DECISION MAKERS AND RATIONALITY

2.1 DECISION MAKERS AND RATIONALITY

Should we invest in a given stock whose returns are hardly predictable? Should we buy an insurance contract in order to protect ourselves from theft? How much should we be willing to pay for such protection? Should we be rational and reach

a decision on the basis of what we know, or combine our prior and subjective assessment with the unfolding evidence? Further, do we have the ability to use a new stream of statistical news and trade intelligently? Or ‘bound’ our procedures? This occurs in many instances, for example, when problems are very complex, outpacing our capacity to analyse them, or when information is so overbearing or so limited that one must take an educated or at best an intuitive guess. In most cases, steps are to be taken to limit and ‘bound’ our decision processes for otherwise no decision can be reached in its proper time. These ‘bounds’ are varied and underlie theories of ‘bounded rationality’ based on the premise that we can only do the best we can and no better! However, when problems are well defined, when they are formulated properly – meaning that the alternatives are well-stated, the potential events well-established, and their conditional con- sequences (such as payoffs, costs, etc.) are determined, we can presume that a rational procedure to decision making can be followed. If, in addition, the uncer- tainties inherent in the problem are explicitly stated, a rational decision can be reached.

What are the types of objectives we may consider? Although there are several possibilities (as we shall see below) it is important to understand that no criterion is the objectively correct one to use. The choice is a matter of economic, individual and collective judgement – all of which may be imbued with psychological and behavioural traits. Utility theory, for example (to be seen in Chapter 3), provides an approach to the selection of a ‘criterion of choice’ which is both consistent and rational, making it possible to reconcile (albeit not always) a decision and its

Risk and Financial Management: Mathematical and Computational Methods. C. Tapiero C 2004 John Wiley & Sons, Ltd ISBN: 0-470-84908-8

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economic and risk justifications. It is often difficult to use, however, as we shall see later on for it requires parameters and an understanding of human decision making processes that might not be available.

To proceed rationally it is necessary for an individual decision-maker (an in- vestor for example) to reach a judgement about: the alternatives available, the sources of uncertainties, the conditional outcomes and preferences needed to order alternatives. Then, combine them without contradicting oneself (i.e. by being rational) in selecting the best course of action to follow. Further, to be ratio- nal it is necessary to be self-consistent in stating what we believe or are prepared to accept and then accept the consequences of our actions. Of course, it is possi- ble to be ‘too rational’. For example, a decision maker who refuses to accept any dubious measurements or assumptions will simply never make a decision! He then incurs the same consequences as being irrational. To be a practical investor, one must accept that there is a ‘bounded rationality’ and that an investment will in the end bear some risk one did not plan on assuming. This understanding is an essential motivation for financial risk management. That is, we can only be satisfied that we did the best possible analysis we could, given the time, the in- formation and the techniques available at the time the decision to invest (or not) was made. Appropriate rational decision-making approaches, whether these are based on theoretical and/or practical considerations, would thus recognize both our capacities and their limit.

2.1.1 The principles of rationality and bounded rationality

Underlying rationality is a number of assumptions that assume (Ariel Rubinstein, 1998):

r knowledge of the problem, r clear preferences, r an ability to optimize, r indifference to equivalent logical descriptions of alternative and choice sets.

Psychologists and economists have doubted these. The fact that decisions are not always rational does not mean that there are no underlying procedures to the decision-making process. A systematic approach to departures from rationality has been a topic of intense economic and psychological interest of particular importance in finance, emphasizing ‘what is’ rather than ‘what ought to be’.

For example, decision-makers often have a tendency to ‘throw good money after bad’, also known as sunk costs. Although it is irrational, it is often practised. Here are a few instances: Having paid for the movie, I will stay with it, even though it is a dreadful and time-consuming movie. An investment in a stock, even if it has failed repeatedly, may for some irrational reason generate a loyalty factor. The reason we are so biased in favour of bringing existing projects to fruition irrespective of their cost is that such behaviour is imbedded in our brains. We resist the conceptual change that the project is a failure and refuse to change our decision process to admit such failure. The problem is psychological: once we

21 have made an irreversible investment, we imbue it with extra value, the price of

DECISION MAKERS AND RATIONALITY

our emotional ‘ownership’. There are many variations of this phenomenon. One is the ‘endowment effect’ in which a person who is offered $10 000 for a painting

he paid only $1000 for refuses the generous offer. The premium he refuses is accounted for by his pride in an exceptionally good judgement—truly, perhaps the owner’s wild fantasy that make such a painting wildly expensive. Similarly, once committed to a bad project one becomes bound to its outcome. This is equivalent to an investor to being OTM (on the money) in a large futures position and not exercising it. Equivalently, it is an alignment, not bounded by limited responsibility, as would be the case for stock options traders; and therefore it leads to maintaining an irrational risky position.

Currently, psychology and behavioural studies focus on understanding and pre- dicting traders’ decisions, raising questions regarding markets’ efficiency (mean- ing: being both rational and making the best use of available information) and thereby raising doubts regarding the predictive power of economic theory. For ex- ample, aggregate individual behaviour leading to herding, black sheep syndrome, crowd psychology and the tragedy of the commons, is used to infuse a certain reality in theoretical analyses of financial markets and investors’ decisions. It is with such intentions that funds such as ABN AMRO Asset Management (a fund house out of Hong Kong) are proposing mutual investment funds based on ‘be- havioural finance principles’ (IHT Money Report, 24–25 February 2001, p. 14). These funds are based on the assumption that investors make decisions based on multiple factors, including a broad range of identifiable emotional and psycho- logical biases. This leads to market mechanisms that do not conform to or are not compatible with fundamental theory (as we shall see later on) and therefore, provide opportunities for profits when they can be properly apprehended. The emotional/psychological factors pointed out by the IHT article are numerous. ‘Investors’ mistakes are not due to a lack of information but because of mental shortcuts inherent in human decision-making that blinds investors. For example, investors overestimate their ability to forecast change and they inefficiently pro- cess new information. They also tend to hold on to bad positions rather than admit mistakes .’ In addition, image bias can keep investors in a stock even when this loyalty flies in the face of balance sheet fundamentals. Over-reaction to news can lead investors to dump stocks when there is no rational reason for doing so. Under-reaction is the effect of people’s general inability to admit mistakes. This is

a trait that is also encountered by analysts and fund managers as much as individ- ual investors. These factors are extremely important for they underlie financial practice and financial decision-making, drawing both on theoretical constructs and an appreciation of individual and collective (market) psychology. Thus, to construct a rational approach to making decisions, we can only claim to do the best we can and recognize that, however thorough our search, it is necessarily bounded.

Rationality is also a ‘bounded’ qualitative concept that is based on essen- tially three dimensions: analysis of information, perception of risk and decision- making. It may be defined and used in different ways. ‘Classical rationality’, underlying important economic and financial concepts such as ‘rational

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expectations’ and ‘risk-neutral pricing’ (we shall attend to this later on in great detail), suppose that the investor/decision maker uses all available information, perceives risk without bias and makes the best possible investment decision he can (given his ability to compute) with the information he possesses at the time the decision is made. By contrast, a ‘Bayesian rationality’, which underlies this chapter, has a philosophically different approach. Whereas ‘rational expectations’ supposes that an investor extrapolates from the available information the true dis- tribution of payoffs, Bayesian rationality supposes that we have a prior subjective distribution of payoffs that is updated through a learning mechanism with un- folding new information. Further, ‘rational expectations’ supposes that this prior or subjective distribution is the true one, imbedding future realizations while the Bayes approach supposes that the investor’s belief or prior distribution is indeed subjective but evolving through learning about the true distribution. These ‘dif- ferences of opinion’ have substantive impact on how we develop our approach to financial decision making and risk management. For ‘rational expectations’, the present is ‘the present of the future’ while Bayesian rationality incorporates learning from one’s bias (prejudice or misconception) into risk measurement and hence decision making, the bias being gradually removes uncertainty as learning sets in. In this chapter we shall focus our attention on Bayes decision making under uncertainty.