The Difference Between Risk and Uncertainty

| 05/14/2009 |
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Recently, we’ve noticed a substantial number of visits referred by search engines from folks trying to understand the difference between risk and uncertainty. In fact, we have a post from April 20, with the tongue-in-cheek title of Learning the Difference Between Risk and Uncertainty, or not.

In that post, we criticize financial firms because they don’t seem to have changed their uncertainty management tactics or methodologies despite the market upheavals and shocks of the past few years. In fact, they still refer to the field as “risk management.”

However, for those looking for something a bit less verbose–but only a bit–we offer the following italicized distinction, which we’ve excerpted from that post.

The following paragraph is repetitive, but reading different phrases that have the same meaning is often the easiest way to learn. That’s why many students learn better in lectures than by solely reading a textbook; the concepts are usually mentioned and presented in a variety of ways in class, whereas often the textbooks strive for parsimony of exposition.1

As usual, we point new readers to our essay, Uncertainty Management, which details our perspective and philosophy on these issues… The main point is that not all uncertainty is measurable, i.e., that measurable uncertainty, or risk, is a proper subset of uncertainty and unknowing. (In other words, specific mathematical conditions must be met for uncertainty to be risk. So, uncertainty is a more general term, i.e., all risk involves uncertainty, but not everything that is uncertain is risky because not all uncertainty is measurable, which, again, has a specific mathematical definition that we don’t care to mention.)

The above definition of risk as quantifiable uncertainty is due to Frank Knight, who developed it in the early-to-mid 20th century.

Uncertain phenomena are often modeled as risky events. While there are a host of other mistakes that one can make in the modeling process, a huge specification error is made when the phenomenon is uncertain and immeasurable, but it is treated as being measurable. That’s especially bad in financial and economic settings because such modeling errors tend to reduce or eliminate the modeled–but not the real–chances of really bad things happening.

To be a bit more precise, note that for some uncertain phenomena, a probability distribution will not exist.

For others, a distribution may exist, but its moments–which one may grossly think of as its common statistics–may not. For example, there are mathematical functions that are probability distributions, but which have no mean or variance (so no standard deviation, either). Many of them look a lot like Normal distribution and density functions–i.e., they have a familiar bell shape like a Normal density–but their “tails” are “too fat,” and extreme events are hundreds or thousands or millions of times more likely than with a Normal distribution. That difference in frequencies of outlying events is why parameters like the expected value and standard deviation don’t exist.2

The problem in real life is that unless one is playing a structured game of chance, one’s never quite certain whether something is uncertain but not risky, or whether it can indeed be quantified.

Regular readers know that we often cite (1) St. James’ admonition in his only epistle that one is like a “puff of smoke,” in the sense that they and their welfare are temporary, ephemeral, and uncertain; and (2) the Problem of Induction, which notes that regardless of the time series of observations, one can never be quite sure of the underlying random process.

That’s why we gave two subtitles to our essay Uncertainty Management: (1) ignoramus et ignorabimus , which means “we do not know and will not know,” and (2) How Trading is Like Playing in a Culvert on a Hot, Sunny, Summer Day, although “trading” can be generalized to any number of activities, including many social ones where, obviously, behavior and sometimes panic come into play.

Copyright © 2009 Spero Consulting.


  1. Depending upon one’s knowledge base, which can be thought of as one’s understanding of words, trying to understand a concept is like looking through a semi-transparent cube to view the underlying idea. The greater one’s knowledge, the less opaque are the cube’s sides. Indeed, depending upon one’s background, approaching from different sides or angles may permit better or worse views of the idea.
  2. Basically, when one tries to add the products of the frequencies and the potential values, the sum becomes infinitely large and can’t be defined.

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