While we link the concept of risk with the notion of uncertainty, risk isn’t synonymous with uncertainty. A person experiencing the flu is not necessarily the same as the virus causing the flu. Risk isn’t the same as the underlying prerequisite of uncertainty. RiskriskUncertainty about a future outcome, particularly the consequences of a negative outcome. (intuitively and formally) has to do with consequences (both positive and negative); it involves having more than two possible outcomes (uncertainty).^[7] The consequences can be behavioral, psychological, or financial, to name a few. Uncertainty also creates opportunities for gain and the potential for loss. Nevertheless, if no possibility of a negative outcome arises at all, even remotely, then we usually do not refer to the situation as having risk (only uncertainty) as shown in Figure 1.2, “Uncertainty as a Precondition to Risk”.

Figure 1.2. Uncertainty as a Precondition to Risk

In general, we widely believe in an a priori (previous to the event) relation between negative risk and profitability. Namely, we believe that in a competitive economic market, we must take on a larger possibility of negative risk if we are to achieve a higher return on an investment. Thus, we must take on a larger possibility of negative risk to receive a favorable rate of return. Every opportunity involves both risk and return.

In a world of uncertainty, we regard risk as encompassing the potential provision of both an opportunity for gains as well as the negative prospect for losses. See Figure 1.3, “Roles (Objectives) Underlying the Definition of Risk”—a Venn diagram to help you visualize risk-reward outcomes. For the enterprise and for individuals, risk is a component to be considered within a general objective of maximizing value associated with risk. Alternatively, we wish to minimize the dangers associated with financial collapse or other adverse consequences. The right circle of the figure represents mitigation of adverse consequences like failures. The left circle represents the opportunities of gains when risks are undertaken. As with most Venn diagrams, the two circles intersect to create the set of opportunities for which people take on risk (Circle 1) for reward (Circle 2).

Figure 1.3. Roles (Objectives) Underlying the Definition of Risk

Identify the overlapping area as the set in which we both minimize risk and maximize value.

Figure 1.3, “Roles (Objectives) Underlying the Definition of Risk” will help you conceptualize the impact of risk. Risk permeates the spectrum of decision making from goals of value maximization to goals of insolvency minimization (in game theory terms, maximin). Here we see that we seek to add value from the opportunities presented by uncertainty (and its consequences). The overlapping area shows a tight focus on minimizing the pure losses that might accompany insolvency or bankruptcy. The 2008 financial crisis illustrates the consequences of exploiting opportunities presented by risk; of course, we must also account for the risk and can’t ignore the requisite adverse consequences associated with insolvency. Ignoring risk represents mismanagement of risk in the opportunity-seeking context. It can bring complete calamity and total loss in the pure loss-avoidance context.

We will discuss this trade-off more in depth later in the book. Managing risks associated with the context of minimization of losses has succeeded more than managing risks when we use an objective of value maximization. People model catastrophic consequences that involve risk of loss and insolvency in natural disaster contexts, using complex and innovative statistical techniques. On the other hand, risk management within the context of maximizing value hasn’t yet adequately confronted the potential for catastrophic consequences. The potential for catastrophic human-made financial risk is most dramatically illustrated by the fall 2008 financial crisis. No catastrophic models were considered or developed to counter managers’ value maximization objective, nor were regulators imposing risk constraints on the catastrophic potential of the various financial derivative instruments.

If we try to get an ex-post (i.e., after the fact) risk measure, we can measure risk as the perceived variability of future outcomes. Actual outcomes may differ from expectations. Such variability of future outcomes corresponds to the economist’s notion of risk. Risk is intimately related to the “surprise an outcome presents.” Various actual quantitative risk measurements provide the topic of Chapter 2, Risk Measurement and Metrics. Another simple example appears by virtue of our day-to-day expectations. For example, we expect to arrive on time to a particular destination. A variety of obstacles may stop us from actually arriving on time. The obstacles may be within our own behavior or stand externally. However, some uncertainty arises as to whether such an obstacle will happen, resulting in deviation from our previous expectation. As another example, when American Airlines had to ground all their MD-80 planes for government-required inspections, many of us had to cancel our travel plans and couldn’t attend important planned meetings and celebrations. Air travel always carries with it the possibility that we will be grounded, which gives rise to uncertainty. In fact, we experienced this negative event because it was externally imposed upon us. We thus experienced a loss because we deviated from our plans. Other deviations from expectations could include being in an accident rather than a fun outing. The possibility of lower-than-expected (negative) outcomes becomes central to the definition of risk, because so-called losses produce the negative quality associated with not knowing the future. We must then manage the negative consequences of the uncertain future. This is the essence of risk management.

Our perception of risk arises from our perception of and quantification of uncertainty. In scientific settings and in actuarial and financial contexts, risk is usually expressed in terms of the probability of occurrence of adverse events. In other fields, such as political risk assessment, risk may be very qualitative or subjective. This is also the subject of Chapter 2, Risk Measurement and Metrics.