Pure higher-order effects in the portfolio choice model

Abstract

This paper examines the e¤ects of higher-order risk attitudes and statistical moments on the optimal allocation of risky assets within the standard portfolio choice model. We derive the expressions for the optimal proportion of wealth invested in the risky asset to show they are functions of portfolio returns third-and fourth-order moments as well as on the investor's risk preferences of prudence and temperance. We illustrate the relative importance that the introduction of those higher-order e¤ects have in the decision of expected utility maximizers using data for the US.JEL classi…cation: C14, G11.

How the Investor’s Risk Preferences Influence the Optimal Allocation in a Credibilistic Portfolio Problem

“…Papers [5], [6] propose solutions in which the Arrow-Pratt index r u , the prudence index P u [7] and the first three moments appear. A form of the solution depending on the first four moments and the indices of risk aversion, prudence and temperance has been proved in [9]. Finally, in [10] we find another form of the solution depending on the first four moments.…”

The Effect of Prudence on the Optimal Allocation in Possibilistic and Mixed Models

“…The following result gives us an approximate expression of α(k): This result can be seen as a possibilistic version of the formula (A.6) of [10], which gives us the optimal allocation of investment in the context of a probabilistic portfolio choice model.…”

“…The approach from [6][7][8] led to forms of the approximate solution which depend on the first three moments, the Arrow-Pratt index r u , and the prudence index P u [9]. The solution found in [10] is expressed according to the first four moments and the indicators of risk aversion, prudence, and temperance of the utility function. Another form of the solution in which the first four moments appear can be found in [11].…”

“…The return of the risky asset is here a fuzzy number, while in [10] it is a random variable. The total utility function of the model is written as a possibilistic expected value.…”

A Portfolio Choice Problem in the Framework of Expected Utility Operators

“…Using Taylor-type approximations, various forms of approximate solutions have been found with respect to two classes of parameters: indicators of the investor's risk performance (absolute risk aversion, prudence, temperance, etc.) and various moments of the return of the risky asset (see [2], [8], [14], [26], [33]).…”