Working with the Wrong Tools

Abstract

Since the 1870s, six innovations have developed and shaped what we know today as Theory of Finance. They are also the basis of fundamental investing fallacies. These are the use of differential analysis, the use of general equilibrium theory, the use of probability theory, the (corruption of the) concept of liquidity, the misunderstanding of sovereign risk and, lastly, systemic risk. All six fallacies are discussed in this chapter.

Appendix

Aesthetics in Infinitesimal Analysis

There is a final aspect of the assumption of continuity in Finance and it is aesthetic. Aesthetics plays a defining role in human behaviour and the Theory of Finance is no exception. Under continuity, compound interest can be expressed as:

$$ {\mathrm{e}}^{rt} $$

Since logarithmic functions are monotonic,⁴⁶ the logarithmic transformation of compound interest comes in handy for regression analysis and results in:

$$ \ln \left({\mathrm{e}}^{rt}\right)={r}^{\ast }t $$

One of the many examples that illustrates this aesthetic use of continuous functions in Finance is the Stochastic Portfolio Theory. In their 2008 paper, “Stochastic Portfolio Theory: An Overview”, Fernholz and Karatzas begin with this basic financial market model:

$$ \mathrm{d}B(t)=B(t)r(t)\ \mathrm{d}t,B(0)=1 $$

The equation above describes a money-market B(·) and stocks, whose prices are driven following a Brownian motion process and a “flow of information” F, where:

$$ F=\left\{F(t)\right\}\kern0.28em 0\le t<\infty $$

Could also be a “filtration” process generated by Brownian motion. Whoever relies a financial analysis on such a model is making the assumption one can earn a return without any jumps, continually, throughout time, and apparently at no cost. The other assumptions, at least, are consistent, because if one is to believe that stocks, which are the legal title to the cash flows produced by real companies, behave completely in a random way, one has to believe too that the information regarding such a market environment is given randomly too and at no cost. This is of course the farthest from reality one can remove oneself, because it is precisely the complete absence of cost-free information and the necessity to produce it or to discover it (in other words, the negation of all the above assumptions) what makes the essence of the entrepreneurial activity and, by transitivity, is reflected in the price of the securities that represent a title on it, namely, stocks. In other words, if economic information was free and its production was random, there would be no need for entrepreneurs or for property titles on their achievements. There would be no need for securities. How any of these portfolio theories have resisted the test of time and experience escapes me. They are however the intellectual foundation for the management of collective pools of savings.

Aesthetics in General Equilibrium Theory

The history of science is full of cases where aesthetics or a singular ideal of beauty played an important role. In Ancient Greece, philosophers were attracted to ideal shapes. In Astronomy, the beauty of the circle led astronomers to believe in circular orbits, which blinded this science until Kepler rediscovered the math behind elliptical orbits. In Economics and Finance, static analysis and the ideal of general equilibrium represent one of such cases, and are well alive to this date.⁴⁷ In the words of Fritz Machlup:

[W]e may define equilibrium, in economic analysis, as a constellation of selected interrelated variables so adjusted to one another that no inherent tendency to change prevails in the model which they constitute.

Equilibrium analysis is an intellectual exercise of dubious utility. To begin, if “no inherent tendency to change prevails” in equilibrium, any Finance practitioner using general equilibrium models is simply ignoring the omnipresent feature that drives value: Change. Also, if time exists (under dynamic equilibrium models), it has a physical not an economic dimension. In this sense, variables within a dynamic equilibrium model are “predestined”, and therefore, no further knowledge is gained by solving dynamic equations.⁴⁸ For instance, take the equation:

$$ Y={x}^{\ast }t+1 $$

Where t is the time variable within the group of whole numbers (i.e. 0, 1, 2…n)

The triplet (1, 2, 3) for (x, t, y) belongs to the group of infinite solutions for this equation, as 1*2+1 = 3. But the triplet (30, 2, 61) also belongs to the universe of possible solutions. The triplet (30, 2, 61) or (35, 3, 106) is already “predestined”; they are simultaneously implied in the equation and are no more valid than the triplet (1, 2, 3). Yet, when in dynamic equilibrium models the t variable is attributed to time, it is believed that further insight can be gained by solving it. This is particularly so in the field of valuation of securities. Equity research analysts, with their dynamic models and respective assumptions, want to project the image of a method, a science that stands out for adding value by discovering where capital is misallocated and constitutes an investment opportunity. But this is an illusion.

What made general equilibrium models so attractive and popular? Firstly, from an analytical perspective, the models allow for optimal states. Every ambitious politician that believes in central planning loves the idea of “optimizing” to make our society more efficient (according to their own criteria, of course). Secondly, general equilibrium models can be run using simple algebra. They are comfortable to work with.

Between 1874 and 1877, the works of Léon Walras surfaced the idea of general equilibrium in Economics. In 1874, Walras published Éléments d’économie politique pure, ou théorie de la richesse sociale, while he taught in Lausanne. His work examined the conditions necessary to reach equilibrium in an economic system, based on a system of simultaneous equations. As this is a book about Finance, not Economics, I cannot be exhaustive and therefore fair to M. Walras.

Plainly speaking, it is understood that a market x is in equilibrium when there is neither an excess of supply or demand.

$$ Sx- Dx=0\ \left(i.e.\kern0.5em Supply\ of\kern0.28em x- Demand\ of\kern0.28em x\right)=0 $$

General equilibrium in an economic system with (n+1) markets implies that if the first n markets are in equilibrium, the last market, n+1, must be in equilibrium as well. Suppose that there were only three markets: If two of them are in equilibrium, the third (i.e. last) will also have to be in equilibrium. Formally:

$$ \left( Sx- Dx\right)+\left( Sy- Dy\right)+\left( Sz- Dz\right)=0 $$

If Sx − Dx = 0 (market x is in equilibrium), and Sy − Dy = 0, then:

$$ Sz- Dz=0 $$

This conclusion is known as the Walras’ Law and it goes to show that it is not necessary that all markets be balanced (i.e. in equilibrium). Only in the particular case of the Walras’ Law, where the n markets show no excess of either demand or supply, will the last one, market (n+1), be balanced too.

There are relevant conceptual errors derived from using general equilibrium models. This mechanistic view demands that we ignore the role of entrepreneurship, precisely when entrepreneurs are the engine behind markets. It also assumes that markets are given and static entities. And it leaves no room to include a theory of prices. To the mainstream Finance practitioner, markets can be described as mathematical finite spaces. But markets are coordination processes. It is entrepreneurs who do the coordination, and in so doing, they develop markets. As I discuss later, it is the entrepreneurs who create, who issue equity or debt and thereby choose a particular capital structure with unique voting control features, design their marketing strategies, take risks and, last but not least, have insider information that the outsider investor doesn’t. Once more, the proof that the idea of equilibrium is foreign to the market process is that the relentless changes effected by entrepreneurs and consumers (every individual is simultaneously a consumer and an entrepreneur) in their selection of means and ends require that we use an institution, that is, money. In a world of general equilibrium and continuity, there is no place for money and barter should be more efficient.

A Word on Indeterminacy

The idea of a general equilibrium brings the implicit recognition of the possibility of indetermination. General equilibrium is formally addressed through equations, whereby the interrelation of variables (as defined by Fritz Machlup above) is exposed. When one isolates a group of equations relevant to the problem examined, one speaks of a system of equations. In algebra, a system is indeterminate if there is more than one solution to it. For ease, let’s think of a one-equation system, where:

$$ y=x+4 $$

For the equation above, the number of solutions is infinite. We cannot say that the pair (2; 6) is more valid than (4; 8) to describe the system.

In 1949, economist Don Patinkin published a work titled The Indeterminacy of Absolute Prices in Classical Economic Theory.⁴⁹ Patinkin decisively demonstrated that under the Walrasian analysis, the absolute level of prices cannot be determined and that markets clear (i.e. supply meets demand) thanks to relative (not absolute) prices. In other words, in the Walrasian analysis, so rooted in today’s mainstream financial models, it is conceivable that multiple solutions solve a system formed by:

$$ \left(S1-D1\right),\left(S2-D1\right),\left(S3-D3\right)\dots ..\left( Sn- Dn\right) $$

But if indeterminate systems are conceivable from a mathematical point of view, indeterminate markets make no sense from an economic standpoint. However, the idea of indetermination is at the core of many contemporary events, like currency wars and currency coordination by central banks, or the use of structured finance products.

In the case of coordination among central banks, the system (USDCAD = 1.45, USDEUR = 1.09, USDJPY = 120…USDCHF= 1.0) is as valid and conceivable as (USDCAD = 1.25, USDEUR = 1.14, USDJPY = 125….USDCHF = 0.90), for instance. To most institutional investors, it is as valid to purchase gold certificates as it is to buy physical gold. The same can be said for those who buy an equity tranche in a structured vehicle, rather than comparable direct equity ownership in its underlying units. This indifference between economic reality and mathematic theory can only last as long as any hint of a physical, non-virtual, insurmountable obstacle is successfully removed from the system. One such hint is the gold market. Because its supply cannot be “printed”, the system:

$$ \left( Sgold- Dgold\right) $$

Remains outside the reach of central bankers. But in time, they learned to cope with this limitation, as I explain later.⁵⁰ They have done so by eliminating the redeemability of gold (from central banks) and allowing the ratio of paper to physical gold to escalate to unimaginable levels. The Walrasian analysis is the formal pillar on which a system where the inventory of paper gold is multiple times that of physical gold is sustainable.