Let’s Get It Straight: Risk, Uncertainty and Likelihood of Loss



Some people take risks. Investors and traders take uncertainties. This awkward turn of phrase draws on the distinction between risk and uncertainty made clear by Frank Knight over 90 years ago.  Only when the precise probability of a random event occurring is known can we call something a risk.  Otherwise it is an uncertainty.

If pricing capital in the face of risk was all that there was to finance, (it) would be as useful as running a regression on a bus timetable.  Source

In one of the best papers I have read in recent years, Professor of Finance Andrew Lo and Physicist Mark Mueller, (2011) explore different levels of uncertainty.  Beware of the investor who only talks in unfalsifiable terms.

• Risk = Known probability of outcome in future
• Uncertainty = Unknown probability of outcome in the future
• Likelihood of Loss = Probability of having a resource taken away

By definition, all animals are very good at calculating risk, on the fly. Example: The source of food is over there – moving, I am here and hungry. My brain has to perform a constant calculation using risk probabilities that my mouth will intercept the food…or I die.

Uncertainty is entirely different. There is no way to calculate the probability of any future event. Thus, the benefits and costs are experienced as open ended. Since catastrophic failure, like death, is one of the possible outcomes – the potential liability of the situation is infinite. Death, or catastrophic loss, may be highly unlikely – but the cost of failure makes any probability aversive. Brains are not risk averse, they manage risk very well, but they are highly uncertainty averse.

Likelihood of loss is what is typically meant when the everyday term “risk” is used. This is a misstatement and misleading. So, some economists have pointed out the damage done in confusing risk with uncertainty thus hiding the likelihood of loss

Since these everyday language terms come from academic discussions, prior to biology developing, we can borrow from economists. Lo and Mueller note: “Knight’s (1921) distinction between “risk” (randomness that can be fully captured by probability and statistics) and “uncertainty” (all other types of randomness)… Fully reducible uncertainty is the kind of randomness that can be reduced to pure risk given sufficient data, computing power, and other resources.” Source

Risk versus Uncertainty: Frank Knight’s “Brute” Facts of Economic Life

By William Janeway

Published on: Jun 07, 2006 –

More than eighty years ago, Frank Knight set out to parse the difference between risk and uncertainty and the significance of that difference. In Risk, Uncertainty and Profit, Knight distinguished between three different types of probability, which he termed: “a priori probability”; “statistical probability” and “estimates”. The first type “is on the same logical plane as the propositions of mathematics”; the canonical example is the odds of rolling any number on a die. “Statistical probability” depends upon the “empirical evaluation of the frequency of association between predicates” and on “the empirical classification of instances”. When “there is no valid basis of any kind for classifying instances”, only “estimates” can be made.1 In contemporary Bayesian parlance, in the first case, the probability distribution of the prior and all its moments are known definitionally; in the second case they are specified by statistical analysis of well-defined empirical data; in the third case such data as exists do not lend themselves to statistical analysis.

This last case is what interested Knight the most, as an economist exploring the world of business and the nature of profit in that world. Knight identified the “confusion” between “the problem of intuitive estimation” with “the logic of probability”, whether a priori or statistical2:

The liability of opinion or estimate to error must be radically distinguished from probability or chance of either type, for there is no possibility of forming in any way groups of instances of sufficient homogeneity to make possible a quantitative determination of true probability. Business decisions, for example, deal with situations which are far too unique, generally speaking, for any sort of statistical tabulation to have any value for guidance. The conception of an objectively measurable probability or chance is simply inapplicable…

“[A]t the bottom of the uncertainty problem in economics”, Knight noted, “is the forward-looking character of the economic process itself.” 4 The post-Keynesian economist Paul Davidson defined the problem as the inapplicability of the “ergodic axiom”:

The economic system is moving through calendar time from an irrevocable past to an uncertain and statistically unpredictable future. Past and present market data do not necessarily provide correct signals regarding future outcomes….”

When Knight turned to the role of profit as the reward to the entrepreneur for bearing inevitable uncertainty, he characterized these facts of economic life in the most stark of terms:

“Profit arises out of the inherent, absolute unpredictability of things, out of the sheer, brute fact that the results of human activity cannot be anticipated and then only in so far as even a probability calculation in regard to them is impossible and meaningless.6

I have documented what Frank Knight meant by “uncertainty” to clarify what is at stake in applying the calculus of financial “risk” to issues of economic and, indeed, social security. More than fifty years ago, “mainstream” economics launched itself on the grand project to formalize the principles of economics in rigorous mathematics. Unsurprisingly, such a system was as incapable of incorporating Knight’s “uncertainty” as it was of addressing the “extreme precariousness” of expectations and confidence described so eloquently in Chapter 12 of Keynes’ General Theory.7

For a time, the “rational expectations hypothesis” (REH) served as a sort of placeholder for serious consideration of the fundamental issues that Knight addressed and the consequences of which Keynes explored. It is not, I believe, an excessive caricature of REH to say that it turns on the assumptions that

(1) all market participants have equal access to the same data;

(2) all market participants share one model of how the world works, application of which translates data into meaningful and actionable information; and

(3) that model happens to be “the truth” (and is identified recursively with “mainstream” general equilibrium theory).

In this world, bubbles and panics cannot exist. All risks can be priced and insured or effectively hedged through the construction of appropriate contingent, derivative securities markets which are assumed to exist.

Application of REH to the capital markets of real economies generates a problem. REH defines a market in which the only occasion for any participant to trade is an externally generated “shock”: price volatility, identified with market risk, should be very low and aligned with the incidence of such shocks. However, empirical studies of the capital markets have identified three “puzzles”: the volatility of stock prices is too great, the risk-free interest rate is too low, and the “equity risk premium” (the return from investing in stocks compared with owning risk-free debt) is far too high to be compatible with REH. And the cluster of capital market shocks around the turn of the millennium seems to have decisively challenged the usefulness of a theory that hardly appeared consistent with the Asian Flu, the Russian Default, the collapse of LTCM, and the great NASDAQ boom and bust. In consequence, a variety of imaginative approaches are being actively deployed to understand the empirical “puzzles” generated by the attempt to explain—or, rather, explain away—the functioning of the capital markets through the application of REH.8 In different ways, this work, which serves to confirm the common sense of the market, is implicitly (sometimes explicitly) re-engaging with Knight, as it variously incorporates such building blocks for theory as “heterogeneous beliefs”, “endogenous uncertainty” and “fat-tailed Bayesian priors”.

When the domain of interest is dominated by uncertain estimates, your (more or less well informed) guess is as good as mine. This is what makes horse races—and securities markets. But, in the case of the stock market, what do you and I each need to guess? In his classic deployment of the metaphor of the “beauty contest”, Keynes captured the challenge:

…[P]rofessional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not a case of choosing those which, to the best of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be.9

Keynes never reduced his intuition, informed by his years of successful investing, to a formal, empirically testable model; indeed, before the development of stochastic calculus and game theory, it may not have been possible for him to do so. But the disparity between financial reality and modern, mathematically formalized economic theory has long been observable to those who have cared to look. A short generation ago, Frank Hahn began a series of lectures on money and finance with an observation pertaining to the social construction of the asset we call “money”:

The most serious challenge that the existence of money poses to the theorist is this: the best developed model of the economy cannot account for it.10

The “precautionary” motive for holding cash is among those enumerated by Keynes in his analysis of liquidity preference and has a long history in the literature on money and banking. Hahn and Solow, in their collaborative Critical Essay on Modern Macroeconomic Theory, elaborate on this:

Uncertainty enters the demand for money in two ways. First, it affects the calculation of the relative advantage of different assets including money. It also enters through considerations of liquidity or flexibility. Transaction costs will make it costly to change a portfolio choice once made. Agents know that as the future unfolds…their probability calculations will change. There is thus a probability that a portfolio choice, once made, is not optimal in light of what will be learned. This consideration, when combined with transaction costs, leads to a premium on “liquid” or low-transaction-cost assets…It is not hard to see how all of this provides a motive for holding money.11

Hahn, alone and with Solow, was observing the disparity between the Arrow-Debreu model and its derivatives—wherein all markets can simultaneously clear because all contingencies can be efficiently and effectively hedged—with the institutionalized reality of cash holdings across all observable economic systems.

Of course, this appreciation of the fine calculations by rational agents as they assess their (changing) optimal portfolios need not conceal the relevance of such analysis to the circumstance of the “agents” who face utter financial loss from the collapse of an Enron or the impact of a Katrina. Holding cash is how people self-insure against the uninsurable uncertainties of economic life, as distinct from the insurable risks. The proliferation of social security systems across the developed world since Bismarck’s innovation in 1891 further confirms the inability of markets to generate adequate hedges, sufficient in scale and distributed fairly enough to pre-empt successful appeal to the political process by market participants threatened with ruin. The evident failure of the Bush administration’s efforts at social security “reform” suggests that, in the nation where market forces are most explicitly respected, popular recognition persists that effective insurance against life’s uncertainties ultimately depends upon the power of the state.

If social security is the explicit institutionalization of state insurance against economic and financial uncertainty, more deeply rooted still in the institutional history of capitalism is the central bank’s role as lender of last resort. In 1873, Walter Bagehot, editor of The Economist, laid out in Lombard Street an analytical description of the British financial system as it had evolved to date. His most controversial and lasting contribution was the detailed discussion of “the duties which the Bank of England is bound to discharge as to its banking reserve”. It was controversial because

first…the Bank has never by any corporate act or authorized utterance acknowledged the duty, and some of its directors deny it; …second (what is even more remarkable) no resolution of Parliament, no report of any Committee of Parliament (as far as I know), no remembered speech of a responsible statesman, has assigned or enforced that duty on the Bank; third (what is more remarkable still), the distinct teaching of our highest authorities has often been that no public duty of any kind is imposed on the Banking Department of the Bank…12

Bagehot provided a succinct definition of and rationale for the Bank’s “duty”:

…the Bank of England is bound…not only to keep a good reserve against a time of panic, but to use that reserve effectively when that time of panic comes. The keepers of the Banking reserve…are obliged then to use that reserve for their own safety. If they permit all other forms of credit to perish, their own will perish immediately and in consequence.13

In the central bank-less United States, the story of how the Panic of 1907 initiated the process that led seven years later to the creation of the Federal Reserve is well known. Equally well known is the world-historical failure of the Federal Reserve to perform its Bagehotian duty in the cumulative crisis of 1931-33: perhaps if the Governors of the Federal Reserve in 1931 had been proprietors of a private banking institution, they would have appreciated that unchecked financial panic means economic ruin. What is not well-known is the story of the first successful exercise of Bagehot’s “duty” by the Federal Reserve some sixty years later. In June 1974, in the context of the first Oil Crisis and the loss of presidential authority due to Watergate, Chairman Arthur Burns—not the most highly regarded of American central bankers—responded to the failure of the German Herstatt Bank and the consequent foreign exchange settlement crisis by quietly but effectively invoking the provisions of the Federal Reserve Act that authorized the regional Reserve Banks to accept as collateral any assets (including , as I recall, desks and chairs) of their member banks. Since 1987, the evolution of the “Greenspan Put” has finally institutionalized the Fed’s role of lender of last resort in an uncertain world.

Access to liquidity, then, is how we seek to deal with Knight’s brute fact. But liquidity is a most perverse substance. First-generation purveyors of “modern portfolio theory” modeled liquidity as a stable attribute of particular securities, statistically derived from observation of price and volume data over time. But, as the partners, clients and counter-parties of LTCM all learned, liquidity—and such other statistical properties of securities as correlations—are, in fact, the variable attributes of markets. And the worst of it is this: liquidity declines more than proportionally with the intensity of the demand for it. The more you need cash, the higher the price you have to pay to get it. And when average opinion comes to believe that average opinion will decide to turn assets into cash, then liquidity may be confidently expected to go to zero. By definition, no market can hedge this risk; no individual participant is rich enough not to need the hedge.

Bagehot defined the need and the remedy that Greenspan has finally institutionalized in America and for the world. But, if the uncertainty that each market participant, each citizen, faces is underwritten by the one power that can create all the liquidity any may require on demand, then the balance between greed and fear has been shifted and shifted materially. The “moral hazard” that arises when the insured farmer no longer need apply himself assiduously to keep his barn from burning becomes a generalized influence on all calculating economic agents. Some 75 years ago, Andrew Mellon gave President Hoover the definitive rationale for refusing to respond to the financial crisis:

Liquidate labor, liquidate stocks, liquidate the farmers, liquidate real estate…People will work harder, live more moral lives.” 14

Mellon’s construct is helpful, at least to the student looking back if not to the well-meaning but bewildered President he was confronting. For it poses the stark choice that both generates and informs political discussion in this domain. A social science that evades Knight’s brute facts and Mellon’s correspondingly brutal prescription will contribute little to those seeking to formulate pragmatic responses to Meredith’s dusty answer. A social science that builds on Knight’s deep intuitions can contribute much.


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