Risk versus Uncertainty, or Mr. Slate versus Great-Aunt Matilda

Taking two quick stops at Webster’s,2 we find the following:

1. risk: “possibility of loss or injury; peril”
2. uncertainty: “indefinite, indeterminate” and “not known beyond a doubt.”

So in common usage, the distinction between the two is that risk denotes a positive probability of something bad happening, while uncertainty does not necessarily imply a value judgment or ranking of the possible outcomes. Fundamentally, though, in common usage both terms refer to a similar situation, in which some aspect of the future cannot be foreseen.

In economics, the definitions of risk and uncertainty are different, and the distinction between the two is clearer. Frank H. Knight established the economic definition of the terms in his landmark book, Risk, Uncertainty, and Profit (1921):

1. risk is present when future events occur with measurable probability
2. uncertainty is present when the likelihood of future events is indefinite or incalculable

Knight arrives at this distinction between risk and uncertainty as part of his analysis of profit and its origins. In his book, Knight seeks to explain the persistent difference between the zero profits predicted as a result of perfect competition in economic theory and the actual positive or negative profits found in reality. In paragraph 24 of Part I, Chapter I, he writes

The primary attribute of competition, universally recognized and evident at a glance, is the “tendency” to eliminate profit or loss, and bring the value of economic goods to equality with their cost…. But in actual society, cost and value only “tend” to equality; it is only by an occasional accident that they are precisely equal in fact; they are usually separated by a margin of “profit,” positive or negative. Hence the problem of profit is one way of looking at the problem of the contrast between perfect competition and actual competition.

Standard economic theory states that in a world of perfect competition and in which all economic agents have complete knowledge, people will make purchase and production decisions that will lead to zero profits. Theories of profit developed prior to Knight argued that profit arises because people do not have perfect knowledge about the future. Harvests may turn out to be good or bad, consumers’ tastes and preferences may change, new and unforeseen products may emerge. Whenever anything happens to make the outcome of events not match with people’s expectations, then the revenues (“values” in the above quote) from the goods or services they produce will not equal costs, and profit will occur. The profits accrue to those parties willing to take on the vagaries of chance.

Let’s look at an example. When Mr. Slate hires Fred to work in his quarry for a fixed wage, Fred has the security of knowing what he will earn, but Mr. Slate cannot easily forecast his profits. Market prices for his output might rise or fall, Fred’s productivity might end up being higher or lower than expected, or any number of other things might occur to make Mr. Slate’s earnings higher or lower than he predicted. These higher or lower earnings, coming about due to the inherent unpredictability of many events, are the positive or negative profits to which Knight refers.

Under Knight’s framework, this is too broad a generalization of what constitutes risk. For him, risk as it is commonly used covers two distinctly different phenomena, and the economic implications of each is decidedly different with regard to the problem of profit. From paragraph 26 of Part I, Chapter 1:

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 shall accordingly restrict the term “uncertainty” to cases of the non-quantitive type. It is this “true” uncertainty, and not risk, as has been argued, which forms the basis of a valid theory of profit and accounts for the divergence between actual and theoretical competition.

So here we have the definitions given above. Knight argues that risk, which under his definition is measurable, will not generate profit. Risk can be quantified, either on a priori grounds (we know without investigation that a flipped coin will come up heads fifty percent of the time) or on the basis of empirical observation (since moving back to St. Louis, I get put on hold one-third of the time when I call for a pizza). Given this, people are able make arrangements to protect themselves against risk, in effect converting risk into certainty, assuming they are free to create the necessary institutions.

Returning to Mr. Slate, let’s suppose it is the case that history (or prehistory, as it were) has told him that in any given number of years, one-quarter of the time quarries lose one thousand dollars, but they make a thousand dollars three-quarters of the time. Assuming that he only owns one quarry, he has a 75% chance of making $1,000 and a 25% of losing $1,000. He can quantify the probabilities of future events, so he is facing risk. But if there are many quarries in the same area, all of which face the same 75%-25% risk, they can come together in some sort of arrangement to convert their collective risk into certainty.

For example, suppose there are 100 quarries in the area, including Mr. Slate’s, and all of them face the same 75%-25% risk. Then the average or expected annual earnings of each quarry are [75%×($1,000) + 25%×(-$1,000)] = $500, but no individual quarry will make that. Each quarry will either make $1,000 or lose $1,000, and at the start of the year, nobody knows which ones will make money and which ones will not.

To eliminate this risk, all of the quarry owners might enter into the following mutual agreement: At the end of each year they will pool all of their positive and negative earnings together and divide the total equally among themselves. Each year, we can expect that about 75 quarries will make money and 25 will lose money, so the total earnings should be [75×($1,000) + 25×(-$1,000)] = $50,000. Divided among the one hundred quarry owners, they each get $500. This is the same amount as each owner would average over time without the agreement, but notice the important difference. Without the pooling of outcomes, a very basic form of insurance, Mr. Slate will make $500 each year on average, but in any given year he does not know whether he will make $1,000 or lose $1,000. With the agreement, he knows that he will make $500 every year, converting his risk into certainty. Because he can eliminate the risk, no profit is generated.

Some might be skeptical of this analysis because in any given year, it is not very likely that exactly 75 quarries will make money and 25 will lose money. While this is true, it is also true that as long as some of the quarries in the agreement win money and some will lose, Mr. Slate’s earnings will always be between $1,000 and -$1,000—play with the numbers yourself to verify this—so the fluctuation in his earnings is reduced. Further, as more quarry owners enter into the agreement, it becomes increasingly likely that the actual outcome will reflect the 75%-25% split. Therefore, even though the risk may not be completely eliminated, it will be substantially reduced, with the risk remaining becoming smaller and smaller as more and more people join together for that purpose.

Note that the above analysis requires that it is possible for the quarries to come together and enter into a mutual arrangement of some kind. Knight deals with this assumption in paragraph 43 of Part I, Chapter II: “If it is objected that practical difficulties may prevent insurance even where the risk is determinate, the reply is that insurance, in the technical sense, is only one method of applying the same principle…. When the technique of business organization has reached a fairly high stage of development… such risks will be borne in groups large enough to reduce the uncertainty to substantially negligible proportions.” In other words, so long as there are no impediments to new markets emerging, people will develop ways to come together to convert risk into certainty. We must also assume that Mr. Slate wants to eliminate risk, something Knight addresses (a bit more dismissively) in the same paragraph: “It is true that the person subject to such a risk may voluntarily choose not to insure, but it is hard to distinguish such a course from deliberate gambling, and economists have not felt constrained to recognize gambling gains in general as a special income category in the theory of distribution.”

So that covers risk. What about uncertainty? Uncertainty is not measurable, and so cannot be quantified and handled through insurance or other arrangements. Uncertainty occurs in circumstances that cannot be analyzed either on a priori grounds, because they are too irregular, or through empirical observation, because they are too unique. To take up a somewhat more current example, let’s say that my Great-Aunt Hortence has made Thanksgiving dinner in my family every year for the last thirty years. In fifteen of those thirty years, or 50% of the time, the turkey has been dry. Looking ahead to this Thanksgiving’s meal, based on my experience I have a very good idea of the likelihood that this year’s turkey will be dry—a situation of risk. If, however, Hortence’s lumbago is flaring up and so Great-Aunt Matilda will be taking over for this year only, I have no idea how the turkey will be. I’ve never had turkey made by Matilda before, so I have no past experience on which to base a probability. Even if I could, because Matilda will be making just this one meal, there is no way for me to enter into an arrangement with other people like Mr. Slate could to handle the unpredictability. This is a situation of uncertainty.

Uncertainty, which cannot be eliminated or insured against, is for Knight the source of profit. He writes in Part III, Chapter X, paragraph 33, that “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.” Faced with uncertainty, a person must rely on his own judgment, having no outside information to which to refer. It is on this resource, good judgment, that profit is earned. A person who can peer into the more unknowable aspects of the future and decide on what reveals itself to be the appropriate course will be awarded with profit; for an inappropriate course, he suffers a loss. But lest those who have been successful at making the right decisions facing uncertainty become too pleased with themselves, Knight remarks in the same paragraph that

The receipt of profit in a particular case may be argued to be the result of superior judgment. But it is judgment of judgment, especially one’s own judgment, and in an individual case there is no way of telling good judgment from good luck, and a succession of cases sufficient to evaluate the judgment or determine its probable value transforms the profit into a wage.

The last point, humbling for an entrepreneur, observes that by the time enough instances of a given situation of uncertainty have occurred to convince people that the entrepreneur’s judgment is sound, there will have been enough time for an uncertainty to have transformed into a risk. The risk being knowable, no profit can be gained, and the person who was once steering through uncertainty for a profit is then managing known risk for a wage.

Knight’s contribution, then, in separating risk from uncertainty, does not represent an overhaul of the theory of profit he initially confronted. For him, profits still arise from the inherent unpredictability of the world around us. The advances due to Knight are the recognition that some of that unpredictability is manageable, and the argument that profit is earned by people who take on endeavors that go beyond that sort of management.