Forecasting risk attitudes: An experimental study using actual and forecast gamble choices

Abstract

We develop and evaluate a simple gamble-choice task to measure attitudes toward risk, and apply this measure to examine differences in risk attitudes of male and female university students. In addition, we examine stereotyping by asking whether a person's sex is read as a signal of risk preference. Subjects choose which of five 50/50 gambles they wish to play. The gambles include one sure thing; the remaining four increase (linearly) in expected payoff and risk. Each subject also is asked to guess which of the five gambles each of the other subjects chose, and is paid for correct guesses. The experiment is conducted under three different frames: an abstract frame where the two highest-payoff gambles carry the possibility of losses, an abstract frame with no losses, and an investment frame that mirrors the payoff structure of the former. We find that women are significantly more risk averse than men in all three settings, and predictions of both women and men tend to confirm this difference. While average guesses reflect the average difference in choices, only 27 percent of guesses are accurate, which is slightly higher than chance.

Introduction

Until very recently, the most popular method for measuring risk attitudes has been a variation on the two-stage preference–revelation mechanism developed by Becker et al. (1964). This mechanism asks subjects to choose a selling price for a lottery. A randomly drawn value then determines whether the subject sells the lottery (if the drawn price exceeds the subject's price) or plays the lottery. Harrison (1986) was first (to our knowledge) to use this technique, which also has been used by other researchers including Kachelmeier and Shehata (1992) for high-stakes gambles in China, Eisenberger and Weber (1995) for valuing ambiguous lotteries, and in our own work on computer extended warranties. However, this mechanism has come under fire for three reasons. First, elicited valuations are sensitive to seemingly irrelevant parameters of the mechanism such as the upper range of possible valuations (Bohm et al., 1997). Second, for valuation of lotteries, subjects have very little incentive to reveal accurate valuations for gambles with low-probability payoffs (Harrison, 1992). Third, the mechanism is sufficiently complex that it can lead to substantial errors in decision-making (Eckel, 1999, Eckel, 2005).

In this paper we present a simple task for measuring risk preferences. Subjects are shown five gambles and asked to choose which of the five they wish to play. The gambles include one sure thing with the remaining four increasing (linearly) in expected payoff and risk (measured by the standard deviation of expected payoff). All are 50/50 gambles. The gambles are represented in a way that is easy for subjects to understand. This measure has several advantages over other means of measuring risk preferences. The use of only 50/50 gambles is designed to keep the task as simple as possible; expected payoffs are easy to calculate, and expected payoff is linear in risk, measured as the standard deviation of payoffs. The increase in variance associated with an increase in expected value is high enough to get subjects’ attention. Although we present subjects with only five alternatives, we nevertheless find considerable heterogeneity in choices.

The advantage of this measure of risk preferences is its simplicity, focusing on expected returns and variance. It should be noted that in opting for simplicity we forgo the ability to address some of the broader aspects of risk addressed in financial economics (see, for example, Alderfer and Bierman, 1970, Harvey and Siddique, 2000, Kraus and Litzenberger, 1976, and Moskowitz and Vissing-Jørgensen, 2002). For example, neither our measure nor other risk reference–revelation mechanisms currently in use are able to address preferences over skewness, which various studies have shown to be favored by gamblers and investors (see, respectively, Garrett and Sobel, 1999 and Åstebro, 2003).

Several additional measures have received recent attention, and it is worthwhile to compare our instrument with those. Our measure is most similar to that developed by Binswanger, 1980, Binswanger, 1981 for use in rural India. He asks subjects to make binary choices between pairs of 50/50 gambles. As with our measure, gains in expected value can be had only with an increase in risk (standard deviation). His choice set is somewhat more extensive, and includes two dominated lotteries. Within the undominated gambles, expected payment has a nonlinear (convex) relationship to risk. In Binswanger (1981) he evaluates the implications of his data for utility theory.²

Holt and Laury (2002) also use a lottery-choice task. In their mechanism subjects make multiple choices between pairs of lotteries that vary in risk and return. This mechanism imposes a finer grid on the subjects’ decisions, and thus produces a more refined estimate of the relevant utility function parameters. However, this comes at a cost of increased complexity, which may lead to errors. Harbaugh et al. (2007) find different patterns of errors depending on whether subjects are presented with valuation or choice tasks, suggesting that failing to account for errors may significantly bias estimated risk preference parameters in ways that are task-dependent.

Ours is the simplest possible task we could design that would give sufficient heterogeneity in choices and at the same time minimize errors. Its simplicity means that it can also be used to assess one person's perceptions of another's risk attitudes. Thus we can use this measure to examine stereotyping in the evaluation of other's risk preferences, a factor that can come into play in negotiations or in situations where an “expert” gives advice to uninformed persons about their possible choices. Financial advisors, for example, routinely tailor their investment advice to perceptions of the client's risk attitudes. In this paper we illustrate the use of our risk measure by comparing the risk attitudes and stereotypes about risk attitudes of women and men.

Each subject chooses a most-preferred gamble and also predicts which of the five gambles each of the other subjects in her session choose for themselves. Our design includes three decision environments: an abstract gamble frame with and without the possibility of losses, and an investment frame with losses, which are explained below. Subjects also complete a commonly-used psychological instrument, the Zuckerman Sensation-Seeking Scale (Zuckerman, 1979, Zuckerman, 1994) for assessing risk preferences. Across all three decision environments, we find a significant sex difference in risk aversion. In addition, both women and men predict greater risk aversion for women. The pattern of errors in forecasts suggests differences in the way women and men perceive each others’ preferences.