Marginal conditional stochastic dominance
Encyclopedia
In finance
, marginal conditional stochastic dominance is a condition under which a portfolio can be improved in the eyes of all risk-averse
investors by incrementally moving funds out of one asset (or one sub-group of the portfolio's assets) and into another. Each risk-averse investor is assumed to maximize the expected value of an increasing, concave von Neumann-Morgenstern utility function. All such investors prefer portfolio B over portfolio A if the portfolio return of B is second-order stochastically dominant
over that of A; roughly speaking this means that the density function of A's return can be formed from that of B's return by pushing some of the probability mass of B's return to the left (which is disliked by all increasing utility functions) and then spreading out some of the density mass (which is disliked by all concave utility functions).
If a portfolio A is marginally conditionally stochastically dominated by some incrementally different portfolio B, then it is said to be inefficient in the sense that it is not the optimal portfolio for anyone. Note that this context of portfolio optimization is not limited to situations in which mean-variance analysis
applies.
The presence of marginal conditional stochastic dominance is sufficient, but not necessary, for a portfolio to be inefficient. This is because marginal conditional stochastic dominance only considers incremental portfolio changes involving two sub-groups of assets — one whose holdings are decreased and one whose holdings are increased. It is possible for an inefficient portfolio to not be second-order stochastically dominated by any such one-for-one shift of funds, and yet to by dominated by a shift of funds involving three or more sub-groups of assets.
-based approach to testing for portfolio inefficiency which works even when the necessary conditional of marginal conditional stochastic dominance is not met. Other similar tests have also been developed.
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, marginal conditional stochastic dominance is a condition under which a portfolio can be improved in the eyes of all risk-averse
Risk aversion
Risk aversion is a concept in psychology, economics, and finance, based on the behavior of humans while exposed to uncertainty....
investors by incrementally moving funds out of one asset (or one sub-group of the portfolio's assets) and into another. Each risk-averse investor is assumed to maximize the expected value of an increasing, concave von Neumann-Morgenstern utility function. All such investors prefer portfolio B over portfolio A if the portfolio return of B is second-order stochastically dominant
Stochastic dominance
Stochastic dominance is a form of stochastic ordering. The term is used in decision theory and decision analysis to refer to situations where one gamble can be ranked as superior to another gamble. It is based on preferences regarding outcomes...
over that of A; roughly speaking this means that the density function of A's return can be formed from that of B's return by pushing some of the probability mass of B's return to the left (which is disliked by all increasing utility functions) and then spreading out some of the density mass (which is disliked by all concave utility functions).
If a portfolio A is marginally conditionally stochastically dominated by some incrementally different portfolio B, then it is said to be inefficient in the sense that it is not the optimal portfolio for anyone. Note that this context of portfolio optimization is not limited to situations in which mean-variance analysis
Modern portfolio theory
Modern portfolio theory is a theory of investment which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets...
applies.
The presence of marginal conditional stochastic dominance is sufficient, but not necessary, for a portfolio to be inefficient. This is because marginal conditional stochastic dominance only considers incremental portfolio changes involving two sub-groups of assets — one whose holdings are decreased and one whose holdings are increased. It is possible for an inefficient portfolio to not be second-order stochastically dominated by any such one-for-one shift of funds, and yet to by dominated by a shift of funds involving three or more sub-groups of assets.
Testing for marginal conditional stochastic dominance
Yitzhaki and Mayshar presented a linear programmingLinear programming
Linear programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model for some list of requirements represented as linear relationships...
-based approach to testing for portfolio inefficiency which works even when the necessary conditional of marginal conditional stochastic dominance is not met. Other similar tests have also been developed.