15 Homogeneous Risk Measures
Lindon Robison
Learning goals. After completing this chapter, you should be able to: (1) define and measure risk; (2) understand how a person’s risk aversion affects his/her resource allocation; (3) distinguish between direct and indirect outcome variables; and (4) evaluate alternative risk response strategies available to financial managers including sharing risky outcomes, purchasing insurance, diversifying investments, purchasing risk reducing investments, and choosing an optimal capital structure.
Learning objectives. To achieve your learning goals, you should complete the following objectives:
- Learn how to describe risky events by assigning a random variable to their outcomes and by assigning a probability density function (pdf) to the random variable.
- Learn how measure the variability and central tendencies of random variables using the expected values and variances of their probability density functions.
- Learn how risk premiums can be used to measure the cost of risk.
- Learn how to describe the risky choice set facing firm managers using expected value-variance (EV) efficient sets.
- Learn about the normal probability density function and understand why it is so important when describing risky events.
- Learn how sharing risk with others can be a useful response to risk.
- Learn how purchasing insurance can be a useful response to risk.
- Learn how diversification can be a useful response to risk.
- Learn how purchasing risk-reducing inputs can be a useful response to risk.
- Learn how leverage affects the level of risk facing the firm.
Introduction
The adjective “uncertain” describes an event (such as a hurricane or a football game) whose outcomes are not known with certainty. An uncertain event must have at least two possible outcomes, and it usually has more. In an earlier time, a distinction was made between risky events and uncertain events based on the information available for identifying an event’s possible outcomes and predicting the probabilities of those outcomes. For example, the flip of a coin is a familiar event with two outcomes: heads (H) and tails (T). Based on past trials or logic, we can infer that the probability of a heads (tails) appearing when a fair coin is tossed is about 50 percent. Some may call this event risky because we have good information about the possible outcomes and the probability of their occurrence.
Now consider a different event: the toss of a thumbtack.[1] What is the probability that the thumbtack will land on its side versus landing on its head? Because we are not familiar with this event and cannot assign probabilities to its outcomes based on our past experience or logic, this event might be called uncertain.
For many, the distinction between risky events and uncertain events is no longer important, and most researchers assign the adjectives uncertain and risky to events interchangeably. One reason many do not distinguish between risky and uncertain events is