Certainty Equivalent

What Is a Certainty Equivalent?

A certainty equivalent is the sure amount of money that a person would consider just as desirable as an uncertain prospect. Instead of facing a payoff that might be high or low, the investor would be indifferent between receiving this guaranteed sum and taking the gamble. The concept comes from decision theory and lets people compare choices with different levels of risk on a common scale. It is closely tied to expected value, which is the average outcome of a risky prospect, weighted by probability.

How It Works

For most people, the certainty equivalent is lower than the expected value. The gap reflects risk aversion, the preference for a steady outcome over an uncertain one with the same average result. The difference between the two figures is called the risk premium:

Certainty Equivalent = Expected Value − Risk Premium

A risk-neutral person has a certainty equivalent equal to the expected value, so the risk premium is zero. Economists often describe a person's attitude toward risk with a utility function, which assigns a level of satisfaction to each amount of money. The certainty equivalent is the guaranteed amount whose utility equals the expected utility of the gamble.

An Example

Consider a prospect that pays $100 with a 50% chance and nothing otherwise. Its expected value is $50. A risk-averse person might say they would rather take a guaranteed $40 than play the gamble. In that case, the certainty equivalent is $40 and the risk premium is $10. A less risk-averse person might accept $45, which produces a smaller risk premium.

Why It Matters to Investors

The certainty equivalent is a theoretical tool rather than a figure reported on any market. It helps explain why investors often expect higher returns from riskier assets and how portfolio choices reflect personal tolerance for uncertainty. Comparing certainty equivalents allows an analyst to rank two investments with different risk profiles on one scale. Because the figure depends on each person's preferences, two investors can look at the same asset and reach different valuations.