Risk premium

A risk premium is the minimum difference between the expected value of an uncertain bet that a person is willing to take and the certain value that he is indifferent to.

Example
Suppose a game show participant may choose one of two doors, one that hides $1,000 and one that hides $0. Further suppose that the host also allows the contestant to take $500 instead of choosing a door. All three options (door 1, door 2, or take $500) have the same expected value of $500, so there is no risk premium for choosing the doors over the guaranteed $500.

A contestant unconcerned about risk is indifferent to these choices. However, a risk averse contestant may be more likely to choose no door and accept the guaranteed $500.

If too many contestants are risk averse, the game show may encourage selection of the riskier choices (door 1 or door 2) by creating a risk premium. If the game show offers $2,000 behind the good door, increasing to $1,000 the expected value of choosing doors 1 or 2, the risk premium becomes $500 (i.e., $1,000 expected value - $500 guaranteed amount). Contestants with a minimum acceptable rate of return of $500 or more will likely choose a door instead of accepting the guaranteed $500.

Finance
In finance, the risk premium can be the expected rate of return above the risk-free interest rate. When measuring risk, a common sense approach is to compare the virtually risk-free return on T-bills and the very risky return on other investments. The difference between these two returns can be interpreted as a measure of the excess return on the average risky asset. This excess return is known as the risk premium.
 * Debt: In terms of bonds it usually refers to the credit spread (the difference between the bond interest rate and the risk-free rate).
 * Equity: In the equity market it is the returns of a company stock, a group of company stock, or all stock market company stock, minus the risk-free rate. The return from equity is the dividend yield and capital gains. The risk premium for equities is also called the equity premium.

The white paper Equity Risk Premium: Expectations Great and Small notes that “it is dangerous to engage in simplistic analyses of historical ERPs to generate ex ante forecasts that differ from the realized mean.”  Standard & Poor’s states “the most correct method is to use an arithmetic average of historical returns.”

If a return represents several periods of growth, use the geometric mean of the periods.