And with this rate hanging in the air, how are
capitalists
to compute an asset's 'true' present value?
Nitzan Bichler - 2012 - Capital as Power
Fluctuations in hype can be several times larger than the growth of actual earnings, so everything else being equal, a dollar invested in changing earning expectations could yield a return far greater than a dollar spent on increasing the earnings themselves.
Pressed to the wall, mainstream finance responded to these anomalies by opening the door to various theories of 'irrationality' - from Herbert Simon's 'bounded rationality' (1955; 1979), through Daniel Ellsberg's 'ambiguity aversion' (1961), to Daniel Kahneman and Amos Tversky's 'prospect theory' (1979), to Richard Thaler's broader delineation of 'behavioural finance' (De Bondt and Thaler 1985). These explanations, though, remain safely within the consensus. Like their orthodox counterparts, they too focus on the powerless individual who passively responds to given circumstances. Unlike his nineteenth-century predecessor, this 'agent' is admittedly imperfect. He is no longer fully informed and totally consistent, he tends to harbour strange preferences and peculiar notions of utility (and may even substitute 'satis- ficing' for 'maximizing'), and he sometimes lets his mood cloud his better judgement.
These deviations, argue their theorists, fly in the face of market efficiency: they show that irrational hype can both exist and persist. But that conclusion, the theorists are quick to add, does not bring the world to an end. As noted in Chapter 10, individual irrationality, no matter how rampant, is assumed to be bounded and therefore predictable. And since predictable processes, no matter how irrational, can be modelled, the theorists can happily keep their jobs.
Of course, what the models cannot tell us (and the financial modellers are careful never to ask) is how these various 'irrationalities' are being shaped, by whom, to what ends and with what consequences. These aspects of capital accumulation have nothing to do with material technology and individual utility. They are matters of organized power. And on this subject, finance theorists and capitalist insiders are understandably tight-lipped. The only way to find out is to develop a radical political economy of hype independent of both.
The discount rate
If putting a number on future income and wealth seems difficult, knowing how much to trust one's prediction is next to impossible - or, at least that is how it was for much of human history. When Croesus, the fabulously rich king of Lydia, asked Solon of Athens if 'ever he had known a happier man than he', the latter refused to be impressed by the monarch's present wealth:
Elementary particles 197
The gods, O king, have given the Greeks all other gifts in moderate degree; and so our wisdom, too, is a cheerful and a homely, not a noble and kingly wisdom; and this, observing the numerous misfortunes that attend all conditions, forbids us to grow insolent upon our present enjoy- ments, or to admire any man's happiness that may yet, in course of time, suffer change. For the uncertain future has yet to come, with every possible variety of fortune; and him only to whom the divinity has continued happiness unto the end, we call happy; to salute as happy one that is still in the midst of life and hazard, we think as little safe and conclusive as to crown and proclaim as victorious the wrestler that is yet in the ring.
(Plutarch 1859, Vol. 1: 196-97, emphasis added)
Solon's caution was not unfounded, for in due course the hubristic Croesus lost his son, wife and kingdom. And in this respect, we can say that little has changed. The future is still uncertain, but the capitalist rulers, like their royal predecessors, continue to convince themselves that somehow they can circum- vent this uncertainty. The main difference is in the methods they use. In pre-capitalist times uncertainty was mitigated by the soothing words of astrologists and prophets, whereas nowadays the job is delegated to the oracles of probability and statistics.
Capitalist uncertainty is built right into the discounting formula. To see why, recall our derivation of this formula in Equations (1) to (6) in Chapter 9. We started by defining the rate of return (r) as the ratio of the known earnings stream (E) to the known dollar value of the invested capital (K), such that r = E/K. The expression is straightforward. It has one equation, one unknown and an obvious solution. Next, we rearranged the equation. Since the rate of interest can be calculated on the basis of the earnings and the original invest- ment, it follows that the original investment can be calculated based on the rate of return and the earnings, so that K = E/r. The result is the discount formula, the social habit of thinking with which capitalists began pricing their capital in the fourteenth century.
Mathematically, the two formulations seem identical, if not circular (recall the Cambridge Controversy). But in reality there is a big difference between them. The first expression is ex post. It computes the realized rate of return based on knowing both the initial investment and the subsequent earnings. The second expression is ex ante. It calculates the present value of capital based on the future magnitude of earnings. These future earnings, however, cannot be known in advance. Furthermore, since capitalists do not know their future earnings, they cannot know the rate of return these earnings will eventually represent. Analytically, then, they are faced with the seemingly impossible task of solving one equation with three unknowns.
In practice, of course, that is rarely a problem. Capitalists simply conjure up two of the unknown numbers and use them to compute the third. The question for us is how they do it and what the process means for accumula-
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tion. The previous section took us through the first step: predicting future earnings. As we saw, these predictions are always wrong. But we also learned that the errors are not unbounded, and that, over a sufficiently long period of time, the estimates tend to oscillate around the actual numbers. The second step, to which we now turn, is articulating the discount rate - the rate that the asset is expected to yield with the forecasted earnings. And it turns out that the two steps are intimately connected. The discount rate mirrors the confi- dence fortunetelling capitalists have in their own forecasts: the greater their uncertainty, the higher the discount rate - and vice versa.
The normal and the risky
What is the 'proper' discount rate? The answer has a very long history, dating back to Mesopotamia in the third millennium BCE (a topic to which we return in the next chapter). 12 Conceptually, the computation has always involved two components: a 'benchmark' rate plus a 'deviation'. The meaning of these two components, though, has changed markedly over time.
Until the emergence of capitalization in the fourteenth century, both components were seen as a matter of state decree, sanctioned by religion and tradition, and modified by necessity. The nobility and clergy set the just lending rates as well as the tolerated zone of private divergence, and they often kept them fixed for very long periods of time (Hudson 2000a, 2000b).
Neoclassicists never tire of denying this 'societal' determination. Scratch the pre-capitalist surface, they insist, and underneath you will find the eternal laws of economics. From the ancient civilizations and early empires, to the feudal world, to our own day and age, the underlying logic has always been the same: the productivity of capital determines the 'normal' rate of return, and the uncertainty of markets determines the 'deviations' from that normal.
This confidence seems unwarranted. We have already seen that the neoclassical theory of profit is problematic, to put it politely. But even if the theory were true to the letter, it would still be difficult to fathom how its purely capitalist concepts could possibly come to bear on a pre-capitalist discount rate. First, prior to the emergence of capitalization in the fourteenth century the productivity doctrine was not simply unknown; it was unthink- able. Second, there were no theoretical tools to conceive, let alone quantify, uncertainty. And, finally, there were no systematic data on either produc- tivity or uncertainty to make sense of it all. In this total blackout, how could anyone calculate the so-called 'economic' discount rate?
12 There is considerable recent literature on the ancient origins of interest, debt and money. These contrarian writings, partly inspired by the work of Mitchell-Innes (1913; 1914), critique the undue imposition of neoclassical logic on pre-capitalist societies and instead emphasize a broader set of political, religious and cultural determinants. Important collec- tions include Hudson and Van de Mieroop (2002), Hudson and Wunsch (2004), Ingham (2004) and Wray (2004).
? Probability and statistics
These concepts have become meaningful only since the Renaissance. The turning point occurred in the seventeenth century, with the twin invention of probability and statistics. 13 In France, Blaise Pascal and Pierre de Ferma, mesmerized by the abiding logic of a game of chance, began to articulate the mathematical law of bourgeois morality. Probability was justice. In the words of Pascal, 'the rule determining that which will belong to them [the players] will be proportional to that which they had the right to expect from fortune. . . [T]his just distribution is known as the division' (cited in Bernstein 1996: 67, emphases added). 14
At about the same time, Englishmen John Graunt, William Petty and Edmund Halley took the first steps in defining the field of practical statistics. The term itself connotes the original goal: to collect, classify and analyse facts bearing on matters of state. And indeed, Graunt, whose 1662 estimate of the population of London launched the scientific art of sampling, was very much attuned to the administrative needs of the emerging capitalist order. His prac- tical language would have been music to the ears of today's chief executives and finance ministers:
It may be now asked, to what purpose tends all this laborious buzzling and groping? . . . I Answer. . . That whereas the Art of Governing, and the true Politiques, is how to preserve the Subject in Peace, and Plenty, that men study onely that part of it, which teacheth how to supplant, and over-reach one another, and how, not by fair out-running, but by trip- ping up each other's heels, to win the Prize. Now, the Foundation, or Elements of this honest harmless Policy is to understand the Land, and the hands of the Territory to be governed, according to all their intrin- sick, and accidental differences. . . . It is no less necessary to know how many people there be of each Sex, State, Age, Religious, Trade Rank, or Degree, &c. by the knowing whereof Trade and Government may be made more certain, and Regular; for, if men know the People as afore- said, they might know the consumption they would make, so as Trade might not be hoped for where it is impossible.
(Graunt 1662: 72-73, original emphases)
Although initially independent, probability and statistics were quickly inter- twined, and in more than one way. The new order of capitalism unleashed multiple dynamics that amplified social uncertainty. Instead of the stable and
13 The social history of these related disciplines is told in Hacking (1975; 1990) and Bernstein (1996). Our account here draws partly on their works.
14 Probability theory in fact was developed a century earlier, by the Italian mathematician Girolamo Cardano. His work, however, was ahead of the times and therefore largely ignored.
Elementary particles 199
? 200 Capitalization
clear hierarchies of feudalism came a new ethic of autonomous individualism and invisible market forces. The slow cycle of agriculture gave rise to bustling industrial cities and rapidly growing populations. The relatively simple struc- tures of personal loyalty succumbed to the impersonal roller coaster of accumulation and the complex imperatives of government finances and regulations. More and more processes seemed in flux. But then, with every- thing constantly changing, how could one tell fact from fiction? What was the yardstick for truth on the path to societal happiness and personal wealth?
The very same difficulty besieged the new sciences of nature. In every field, from astronomy and physics to chemistry and biology, there was an explo- sion of measurement. But the measurements rarely turned out to be the same - so where was truth? With so many 'inaccuracies', how could one pin down the ultimate laws of nature?
The solution, in both society and science, came from marrying logical probability with empirical statistics. According to this solution, truth is hidden in the actual statistical facts, and probability theory is the special prism through which the scientist can see it. Any one measurement may be in error. But when the errors are random they tend to cancel each other out, and if we increase the size of the sample we can get as close to the truth as we wish. Moreover, and crucially for our purpose here, probability theory can also tell us how wrong our pronouncement of truth is 'likely' to be. It tosses the al-zahr - Arabic for 'dice' - to reckon the hazards.
This marriage of logic and measurement changed the concept of the unknown, making it seem less intimidating. Of course, the fear is still very much there: 'Unless you are running scared all the time, you're gone', explains the quintessential forward-looking capitalist, Bill Gates (1994). But the unknown, having been mediated through probability and statistics, has become less mysterious and, in that sense, less menacing. For the first time in history, uncertainty has been given a shape: it has a 'distribution'. Probability and statistics draw a clear relationship between the 'normal' and the 'disper- sion' around it, between what is supposedly 'natural' and 'true' and what is 'distorted' and 'devious', between the rulers at the 'centre' and the rebels and radicals at the 'margins'. They translate the unknown into seemingly precise 'standard deviations', and by so doing give human beings a comforting 'measure of their ignorance'.
The effect of this newly found confidence has been nothing short of revo- lutionary. It has opened the door to massive advances in the natural sciences. Virtually every field - from geodesy and astronomy, to classical and quantum statistical mechanics, to the biostatistics of evolution and medicine - has been rewritten by the new technique. And the same has happened in political economy. Every aspect of capitalism - from insurance, to engineering, to production, salesmanship, finance, public management, weapon develop- ment, population control, health care, mass psychology, the media and education, to name a few - has been re-articulated and further developed to leverage the power of probability and statistics. The belief that one can at
Elementary particles 201
least sketch the unknown has encouraged social imitative and intellectual creativity. The sense of knowing the 'odds' has made it much easier to dare to take a risk.
Averting risk: the Bernoullian grip
For the running-scared capitalist, though, probability and statistics are a mere starting point. They pretend to give the odds - but the odds alone are still devoid of meaning. And that is where utilitarianism comes into the picture.
The issue can be illustrated with a simple example. Suppose Bill Gates considers acquiring one of two software companies, Civilsoft and Weaponsoft. Civilsoft sells in the open market and is a bit volatile. The analysts tell Gates that, in their view, it has a 50 per cent chance of generating annual earnings of $50 million and a 50 per cent chance of generating annual earnings of $150 million. Weaponsoft is different. It sells to the military and has recently managed to secure a long term contract with the U. S. Department of Defense. According to the analysts, it is certain to generate $100 million annually. Now, probability calculations make the two firms equally attractive: mathematically, both have expected annual earnings of $100. 15 And, so, if Gates believes his analysts he should be indifferent as to which of the two he should acquire.
Not so, argued Daniel Bernoulli (1738). In his seminal paper, published more than two centuries before Gates was born, he stipulated that the measurement of risk involves more than the mere statistical odds. It requires that we put a 'moral' judgement on the expected dollars and cents - a judge- ment that he insisted must be based on diminishing marginal utility.
According to this logic, Gates, like the rest of us, should contemplate not the expected dollar earnings the companies will generate, but the expected utility he will get from consuming those earnings. This modification makes a big difference. '[A]ny increase in wealth no matter how insignificant', wrote Bernoulli, 'will always result in an increase in utility which is inversely propor- tionate to the quantity of goods already possessed' (p. 25). So the first dollar Gates earns generates more utility than the second, the second more than the third, and so on all the way to the billionth dollar and beyond.
To illustrate the consequence of this stipulation, let us split the expected earnings into $50 million chunks and assume for simplicity that with dimin- ishing marginal utility the first chunk gives Gates 3,000 utils, the second 2,000 utils and the third 1,000 utils. With this assumption, the takeover targets no longer look equally attractive: the less risky Weaponsoft is expected to generate 5,000 utils, whereas the more volatile Civilsoft is likely to give only
15 Mathematically, the expected earnings of Civilsoft are: $50 million * 0. 5 + $150 million * 0. 5 = $100 million, the same as Weaponsoft's.
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4,500. 16 And since ultimately all Mr Gates cares about is hedonic consump- tion, it is better for him to acquire the military contractor. It is likely to give him 500 more utils per annum.
Finance theory has never managed to shake loose of the Bernoulli grip. His paper triggered a deluge of publications on risk, many of which modified and revised his original formulation. But most remain locked behind his three subjectivist tenets. First, risk ultimately is a personal matter. Second, attitude to risk is rooted in the individual's hedonic preferences. And third, because of diminishing marginal utility, most individuals tend to be risk averse. This grip keeps the risk analysis of contemporary capitalist power hostage to the eighteenth-century belief in individual utilitarianism.
The unknowable
Of course, most theorists of capitalism ignore power. So before continuing we should point out that Bernoulli's mechanical hedonism may be inappropriate for the study of risk quite apart from the absence of power. First, there is the question of the odds. Capitalists are concerned with the future, yet statistical estimates of probabilities can only be drawn from the past. This is a crucial mismatch. As David Hume's Treatise of Human Nature (1739) tells us, the mere fact that all past experiments have found water to boil at 100 degrees Celsius does not mean that the same will happen next time we put the kettle on the stove. Natural scientists have managed to assume this challenge away by stipulating the stability of natural laws (whether deterministic or stochastic), but this stipulation seems a bit stretched when applied to society.
The inherent difficulty of calculating the social odds was heightened during the first half of the twentieth century. The combined onslaught of revo- lutions, financial crises, a Great Depression and two world wars suggested that the problem was not merely one of assigning odds to possible outcomes, but of specifying what those outcomes might be in the first place.
According to Frank Knight (1921), risk calculations presuppose a known set of odds. But in society, the future contains an element of novelty, and novelty cannot be pre-assigned a probability: it is unique and therefore inher- ently uncertain. Even Keynes, whose belief in the existence of so-called objec- tive social probability survived the First World War, caved in after the Second. In matters of society, he confessed, the future is largely unknowable:
By 'uncertain' knowledge, let me explain, I do not mean merely to distin- guish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty; nor is the prospect of
16 For Weaponsoft, the expected utility is the sum of 3,000 utils for the first $50 million chunk and 2,000 utils for the second. For Civilsoft, the computation is: 3,000 utils * 0. 5 + (3,000 utils + 2,000 utils + 1,000 utils) * 0. 5.
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a Victory bond being drawn. Or, again, the expectation of life is only slightly uncertain. Even the weather is only moderately uncertain. The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention, or the position of private wealth-owners in the social system in 1970. About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know.
(Keynes 1937: 213-14, emphasis added)
And then there is the second problem. Even if we convince ourselves that the mathematical odds exist and that we can somehow know them, there is still the task of assigning to these odds utilitarian weights. Without these weights, there is no point talking about Bernoullian risk. Yet these weights, made up of utils, vary from person to person and from moment to moment, and this fluidity has implications. Any given asset must be seen as having not one, but many quantities of risk (as many as there are potential capitalists). Furthermore, the quantity of risk, being partly subjective, will change with preferences even if the so-called objective odds remain unaltered. This ever- shifting multiplicity makes it difficult to pin down the 'correct' risk premium and therefore to specify the 'proper' discount rate.
And with this rate hanging in the air, how are capitalists to compute an asset's 'true' present value?
The capital asset pricing model
These logical challenges proved no match for the capitalist nomos. Although investors may be unable to calculate risk on their own, they can ask the know- all market to do it for them. All they need is a bureaucratic blueprint disguised as theory, and Lord Keynes was prescient enough to anticipate what it would take to produce one. His checklist was short: (1) believe that the present odds are a reliable guide to future ones; (2) assume that other investors got those odds right; and (3) conclude that their relevant computations are already reflected in asset prices (Keynes 1937: 214). The instructions were simple enough, and when a year later Paul Samuelson (1938) announced that prices reveal to us what we desire but cannot express ('revealed preferences'), the road for an operational theory of risk was finally wide open.
The glory went to Harry Markowitz and William Sharpe. Markowitz (1952; 1959) gave investors a quantitative definition of risk and told them how to 'optimize' risk and return through diversification. Sharpe (1964), building on Markowitz's insight, showed capitalists how to tease out of the market the 'true' risk premium with which to discount their assets. These contributions closed the circle. The capitalization ritual was now fully articu- lated, and the two inventors went on to collect the Sveriges Prize in Economic Sciences in Memory of Alfred Nobel.
204 Capitalization
Portfolio selection
Markowitz's manuals focused on the Bernoullian individual: the risk-averse investor. In buying and selling financial assets, he said, 'the investor does (or should) consider expected return a desirable thing and variance of return an undesirable thing' (1952: 77, original emphasis). And the best method to achieve both goals, he concluded, is to diversify.
Although Markowitz himself spoke merely of the 'variance' of returns - defined as the squared deviation of the rate of price change from its own mean value - the term was quickly adopted as a synonym for risk. This in itself was a major achievement. Until Markowitz, there was no quantitative definition for risk, let alone one that everyone agreed on. 17 So the fact that he was able to galvanize the 'investment community' around this concept - even if he never intended to - is already worth a Nobel.
But Markowitz did much more than that. By showing why risk should be handled through diversification, he provided the justification for an old practice and helped underwrite the new trend of institutional investing. To illustrate his logic, consider a portfolio comprising different financial assets. If the market prices of these assets do not move completely in tandem (so that the correlations between their rates of change are less than 1), their unique fluctuations will partly offset one another. This partial offsetting has a great benefit: it causes the price volatility of the portfolio as a whole to be smaller than the average volatility of the individual assets. By owning a portfolio of different assets, therefore, the capitalist can enjoy their average return while suffering less than their average 'risk'. Diversification, it now seemed, offered an entirely free lunch.
Which portfolio should the capitalist own? Conceptually, it is possible to plot on a two-dimensional chart the return/variance attributes of all possible portfolios. Of these endless combinations, there is a subset that Markowitz identified as 'efficient'. These are the best deals. Each efficient portfolio offers the minimum variance for a given return - or, alternatively, the maximum return for a given variance. The only way to do better on one attribute is to give up on the other, and vice versa. Conveniently, all efficient portfolios lie on a well-defined 'efficient frontier', and the Bernoullian capitalist simply needs to pick the one that equilibrates her very own greed and fear.
A few years after Markowitz made his mark, James Tobin (1958) offered an even sweeter deal. If investors are able to borrow and lend at a 'risk-free' rate of interest (such as the rate on US T-bills) they can in fact outperform the efficient frontier. All it takes is two easy steps. First, they need to single out on the efficient frontier that particular portfolio (labelled M for convenience) which, when combined with borrowing or lending, yields the highest return
17 Ricciardi (2004) managed to collate a list of no less than 150 unique risk indicators - hardly an indication of unanimity.
? Elementary particles 205
for every level of volatility. And then they make their move. Those who are more risk averse can invest part of their money in M, putting the rest of it into risk-free assets (i. e. lending it to the central bank). And those who are less risk averse can borrow at the risk-free interest rate and invest the extra cash in additional units of M. Life has never been simpler.
CAPM
These guidelines, though, are still limited. Their target is the individual investor who already possesses definite expectations on return and variance and merely awaits instructions on how to diversify. The guidelines are silent, however, on how investors formed these expectations to begin with, and on the market consequences should they all follow the diversification advice. These latter questions were taken up by William Sharpe (1964) and John Lintner (1965) in their capital asset pricing model, or CAPM for short.
On the face of it, the questions seem unanswerable. Since individual inves- tors are assumed to be autonomous, their return/variance expectations are open-ended and can take any value whatsoever. And given that the expecta- tions are unbounded, the consequences of acting on them become unpredict- able. So Sharpe and Linter decided to simplify. What would happen, they asked, if all investors happened to share the same expectations regarding return and variance - and, moreover, if their expectations were the same as the true distribution of outcomes (i. e. if investors knew the stochastic generator of history)?
The scenario is admittedly odd. After all, what can one learn about uncer- tainty by assuming it away? Indeed, what would generate a future variance if all capitalists were the same and if all knew the future variance? Recall, however, that we are dealing here with the articulation of the capitalist nomos. The ultimate task is not to theorize capitalists, but to give them a bureaucratic blueprint. And if you revisit the previous section you will see that, in pursuing this goal, Sharpe and Linter were merely following Keynes' checklist.
And indeed, the answers they gave emerged directly from their assump- tions. If investors all see the world eye to eye, they will all own the same effi- cient portfolio M, and nothing but M. And since they all own only units of M, every owned stock in the market must be part of M. The only portfolio that satisfies these conditions is the market as a whole. So in Sharpe and Lintner's world, investors are fully diversified, each holding onto a propor- tion of the entire market.
Now, recall that diversification reduces volatility because the price move- ments of different assets partly offset each other. Why is the offsetting only partial? The reason is that price volatility is seen as stemming from two distinct sources: one that is unique to the asset itself, and another that is common to the market as a whole. A sufficiently diverse portfolio - which M obviously is - eliminates all unique volatility. Thus, following Sharpe and Lintner, portfolio investors can disregard all price volatility that is out of sync
206 Capitalization
with the market. But no matter how diverse their portfolio, they can never eliminate market volatility, by definition.
In other words, every asset carries in its genes a definite quantum of market volatility, a quantum which in turn is passed on to the portfolio as a whole. 'The risk of a well-diversified portfolio', declare Brealey, Myers and Allen in their Principles of Corporate Finance (2008: 193), 'depends on the market risk of the securities included in the portfolio'. This is not something one argues about: 'Tattoo that statement on your forehead if you can't remember it any other way', they warn. 'It is one of the most important ideas in this book'.
Conveniently, this logic is fully invertible. Since individual assets contri- bute to the market portfolio their own market risk, their contribution can be deduced from the market. Recall that unique risk has been diversified away, so the only thing that makes one asset more or less risky than another is its 'sensitivity' to the overall market. This sensitivity is called beta, and it can easily be measured, or so we are told. The greater the market risk of the asset, the higher beta - and vice versa. 18
Now, if the measured historical beta is equal to the 'true' timeless beta, as the CAPM proclaims, we can calculate the asset's risk premium. By defini- tion, beta expresses the ratio between, on the one hand, the 'excess' return of the asset over and above 'risk-free' assets (asset excess return = r -rrf) and, on the other hand, the 'excess' return of the market over and above 'risk-free' assets (market excess return = rm - rrf):
5. beta = r - rrf rm - rrf
Rearranging Equation (5), the capitalist can obtain the risk premium for the asset:
6. risk premium = r - rrf = beta (rm - rrf)
And, finally, with one more reshuffle, the overall discount rate (r):
7. r = rrf + beta (rm - rrf)
The first component on the right is the 'risk-free' benchmark (rrf), while the second component is the compensation for the asset's risky 'deviations' (beta (rm - rrf)).
18 Beta can be derived in two easy steps. First, assume that all investors consider historical volatility equal to 'true' volatility. Second, run a linear regression with the historical rate of change of the asset price as the dependent variable, and with a constant and the historical rate of change of the market price as the independent variables. Beta is the estimated slope coefficient of this regression.
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And that is pretty much it. All that the capitalist now has to do is take the 'risk-free' rate of interest (rrf), the market return (rm) and the estimated beta and plug them into Equation (7). And since all capitalists are assumed to be drones and therefore to do the very same maths with the very same numbers, they all end up with the same discount rate (r). 19 This number is then put into the denominator of the discount formula in Equations (3) and (4) to give the 'true' capitalized value of the asset.
Circularity
CAPM has been a smashing business success. Within a few decades, it has become the basis on which corporate finance courses are structured. Often, it is the only model that MBA students rehearse in some detail. And as the students turn into managers, executives and government officials, they apply what they learnt. In the early 1980s, less than one third of large US firms used the CAPM to compute the cost of equity. By the early 2000s, the proportion was well over 70 per cent, although, to be on the safe side, other formulae are used as well (Gitman and Mercurio 1982; Graham and Harvey 2001).
This success is all the more remarkable given the model's dismal empirical showing. Recall that Sharpe and Lintner assumed that investors know the 'true' variance of returns, and therefore also the 'true' beta - yet that, in prac- tice, they all take a shortcut and use the historical beta instead. No wonder the model crumbles.
First, there is the 'equity premium puzzle': it turns out that, taken as an asset class, equities outperform government bonds by much more than their extra volatility would demand (Mehra and Prescott 1985). And then the puzzle becomes embarrassing. Comparisons of different classes of equities often show returns to be uncorrelated and sometimes negatively correlated with beta values! 'The problems are serious enough', conclude efficient market theorists Fama and French, 'to invalidate most applications of the CAPM' (2004: 43).
Given these difficulties, the CAPM has been refurbished, extended and modified with new and improved techniques and a never-ending flow of fresh data. 20 But the new models share with the old one key feature: circularity. Excess return is the compensation for risk, while risk is measured by excess return. This correspondence holds simply because it should:
[F]ew people quarrel with the idea that investors require some extra return for taking on risk. That is why common stocks have given on
19 Equation (7) produces two special cases. One is for 'risk-free' assets, which, being uncorre- lated with the market, have a beta of 0 and therefore a discount rate of rrf. The other is for the market index itself, whose beta is 1 and whose yield is therefore rm.
20 Two famous extensions/alternatives are Ross' Arbitrage Price Theory (1976) and the augmented CAPM of Fama and French (1995).
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average a higher return than US Treasury bills. Who would want to invest in risky common stocks if they offered only the same expected returns as bills?
(Brealey, Myers, and Allen 2008: 217, first emphasis added)
It is just like Lamarckian evolution. A giraffe grows its neck to reach the high leaves on the tree, and so does the market: it makes prices of volatile assets rise faster in order to give investors a reason to own them.
Risk and power
The issue here is not circularity as such, but the worldview that underlies it. The framework of mainstream financial theories is neoclassical. Its basic units are risk-averse, utility maximizing investors. These individuals are powerless. They are too small to affect the circumstances and hence take them as given. Their only possible course of action is reaction: buying stocks whose return/risk attributes are attractive and selling those that are unattractive (that is, until the market equilibrates their prices to their natural levels). Their focus is price, and only price. The price tells them everything they need to know about return and risk. Whatever lies beneath it is irrelevant. And so the discount formula disappears.
The CAPM reasons the link between return and risk in moral terms: the capitalist 'deserves' higher returns to compensate for higher risk. But if we abandon the fairy tale of perfect competition and efficient markets and return to the real world of organized capitalist power, the capitalization formula comes back into focus and the relationship between risk and return assumes a rather different meaning.
Back on earth, the sequence is as follows: earnings are a matter of power and conflict; the conflict over earnings invites resistance; and resistance breeds volatility and uncertainty. In this way, the capitalist struggle to increase earnings is inextricably bound up with uncertainty regarding their eventual level. The numerator of the capitalization formula becomes inti- mately tied to its denominator.
The degree of confidence
Recall that in capitalism the ownership of an asset is a claim on future earn- ings. The price of the asset, expressed as present value, is merely the capitalist assessment of those earnings. Underlying this assessment are two key con- siderations. One is the level of earnings capitalists expect to receive; the other is the degree of confidence capitalists have in their own predictions. In order to make this degree of confidence explicit, we rewrite Equations (3) and (4), such that:
8. Kt = EE = E * H r rc * ?
? ? 9. Pt = EEPS = EPS * H r rc * ?
In this reformulation, capitalist confidence is expressed in two basic ways. At any given social conjunction, there is a certain benchmark, a rate of return that capitalists feel confident they can get. We denote it accordingly by rc. Finance theory refers to this rate as 'risk-free' - yet explains neither why it is free of risk nor what determines its level. Neoclassicists must resist the temp- tation to equate this rate to the marginal productivity of capital - not only because the latter is logically impossible and empirically invisible, but also because the absence of 'risk' here is secured by . . . the government! As we shall argue in the next part of the book, what enables capitalist governments to set a 'risk-free' rate in the first place - and what makes capitalists view this rate with approval and confidence - is neither 'productivity' nor statist 'distortions', but the overall structure of power in society.
Of course, with the exception of short-term government instruments, capi- talist income is always uncertain (hence the ever-present hype). The conflict that underlies earnings is multifaceted and can develop in many directions. Sometimes capitalist power is sufficiently secure to make capitalists certain of their strategy and the earnings it will generate; at other times, their power is tenuous and future predictions more hesitant. The degree of confidence that emerges from these considerations is expressed, inversely, by the 'risk coeffi- cient' (? ). When capitalists are fully confident, ? is 1. Otherwise, ? is bigger than 1, and it increases as confidence decreases.
Note that this risk coefficient is not the same as the so-called 'risk premium' of finance theory. First, whereas the risk premium pertains to the asset price on the left-hand side of the capitalization equation, the risk coefficient pertains to earnings on the right-hand side. Since the price of the asset involves more than earnings, the two risk concepts cannot be the same.
Second, whereas the 'risk premium' is the designated return for actual volatility, the risk coefficient denotes the confidence capitalists have in their predictions. Of course, volatility and confidence are related, but their corre- spondence is anything but simple. To start with, volatility per se does not generate uncertainty. It is the pattern of volatility that does. The annual earning cycle of ski resorts may be much more volatile - yet far more certain - than the profits of airlines. Insofar as seasonal weather variations prove easier to predict than the vagaries of world travel, capitalists will judge the larger volatility of the former less risky than the smaller volatility of the latter. The other reason is that the past is only a partial guide to the future. This fact has been pointed out by Knight and Keynes, but it takes on a whole new dimen- sion once we bring power into the picture. In the next part of the book we argue that the very purpose of power-driven capitalist accumulation is to reshape society. Capitalists realize that the very nature of their enterprise is to defy prediction, and they therefore take even the most successful forecasting models with a grain of salt.
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? ? 210 Capitalization
Lastly, whereas in financial theory a higher risk begets a higher 'risk premium', higher earnings volatility does not imply higher earnings growth, or vice versa. Over the past half-century, the earnings of General Electric rose 10 times faster than those of General Motors - though the volatility of GE's earning growth was far smaller than GM's (Bichler and Nitzan 2006). Contrary to Lamarckian finance, earnings volatility does not entail a 'premium'. And the reason, again, is at least partly associated with power. Bernoulli's capitalists are risk averse because their goal is hedonic consump- tion: their next yacht is assumed to be slightly less enjoyable than the previous one. But power-driven capitalists are very different. As we shall see, their goal is not more income, but a larger distributive share of income. Redistribution, however, does not obey the laws of diminishing marginal utility, so there is no longer reason to assume that capitalists are risk averse.
Most of the world's leading capitalists, including some of the biggest so- called portfolio investors, are not very diversified. In fact, many are highly focused. The reason they have 'made it' is that, unlike the passive individuals that populate the CAPM, they are active. 'Speculating and playing with power is more exciting than playing roulette', writes Traven in The White Rose: 'At roulette influence cannot be exercised' (1929: 96). Big capitalists do not take the odds as given; they try to change them. They struggle to increase their earnings and surrounding hype, and they similarly try to tame volatility. They are not only risk takers, they are also risk shapers. And as they embrace risk rather than shy away from it, the moral link between earnings volatility and earnings growth breaks down.
For the large capitalists, reducing earning volatility is a major obsession. But the reason is not hedonic payoff, but predictability and control. Knight and Keynes identified the problem: the unbridgeable gap between uncertainty and risk. Organized capitalist power is an attempt to defy the problem, if only in appearance: by shaping society, capitalist power 'translates' undefined uncertainty into seemingly quantitative risk. Capitalism is uncertain partly because the conflictual power logic of accumulation makes it so.
Pressed to the wall, mainstream finance responded to these anomalies by opening the door to various theories of 'irrationality' - from Herbert Simon's 'bounded rationality' (1955; 1979), through Daniel Ellsberg's 'ambiguity aversion' (1961), to Daniel Kahneman and Amos Tversky's 'prospect theory' (1979), to Richard Thaler's broader delineation of 'behavioural finance' (De Bondt and Thaler 1985). These explanations, though, remain safely within the consensus. Like their orthodox counterparts, they too focus on the powerless individual who passively responds to given circumstances. Unlike his nineteenth-century predecessor, this 'agent' is admittedly imperfect. He is no longer fully informed and totally consistent, he tends to harbour strange preferences and peculiar notions of utility (and may even substitute 'satis- ficing' for 'maximizing'), and he sometimes lets his mood cloud his better judgement.
These deviations, argue their theorists, fly in the face of market efficiency: they show that irrational hype can both exist and persist. But that conclusion, the theorists are quick to add, does not bring the world to an end. As noted in Chapter 10, individual irrationality, no matter how rampant, is assumed to be bounded and therefore predictable. And since predictable processes, no matter how irrational, can be modelled, the theorists can happily keep their jobs.
Of course, what the models cannot tell us (and the financial modellers are careful never to ask) is how these various 'irrationalities' are being shaped, by whom, to what ends and with what consequences. These aspects of capital accumulation have nothing to do with material technology and individual utility. They are matters of organized power. And on this subject, finance theorists and capitalist insiders are understandably tight-lipped. The only way to find out is to develop a radical political economy of hype independent of both.
The discount rate
If putting a number on future income and wealth seems difficult, knowing how much to trust one's prediction is next to impossible - or, at least that is how it was for much of human history. When Croesus, the fabulously rich king of Lydia, asked Solon of Athens if 'ever he had known a happier man than he', the latter refused to be impressed by the monarch's present wealth:
Elementary particles 197
The gods, O king, have given the Greeks all other gifts in moderate degree; and so our wisdom, too, is a cheerful and a homely, not a noble and kingly wisdom; and this, observing the numerous misfortunes that attend all conditions, forbids us to grow insolent upon our present enjoy- ments, or to admire any man's happiness that may yet, in course of time, suffer change. For the uncertain future has yet to come, with every possible variety of fortune; and him only to whom the divinity has continued happiness unto the end, we call happy; to salute as happy one that is still in the midst of life and hazard, we think as little safe and conclusive as to crown and proclaim as victorious the wrestler that is yet in the ring.
(Plutarch 1859, Vol. 1: 196-97, emphasis added)
Solon's caution was not unfounded, for in due course the hubristic Croesus lost his son, wife and kingdom. And in this respect, we can say that little has changed. The future is still uncertain, but the capitalist rulers, like their royal predecessors, continue to convince themselves that somehow they can circum- vent this uncertainty. The main difference is in the methods they use. In pre-capitalist times uncertainty was mitigated by the soothing words of astrologists and prophets, whereas nowadays the job is delegated to the oracles of probability and statistics.
Capitalist uncertainty is built right into the discounting formula. To see why, recall our derivation of this formula in Equations (1) to (6) in Chapter 9. We started by defining the rate of return (r) as the ratio of the known earnings stream (E) to the known dollar value of the invested capital (K), such that r = E/K. The expression is straightforward. It has one equation, one unknown and an obvious solution. Next, we rearranged the equation. Since the rate of interest can be calculated on the basis of the earnings and the original invest- ment, it follows that the original investment can be calculated based on the rate of return and the earnings, so that K = E/r. The result is the discount formula, the social habit of thinking with which capitalists began pricing their capital in the fourteenth century.
Mathematically, the two formulations seem identical, if not circular (recall the Cambridge Controversy). But in reality there is a big difference between them. The first expression is ex post. It computes the realized rate of return based on knowing both the initial investment and the subsequent earnings. The second expression is ex ante. It calculates the present value of capital based on the future magnitude of earnings. These future earnings, however, cannot be known in advance. Furthermore, since capitalists do not know their future earnings, they cannot know the rate of return these earnings will eventually represent. Analytically, then, they are faced with the seemingly impossible task of solving one equation with three unknowns.
In practice, of course, that is rarely a problem. Capitalists simply conjure up two of the unknown numbers and use them to compute the third. The question for us is how they do it and what the process means for accumula-
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tion. The previous section took us through the first step: predicting future earnings. As we saw, these predictions are always wrong. But we also learned that the errors are not unbounded, and that, over a sufficiently long period of time, the estimates tend to oscillate around the actual numbers. The second step, to which we now turn, is articulating the discount rate - the rate that the asset is expected to yield with the forecasted earnings. And it turns out that the two steps are intimately connected. The discount rate mirrors the confi- dence fortunetelling capitalists have in their own forecasts: the greater their uncertainty, the higher the discount rate - and vice versa.
The normal and the risky
What is the 'proper' discount rate? The answer has a very long history, dating back to Mesopotamia in the third millennium BCE (a topic to which we return in the next chapter). 12 Conceptually, the computation has always involved two components: a 'benchmark' rate plus a 'deviation'. The meaning of these two components, though, has changed markedly over time.
Until the emergence of capitalization in the fourteenth century, both components were seen as a matter of state decree, sanctioned by religion and tradition, and modified by necessity. The nobility and clergy set the just lending rates as well as the tolerated zone of private divergence, and they often kept them fixed for very long periods of time (Hudson 2000a, 2000b).
Neoclassicists never tire of denying this 'societal' determination. Scratch the pre-capitalist surface, they insist, and underneath you will find the eternal laws of economics. From the ancient civilizations and early empires, to the feudal world, to our own day and age, the underlying logic has always been the same: the productivity of capital determines the 'normal' rate of return, and the uncertainty of markets determines the 'deviations' from that normal.
This confidence seems unwarranted. We have already seen that the neoclassical theory of profit is problematic, to put it politely. But even if the theory were true to the letter, it would still be difficult to fathom how its purely capitalist concepts could possibly come to bear on a pre-capitalist discount rate. First, prior to the emergence of capitalization in the fourteenth century the productivity doctrine was not simply unknown; it was unthink- able. Second, there were no theoretical tools to conceive, let alone quantify, uncertainty. And, finally, there were no systematic data on either produc- tivity or uncertainty to make sense of it all. In this total blackout, how could anyone calculate the so-called 'economic' discount rate?
12 There is considerable recent literature on the ancient origins of interest, debt and money. These contrarian writings, partly inspired by the work of Mitchell-Innes (1913; 1914), critique the undue imposition of neoclassical logic on pre-capitalist societies and instead emphasize a broader set of political, religious and cultural determinants. Important collec- tions include Hudson and Van de Mieroop (2002), Hudson and Wunsch (2004), Ingham (2004) and Wray (2004).
? Probability and statistics
These concepts have become meaningful only since the Renaissance. The turning point occurred in the seventeenth century, with the twin invention of probability and statistics. 13 In France, Blaise Pascal and Pierre de Ferma, mesmerized by the abiding logic of a game of chance, began to articulate the mathematical law of bourgeois morality. Probability was justice. In the words of Pascal, 'the rule determining that which will belong to them [the players] will be proportional to that which they had the right to expect from fortune. . . [T]his just distribution is known as the division' (cited in Bernstein 1996: 67, emphases added). 14
At about the same time, Englishmen John Graunt, William Petty and Edmund Halley took the first steps in defining the field of practical statistics. The term itself connotes the original goal: to collect, classify and analyse facts bearing on matters of state. And indeed, Graunt, whose 1662 estimate of the population of London launched the scientific art of sampling, was very much attuned to the administrative needs of the emerging capitalist order. His prac- tical language would have been music to the ears of today's chief executives and finance ministers:
It may be now asked, to what purpose tends all this laborious buzzling and groping? . . . I Answer. . . That whereas the Art of Governing, and the true Politiques, is how to preserve the Subject in Peace, and Plenty, that men study onely that part of it, which teacheth how to supplant, and over-reach one another, and how, not by fair out-running, but by trip- ping up each other's heels, to win the Prize. Now, the Foundation, or Elements of this honest harmless Policy is to understand the Land, and the hands of the Territory to be governed, according to all their intrin- sick, and accidental differences. . . . It is no less necessary to know how many people there be of each Sex, State, Age, Religious, Trade Rank, or Degree, &c. by the knowing whereof Trade and Government may be made more certain, and Regular; for, if men know the People as afore- said, they might know the consumption they would make, so as Trade might not be hoped for where it is impossible.
(Graunt 1662: 72-73, original emphases)
Although initially independent, probability and statistics were quickly inter- twined, and in more than one way. The new order of capitalism unleashed multiple dynamics that amplified social uncertainty. Instead of the stable and
13 The social history of these related disciplines is told in Hacking (1975; 1990) and Bernstein (1996). Our account here draws partly on their works.
14 Probability theory in fact was developed a century earlier, by the Italian mathematician Girolamo Cardano. His work, however, was ahead of the times and therefore largely ignored.
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? 200 Capitalization
clear hierarchies of feudalism came a new ethic of autonomous individualism and invisible market forces. The slow cycle of agriculture gave rise to bustling industrial cities and rapidly growing populations. The relatively simple struc- tures of personal loyalty succumbed to the impersonal roller coaster of accumulation and the complex imperatives of government finances and regulations. More and more processes seemed in flux. But then, with every- thing constantly changing, how could one tell fact from fiction? What was the yardstick for truth on the path to societal happiness and personal wealth?
The very same difficulty besieged the new sciences of nature. In every field, from astronomy and physics to chemistry and biology, there was an explo- sion of measurement. But the measurements rarely turned out to be the same - so where was truth? With so many 'inaccuracies', how could one pin down the ultimate laws of nature?
The solution, in both society and science, came from marrying logical probability with empirical statistics. According to this solution, truth is hidden in the actual statistical facts, and probability theory is the special prism through which the scientist can see it. Any one measurement may be in error. But when the errors are random they tend to cancel each other out, and if we increase the size of the sample we can get as close to the truth as we wish. Moreover, and crucially for our purpose here, probability theory can also tell us how wrong our pronouncement of truth is 'likely' to be. It tosses the al-zahr - Arabic for 'dice' - to reckon the hazards.
This marriage of logic and measurement changed the concept of the unknown, making it seem less intimidating. Of course, the fear is still very much there: 'Unless you are running scared all the time, you're gone', explains the quintessential forward-looking capitalist, Bill Gates (1994). But the unknown, having been mediated through probability and statistics, has become less mysterious and, in that sense, less menacing. For the first time in history, uncertainty has been given a shape: it has a 'distribution'. Probability and statistics draw a clear relationship between the 'normal' and the 'disper- sion' around it, between what is supposedly 'natural' and 'true' and what is 'distorted' and 'devious', between the rulers at the 'centre' and the rebels and radicals at the 'margins'. They translate the unknown into seemingly precise 'standard deviations', and by so doing give human beings a comforting 'measure of their ignorance'.
The effect of this newly found confidence has been nothing short of revo- lutionary. It has opened the door to massive advances in the natural sciences. Virtually every field - from geodesy and astronomy, to classical and quantum statistical mechanics, to the biostatistics of evolution and medicine - has been rewritten by the new technique. And the same has happened in political economy. Every aspect of capitalism - from insurance, to engineering, to production, salesmanship, finance, public management, weapon develop- ment, population control, health care, mass psychology, the media and education, to name a few - has been re-articulated and further developed to leverage the power of probability and statistics. The belief that one can at
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least sketch the unknown has encouraged social imitative and intellectual creativity. The sense of knowing the 'odds' has made it much easier to dare to take a risk.
Averting risk: the Bernoullian grip
For the running-scared capitalist, though, probability and statistics are a mere starting point. They pretend to give the odds - but the odds alone are still devoid of meaning. And that is where utilitarianism comes into the picture.
The issue can be illustrated with a simple example. Suppose Bill Gates considers acquiring one of two software companies, Civilsoft and Weaponsoft. Civilsoft sells in the open market and is a bit volatile. The analysts tell Gates that, in their view, it has a 50 per cent chance of generating annual earnings of $50 million and a 50 per cent chance of generating annual earnings of $150 million. Weaponsoft is different. It sells to the military and has recently managed to secure a long term contract with the U. S. Department of Defense. According to the analysts, it is certain to generate $100 million annually. Now, probability calculations make the two firms equally attractive: mathematically, both have expected annual earnings of $100. 15 And, so, if Gates believes his analysts he should be indifferent as to which of the two he should acquire.
Not so, argued Daniel Bernoulli (1738). In his seminal paper, published more than two centuries before Gates was born, he stipulated that the measurement of risk involves more than the mere statistical odds. It requires that we put a 'moral' judgement on the expected dollars and cents - a judge- ment that he insisted must be based on diminishing marginal utility.
According to this logic, Gates, like the rest of us, should contemplate not the expected dollar earnings the companies will generate, but the expected utility he will get from consuming those earnings. This modification makes a big difference. '[A]ny increase in wealth no matter how insignificant', wrote Bernoulli, 'will always result in an increase in utility which is inversely propor- tionate to the quantity of goods already possessed' (p. 25). So the first dollar Gates earns generates more utility than the second, the second more than the third, and so on all the way to the billionth dollar and beyond.
To illustrate the consequence of this stipulation, let us split the expected earnings into $50 million chunks and assume for simplicity that with dimin- ishing marginal utility the first chunk gives Gates 3,000 utils, the second 2,000 utils and the third 1,000 utils. With this assumption, the takeover targets no longer look equally attractive: the less risky Weaponsoft is expected to generate 5,000 utils, whereas the more volatile Civilsoft is likely to give only
15 Mathematically, the expected earnings of Civilsoft are: $50 million * 0. 5 + $150 million * 0. 5 = $100 million, the same as Weaponsoft's.
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4,500. 16 And since ultimately all Mr Gates cares about is hedonic consump- tion, it is better for him to acquire the military contractor. It is likely to give him 500 more utils per annum.
Finance theory has never managed to shake loose of the Bernoulli grip. His paper triggered a deluge of publications on risk, many of which modified and revised his original formulation. But most remain locked behind his three subjectivist tenets. First, risk ultimately is a personal matter. Second, attitude to risk is rooted in the individual's hedonic preferences. And third, because of diminishing marginal utility, most individuals tend to be risk averse. This grip keeps the risk analysis of contemporary capitalist power hostage to the eighteenth-century belief in individual utilitarianism.
The unknowable
Of course, most theorists of capitalism ignore power. So before continuing we should point out that Bernoulli's mechanical hedonism may be inappropriate for the study of risk quite apart from the absence of power. First, there is the question of the odds. Capitalists are concerned with the future, yet statistical estimates of probabilities can only be drawn from the past. This is a crucial mismatch. As David Hume's Treatise of Human Nature (1739) tells us, the mere fact that all past experiments have found water to boil at 100 degrees Celsius does not mean that the same will happen next time we put the kettle on the stove. Natural scientists have managed to assume this challenge away by stipulating the stability of natural laws (whether deterministic or stochastic), but this stipulation seems a bit stretched when applied to society.
The inherent difficulty of calculating the social odds was heightened during the first half of the twentieth century. The combined onslaught of revo- lutions, financial crises, a Great Depression and two world wars suggested that the problem was not merely one of assigning odds to possible outcomes, but of specifying what those outcomes might be in the first place.
According to Frank Knight (1921), risk calculations presuppose a known set of odds. But in society, the future contains an element of novelty, and novelty cannot be pre-assigned a probability: it is unique and therefore inher- ently uncertain. Even Keynes, whose belief in the existence of so-called objec- tive social probability survived the First World War, caved in after the Second. In matters of society, he confessed, the future is largely unknowable:
By 'uncertain' knowledge, let me explain, I do not mean merely to distin- guish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty; nor is the prospect of
16 For Weaponsoft, the expected utility is the sum of 3,000 utils for the first $50 million chunk and 2,000 utils for the second. For Civilsoft, the computation is: 3,000 utils * 0. 5 + (3,000 utils + 2,000 utils + 1,000 utils) * 0. 5.
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a Victory bond being drawn. Or, again, the expectation of life is only slightly uncertain. Even the weather is only moderately uncertain. The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention, or the position of private wealth-owners in the social system in 1970. About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know.
(Keynes 1937: 213-14, emphasis added)
And then there is the second problem. Even if we convince ourselves that the mathematical odds exist and that we can somehow know them, there is still the task of assigning to these odds utilitarian weights. Without these weights, there is no point talking about Bernoullian risk. Yet these weights, made up of utils, vary from person to person and from moment to moment, and this fluidity has implications. Any given asset must be seen as having not one, but many quantities of risk (as many as there are potential capitalists). Furthermore, the quantity of risk, being partly subjective, will change with preferences even if the so-called objective odds remain unaltered. This ever- shifting multiplicity makes it difficult to pin down the 'correct' risk premium and therefore to specify the 'proper' discount rate.
And with this rate hanging in the air, how are capitalists to compute an asset's 'true' present value?
The capital asset pricing model
These logical challenges proved no match for the capitalist nomos. Although investors may be unable to calculate risk on their own, they can ask the know- all market to do it for them. All they need is a bureaucratic blueprint disguised as theory, and Lord Keynes was prescient enough to anticipate what it would take to produce one. His checklist was short: (1) believe that the present odds are a reliable guide to future ones; (2) assume that other investors got those odds right; and (3) conclude that their relevant computations are already reflected in asset prices (Keynes 1937: 214). The instructions were simple enough, and when a year later Paul Samuelson (1938) announced that prices reveal to us what we desire but cannot express ('revealed preferences'), the road for an operational theory of risk was finally wide open.
The glory went to Harry Markowitz and William Sharpe. Markowitz (1952; 1959) gave investors a quantitative definition of risk and told them how to 'optimize' risk and return through diversification. Sharpe (1964), building on Markowitz's insight, showed capitalists how to tease out of the market the 'true' risk premium with which to discount their assets. These contributions closed the circle. The capitalization ritual was now fully articu- lated, and the two inventors went on to collect the Sveriges Prize in Economic Sciences in Memory of Alfred Nobel.
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Portfolio selection
Markowitz's manuals focused on the Bernoullian individual: the risk-averse investor. In buying and selling financial assets, he said, 'the investor does (or should) consider expected return a desirable thing and variance of return an undesirable thing' (1952: 77, original emphasis). And the best method to achieve both goals, he concluded, is to diversify.
Although Markowitz himself spoke merely of the 'variance' of returns - defined as the squared deviation of the rate of price change from its own mean value - the term was quickly adopted as a synonym for risk. This in itself was a major achievement. Until Markowitz, there was no quantitative definition for risk, let alone one that everyone agreed on. 17 So the fact that he was able to galvanize the 'investment community' around this concept - even if he never intended to - is already worth a Nobel.
But Markowitz did much more than that. By showing why risk should be handled through diversification, he provided the justification for an old practice and helped underwrite the new trend of institutional investing. To illustrate his logic, consider a portfolio comprising different financial assets. If the market prices of these assets do not move completely in tandem (so that the correlations between their rates of change are less than 1), their unique fluctuations will partly offset one another. This partial offsetting has a great benefit: it causes the price volatility of the portfolio as a whole to be smaller than the average volatility of the individual assets. By owning a portfolio of different assets, therefore, the capitalist can enjoy their average return while suffering less than their average 'risk'. Diversification, it now seemed, offered an entirely free lunch.
Which portfolio should the capitalist own? Conceptually, it is possible to plot on a two-dimensional chart the return/variance attributes of all possible portfolios. Of these endless combinations, there is a subset that Markowitz identified as 'efficient'. These are the best deals. Each efficient portfolio offers the minimum variance for a given return - or, alternatively, the maximum return for a given variance. The only way to do better on one attribute is to give up on the other, and vice versa. Conveniently, all efficient portfolios lie on a well-defined 'efficient frontier', and the Bernoullian capitalist simply needs to pick the one that equilibrates her very own greed and fear.
A few years after Markowitz made his mark, James Tobin (1958) offered an even sweeter deal. If investors are able to borrow and lend at a 'risk-free' rate of interest (such as the rate on US T-bills) they can in fact outperform the efficient frontier. All it takes is two easy steps. First, they need to single out on the efficient frontier that particular portfolio (labelled M for convenience) which, when combined with borrowing or lending, yields the highest return
17 Ricciardi (2004) managed to collate a list of no less than 150 unique risk indicators - hardly an indication of unanimity.
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for every level of volatility. And then they make their move. Those who are more risk averse can invest part of their money in M, putting the rest of it into risk-free assets (i. e. lending it to the central bank). And those who are less risk averse can borrow at the risk-free interest rate and invest the extra cash in additional units of M. Life has never been simpler.
CAPM
These guidelines, though, are still limited. Their target is the individual investor who already possesses definite expectations on return and variance and merely awaits instructions on how to diversify. The guidelines are silent, however, on how investors formed these expectations to begin with, and on the market consequences should they all follow the diversification advice. These latter questions were taken up by William Sharpe (1964) and John Lintner (1965) in their capital asset pricing model, or CAPM for short.
On the face of it, the questions seem unanswerable. Since individual inves- tors are assumed to be autonomous, their return/variance expectations are open-ended and can take any value whatsoever. And given that the expecta- tions are unbounded, the consequences of acting on them become unpredict- able. So Sharpe and Linter decided to simplify. What would happen, they asked, if all investors happened to share the same expectations regarding return and variance - and, moreover, if their expectations were the same as the true distribution of outcomes (i. e. if investors knew the stochastic generator of history)?
The scenario is admittedly odd. After all, what can one learn about uncer- tainty by assuming it away? Indeed, what would generate a future variance if all capitalists were the same and if all knew the future variance? Recall, however, that we are dealing here with the articulation of the capitalist nomos. The ultimate task is not to theorize capitalists, but to give them a bureaucratic blueprint. And if you revisit the previous section you will see that, in pursuing this goal, Sharpe and Linter were merely following Keynes' checklist.
And indeed, the answers they gave emerged directly from their assump- tions. If investors all see the world eye to eye, they will all own the same effi- cient portfolio M, and nothing but M. And since they all own only units of M, every owned stock in the market must be part of M. The only portfolio that satisfies these conditions is the market as a whole. So in Sharpe and Lintner's world, investors are fully diversified, each holding onto a propor- tion of the entire market.
Now, recall that diversification reduces volatility because the price move- ments of different assets partly offset each other. Why is the offsetting only partial? The reason is that price volatility is seen as stemming from two distinct sources: one that is unique to the asset itself, and another that is common to the market as a whole. A sufficiently diverse portfolio - which M obviously is - eliminates all unique volatility. Thus, following Sharpe and Lintner, portfolio investors can disregard all price volatility that is out of sync
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with the market. But no matter how diverse their portfolio, they can never eliminate market volatility, by definition.
In other words, every asset carries in its genes a definite quantum of market volatility, a quantum which in turn is passed on to the portfolio as a whole. 'The risk of a well-diversified portfolio', declare Brealey, Myers and Allen in their Principles of Corporate Finance (2008: 193), 'depends on the market risk of the securities included in the portfolio'. This is not something one argues about: 'Tattoo that statement on your forehead if you can't remember it any other way', they warn. 'It is one of the most important ideas in this book'.
Conveniently, this logic is fully invertible. Since individual assets contri- bute to the market portfolio their own market risk, their contribution can be deduced from the market. Recall that unique risk has been diversified away, so the only thing that makes one asset more or less risky than another is its 'sensitivity' to the overall market. This sensitivity is called beta, and it can easily be measured, or so we are told. The greater the market risk of the asset, the higher beta - and vice versa. 18
Now, if the measured historical beta is equal to the 'true' timeless beta, as the CAPM proclaims, we can calculate the asset's risk premium. By defini- tion, beta expresses the ratio between, on the one hand, the 'excess' return of the asset over and above 'risk-free' assets (asset excess return = r -rrf) and, on the other hand, the 'excess' return of the market over and above 'risk-free' assets (market excess return = rm - rrf):
5. beta = r - rrf rm - rrf
Rearranging Equation (5), the capitalist can obtain the risk premium for the asset:
6. risk premium = r - rrf = beta (rm - rrf)
And, finally, with one more reshuffle, the overall discount rate (r):
7. r = rrf + beta (rm - rrf)
The first component on the right is the 'risk-free' benchmark (rrf), while the second component is the compensation for the asset's risky 'deviations' (beta (rm - rrf)).
18 Beta can be derived in two easy steps. First, assume that all investors consider historical volatility equal to 'true' volatility. Second, run a linear regression with the historical rate of change of the asset price as the dependent variable, and with a constant and the historical rate of change of the market price as the independent variables. Beta is the estimated slope coefficient of this regression.
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And that is pretty much it. All that the capitalist now has to do is take the 'risk-free' rate of interest (rrf), the market return (rm) and the estimated beta and plug them into Equation (7). And since all capitalists are assumed to be drones and therefore to do the very same maths with the very same numbers, they all end up with the same discount rate (r). 19 This number is then put into the denominator of the discount formula in Equations (3) and (4) to give the 'true' capitalized value of the asset.
Circularity
CAPM has been a smashing business success. Within a few decades, it has become the basis on which corporate finance courses are structured. Often, it is the only model that MBA students rehearse in some detail. And as the students turn into managers, executives and government officials, they apply what they learnt. In the early 1980s, less than one third of large US firms used the CAPM to compute the cost of equity. By the early 2000s, the proportion was well over 70 per cent, although, to be on the safe side, other formulae are used as well (Gitman and Mercurio 1982; Graham and Harvey 2001).
This success is all the more remarkable given the model's dismal empirical showing. Recall that Sharpe and Lintner assumed that investors know the 'true' variance of returns, and therefore also the 'true' beta - yet that, in prac- tice, they all take a shortcut and use the historical beta instead. No wonder the model crumbles.
First, there is the 'equity premium puzzle': it turns out that, taken as an asset class, equities outperform government bonds by much more than their extra volatility would demand (Mehra and Prescott 1985). And then the puzzle becomes embarrassing. Comparisons of different classes of equities often show returns to be uncorrelated and sometimes negatively correlated with beta values! 'The problems are serious enough', conclude efficient market theorists Fama and French, 'to invalidate most applications of the CAPM' (2004: 43).
Given these difficulties, the CAPM has been refurbished, extended and modified with new and improved techniques and a never-ending flow of fresh data. 20 But the new models share with the old one key feature: circularity. Excess return is the compensation for risk, while risk is measured by excess return. This correspondence holds simply because it should:
[F]ew people quarrel with the idea that investors require some extra return for taking on risk. That is why common stocks have given on
19 Equation (7) produces two special cases. One is for 'risk-free' assets, which, being uncorre- lated with the market, have a beta of 0 and therefore a discount rate of rrf. The other is for the market index itself, whose beta is 1 and whose yield is therefore rm.
20 Two famous extensions/alternatives are Ross' Arbitrage Price Theory (1976) and the augmented CAPM of Fama and French (1995).
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average a higher return than US Treasury bills. Who would want to invest in risky common stocks if they offered only the same expected returns as bills?
(Brealey, Myers, and Allen 2008: 217, first emphasis added)
It is just like Lamarckian evolution. A giraffe grows its neck to reach the high leaves on the tree, and so does the market: it makes prices of volatile assets rise faster in order to give investors a reason to own them.
Risk and power
The issue here is not circularity as such, but the worldview that underlies it. The framework of mainstream financial theories is neoclassical. Its basic units are risk-averse, utility maximizing investors. These individuals are powerless. They are too small to affect the circumstances and hence take them as given. Their only possible course of action is reaction: buying stocks whose return/risk attributes are attractive and selling those that are unattractive (that is, until the market equilibrates their prices to their natural levels). Their focus is price, and only price. The price tells them everything they need to know about return and risk. Whatever lies beneath it is irrelevant. And so the discount formula disappears.
The CAPM reasons the link between return and risk in moral terms: the capitalist 'deserves' higher returns to compensate for higher risk. But if we abandon the fairy tale of perfect competition and efficient markets and return to the real world of organized capitalist power, the capitalization formula comes back into focus and the relationship between risk and return assumes a rather different meaning.
Back on earth, the sequence is as follows: earnings are a matter of power and conflict; the conflict over earnings invites resistance; and resistance breeds volatility and uncertainty. In this way, the capitalist struggle to increase earnings is inextricably bound up with uncertainty regarding their eventual level. The numerator of the capitalization formula becomes inti- mately tied to its denominator.
The degree of confidence
Recall that in capitalism the ownership of an asset is a claim on future earn- ings. The price of the asset, expressed as present value, is merely the capitalist assessment of those earnings. Underlying this assessment are two key con- siderations. One is the level of earnings capitalists expect to receive; the other is the degree of confidence capitalists have in their own predictions. In order to make this degree of confidence explicit, we rewrite Equations (3) and (4), such that:
8. Kt = EE = E * H r rc * ?
? ? 9. Pt = EEPS = EPS * H r rc * ?
In this reformulation, capitalist confidence is expressed in two basic ways. At any given social conjunction, there is a certain benchmark, a rate of return that capitalists feel confident they can get. We denote it accordingly by rc. Finance theory refers to this rate as 'risk-free' - yet explains neither why it is free of risk nor what determines its level. Neoclassicists must resist the temp- tation to equate this rate to the marginal productivity of capital - not only because the latter is logically impossible and empirically invisible, but also because the absence of 'risk' here is secured by . . . the government! As we shall argue in the next part of the book, what enables capitalist governments to set a 'risk-free' rate in the first place - and what makes capitalists view this rate with approval and confidence - is neither 'productivity' nor statist 'distortions', but the overall structure of power in society.
Of course, with the exception of short-term government instruments, capi- talist income is always uncertain (hence the ever-present hype). The conflict that underlies earnings is multifaceted and can develop in many directions. Sometimes capitalist power is sufficiently secure to make capitalists certain of their strategy and the earnings it will generate; at other times, their power is tenuous and future predictions more hesitant. The degree of confidence that emerges from these considerations is expressed, inversely, by the 'risk coeffi- cient' (? ). When capitalists are fully confident, ? is 1. Otherwise, ? is bigger than 1, and it increases as confidence decreases.
Note that this risk coefficient is not the same as the so-called 'risk premium' of finance theory. First, whereas the risk premium pertains to the asset price on the left-hand side of the capitalization equation, the risk coefficient pertains to earnings on the right-hand side. Since the price of the asset involves more than earnings, the two risk concepts cannot be the same.
Second, whereas the 'risk premium' is the designated return for actual volatility, the risk coefficient denotes the confidence capitalists have in their predictions. Of course, volatility and confidence are related, but their corre- spondence is anything but simple. To start with, volatility per se does not generate uncertainty. It is the pattern of volatility that does. The annual earning cycle of ski resorts may be much more volatile - yet far more certain - than the profits of airlines. Insofar as seasonal weather variations prove easier to predict than the vagaries of world travel, capitalists will judge the larger volatility of the former less risky than the smaller volatility of the latter. The other reason is that the past is only a partial guide to the future. This fact has been pointed out by Knight and Keynes, but it takes on a whole new dimen- sion once we bring power into the picture. In the next part of the book we argue that the very purpose of power-driven capitalist accumulation is to reshape society. Capitalists realize that the very nature of their enterprise is to defy prediction, and they therefore take even the most successful forecasting models with a grain of salt.
Elementary particles 209
? ? 210 Capitalization
Lastly, whereas in financial theory a higher risk begets a higher 'risk premium', higher earnings volatility does not imply higher earnings growth, or vice versa. Over the past half-century, the earnings of General Electric rose 10 times faster than those of General Motors - though the volatility of GE's earning growth was far smaller than GM's (Bichler and Nitzan 2006). Contrary to Lamarckian finance, earnings volatility does not entail a 'premium'. And the reason, again, is at least partly associated with power. Bernoulli's capitalists are risk averse because their goal is hedonic consump- tion: their next yacht is assumed to be slightly less enjoyable than the previous one. But power-driven capitalists are very different. As we shall see, their goal is not more income, but a larger distributive share of income. Redistribution, however, does not obey the laws of diminishing marginal utility, so there is no longer reason to assume that capitalists are risk averse.
Most of the world's leading capitalists, including some of the biggest so- called portfolio investors, are not very diversified. In fact, many are highly focused. The reason they have 'made it' is that, unlike the passive individuals that populate the CAPM, they are active. 'Speculating and playing with power is more exciting than playing roulette', writes Traven in The White Rose: 'At roulette influence cannot be exercised' (1929: 96). Big capitalists do not take the odds as given; they try to change them. They struggle to increase their earnings and surrounding hype, and they similarly try to tame volatility. They are not only risk takers, they are also risk shapers. And as they embrace risk rather than shy away from it, the moral link between earnings volatility and earnings growth breaks down.
For the large capitalists, reducing earning volatility is a major obsession. But the reason is not hedonic payoff, but predictability and control. Knight and Keynes identified the problem: the unbridgeable gap between uncertainty and risk. Organized capitalist power is an attempt to defy the problem, if only in appearance: by shaping society, capitalist power 'translates' undefined uncertainty into seemingly quantitative risk. Capitalism is uncertain partly because the conflictual power logic of accumulation makes it so.
