# Risk Preference and Utility

14 Pages Posted: 21 Oct 2008

See all articles by Samuel E. Bodily

## Samuel E. Bodily

University of Virginia - Darden School of Business

### Abstract

This introduction to methods for treating risk illustrates the assessment and use of a utility function and gives simplified techniques for typical forms of risk aversion. Some associated risk-preference exercises (UVA-QA-0253) can be used with this note.

Excerpt

UVA-QA-0232

RISK PREFERENCE AND UTILITY

Many risky opportunities are evaluated solely by the average of the possible financial outcomes, that is, by the EMV or expected monetary value. The EMV is a convenient single number to help compare alternatives that have complicated risk profiles, but very few people in reality are willing to play the averages when making decisions of any importance. For example, most people would sell for less than \$ 500 a lottery ticket that gave them a 50% chance at winning \$ 1,000.

In this chapter, methods are presented for explicitly factoring risk into decision making in a consistent, systematic way. The approach is to assess the decision maker's degree of risk tolerance and to identify an appropriate model of his or her risk preferences. This is done using a so-called utility function, which scores the “utility” of various outcomes. The best action is the one with the highest probability-weighted or “expected” utility. The power of the utility method is that we can represent a rich variety of risk tolerances within a single unifying concept and set of procedures. With this approach we can determine how much below the \$ 500 average value is acceptable for the above-mentioned lottery ticket. And we can similarly put a price on a complicated risk profile that is consistent with the price placed on the lottery ticket.

The Utility of Monetary Consequences

Consider a risky opportunity (call it a lottery for simplicity) that has equally likely possible outcomes of \$ 2,500 and \$ 10,000, The expected monetary value is .5(10,000) + .5(2,500) or \$ 6,250. Would you pay \$ 6,250 to purchase this lottery? Most people would not. Not even close. We all use something besides monetary value and probability to evaluate uncertain prospects. Our evaluation usually involves a third factor: our willingness to face risk.

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Keywords: decision theory, management decision models, risk analysis, risk management

Suggested Citation

Bodily, Samuel E., Risk Preference and Utility. Darden Case No. UVA-QA-0232. Available at SSRN: https://ssrn.com/abstract=911832