Mean-Variance Preferences and Investor Behavior

Portfolio allocation and asset demand with mean-variance preferences

“…the marginal rate of substitution between σ and µ, which is the MV analogue of the Arrow-Pratt measure of absolute risk aversion (Lajeri and Nielsen 2000;Ormiston and Schlee 2001). From α we derive…”

“…Given that α is positive, ε µ > 0 is equivalent to α µ > 0, which reflects increasing absolute risk aversion (IARA; see Ormiston and Schlee, 2001). The first part of Proposition 2 then conveys that assets X and Z are substitutes (i.e., the investor will always reduce her exposure to a riskincreasing asset if the mean return to a risk-reducing asset increases) if and only if the investor's preferences display IARA.…”

“…2 While the decomposition into income and substitution effects clearly provides many insights into the motives that drive the properties of asset demand, it does not answer the potentially more relevant question for the types of risk preferences that lead to "clear" properties of asset demand functions, i.e., that decide which of the sides dominates in Tobin's "ubiquitous conflict". To the best of our knowledge only Ormiston and Schlee (2001) and Lajeri-Chaherli (2003) deal with these issues in a MV framework. For so-called standard portfolio problems (one safe and one risky asset), Ormiston and Schlee (2001) and Lajeri-Chaherli (2003) derive sufficient conditions (basically, the analogue to the EU-concept of decreasing absolute risk aversion) 1 In portfolio analyses, "mean-variance analysis" is often confined either to the search for mean-variance efficient portfolios or to the (implausible) case of separable utility functions that are linear in the expected value and the variance of final wealth.…”

“…To the best of our knowledge only Ormiston and Schlee (2001) and Lajeri-Chaherli (2003) deal with these issues in a MV framework. For so-called standard portfolio problems (one safe and one risky asset), Ormiston and Schlee (2001) and Lajeri-Chaherli (2003) derive sufficient conditions (basically, the analogue to the EU-concept of decreasing absolute risk aversion) 1 In portfolio analyses, "mean-variance analysis" is often confined either to the search for mean-variance efficient portfolios or to the (implausible) case of separable utility functions that are linear in the expected value and the variance of final wealth. For this paper, "mean-variance analysis" refers to the (constrained) maximization of utility functions that depend on the first two moments of the wealth distribution.…”

“…For the (not implausible) cases where problems of portfolio choice meet these restrictions (see Meyer and Rasche, 1992), MV analysis constitutes a perfect substitute for the EU approach. Generally, however, MV analysis should be interpreted as a genuine and insightful approach to decision making under risk that can stand on its own (Nielsen, 1990;Ormiston and Schlee, 2001). As such, it has experienced a recent renaissance in the theoretical literature (see Eichner, 2008, for an overview).…”