Adequate Decision Rules for Portfolio Choice Problems

Hidden beneath its many facets and different aspects, veiled by inexhaustibly many contributions on all those different aspects, and obscured by a swarm of buzz words originating from the trading floors and back offices of the investment community, lies the plain core problem of portfolio choice theory: how to choose. Portfolio choice, or portfolio selection, is concerned with how much of a given wealth to devote to individual assets, that is, which weights to assign to each asset, that is, which portfolio to choose. Portfolio choice theory is thus nothing but an application of decision theory. It should be treated within this framework, unperturbed by all the buzzing.

Every investor faces a decision regarding which assets to choose for his or her portfolio. Portfolio choice theory is thus about making decisions, and an application of decision theory. It seems appropriate to treat portfolio choice problems as decisions that are to be made in an uncertain environment.

Portfolio choice problems have been shown to be special cases of decisions under Knightian risk. Investments are gambles, because the investments’ results, and the utility they provide, depend on the outcome of a chance experiment. If portfolio selection is a special case of decision theory, and if Debreu’s axioms are taken as valid, portfolio selection problems may be solved by applying decision rules. The decision rules that have, or have had, some importance in portfolio choice theory will now be characterised. They will be analysed in the following chapters.

Normative decision rules are commonly deemed reasonable for decisions under Knightian risk if and only if they comply with the EU principle and obey the EU principle’s definition of ‘rationality’. This convention has been criticised here. Normative ideals are but mere convictions on how individuals should make a decision, and convictions cannot be justified conclusively. Terms like ‘rationality’ and ‘plausibility’, frequently used to justify or refute specific decision rules, are empty phrases. Meaning is given to them solely by opinion. No arguments can be provided to make a decision rule accepted as ‘rational’ by any two people not sharing the same opinion on rationality, especially no reference to logic or to any framework deducible from it. Discussions on which decision rule should be accepted as ‘rational’ thus cannot reach any conclusion. Any decision rule may be labelled ‘rational’ and recommended. Judging decision rules by their congruence with the EU principle is thus futile. There is no reason to necessarily accept the EU principle as the yardstick for ‘rationality’.

As the preceding analyses show, any recommendation on how to select a portfolio must first be based on a thorough analysis of the decision situation at hand. This analysis must include three aspects: the general theoretical framework that is to be applied, the characteristics of the decision situation, and a statement on which results of the action should matter to the decision-making individual.