Satisficing Measures for Analysis of Risky Positions

Abstract

I n this work we introduce a class of measures for evaluating the quality of financial positions based on their ability to achieve desired financial goals. In the spirit of Simon (Simon, H. A. 1959. Theories of decisionmaking in economics and behavioral science. Amer. Econom. Rev. 49(3) 253-283), we call these measures satisficing measures and show that they are dual to classes of risk measures. This approach has the advantage that aspiration levels, either competing benchmarks or fixed targets, are often much more natural to specify than risk tolerance parameters. In addition, we propose a class of satisficing measures that reward diversification. Finding optimal portfolios for such satisficing measures is computationally tractable. Moreover, this class of satisficing measures has an ambiguity interpretation in terms of robust guarantees on the expected performance because the underlying distribution deviates from the investor's reference distribution. Finally, we show some promising results for our approach compared to traditional methods in a real-world portfolio problem against a competing benchmark.

Robust portfolios: contributions from operations research and finance

“…This robust technique has obtained prodigious success since the late 1990s, especially in the field of optimization and control with uncertainty parameters Nemirovski 1998, 1999;El Ghaoui and Lebret 1997;Goldfarb and Iyengar 2003a). With respect to portfolio selection, the major contributions have come in the 21st century (see, for example, Rustem et al 2000;Costa and Paiva 2002;Ben-Tal et al 2002;Goldfarb and Iyengar 2003b;El Ghaoui et al 2003;Tütüncü and Koenig 2004;Pinar and Tütüncü 2005;Lutgens and Schotman 2006;Natarajan et al 2009;Garlappi et al 2007;Pinar 2007;Calafiore 2007;Huang et al 2008;Natarajan et al 2008a;Brown and Sim 2008;Natarajan et al 2008b;Shen and Zhang 2008;Elliott and Siu 2008;Zhu and Fukushima 2008). For a complete discussion of robust portfolio management and the associated solution methods, see Fabozzi et al (2007), Föllmer et al (2008), and the references therein.…”

Aspirational Preferences and Their Representation by Risk Measures

“…This bias involves a switch between risk attitudes and therefore relies on a model that has both risk aversion and risk seeking. Lastly, Brown and Sim (2009) do not explore any descriptive implications, whereas here we do.…”

“…Although this paper builds upon Brown and Sim (2009), there are a number of important differences. First, Brown and Sim (2009) assume a given probability distribution and therefore cannot handle ambiguity; the AP model does not rely on a given probability distribution. Second, Brown and Sim explicitly enforce properties (which they call "attainment content" and "nonattainment apathy") relative to an exogenous target.…”

“…This can be important in applications. For instance, Brown and Sim (2009) discuss a debt management problem and mention that when the liabilities are too large, they cannot use satisficing measures to choose among investment strategies because all options have a net negative expected value and are indistinguishable in such a model. More recently, Chen and Long (2012) show that a decision bias in newsvendor problems (reported empirically in Schweitzer and Cachon 2000), which cannot be resolved by expected utility theory, can be explained by SAM.…”

Routing Optimization Under Uncertainty

“…It is a particular case of the satisficing measure proposed by Sim (2009) andBrown et al (2012) for evaluating uncertain monetary outcomes and has been applied in project selection by Hall et al (2014). We use the RV Index as an optimization criterion to formulate the problem as follows.…”