Essays on modern portfolio theory and decision making under risk
Samartzis, George K.
KeywordsΣύγχρονη θεωρία χαρτοφυακίου ; Κριτήρια στοχαστικής κυριαρχίας ; Κρίτηριο Markowitz ; Βαθμός απόλυτης αποστροφής κινδύνου ; Βαθμός σχετικής αποστροφής κινδύνου
Two fundamental questions of particular concern to the economists are: (i) how an economic unit (decision maker or investor) makes its decisions, and (ii) the "risk" tolerance that the economic unit has. In 1944, Von Neumann - Morgenstern founded the Theory of Decision Making under Risk. This theory studies how an economic unit chooses between different lotteries (random variables). In contrast to Decision Making under uncertainty, under "risk" an economic unit knows the objective probabilities of the lotteries. This means that every economic unit faces the same odds and there is no disagreement between the economic units about how likely each lottery event is. Thus, the uncertainty in this context is objectively calculable and is therefore called "risk". The main assumption that the objective probabilities of lotteries are known leads to the Von Neumann - Morgenstern Representation Theorem. The Theorem proves that under "risk", every rational economic unit wishes to maximize its expected utility. However, the utilization of this Theorem, as it stands, presupposes the exact knowledge of the utility function. The various Stochastic Dominance Criteria, as defined in the framework of the Representation Theorem, circumvent this obstacle. They do this by each time setting a rule between the cumulative distributions of two lotteries which should be used by a particular set of investors wishing to maximize their expected utility. A product of the Von Neumann - Morgenstern Representation Theorem is the Modern Portfolio Theory, which was founded by Markowitz in 1952. The main feature of this Theory is that under specific assumptions, the utility function of an investor depends exclusively on the mean and the variance a lottery. This means that the Criterion used by a risk-averse investor who wishes to maximize his expected utility relies solely on the relationships between the means and variances of two lotteries. Once the appropriate Decision Criterion has been identified for a decision maker, the next step is to study his degree of "risk" aversion. In this regard, Arrow - Pratt (1964,1965) define measures of the degree of absolute and relative risk aversion of an investor. These measures essentially study how a decision maker's degree of risk aversion changes with respect to different levels of wealth. The purpose of this doctoral thesis is divided into three parts. First, to examine and evaluate the various theoretical and empirical findings arising from already existing research works in the framework of the Modern Portfolio Theory and more generally of the Theory of Decision Making under Risk. Then, to answer important questions that either the literature has ignored, or the answers given to them are in doubt. And finally, to propose some new methods which contribute to the study and interpretation of the behavior of investors under risk.