Individual differences in risk aversion and anxiety

Amy E. Eisenberg[+]

Jonathan Baron

Martin E. P. Seligman



University of Pennsylvania

In two studies, college-student subjects completed a questionnaire about what they would do in hypothetical decisions pitting a risky option against a safe one. The risky option sometimes involved an action and sometimes an omission, so that risk aversion could be unconfounded from passivity. Anxiety correlated with risk aversion, as did depressive symptoms, but the latter correlation was mediated by the correlation of depressive symptoms with anxiety. Risk aversion was correlated with the tendency to believe that bad outcomes were both likely and particularly bad, and these beliefs were correlated with depressive symptoms and with pessimistic attributional style. All of these relations were confined to beliefs about the self: they disappeared when the questionnaire involved a hypothetical other person.

Anxiety is usually conceived as an emotional state, accompanied by expectations of bad outcomes or concerns about how terrible those outcomes could be (e.g., Beck, 1976). Measures of anxiety as a state or a personality trait typically assess emotions and associated concerns. The State-Trait Anxiety Inventory, for example, asks subjects whether they feel calm, secure, tense, strained, whether they take disappointments keenly, and whether they are in a state of tension or turmoil (Spielberger et al., 1970). It does not ask specifically about decision making.

Risk aversion in decision making is the tendency to avoid options associated with uncertain outcomes that differ in their desirability (Baron, 1994). It would stand to reason that anxious people would avoid risks, because they would think that bad outcomes are both likely and particularly bad. We know of no previous study that has shown a correlation between anxiety as an emotional tendency and risk aversion in decision making.

We describe here a questionnaire measure of individual differences in risk aversion, and we show that it correlates with anxiety. The new measure asks subjects to consider choices typical of those that people make in their daily lives, each between a risky option and a safe option. The safe option has some moderate utility - that is, it leads with certainty to an outcome that is neither highly desirable nor highly undesirable. The risky option could lead to a better outcome or a worse one. Rational decision makers consider both the utility of the three possible outcomes and their probability that the risky option will result in the better outcome (Baron, 1994). If anxiety makes people less likely to choose the risky option, it could do this by increasing their probability that the risk would result in the bad outcome, by making the bad outcome seem worse (lower in utility) or by making the utility of the good outcome seem not as good (lower in utility). We examine these effects by asking subjects directly about probability and utility of outcomes.

Previous studies of individual differences in risk aversion have typically used gambles for money (Bromley & Curley, 1992; Schoemaker, 1993). Although consistent individual differences have sometimes been found, none of these studies has examined the role of anxiety. Moreover, such money gambles are untypical of everyday risks both because they are subject to cultural attitudes toward gambling and because most experiments involve gains only, although risks in everyday life typically involve potential losses as well.

Kogan and Wallach (1964) developed a more general questionnaire concerning risk taking in everyday life. A typical item (much abbreviated) was, ``Mr. A, ...is offered a job with a small, newly founded company which has a highly uncertain future. The new job would pay more to start and would offer the possibility of a share in the ownership if the company survived .... Imagine that you are advising Mr. A. Listed below are several probabilities or odds of the new company's proving financially sound. Please check the lowest probability that you would consider acceptable to make it worthwhile for Mr. A to take the new job.'' Checking higher probabilities indicated more risk-aversion. Risk-aversion measured with their questionnaire correlated with risk-aversion in gambling tasks (p. 38) and in skill tasks (p. 41). Kogan and Wallach measured test anxiety (not general anxiety) because they hypothesized that it would moderate other relationships. Apparently, test anxiety correlated somewhat with risk-aversion, significantly for females but not for males (Appendices A-2 and A-3). Such a correlation would result if anxious people (relative to nonanxious people) thought that bad outcomes were particularly bad, or good outcomes not so good. For anxious people to take a risk under such conditions, the probability of the good outcome would have to be high.

Butler and Matthews (1987) looked at the other side of the question, asking subjects for outcome probabilities of good and bad events, rather than asking for a probability cutoff in the manner of Kogan and Wallach. Butler and Matthews found that more anxious subjects gave lower probabilities for good events and higher probabilities for bad events. This result was restricted to events happening to the self. The events in question did not all result from decisions. The result was not found for events happening to others. (Within the category of self-events, the result held equally for events that were caused by the self and those that were externally caused. We do not examine this distinction here.) Butler and Matthews (1983) found that both anxious and depressed patients had higher probabilities for bad events than controls did. This was restricted to events happening to the self. There was no difference for events happening to others. It was not clear whether this correlation between probability of bad events and depression was mediated by the correlation between probability and anxiety, given that anxiety and depression are highly correlated.

We also take the opportunity to examine correlations between risk aversion and depressive symptoms. Pietromonaco and Rook (1987) examined this correlation in college students. Their items, also from a variety of domains, presented subjects with hypothetical situations involving risky action, e.g.: ``There is a personal matter that has been troubling you quite a bit recently. You are wondering what would happen if you discussed this problem with your new roommate ....'' Subjects rated the importance, probability, and goodness/badness of each of a few benefits and risks of each action. Subjects with more depressive symptoms were less likely to take the action than were subjects with fewer symptoms, and they thought that the risks were more important and the benefits less important. Separate analyses of probability, goodness, and badness were not reported.

In all of Pietromonaco and Rook's items, the risky option was the more active one. The correlation between depressive symptoms and risk aversion could therefore be explained if depressive symptoms were correlated with passivity rather than with risk aversion, as learned-helplessness theory (Seligman, 1975) suggests. Moreover, if there is a correlation between depressive symptoms and risk aversion, it could be mediated by the correlation of both with anxiety, which was not measured. In our study, we measured both anxiety and depressive symptoms, and we included items involving both actions that increased risk and actions that reduced risk, thus unconfounding action vs. inaction from risk seeking vs.\ aversion.

Our questionnaire, like that of Kogan and Wallach and of Pietromonaco and Rook, used a variety of hypothetical decisions situations drawn from the everyday lives of our subjects. We did not provide critical probabilities. We provided a description of the situation, and then we asked subjects the probability of their taking a risk (or of taking an action to avoid a risk) and of a good outcome if they took the risk. Anxiety may affect perceived probabilities of good outcomes, and, if it did, the original Kogan/Wallach measure could not detect this. Another difference between our questionnaire and that of Kogan and Wallach was that we asked what the subjects would do in the situation, rather than asking how they would advise someone else. (In Experiment 2, however, we asked what others would do.)

Each item of our questionnaire presented a hypothetical decision with a risky option and a safe option. For example, in the student version, ``You would like to join a certain organization on campus. It is not possible to just `sign up.' You must go through a selection process consisting of three interviews along with many others who would also like to become members.'' Subjects were asked the probability that they would act, the probability that, if they took the risky option, they would succeed, how good it would be if they took the risk and succeeded (on a ten-point scale), and how bad it would be if they failed. For half of the items, the risky option was an action, and for half it was an omission. An example of the latter was buying vs. not buying a computer disk to back up a course paper just written on a computer. Our measure of risk aversion was the subject's probability that she would choose the less risky option if she were faced with a situation like the one described.

We also asked whether individual differences in risk aversion are determined in part or in full by differences in expected probability of success. The last two questions following each item allow us to ask whether such differences are also a function of anticipated utilities of good and bad outcomes. People who are more risk averse may find bad outcomes to be particularly bad, or they may find good outcomes to be not so good. We might expect depressive symptoms to correlate with these measures, with higher levels of depressive symptoms correlating with more negative ratings for the bad outcome. Similarly, we might expect pessimistic attributional style to correlate with very negative ratings of bad outcomes: people who blame outcomes on themselves might find these outcomes particularly aversive.

We report two studies using college students. The first of these gave many of the students the Attributional Style Questionnaire (ASQ; Peterson et al., 1982), so we were able to ask about the relation between attributional style and components of risk aversion. The second study used two parallel forms of the risk questionnaire, one concerning the self and one concerning a hypothetical other person. This allowed us to ask whether attitudes toward risk are better characterized as being limited to the self or about what is rational to do in the world. Butler and Matthews (1983, 1987) made this comparison for risk beliefs (in contrast to decisions) and found that the effects of anxiety and depression were confined to beliefs about the self.

Scenario 1 read, in entirety:

1. You have recently become acquainted with a person in your class. You find this person attractive and would like to ask him/her out on a date.

A) What is the probability that you will ask this person out? (0-100%)

B) If you do ask this person out, how likely is it that the person will accept your offer? (0-100%)

C) How good would you feel if the person accepted your offer? (1=not good at all, 5=moderately good, 10=extremely good)

D) How bad would you feel if the person rejected your offer? (1=not bad at all, 5=moderately bad, 10=extremely bad)

In ten of the scenarios, like this one, action was risky, and inaction was safe. In eight others, inaction was risky and action was safe. For example, scenario 2 began, ``A very serious virus is predicted to hit your area. A vaccination is available which eliminates your risk of catching the virus. It involves a series of three shots spaced over three weeks.'' Question B was written so that a high number favored action, e.g., ``If you don't get vaccinated, how likely is it that you will get the virus?'' Questions C-D referred to the risky option: ``If you do not get the vaccine, how good would you feel about not getting the virus?'' ``If you do not get the vaccine, how bad would you feel about getting the virus?''

The other 16 items concerned, respectively: applying for a small grant for a student research project; entering the selection process to join a student organization; going out to buy a diskette to make a backup of a paper; running for president of the student body; complaining to a professor about a poor grade; going to get stitches for a very bad cut; going to court to recover a loan from a friend; switching out of a class with a tough grader into a less-interesting one with an easy grader; investing $500 in a friend's business venture; selling an old car that is starting to need repairs; switching to a less interesting but more secure job; switching to a safer but longer way of walking to campus; switching to a more interesting class with a tougher grader; evacuating from a hurricane zone; having risky surgery for a condition that impairs sports performance; and playing a coin-flip game in which heads leads to $100 and tails leads to a $30 loss.

We found two main results:

1. People who are more risk averse are more anxious, and people who are less active show more depressive symptoms. These symptoms, in turn, are more common in people with pessimistic attributional style.

2. The Decision Questionnaire is internally consistent. People who are more risk averse think that bad events are more likely (Probability, question B) and worse if they happen (Badness, question D). However, risk averse people do not think that good events are not as good if they happen (Goodness, question C). People who think of themselves as more active also believe that better outcomes are more likely to result from action than from inaction, that bad outcomes resulting from action are less bad, and those resulting from inaction are worse.

r=.26

p=.001

r=.22

p=.008

r=.58

p=.000

r=.28

p=.000

We would expect Activeness to correlate with the belief that bad events were unlikely when action was associated with risk but likely when inaction was associated with risk. Likewise, Activeness might be associated positively with Goodness for risky acts and negatively for risky omissions, and the reverse with Badness. To test these hypotheses, we analyzed questions B-D as relevant to activeness vs. passivity, as opposed to risk seeking vs. aversion. Thus we formed new composite variables for predicting Activeness, coded in these ways: Act Probability, Act Goodness, and Act Badness. Activeness correlated in the expected direction with Act Probability ( r=.60 , p=.000 ): more active subjects thought that good outcomes would be more likely with risky action and bad outcomes more likely with risky omission. Activeness also correlated with Act Badness ( r=.21 , p=.010 ): more active subjects were inclined to think that the bad consequences of taking a risk are less bad when the risk results from action than when it results from inaction. There was no correlation with Act Goodness ( r=-.05 ).

To score the STAI, state and trait measures were combined into a single measure of Anxiety. (State and trait measures behaved similarly in separate analyses and were correlated, r=.77 .) Anxiety and depressive symptoms (BDI) were highly correlated ( r=.72 ). Both depressive symptoms and Anxiety correlated negatively with Activeness - more depressive symptoms and more anxiety went with less tendency to act - but the depressive-symptoms correlation was somewhat greater ( r=-.25 , -.20; p=.002 , .013, respectively). Both depressive symptoms and Anxiety correlated positively with Risk-aversion - more symptoms and anxiety went with more risk aversion - but only the latter correlation was significant ( r=.12 , .26; NS, p=.001 , respectively).

Canonical correlation in which depressive symptoms and Anxiety were correlated with Risk-aversion and Activeness revealed two significant canonical correlates ( p=.000 and .037, respectively). In other words, the best weights for predicting Risk-aversion from symptoms and Anxiety were significantly different from the best weights for predicting Activeness from symptoms and Anxiety. The standardized regression weights for predicting Activeness were -.22 for depressive symptoms and -.04 for Anxiety; the weights for predicting Risk-aversion were -.14 for symptoms and .36 for Anxiety. These weights take into account the high correlation between depressive symptoms and Anxiety, of course. Except for this correlation, it seems that depressive symptoms are related only to passivity and anxiety is related only to Risk-aversion. (We note, however, that the separation of variables did not succeed in the second study.)

Further analysis suggested that the effect of Anxiety on Risk-aversion was mediated by its effect on Probability, but the effect of depressive symptoms on Activeness was direct. Specifically, when Anxiety was regressed on Risk-aversion and Probability, only the latter coefficient was significant; and when depressive symptoms were regressed on Activeness and Act Probability, only the former coefficient was significant. Details are omitted because these analyses are speculative, and tests of mediation were not quite significant.

r=-.48

r=-.57

r=-.25

r=.29

p<.01

Probability (of the bad event) was correlated negatively with Optimism ( r=-.49 , p=.000 ), and including Probability in the regression of Risk-aversion on Optimism reduced the coefficient from -.25 to .08 (a reversal of direction). These results suggest that optimism reduces risk-aversion entirely by increasing the belief that bad events are unlikely. Optimism also correlated significantly with Badness ( r=-.31 , p=.001 ): more optimistic subjects thought that bad events were less bad, and this would make it more rational for them to take risks. Act Probability was also correlated with Optimism ( r=.22 , p=.018 ): more optimistic subjects were more disposed to think that acts were more likely than omissions to lead to good outcomes. In this case, however, Optimism was still a significant predictor of Activeness when Act Probability was included. Optimism therefore seems to affect Activeness directly, just as depressive symptoms do.

In sum, we are left with a general model in which Risk-aversion is determined by the belief that bad events are likely to happen. A complex of traits that include anxiety and pessimistic attributional style make individuals believe that bad events are more likely. Passivity, on the other hand, is more closely related to depressive symptoms alone, which, in turn, are also related to pessimistic attributional style.

Experiment 2 replicated Experiment 1, but with an additional decision questionnaire, following the first, completed from the viewpoint of another person. This allowed us to ask whether anxiety is related to a belief in the general perverseness of the world, for anyone, or to a belief that the world is perverse for the individual alone. Because of the additional length of the questionnaire, we did not administer the ASQ.

We modified the Decision Questionnaire, replacing some questions and adding others, so that it contained 11 risky acts and 9 risky omissions. The Probability question was phrased in terms of the good outcome rather than the bad outcome (except for three questions, for which we reversed the answers). Immediately following the Decision Questionnaire, subjects completed a second version in which each item involved a third person with a sex-neutral name (Terry, Alex, etc.). Then subjects completed the BDI and STAI. Subjects were drawn from classes and from paid volunteers who came to a laboratory to fill out questionnaires for $6/hour. A total of 175 subjects, all students solicited as in Experiment 1, completed the questionnaires. Unlike Experiment 1, subjects indicated their sex.

The major results of Experiment 1 were replicated, with some complications. The results were largely limited to the self. We deal with the results for the self first, then the results for another person.

r=.77

r=.27

p=.000

r=.30

p=.000

As in Experiment 1, activeness (probability of acting) in the action items and activeness in the inaction items were positively correlated, although not quite significantly ( r=.14 , p=.070 ). Reliabilities of the main measures were somewhat lower than in Experiment 1: .54 for Activeness and .48 for Risk-aversion. Risk-aversion was again correlated with Probability ( r=.36 , p=.000 ) and badness ( r=.23 , p=.003 ). Activeness was again correlated with Act Probability, the tendency to believe that action is more likely than inaction to lead to good outcomes ( r=.27 , p=.000 ), but Activeness was not correlated with Act Goodness or Act Badness. (Experiment 1 did find a correlation with Act Badness.) There were no sex differences in any of the risk measures.

r=.19

r=.45

The risk aversion measures were internally consistent. Risk-aversion correlated negatively with Probability ( r=.33 , p=.000 ) and positively with Badness ( r=.18 , p=.018 ). The correlation with Goodness was not significant (although, as in Experiment 1, in the wrong direction, r=.12 ).

Likewise, Activeness was correlated with Act Probability ( r=.30 , p=.000 ). It was not correlated with Act Badness ( r=-.05 ) and was correlated in the wrong direction with Act Goodness ( r=-.26 ).

None of the risk-aversion measures for Other was correlated significantly with Anxiety. Anxiety thus seems to affect risk beliefs about the self, and risk aversion for oneself alone. Activeness was correlated positively (the wrong direction) with depressive symptoms, however ( r=.21 ): subjects with many symptoms seemed to think that other people were more active. Otherwise, none of the activeness measures correlated with depressive symptoms.

Most important, the correlation between Anxiety and Risk-aversion for Self ( r=.30 ) was significantly higher than that between Anxiety and Risk-aversion for Other ( r=.03 ; t=2.89 , p=.005 , using the method recommended by Steiger, 1980).

Greater anxiety correlates greater risk aversion by our measure. This correlation is separate from that between depressive symptoms and risk aversion. In both experiments, depressive symptoms correlated with risk aversion only because of its correlation with anxiety.

In Experiment 1, depressive symptoms correlated separately with a general passivity, a tendency not to act. Although this was not replicated in Experiment 2, perhaps further studies are warranted using people with greater degrees of depressive symptoms.

We defined risk aversion as a tendency to make choices that avoid risk. Risk aversion was high when the belief that bad events were likely if risks were taken was strong. The effect of anxiety on risk aversion seemed to be mediated largely through an effect on this belief.

Greater risk aversion was also correlated with the expectation that bad outcomes of risky choices would be particularly bad. This, in turn, was influenced by anxiety and depressive symptoms. Risk aversion was not correlated with the expectation that good outcomes would not be particularly good. In fact, a reverse correlation was sometimes observed. It seems that individual differences in risk aversion (and its converse, risk seeking) have more to do with differences in how people think of bad outcomes than with differences in how they think of good outcomes.

In conclusion, we suggest that individual differences in anxiety are broader than those that concern emotion. Anxiety, as measured by a scale concerned primarily with emotion, is correlated with acknowledged tendencies to avoid risks, whether risk avoidance requires action or inaction. This correlation seems to be mediated by beliefs that bad outcomes are both particularly bad and particularly likely. These beliefs, in turn, may be caused by the emotion of anxiety itself. Anxious people may avoid taking risks, even when they should.

Although the present study is correlational, it suggests that experimental studies are worth doing, and it provides measures that might be useful in such studies. In particular, it would be interesting to examine the effect of therapy for anxiety - either drugs or psychotherapy - on the management of risks in daily life. If the causal mechanism goes, as we suggest, from the emotional effects to the decisions, then further attempts to deal with decision making itself may not be necessary.

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Individual differences in risk aversion and anxiety

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...Eisenberg This research was partially supported by N.S.F. grant SES91-09763 to J. Baron and N.I.H.\ grant MH19604 to M. Seligman. We acknowledge the significant contribution of Dr. Mary Ann Layden to the authorship of the ASQ. Send correspondence to Jonathan Baron, Department of Psychology, University of Pennsylvania, 3815 Walnut St., Philadelphia, PA 19104-6196, or (e-mail) baron@cattell.psych.upenn.edu.

Jonathan M Baron

Wed Jan 21 07:11:13 EST 1998