As decision makers ponder the possible outcomes of their decisions they often think about risk, which is the possibility of an undesirable result. In discussing this, it is convenient to consider the notion of arisk-neutral decision maker. Someone who is risk neutral is willing to play the long-run odds when making decisions, and will evaluate alternatives according to their expected values.
For example, such a decision maker would be indifferent between receiving $1 for certain and an alternative with equal chances of yielding $0 and $2, since this is the average amount that the alternative would yield if repeated many times.
While an insurance company may evaluate individual policies as if it were risk-neutral, for alternatives with substantial risks, decision makers are oftenrisk averse, which means that they value alternatives at less than their expected values. To make this definition of value precise, we define the certain equivalent, (or certainty equivalent) of an alternative as the amount that the decision maker would be indifferent between (1) having that monetary amount for certain or (2) having the alternative with its uncertain outcome.
For example, a risk-averse decision maker might have a certain equivalent of $500,000 for an alternative with equal chances of yielding $0 and $2,000,000, even though the expected value for this alternative is $1,000,000. In thinking about risk aversion, it is important to remember that different decision makers have different attitudes toward risk. While this gamble with equal chances of yielding $0 and $2,000,000 may be very risky for me, a billionaire or a big company may not view these stakes as large and may have a certain equivalent close to the expected value.
Decisions where risk aversion holds can be analysed using a utility function, which encodes a decision maker’s attitude toward risk taking in mathematical form by relating the decision maker’s satisfaction with the outcome (or “utility” associated with the outcome) to the monetary value of the outcome itself. These utility functions can be indexed by their risk tolerance, which is a technical term describing the decision maker’s attitude toward risk. The greater the decision maker’s risk tolerance, the closer the certain equivalent of a gamble will be to its expected value. The risk tolerance is a mathematical quantity that describes the decision maker’s attitude towards risk; it is not the maximum amount that the decision maker can afford to lose, though generally decision makers with greater wealth will have larger risk tolerances. The decision maker needs to think about his risk tolerance only in cases where the stakes are large and he is not comfortable basing his decision on the expected monetary value.
Key distinction: certain equivalent vs. expected NPV
Example: The certain equivalent for a risky new product is the smallest sum of money for which the decision maker would be willing to sell rights to that product. The expected NPV for the product is the hypothetical average NPV from numerous independent launches of identical projects.
Why it’s important: Most projects cannot be repeated and even if they could, when the stakes are large, most decision makers value gambles at less than their expected values. Precisely how much less than their expected value depends on the decision maker’s attitude towards risk. This attitude towards risk varies from decision maker to decision maker and, even for a specific decision maker, may vary over time.