which of the following functions is a key element of prospect theory
Answers
Prospect theory replaces the utility function u(·) over states of wealth with a value function v(·) over gains and losses relative to a reference point, with v(0)=0. According to prospect theory, the value function v(·) exhibits the psychophysics of diminishing sensitivity. That is, the marginal impact of a change in value diminishes with the distance from a relevant reference point. For monetary outcomes, the status quo generally serves as the reference point distinguishing losses from gains, so that the function is concave for gains and convex for losses (see Figure 11.2a). Concavity for gains contributes to risk aversion for gains, as with the standard utility function (Figure 11.1). Convexity for losses, on the other hand, contributes to risk seeking for losses. For instance, the disvalue of losing $50 is more than half the disvalue of losing $100, which will contribute to a preference for the gamble over the sure loss. This tendency to be risk averse for moderate-probability gains and risk seeking for moderate-probability losses may contribute to the “disposition effect,” in which investors have a greater tendency to sell stocks in their portfolios that have risen rather than fallen since purchase (Odean, 1998; but see also Barberis and Xiong, 2006).
The prospect theory value function is steeper for losses than gains – a property known as loss aversion. People typically require more compensation to give up a possession than they would have been willing to pay to obtain it in the first place (see, for example, Kahneman et al., 1990). In the context of decision under risk, loss aversion gives rise to risk aversion for mixed (gain–loss) gambles so that, for example, people typically reject a gamble that offers a .5 chance of gaining $100 and a .5 chance of losing $100, and require at least twice as much “upside” as “downside” to accept such gambles (see Table 11.2b). In fact, Rabin (2000) showed that a concave utility function over states of wealth cannot explain the normal range of risk aversion for mixed gambles, because this implies that a decision maker who is mildly risk averse for small-stakes gambles over a range of states of wealth must be unreasonably risk averse for large-stakes gambles. This tendency to be risk averse for mixed prospects has been used by Benartzi and Thaler (1995) to explain why investors require a large premium to invest in stocks rather than bonds (the “equity premium puzzle”): because of the higher volatility of stocks than bonds, investors who frequently check their returns are more likely to experience a loss in nominal value of their portfolios if they are invested in stocks than bonds (see also Barberis et al., 2001).
It is important to note that loss aversion, which gives rise to risk aversion for mixed (gain–loss) prospects (e.g., most people reject a 50–50 chance to gain $100 or lose $100) should be distinguished from convexity of the value function for losses, which gives rise to risk-seeking for pure loss prospects (e.g., most people prefer a 50–50 chance to lose $100 or nothing, to losing $50 for sure).