Models and Paradigms




Contents:

Models

In this work, we develop models designed to enable the Analyst to better counsel an Investor. Before embarking on this task, it is useful to consider the role of theory in practical affairs.

This work is concerned with theory. To understand a complex financial economy, one must begin with a simple one. All economic theory uses abstraction. Key elements of a process are investigated in the hope that resulting implications will help illuminate the issues being addressed. In effect, the financial economist builds a simplified model to help answer one or more questions. Not surprisingly, different questions may be addressed most effectively with different models.

Financial economics is concerned with the terms under which financial trades take place. Determining such terms is often called valuation. Financial economics is concerned with both the trades that people do make and those that they should make. Valuation and analysis of trades that are made fall in the domain of positive financial economics (analysis of what is). Analysis of trades that people should make falls in the domain of normative financial economics (analysis of what should be).

The ultimate test of a positive model is the consistency with reality of its implications concerning the questions asked. The ultimate test of a normative model is its ability to provide better outcomes in the areas for which it is intended.

Often financial economists assume that people make trades optimally, given certain assumed objectives. The implications of such behavior are then examined. In such cases, normative financial economics provides a base for positive financial economics.

It is useful to analyze situations in which (1) trades can be made without any cost and (2) a specific body of information is known to all members of a society. In such a world, there are no transactions costs and anyone can swap X for Y on the same terms as he or she can swap Y for X.

In the real world, this is rarely the case. Consider foreign exchange. One might be able to buy 1 franc for $0.21 but sell 1 franc for only $0.19. A currency dealer covers costs by bidding only $0.19 for a franc but asking $0.21. The bid-ask spread represents the cost of transacting. The average of the bid and ask prices (e.g. $0.20) approximates the price that might prevail in an idealized (transactions cost-free) world.

Financial institutions provide transactions services, broadly construed. To do business, such an institution must find a way to arrange a set of trades more efficiently than can those with whom it does business. To compete effectively, an institution must also do this at least as efficiently as other institutions.

Were there no transactions costs, there would be no financial institutions. Advances in communications, computation, and financial economics have greatly increased the competition among such institutions and provided accompanying decreases in transactions costs.

Paradigms

It would be convenient if every investment problem could best be analyzed with a model derived from a single overarching paradigm (pattern). For some issues, one paradigm will prove more practical; for other issues, another.

One useful classification of paradigms used in financial economics identifies major types, based on the treatment of time and outcomes. For each of these elements, one may consider discrete alternatives or a continuum of possibilities.

The most straightforward approach treats time and outcomes as discrete. For example, one identifies time period 0 (today), time period 1 (e.g. next year), time period 2 (two years hence), etc.. Each time period is associated with a limited number of possible outcomes. For example, good weather and bad weather; stocks rise 10%, rise 5%, fall 5%, fall 10%, etc.. The discrete time, discrete outcome approach is often termed the time-state paradigm or the Arrow- Debreu paradigm, after the two Nobel prize-winning authors who developed its basic characteristics.

A second approach retains the notion of discrete time, but treats outcomes as continuous. For example, at time 1 the stock market might be assumed to return any amount between -50% and +100%, with any intermediate value (such as 10.34123%) possible. To make such an approach feasible, Analysts generally characterize prospective outcomes using probability distributions. Thus the stock market might be assumed to offer a return characterized by a normal (bell-shaped) distribution with an expected value (mean) of 11% and a likely range (standard deviation) of 15%. Related to the standard deviation measure of risk is its square, the variance. The discrete time, continuous outcome approach is often termed the mean-variance paradigm or the Markowitz paradigm after the Nobel prize-winning author who proposed it and showed how it could be used in the investment process.

A combination involving continuous time and discrete outcomes makes little sense and hence is not utilized. However, considerable work in financial economics has utilized models in which both time and outcomes are assumed to be continuous. This is generally known as the continuous time paradigm.

In practice, the mean-variance approach is widely used in applications involving investment portfolios, and the continuous time approach in applications involving derivative contracts. Procedures deriving from the time-state approach are also widely used for the analyses of derivatives.

Continuous-time models are of substantial importance in financial economics, and especially so in theoretical work. However, the mathematical sophistication required for a full understanding of this approach is substantial. Fortunately, most of the key economic aspects of issues relevant to Investors can be understood as well or better using one or both of the alternative paradigms. From the viewpoint of the Analyst, the continuous time formulas of practical relevance can generally be regarded as limiting cases of related time-state formulations in which the number of time periods becomes very large and the length of each period very small; we generally present them as such, without detailed discussion of the limiting process.

The time-state paradigm provides considerable generality, yet its understanding requires little in the way of mathematical sophistication. We rely on it heavily when establishing principles concerning the key economic relationships that should be fully understood by the Analyst. The mean-variance paradigm is more limited in scope, but is well-suited for applications in which numeric values must be estimated in order for investment decisions to be made appropriately. Accordingly, we will devote a great deal of attention to it as well.

Philosophically, one may consider mean-variance approaches as special cases of time-state approaches in which the number of possible states of the world is very large and can only be practically dealt with using summary measures based on probabilities. Given this view, it is important to begin with time-state formulations, then move to mean-variance approaches.

Plan of the Work

Skillful Macro Investment Analysis requires an understanding of many aspects of Financial Economics and an ability to apply a wide range of techniques. Organization of the requisite body of material is not a simple task.

We have chosen an arrangement built on major themes, with an understanding that the reader who fails to proceed in sequence does so at his or her peril.

The title of each section is deceptively short -- an alternative that seems preferable to the usual long list of subjects separated by the usual sets of colons and semicolons. Be forewarned, however, that subjects often appear in unexpected places and that some issues are treated in increasing detail in two or more places.