Defining risk, an allegedly impossible task

Glyn A. Holton, a contributor to Haslett’s Risk Management, tackles a fundamental conceptual problem, “Defining Risk” (pp. 113-123). His thesis is that risk lies at the intersection of subjective probability and operationalism.

He starts with Hume, who laid the philosophical foundation for both streams when he wrote: “Though there be no such thing as Chance in the world; our ignorance of the real cause of any event has the same influence on the understanding, and begets a like species of belief or opinion.”

Holton then criticizes objectivists such as Frank Knight and Keynes who believed that risk is real. Knight distinguished between objective or measurable probabilities and subjective or unmeasurable probabilities, designating the former as risk and the latter as uncertainty. For Keynes probabilities apply not to individual propositions but to pairs of propositions where one proposition is not known to be true or false and the second is the evidence for the first.

It’s not important to go into Holton’s arguments against objectivism; we can skip straight to his own efforts to define risk. As a first stab, he suggests that risk has two essential components: exposure (a person has a personal interest or stake in what transpires) and uncertainty. He admits, however, that to define risk as “exposure to a proposition of which one is uncertain” is flawed.

It is indeed flawed if one accepts Percy Bridgman’s philosophy of operationalism, developed in his 1927 book The Logic of Modern Physics, which contends that “we mean by any concept nothing more than a set of operations.” From Bridgman’s viewpoint, Holton’s preliminary definition of risk would be inadequate because it is intuitive; it “depends on the notions of exposure and uncertainty, neither of which can be defined operationally.”

The paper’s conclusion is that there is no true risk. “At best, we can operationally define our perception of risk.” Therefore, when assessing risk metrics such as delta, value-at-risk, or beta in financial applications, we can never ask whether they capture true risk or whether they misrepresent risk. The most we can ask is whether a particular risk metric is useful, whether it will “promote behavior that management considers desirable.”

Holton’s conclusion may seem intellectually unsatisfactory, but at least it’s a position worth arguing against.