UNCERTAINTY :

Uncertainty is at the very core of the concept of risk itself. It is uncertainty about the outcome in a given situation. Uncertainty does not exist in the natural order of things though there are a number of outcomes, which are uncertain. For example: the weather for the test match; the possibility of being made redundant; the risk of having an accident. There is surely uncertainty surrounding all of these events.

In 1921, Frank Knight summarized the difference between risk and uncertainty thus: “… Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated. … 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 phenomena 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 un-measurable one that it is not in effect an uncertainty at all.”

Risk is incorporated into so many different disciplines from insurance to engineering to portfolio theory that it should come as no surprise that it is defined in different ways by each one. It is worth looking at some of the distinctions:

(a) Risk versus Probability: While some definitions of risk focus only on the probability of an event occurring, more comprehensive definitions incorporate both the probability of the event occurring and the consequences of the event. Thus, the probability of a severe earthquake may be very small but the consequences are so catastrophic that it would be categorized as a high-risk event.

(b) Risk versus Threat: In some disciplines, a contrast is drawn between risk and a threat. A threat is a low probability event with very large negative consequences, where analysts may be unable to assess the probability. A risk, on the other hand, is defined to be a higher probability event, where there is enough information to make assessments of both the probability and the consequences.

(c) All outcomes versus Negative outcomes: Some definitions of risk tend to focus only on the downside scenarios, whereas others are more expansive and consider all variability as risk. The engineering definition of risk is defined as the product of the probability of an event occurring, that is
viewed as undesirable, and an assessment of the expected harm from the event occurring.

Risk = Probability of an accident * Consequence in lost money/deaths

In contrast, risk in finance is defined in terms of variability of actual returns on an investment around an expected return, even when those returns represent positive outcomes. Building on the last distinction, we should consider broader definitions of risk that capture both the positive and negative outcomes