Risk premium

For an individual, a risk premium is the minimum amount of money by which the expected return on a risky asset must exceed the known return on a risk-free asset in order to induce an individual to hold the risky asset rather than the risk-free asset. It is positive if the person is risk averse. Thus it is the minimum willingness to accept compensation for the risk.

The certainty equivalent, a related concept, is the guaranteed amount of money that an individual would view as equally desirable as a risky asset.

For market outcomes, a risk premium is the actual excess of the expected return on a risky asset over the known return on the risk-free asset.

Let an individual's increasing, concave von Neumann-Morgenstern utility function be u, let r_f be the return on the risk-free asset, and let r be the random return on the risky asset. Write r as the sum of its expected return r_f + ${\displaystyle \pi }$, necessary for indifference between the risky and risk-free assets, and its zero-mean risky component x. Then the risk premium ${\displaystyle \pi }$ is defined by

Here the left side is the degree of attractiveness of the risk-free asset—the known utility of its known return—and the right side is the degree of attractiveness of the risky asset—the expected utility of its risky return. Thus the risk premium is the amount by which the risky asset's expected return must in fact exceed the risk-free return in order to make the risky and risk-free assets equally attractive.

...
Wikipedia