# 4.4 Alternative Risk Definitions

We subscribe to the classic definition of risk as the expected loss –1) in its mathematical definition as the mean value of a probability distribution of losses, 2) in the significance of it representing the long term loss (as determined by the central limit theorem and law of large numbers -discussed below) and 3) in it being the most common understanding of risk as the possibility of losing something of value. We briefly describe and give reason(s) for dismissing other definitions below.

4.4.1.1 Knight’s definition of risk as uncertainty when probabilities are known

In 1921 Frank Knight defined risk as uncertainty when probabilities are known. Unfortunately, many people abandoned the classic definition of risk and adopted Knight’s definition. Aside from Knight’s definition not possessing the benefits of the classic definition discussed above, one major shortcoming of his definition is that it does not require a loss. Thus, for example, someone watching people playing poker on tv would, by Knight’s definition, have a risk.

As noted by Hubbard[1]

Frank Knight was an influential economist of the early 20th century who wrote a text titled Risk, Uncertainty and Profit (1921). The book, which expanded on his 1917 doctoral dissertation, has become what many economists consider a classic. In it, Knight makes a distinction between uncertainty and risk that still influences a large circle of academics and professionals today: [To differentiate] the measurable uncertainty and an unmeasurable one we may use the term “risk” to designate the former and the term “uncertainty” for the latter. According to Knight, we have uncertainty when we are unable to quantify the probabilities of various outcomes whereas risk applies to situations where the odds of various possible outcomes can be known.

Why not use Knight’s definition? For one thing, it contradicts the classical mathematical definition of risk as the expected loss that is still subscribed to by most statisticians and scientists today. But equally as important, as Hubbard points out, Knight’s definition would classify an uncertain event with no loss as a risk. This is not reasonable, because, for example, most people would not consider it a risk to simply watch a roulette wheel at a casino if they did not place a bet and hence had no possibility of a loss. Surely there is uncertainty, the odds are known, but nothing is at risk. Hilson[1], who is one of the authors of the ISO and PMI standards explains that all risks are uncertain but not all uncertainties are risks. A risk is an uncertainty that matters.

4.4.1.2 Defining risk as both upside as well as a downside

For most people, risks are something to worry about. They consider risks as potential losses, such as the risk of dying, the risk of being in an accident, the risk of a stock or portfolio of stocks they own declining in value. Cyber risk, today a major concern, is about preventing losses in the form of confidentiality, integrity, or availability of information, all of which are ‘losses’. Defining ‘upside risks’ is contradictory to such common usage of the word risk. The primary dictionary definitions of risk do not include ‘upside’. For example, the Webster dictionary defines risk as:

*1*: possibility of loss or injury: peril

*2*: someone or something that creates or suggests a hazard

*3*

*a*: the chance of loss or the perils to the subject matter of an insurance contract; *also*: the degree of probability of such loss

*b* : a person or thing that is a specified hazard to an insurer

*c* : an insurance hazard from a specified cause or source war *risk*

*4*: the chance that an investment (such as a stock or commodity) will lose value

4.4.1.3 Economists definition of risk as variability.

Economists use variability as risk in two different ways – 1) modern portfolio theory, where a linear programming optimization is used to either minimize the variability (risk) of a portfolio of investments for a given expected return, or maximize the expected return for the portfolio for a given variability of the portfolio; and 2) in options theory where the risk of an investment (as represented by the variability of the investment in a log-normal distribution) is used to price an option. Without going into a discussion of some of the questionable assumptions of each of these theories, the use of variability as risk is questionable since it includes variability above the mean as well as below the mean. In fact, some criticisms of modern portfolio theory have led to the use of ‘semi-variance’ rather than variance as a measure of risk. As we will discuss below, using the definition of risk as the expected loss is our favored definition. Risk is a long-term measure, corresponding to the expected return in modern portfolio theory. Value at risk, which we will also discuss below, is a short-term measure of risk that corresponds to the ‘risk’ of modern portfolio theory.

4.4.1.4 Using just the classical definition of risk as the expected loss.

Defining risk as Expected loss alone precludes the consideration of opportunities when making decisions and doing strategic planning. Taking risks is an important ingredient of success. When viewed as such, risk is an ‘upside’ objective. If we were to limit the definition of ‘risk’ only to the downside, then the role of risk assessment and management in decision making and strategic planning would be limited. Risk managers should be an integral part of decision making as well as being responsible for minimizing expected losses. We can overcome this dilemma as follows.

[1] Hillson, David, *Managing Risk in Projects, Routledge Taylor & Francis Group, London and New York, 2009*

[1] Hubbard, Douglas W., 2009, *The Failure of Risk Management – Why It’s Broken and How to Fix It*, Wiley.