The Nature of Risk

Risk is inextricably bound up with wealth destruction, and yet, risk measures are agnostic, treating risk as if investors are indifferent to gains and losses. This tortured contradiction is recognised by investors and managers, who intuitively understand that risk must be seen in terms of the possibility of forever losing one’s capital, or of missing out on a defined target. This contradiction between the risk measures in wide currency and intuitive and logical sense of risk, is often ignored because so little attention is paid to understanding the nature of risk. It is agreed that risk is, fundamentally, an epistemic problem, a problem of not knowing enough. The statistical expressions of risk, volatility-based measures, are founded on the assumption that risk is a forecasting problem, a question of not knowing enough about the future. That view is obviously false, and not only false, dangerous, for it leads to a view of risk that is too genteel and kind, blind to the dangers of wealth destruction. In trying to disentangle risk from uncertainty, a view has congealed that risk is measurable, enumerable and therefore objective, and so, its analysis has proceeded along purely statistical lines. In this view, an asset or venture’s risk is the same for everyone, and in a trade, someone always walks away the loser. There is no space for subjectivity of risk in this view, no recognition that that the risk for one party may be an opportunity for another, that this can be the basis of trade. Perhaps no event better demonstrates this than the widespread misunderstanding that Berkshire Hathaway faced when it sold off its airline stock in the wake of the pandemic crash.

The Knightian Consensus 

… Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated. The term ‘risk,’ as loosely used in everyday speech and in economic discussion, really covers two things which, functionally at least, in their causal relations to the phenomena of economic organisation, are categorically different. … The essential fact is that ‘risk’ means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomenon depending on which of the two is really present and operating. … It will appear that a measurable uncertainty, or “risk” proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all. We … accordingly restrict the term “uncertainty” to cases of the non-quantitative type.:

Frank Knight

With these canonical words, penned in one of economics’ great texts, Risk, Uncertainty and Profit, Knight segregated risk and uncertainty. Since then, the Knightian consensus has been that risk refers to what is measurable and tractable, with knowable probability distributions and unknowable specific outcomes, and uncertainty to what is immeasurable and intractable, with unknowable probability distributions and unknowable specific outcomes. Economists of every school, such as John Maynard Keynes, F.A. Hayek and Milton Friedman, have been indebted to him. Even his critics, few as they are, are profoundly Knightian in their views. Today, it is fashionable to talk about “radical uncertainty” and “Black Swans” and central bankers and investors chide themselves for excesses of certainty. Only mad men believe that uncertainty is susceptible to measurement.

Wealth Marches Toward Its Destruction

It can be said that Knight does not so much as define risk and uncertainty, as state whether they can be measured or not, but in doing so, he opens the door to the ridiculous, to what are now known as “downside” and “upside” risks. 

Since Harry Markowitz’s seminal 1952 paper, “Portfolio Selection”, it is generally accepted that risk is best measured in terms of a “volatility of returns”, in other words, the upward and downward swings in prices. Under this measure, if one expects a return of 10% from an investment, both the chance that the return will be lower, or higher than that expected return, are classed as risk! Few investors and managers, if any, would accept this view. Just eighteen years after Markowitz’ paper, one survey found that, across eight industries, most managers said they believed that semivariance, a measure of “downside risk”, was a more plausible measure of risk than variance. Decades later, that unease with theory remains. This notion of risk clearly goes against our intuition. One does not say, “There is a risk I will make a return greater than expected on this investment”. This notion of risk is also self-contradictory: it would seem perverse to imagine as rational behaviour a situation in which a person sought to limit all their risk, that is, both downside and “upside” risk. Defenders of the position would claim that when they refer to risk, they are of course referring to downside risk, which begs the question why the scope of this definition of “risk” allows for “upside risk” to be defined as such. It is not a merely academic argument: investors and managers make decisions based on risk measures that imply this very logic. It seems evident that whereas a person would want to limit their downside risk, they would be happy to have their profits run far in excess of what they expected. 

The idea of risk as composed of upside risk and downside risk is a very agnostic view of risk, like a man who does not know if he wants to turn left or right but zigs and zags. Downside risk is the only legitimate risk. Even Markowitz could not defend his risk measure from a logical point of view. The great man was aware of the inherent absurdity of so catholic a notion of risk, saying that semi-variance was a “more plausible measure of risk”. Seventy years since Markowitz launched modern portfolio theory, this notion of agnostic view of risk is pervasive, partly because Markowitz himself continued to advance variance as a measure of risk, arguing that practitioners needed to become more familiar with the simpler measure of variance, before they could advance to the more plausible notion of risk. 

The economist, A.D. Roy’s criticism of risk theory as being “set against a background of ease and safety”, rather than “poorly chartered waters” or hostile jungles, assumes “economic survival”, and thus incapable of understanding why investors act as if they see disaster everywhere, still rings true. 

Properly understood, risk should be viewed myopically, as being primarily the possibility of incurring a loss (the moment and existence of loss are more important than the knowledge of it), and secondarily, the possibility of underperforming some target rate of return. By loss is meant a decay or decline in prior wealth, where wealth represents one’s assets, a part of which is risked in some venture. This myopic view of risk becomes even more important in light of advances in behavioural economics in recent decades. Daniel Kahneman and Amos Tversky found that people are more fearful of losses than they are desirous of making corresponding gains, something they called, “loss aversion”. Loss aversion is often treated as irrational, and managers have been encouraged to overcome their loss aversion in search of superior returns. By way of example, in Applied Corporate Finance, Aswath Damodaran makes that argument, and so too do Tim Koller, Marc Goedhart, and David Wessels in their textbook, Valuation. However, if risk is defined not just by the question of its tractability, but also by the possibility of loss, then loss aversion is a rationally obligatory response, whereas, if risk is merely a forecasting error about a range of outcomes, good and bad, then, as prospect theory argues, and as managers are taught to believe, loss aversion is an irrational bias that should be overcome. 

Centuries ago, the Swiss mathematician, Daniel Bernoulli proved that wealth compounds, is “multiplicative” to use the more technical and uglier wording, and that, in terms of risk, tends toward its own destruction. This is the most likely long-term outcome for most capital allocators, which leads naturally to the conclusion that in reducing risk, we increase our possibility of building wealth. This is, of course, at odds with the, “no reward without risk” paradigm that is in such wide currency. Yet, logically, if risk is primarily defined by the likelihood of loss, then piling risk on top of more risk should surely lead to a portfolio’s destruction. 

Losses impact portfolios more profoundly than corresponding gains. In truth, although perhaps controversial, this can be shown with very elementary arithmetic: a decay in wealth of 10% requires an 11.11% gain just for an investor to break even, while a 20% decline requires a 25% gain, a 50% decline demands a 100% gain, and a 99% decline requires a miracle. As losses mount, the gains needed just to break even escalate asymmetrically. Whether these losses come in one fell swoop, or in dribs and drabs over time, the demands on a portfolio to earn asymmetrically greater returns soar. Managers and investors are rationally obliged to avoid risk, investing only when they have an edge, and, when doing so, investing in concentrated portfolios, while diversifying across time. 

Losing money is the dominant state of most investors and businesses. In his 2018 paper, “Do Stock Outperform Treasury Bills?”, Hendrik Bessembinder observed that just 4% of publicly traded companies in the CRSP database account for the net gain for the U.S. stock market between 1926 and 2018, with the other stocks having returns equal to those of Treasury bills. More precisely, 96% of stocks, if held across their lifetime, cannot match the returns of Treasury bills. Wealth destruction is the order of the day.

Measurable and Uncertain

There is a certain comfort to be derived from Knight’s notion of risk: with robust techniques and enough data, one can arrive at a measure of risk within an acceptable margin of error. Yet, data is often either scarce, or very difficult or expensive to get. For instance, gravitational waves were first proposed by Oliver Heaviside in 1893, and then by Henri Poincaré in 1905, before being predicted by Albert Einstein in 1916. Yet, the first indirect evidence for gravitational waves only came in 1974, and the first direct observation of them was made in 2015 by the LIGO project, over a century after Heaviside’s work. On the basis of a paucity of data, a scientist in 2014 could have reasonably rejected the idea of gravitational waves, and that scientist would have been wrong. In the second century A.D., Juvenal wrote, “Rara avis in terris, nigroque simillima cygno [a bird as rare upon the earth as a black swan]!”, and since then, “black swan” has been an apt metaphor for rare events. Since 1697, when a team of Dutch explorers led by Willem de Vlamingh saw black swans in Western Australia, becoming the first Europeans to see them, black swans have taken on a different meaning, being, not simply rare events, but rare events which are the undoing of systems of thought. That is the first chink in Knight’s armour: a thing may be measurable, and uncertain, given data constraints. Indeed, a false thing can possess more data in its favour than a true thing.

The Subjectivity of Risk

The view that probability is measurable, and therefore objective, is driven by the Industrial Revolution and the needs of factory managers to optimise their processes. The Student’s t-test, for instance, came from the work of William S. Gossett, a brewer at Guiness in the late-nineteenth century. At present, the dominant paradigm in probability theory is the frequentist interpretation, in which the probability of some outcome is the limit of its relative frequency of occurrence over repeated trials under similar conditions. In that framing, if, for instance, a bottle-maker faces a risk of 0.5% of 1 of 10000 bottles breaking, that risk is determined by observations of the bottle making process. However, this view of probability does not have a universal application: not all probabilities are a function of the physical properties of the phenomenon being studied. The most typical thought experiment that is often presented involves either a die or coin, where the chances of a side turning up is a function of the physical properties of the die or coin.

The most significant issue with the frequentist interpretation is that these probabilities are somewhat circular and subjective. Take the chance of an earthquake: P.B. Stark and D.A. Freedman argue that it is not possible to actually have a large number of trials to forecast the relative frequency of earthquakes within the next thirty years. Those “trials” are not laboratory experiments. This is even more significant when one considers that earthquakes are rare, unlike changes in the weather, with recurrence over periods of hundreds of years. They hold that probability should be seen as a property of a mathematical model that seeks to describe features of the natural world, rather than an expression of the natural world. In doing so, one is forced to accept that risk cannot be so easily segregated from uncertainty, because no mathematical model can perfectly express the natural world. Rather, mathematical models are founded upon assumptions made by the modeller, assumptions which cannot be tested. For investors and managers, this is especially true: risk measures are not the natural expression of the market, they are constructs, and thus, the measures are not pure objective creatures, instead, they commingle our subjective ideas with objective facts, and so, they are less reliable than is often discussed. Uncertainty is a feature of risk, not a separate category. 

Not only are many choices made within a mathematical model untestable, they may even seem arbitrary. For instance, Markowtiz’s decision to use “volatility of returns” of returns was guided, not by the logic of risk, but, as he detailed in 1959 book, Portfolio Selection, by fears that the computing power available at the time did not allow him to calculate the more plausible semivariance. 

The modelling decisions that one makes, the decision to use one risk measure over another, or the credence given to one theory over another, are all examples of areas in which one is forced to weigh evidence without recourse to some final test that says what is true, or more likely. The Knightian segregation of risk and uncertainty overstates the gulf between the two, and leads to overconfidence about risk measures. There are unquantifiable risks that are distinct from uncertainty that managers face. For example, investors have a smorgasbord of risk measures to use, but the risk of selecting the wrong risk measure cannot be measured. A theory, concept or argument may be wrong, even if the underlying data is perfect, and there is no way to arrive at a probability that one argument is more likely than another. These unquantifiable risks are, nevertheless, tractable within the framework of plausible reasoning.  The nature of these risks is that they lead to only partial entailment or partial belief, which is to say, uncertainty is implicated in their formation. Thus, we are compelled to embrace uncertainty as a component of risk, and the immeasurability of aspects of risk.

Finally, risk is subjective not simply from an ontological point of view, but from a positional perspective with a trade. It matters whether one is buying or selling an asset, because the risks are opposed. Take Warren Buffett’s April 2020 decision to sell Berkshire Hathaway’s holdings in Delta Air Lines (DAL), United Airlines (UAL), American Airlines (AAL) and Southwest Airlines (LUV), realising a loss of $5 billion, having bought them for $9.3 billion between mid-2016 and early 2017. Between 2019 when Berkshire Hathaway invested in the airlines, and the decision to sell, American Airlines fell 62.9%, Delta Air Lines fell 58.7%, Southwest Airlines fell 45.8%, and United Airlines fell 69.7%, for an average decline of 59.28%, assuming equal-weights for the sake of simplicity. 

Selling these stocks seemed at odds with Buffett’s philosophy of striking in times of fear, and of the diminishing risk entailed in falling valuations. Had the man who scoffed at volatility as a measure of risk lost his nerve at the moment of maximum volatility? Surely it was obvious to the far-sighted investor that airlines would fly again? Buffett’s decision was placed in harsher light when, within a year, American Airlines and Southwest Airlines were both up more than 80%, and United Airlines and Delta Air Lines were up around 70%. An investor who bought at the May 25, 2020 bottom would have earned a 200% return from United Airlines, and a 190% return from American Airlines. Results are their own defence, and they seemed to damn a man considered by many as the greatest investor ever. 

However, simple arithmetic reveals the subjectivity of risk, that it matters whether one is buying or selling, and explodes the notion that Buffett’s decision to sell was imprudent: having experienced a decline of 59.28% in its airline portfolio, Berkshire Hathaway needed a gain of 245.55% just to break even, which is to say, the disutility or pain of loss, is greater than the utility or usefulness of a gain. Hope may have feathers, but that is no reason for the prudent investor to let it perch on the soul. A decision to stay the course would, in effect, be a bet that not only would airlines enjoy staggering returns, but that the post-pandemic climate for airlines would be markedly better than the pre-pandemic climate.