Several speakers pointed out that behavioral finance has no theory but a great deal of empirical evidence to indicate how investors actually make choices under conditions of uncertainty. Traditional finance has a lot of theories to explain how people should behave if they are rational.  Unfortunately, when these theories are tested empirically, they don't seem to hold water.  For example, Amos Tversky, one of the pioneers in this field, conducted investigations to determine how people made choices in a risk-return framework and found that their choices did not conform to axioms of choice described in expected utility theory. The most widely used utility function in finance is the quadratic utility function.shown in Figure 1.

Figure 1

The first half of the curve indicates that investors should be risk averse, their utility function curves downword as they incur losses.  However, beyond the mid-point, they also experience a disutility for gains.  This pathalogical behavior of hating an increase in wealth has long been a source of criticism, which led to the development of numerous other utility functions.  One of these was Peter Fishburn, who proposed a utility function that exhibited risk-averse behavior below some minimal acceptable return (MAR), but was risk neutral above the MAR.  In other words, investors should be risk-averse to losses but should not consider gains to be risky.   We have adopted the Fishburn utility function in our work at PRI..   Tversky found that investors actually had a utility function that resembled an S curve, as shown in Figure 2. Figure 2

  It is called prospect theory, but it is not a normative theory, i.e., it does not proport to explain how people should behave.  It is an operative theory that predicts how they will behave based on past experience. The S curve indicates investors are risk-averse for relatively small losses (close to the MAR) but are actually risk takers for large losses (bottom of the S).  If told they could lose a bundle investing in Indonesia they would gladley take on this high risk for the chance of moderate gains.  However, the S curve above the MAR shows they are also averse to very large gains.  Tversky pointed out that this behavior can lead to suboptimal results.

Why do people behave in this bizarre manner?  Werner De Bondt claimed people intend to be rational, but are limited to do so.  They have bounded rationality.  They do not have all the external information they need, and they have limited capacity to process the information they do have. 

Meir Statman said recent research shows investors seek upside potential with downside protection.  This view is echoed by Robert Olsen in the March 1998 FAJ who claimed investors seek consistency of returns as opposed to maximizing the expected return.  We believe this behavioral attitude can be incorporated in the Fishburn utility function and will be testing this in the coming year.

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