings in
financial asset values may be related to
the use of less formal heuristic devices,
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where R(B) is a positive function of the
variance of stock returns (including
growth rate variability) in a portfolio
NovernbedDecember 2003
101
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most likely as a result of the even more
pervasive financial market noise in the
short term (i.e,, Type C uncertainty).
The tendencies of decision makers to
base expectations on representativeness
and availability are well documented in
the experimental 1iteratu1-e.~
The former
refers to categorization of events on the
basis of stereotypical features without
regard to the a priori probabilities of
these events, whereas the latter occurs
when agents estimate the likelihood of
an event according to the ease with
which they can recall examples of it.
These heuristics are often labeled as
biases because they may lead the decision maker to ignore important information. In a world of Type C uncertainty,
however, agents may not have confident
access to such information or may not
even know that it exists. Theories of
“optimal” search for information cannot
account for these situations because one
would not expect agents to expend
resources to search for something about
which they have no knowledge, without
some information about the potential
benefits of the search.
Conclusion
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basis for doing so. This would be an example of
Type D uncertainty.
4. Many of these nonmainstream analyses are
based on earlier insights from economists such as
Knight (1921).
5. See Schoemaker, 1982, p. 551. The seminal
works are Kahneman and Tversky (1972) and
Tversky and Kahneman (1973).
REFERENCES
Barsky, R. B., & De Long, J. B. (1990). Bull and
bear markets in the twentieth century. Journal
of Economic History, 50(2), 265-28 1.
Caplan, B. (1999). The Austrian search for realistic foundations. Southern Economic Journal,
65, 823-838.
Dempster, G . M. (1999). Austrians and post Keynesians: The questions of ignorance and uncertainty. Quarterly Journal of Austrian Economics, 2(4), 73-8 1.
Kahneman, D., & Tversky, A. (1972). Subjective
probability: A judgment of representativeness.
Cognitive Psychology, 3(3), 430-454.
Knight, F. (1921). Risk, uncertainty, and projt.
New York: Houghton Mifflin.
Lucas, R. (1981). Studies in business cycle theory.
Cambridge, MA: MIT Press.
Morgan, M. G., & Henrion, M. (1990). Uncertainty. New York: Cambridge University Press.
Neilson, W. S. (1993). An expected utility-user’s
guide to nonexpected utility experiments. Easrern Economic Journal, 19(3), 257-274.
Schoemaker, P. J. H. (1982). The expected utility
model: Its variants, purposes, evidence, and
limitations. Journal of Economic Literature, 20,
529-563.
Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability. Cognitive Psychology, 5(2), 207-232.
Von Neumann, J., & Morganstern, 0. (1944). The
theory of games and economic behavior.
Princeton, NJ: Princeton University Press.
zyx
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In sum, the approach to uncertainty
that we have posited is not one in which
102
agents engage in actions “absent any
knowledge of the probabilities of different events . . . ” (Caplan, 1999, p. 832,
italics ours). Rather, it is an approach that
recognizes the reality of decision making
by agents who realize that they do not
know enough to form complete probability distributions describing all possible
outcomes of their actions. A more realistic presentation of the uncertainty problem to undergraduate students will allow
them to understand better the assumptions in theoretical models and their relevance to financial problems. Such an
approach, we believe, is a long overdue
adjustment to the standard practice of
modeling decision making as if agents
live in a world of probabilistic certainty,
and it forms an essential part of a realworld approach to economic and financial instruction in the classroom.
Journal of Education for Business
NOTES
1. Two excellent summaries of the issues and
evidence associated with the expected utility
model are Schoemaker (1982) and Neilson
(1993).
2. In finance, rational expectations are used in
the context of the Efticient Markets Hypothesis.
3. A fourth possibility, although one that is
more likely to be of philosophical interest primarily, is that agents may actually “impose” order on
reality (i.e., form subjective probability distributions to describe it) where there is no objective
ISSN: 0883-2323 (Print) 1940-3356 (Online) Journal homepage: http://www.tandfonline.com/loi/vjeb20
A Note on the Treatment of Uncertainty in
Economics and Finance
Anthony M. Carilli & Gregory M. Dempster
To cite this article: Anthony M. Carilli & Gregory M. Dempster (2003) A Note on the Treatment
of Uncertainty in Economics and Finance, Journal of Education for Business, 79:2, 99-102, DOI:
10.1080/08832320309599096
To link to this article: http://dx.doi.org/10.1080/08832320309599096
Published online: 31 Mar 2010.
Submit your article to this journal
Article views: 12
View related articles
Citing articles: 1 View citing articles
Full Terms & Conditions of access and use can be found at
http://www.tandfonline.com/action/journalInformation?journalCode=vjeb20
Download by: [Universitas Maritim Raja Ali Haji]
Date: 12 January 2016, At: 23:00
A Note on theTreatment of
Uncertainty in Economics
and Finance
ANTHONY M. CARlLLl
GREGORY M. DEMPSTER
Hampden-Sydney College
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:00 12 January 2016
Hampden-Sydney, Virginia
E
zyxw
zy
zyxwvutsrqp
zyxwvutsr
zyxwvut
ver since John von Neumann and
Oskar Morganstern published their
groundbreaking work, The Theory of
Games and Economic Behavior (1944),
the treatment of uncertainty in the classrooms of economics and finance has
been dominated by the application of
risk theory to the utility-maximization
framework. In defending the advantages
of this approach, some economists have
gone so far as to deny the coherence of
any distinction between risk and uncertainty, whereas others have maintained
that, in situations where risk theory is
inapplicable, behavior “may not be
explainable in terms of economic theory” (Lucas, 1981, p. 223). The most
common defense of risk theory, however, is on instrumentalist grounds and is
supported by the undeniable value of
the expected utility model as a normative theory of decision making.
Nevertheless, the relevance of the
standard risk model as a positive description of economic decision making
increasingly is being called into question
in theoretical work. Persistent evidence
from experimental psychology and economics suggests that the principles of
actual decision making are often inconsistent with the axioms of the standard
theory.’ Our purpose in this article is to
provide a method of categorizing the
types of uncertainty as well as to summarize various approaches to the problem for the educated businessman.As the
ABSTRACT. The treatment of uncertainty in the business classroom has
been dominated by the application of
risk theory to the utility-maximization
framework. Nonetheless, the relevance
of the standard risk model as a positive
description of economic decision making often has been called into question
in theoretical work. ’ In this article, the
authors offer an instructional approach
that recognizes the reality of decision
making by agents who know that they
do not know enough to form complete
probability distributions describing all
possible outcomes of their actions.
Students must recognize the fundamental difference between risk and the
broader concept of uncertainty. This
realistic presentation of the uncertainty
problem will allow undergraduate students to better understand the assumptions involved in modeling and their
relevance to economic and financial
problems.
tations, which means that the agents (a)
have access to all the information necessary to approach the economic problem
with which they are faced and (b) make
use of the information in a manner consistent with the standard axioms of rational decision theory.2 In the terminology
of Bayesian probability theory, this situation implies convergence between the
objective probability distributions governing real-world outcomes and agents’
subjectively formed assessments of those
objective conditions. Therefore, agents
do not make systematic errors in the forecasting of potential outcomes. Agents
make decisions that lead to suboptimal
outcomes not because of any entrenched
bias in the decision-making process, but
only because the actual outcomes usually will be different from the ex ante
expected (average) value dictated by
their assessments. In other words, even
with full knowledge of all possible outcomes and their associated probabilities,
decisions are still risky because we do
not know which of the possible outcomes
will materialize.
We have characterized risk in this
way to contrast it with the more general
phenomenon of uncertainty. First and
foremost, uncertainty refers to the
inability of the agent to accurately predict future outcomes. The phenomenon
of risk described above is one manner in
which uncertainty may manifest itself in
decision making. Thus, we can label
zyxwvutsrq
demands of a competitive marketplace
prompt business professionals to adopt
more and more complex methods of
forecasting and planning, a working
knowledge of these alternative approaches will be of great value. We conclude
with a discussion of the importance of
these approaches for economic and
financial analysis and an example of how
such alternatives might be introduced in
an undergraduate classroom setting.
Degrees of Uncertainty
Most modem economic and financial
models posit agents with rational expec-
zyxw
November/December 2003
99
Downloaded by [Universitas Maritim Raja Ali Haji] at 23:00 12 January 2016
risk as one category, or type, of uncertainty and designate it as Type A. But
there are circumstances under which
risk analysis cannot fully explain the
deviation between expected and actual
outcomes. One such circumstance
involves the possibility that subjectively
formed distributions may be systematically biased; that is, there may be a lack
of convergence between those assessments and the objective distributions
that govern reality. We can call this situation Type B uncertainty. Another possibility is that economic agents may fail
to form complete probability distributions as part of their subjective assessments because either (a) they do not
believe an objective distribution exists
or (b) they do not believe that they have
enough information about objective
conditions to form a subjective distribution that would remotely describe those
conditions. We designate this uncertainty as Type C3
One might categorize these “degrees”
of additional uncertainty by the amount
of information available to the economic
agent. Type B involves a deviation from
rational expectations but not a departure
from the axioms of rational choice.
Agents still make decisions based on risk
analysis, but the expected values of their
subjectively formed distributions are
biased because they lack some important
information about objective conditions.
On the other hand, Type C does involve a
departure from the axioms of expected
utility. In this sense, it is somewhat more
fundamental than Type B uncertainty.
Type C agents possess some information
that they believe is relevant for decision
making, but they realize that they do not
possess enough to form a complete subjective distribution of outcomes that is
even moderately accurate in representing
the actual realm of possibilities.
Dempster (1999) argued that these
types of uncertainty also might be distinguished on the basis of their root causes.
For Type B, the cause of the additional
uncertainty is faulty perceptions of
potential outcomes and their probabilities, so that subjectively formed distributions fail to converge with their objective
counterparts. Type C uncertainty, on the
other hand, arises because of the uniqueness (or “specificity”) of the situation at
hand. Without either some a priori
knowledge of the probabilities associated
with potential outcomes (as in a game of
dice) or some experience in similar situations (as in the case of insurable contingencies), there is no foundation for subjective outcome distributions upon which
actions can be based.
What Caplan and other proponents of
risk theory ignore, however, is the fact
that its application to decision making
requires a complete probability distribution, listing all of the possible outcomes
of a random variable and their associated probabilities. The random variable
must be defined by a set of mutually
exclusive outcomes whose probabilities
sum to one. If either an outcome or a
probability is unknown, expected values
and variances cannot be calculated. And
if expected values and variances cannot
be calculated, there is no basis from
which to make a decision under risk theory. In other words, to treat situations of
uncertainty as risky, it is necessary to
define both columns of the probability
distribution.
It is quite obvious that agents are
unable to assign probabilities to events
about which they are completely unaware, and therefore they cannot calculate expected values or variances that
will converge toward any objective values. If an agent is at least aware that
such unknown events are likely to exist,
he or she will also realize that one cannot decide, for example, on the maximum price to pay for a known opportunity on the basis of risk theory. It would
be reasonable for such an agent to make
a decision on the basis of intuition or
simple heuristics. Thus, consistent findings of economic behavior that contradict the standard model of decision
making may be a result, in part, of an
awareness on the part of economic
agents that their information set is
incomplete with regard to possible outcomes of their actions.
But it is also true that agents might
not assign probabilities to all possible
events of which they are aware. Perhaps
an example will be helpful here. Let us
assume that an agent faces three possible outcomes of a decision: (a) winning
$100 with a probability of 50%, (b)
winning $25 with an unknown probability, or (c) losing $90 with an unknown
probability. We represent this probability distribution in Table 1.
It is easy to see that no variance or
expected value can be calculated.
Therefore, risk theory provides no basis
for an optimal decision. This does not
mean, however, that the agent completely lacks information upon which to base
zyxwvu
Alternative Approaches
to Uncertainty
Unfortunately, the distinction between
the various degrees of uncertainty has
been blurred in the standard classroom
treatment of decision making. There are
generally two reasons given for the abandonment of such distinctions: (a) the
belief that few real-world situations
involve true uncertainty, so that the distinction, although valid, may be usefully
ignored; and (b) the fact that risky, rather
than truly uncertain, situations make certain economic models tractable. The sum
of these two general attitudes is neatly
expressed by Robert Lucas, who has
done much to bring the application of
risk models into mainstream economics
via rational expectations. Lucas acknowledged the validity of the distinction when
he admitted that his treatment of expectations is not relevant to situations of true
uncertainty. He concluded, however, that
in such cases “economic reasoning will
be of no value” (1981, p. 224).
True uncertainty is difficult to model
because it “renders the theory of probability virtually inapplicable to real-world
decision making,” and thus it is generally
thought that the risk-uncertainty distinction is “unhelpful” (Morgan & Henrion,
1990, p. 49). A number of non- mainstream traditions in economics and
finance nevertheless continue to maintain
that many situations involve choice under
true uncertainty and that mainstream practitioners are assuming away an important
distinction for the sake of convenience?
Some recent research continues to reinforce this dichotomy in economic
approaches. For example, Caplan (1999)
acknowledged that the standard treatment
“sounds implausible at first” (p. 836), but
then he actually went further than most
mainstream counterparts by questioning
the very coherence of the distinction
between risk and uncertainty and suggesting that the risk model is an accurate and
sufficient model for decision making.
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Journal of Education for Business
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TABLE 1. Probability Distribution No. 1
Value
(value)
Value*p
(value)
$100
50%
$50
?
?
?
?
P
$25
($90)
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TABLE 2. Probability Distribution No. 2
Value
$100
Not $100
P
(value)
Value*p
(value)
50%
50%
$50
?
a decision, for he or she knows (or
believes that he or she knows) that there
is a 50% chance of winning $100. And
although the agent does not have
enough information to assign probabilities to the other outcomes, he nonetheless may be willing to act or not act in a
certain manner solely on the basis of
intuition, a hunch, or even a heuristic
that has proved useful in the past.
It may be argued that the agent subjectively will assign probabilities to all
outcomes despite the absence of any
basis for their values. But why would
an agent expend resources (mental
effort, etc.) to form a subjective probability distribution that he knows to have
no connection with any actual state of
affairs? Will the agent necessarily be
made better off by doing so? Is it not
much more likely that the agent will
use trusted heuristics as a basis for
decision making rather than act on a
probability distribution he or she knows
to be false? To assert that probability
calculus will be used in such a situation
is to make the heroic assumption that
some estimation of probabilities, no
matter how significantly they might
bias the subjectively determined
expected value from its actual value, is
always preferred to none. Note, for
example, what would happen if we
assume that agents “divide the world
into two events”-for example, earning
$100 and not earning $100 (Caplan,
1999, p. 832). Such a decision process
would lead to the distribution that we
represent in Table 2.
This decision process leaves us no
better off than we were before, with no
expected value or variance that can be
calculated, so risk analysis provides no
basis for decision making. And there is
no reason to believe that arbitrarily
assigning a value to the unknown parameter will make the agent better off.
Therefore, one approach we can take
to the problem of incomplete probability
distributions is to allow for Type B or
Type C uncertainty involving biased
subjective evaluations. In this approach,
we might assume that agents act according to some basic heuristics in making
decisions characterized by incomplete
probability distributions. What kinds of
heuristics might be used in such a situation? Experimental tests in psychology
and economics suggest a number of possibilities, ranging from the familiar representativeness and availability heuristics to more formal (but still less than
fully “rational” in the standard economic sense) decision-making rules.
Uncertainty and Financial
Analysis
Recognition of the broader uncertainty concept can have profound implications for economic and financial analysis and can be demonstrated fairly easily
in a classroom setting. Consider, for
example, a standard formulation of
stock price determination under risk:
where P, is the current price, D, is the current l -year cash flow, R, is the annualized
interest rate on the financial asset, and
E[G,I is the expected growth rate in cash
flows. Standard risk analysis implies that
E[GJ equals the sum of all possible outcomes for G, times their respective probabilities. The interest rate is often
expressed as a function of an underlying
risk-free rate and a risk premium:
context. If R(B) is a linear function of
market risk in the long run, then we
have the familiar Capital Asset Pricing
Model (CAPM) formulation of risk and
return.
CAPM is used widely as a tool for financial analysis. Corporate finance officers use it to determine the long-run rate
of return they should expect to pay on
common stock. Securities analysts use it
to make judgments about whether
stocks are over- or undervalued. Although some academics have identified
theoretical problems with CAPM, it
continues to be a standard part of the
finance toolkit and curriculum. Little
work has been done, however, in regard
to the effects of alternative forms of
uncertainty on CAPM.
For example, consider the case in
which growth rates are subject to Type B
uncertainty. In dealing with insufficient
information for estimating objective
probabilities, agents may rely on heuristics that make use of past and present
information in some systematic way. An
example of a formal heuristic is provided by Barsky and De Long (1990) in
their important work on long swings in
financial asset markets. Consider their
hypothesized forecasting rule for the
natural log of dividend growth in a given
year:
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E[G,I= (1 - 0 ) C. 8’
(for i = O...
m,
0c8c I]
where
is the natural log of the proportional rate of dividend growth from
year t - i - 1 to year t - i. Note that GI is
formulated as an expectation based
solely on past and present dividends.
What is interesting about this forecasting rule is that it provides for a built-in
momentum in financial asset valuations
and can, as Barsky and De Long indicated, lead to wide swings in asset markets on the basis of predicted fundamental values rather than any sort of
“irrational” behavior. It is a perfectly
rational way to forecast when agents
realize that they simply are not able to
uncover the objective values that apply
to a given situation.
Finally, even short-term swings in
financial asset values may be related to
the use of less formal heuristic devices,
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variance of stock returns (including
growth rate variability) in a portfolio
NovernbedDecember 2003
101
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most likely as a result of the even more
pervasive financial market noise in the
short term (i.e,, Type C uncertainty).
The tendencies of decision makers to
base expectations on representativeness
and availability are well documented in
the experimental 1iteratu1-e.~
The former
refers to categorization of events on the
basis of stereotypical features without
regard to the a priori probabilities of
these events, whereas the latter occurs
when agents estimate the likelihood of
an event according to the ease with
which they can recall examples of it.
These heuristics are often labeled as
biases because they may lead the decision maker to ignore important information. In a world of Type C uncertainty,
however, agents may not have confident
access to such information or may not
even know that it exists. Theories of
“optimal” search for information cannot
account for these situations because one
would not expect agents to expend
resources to search for something about
which they have no knowledge, without
some information about the potential
benefits of the search.
Conclusion
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basis for doing so. This would be an example of
Type D uncertainty.
4. Many of these nonmainstream analyses are
based on earlier insights from economists such as
Knight (1921).
5. See Schoemaker, 1982, p. 551. The seminal
works are Kahneman and Tversky (1972) and
Tversky and Kahneman (1973).
REFERENCES
Barsky, R. B., & De Long, J. B. (1990). Bull and
bear markets in the twentieth century. Journal
of Economic History, 50(2), 265-28 1.
Caplan, B. (1999). The Austrian search for realistic foundations. Southern Economic Journal,
65, 823-838.
Dempster, G . M. (1999). Austrians and post Keynesians: The questions of ignorance and uncertainty. Quarterly Journal of Austrian Economics, 2(4), 73-8 1.
Kahneman, D., & Tversky, A. (1972). Subjective
probability: A judgment of representativeness.
Cognitive Psychology, 3(3), 430-454.
Knight, F. (1921). Risk, uncertainty, and projt.
New York: Houghton Mifflin.
Lucas, R. (1981). Studies in business cycle theory.
Cambridge, MA: MIT Press.
Morgan, M. G., & Henrion, M. (1990). Uncertainty. New York: Cambridge University Press.
Neilson, W. S. (1993). An expected utility-user’s
guide to nonexpected utility experiments. Easrern Economic Journal, 19(3), 257-274.
Schoemaker, P. J. H. (1982). The expected utility
model: Its variants, purposes, evidence, and
limitations. Journal of Economic Literature, 20,
529-563.
Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability. Cognitive Psychology, 5(2), 207-232.
Von Neumann, J., & Morganstern, 0. (1944). The
theory of games and economic behavior.
Princeton, NJ: Princeton University Press.
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In sum, the approach to uncertainty
that we have posited is not one in which
102
agents engage in actions “absent any
knowledge of the probabilities of different events . . . ” (Caplan, 1999, p. 832,
italics ours). Rather, it is an approach that
recognizes the reality of decision making
by agents who realize that they do not
know enough to form complete probability distributions describing all possible
outcomes of their actions. A more realistic presentation of the uncertainty problem to undergraduate students will allow
them to understand better the assumptions in theoretical models and their relevance to financial problems. Such an
approach, we believe, is a long overdue
adjustment to the standard practice of
modeling decision making as if agents
live in a world of probabilistic certainty,
and it forms an essential part of a realworld approach to economic and financial instruction in the classroom.
Journal of Education for Business
NOTES
1. Two excellent summaries of the issues and
evidence associated with the expected utility
model are Schoemaker (1982) and Neilson
(1993).
2. In finance, rational expectations are used in
the context of the Efticient Markets Hypothesis.
3. A fourth possibility, although one that is
more likely to be of philosophical interest primarily, is that agents may actually “impose” order on
reality (i.e., form subjective probability distributions to describe it) where there is no objective