A General Measure of Risk with a Behavioral Foundation

We present a general measure of risk that is rooted in behavioral considerations about the way individuals value uncertain outcomes, and that fulfills fundamental requirements for prescriptive use. The psychological postulate is that, in contemplating a risky situation, individuals care about how they will come out relative to all prospective outcomes of the situation, not just a specific benchmark as is commonly assumed in measuring risk. Our model includes, or relates to, some classic measures of risk, such as the variance, Gini mean difference, or Fishburn's (1977) α-t, but it is distinct from the traditional families of risk measures. We provide necessary and sufficient conditions for the risk measure to satisfy first and second order stochastic dominance, two essential criteria for ordering prospects, thereby generalizing important results on the Gini risk measure. We also provide conditions for our risk measure to be a coherent or a convex risk measure, thus providing an alternative to other measures used for the management and regulation of risk. We show that the risk measure can produce both corner or interior solutions to the asset allocation problem, thus allowing more flexibility than traditional models. Finally, we obtain some evidence on the empirical form assumed by the risk measure by fitting it to experimental preference data.