Risk premium

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

The certainty equivalent is the guaranteed payoff at which a person is "indifferent" between accepting the guaranteed payoff and a higher but uncertain payoff. (It is the amount of the higher payout minus the risk premium.)

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. The two options (choosing between door 1 or 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 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.

• Equity: In the equity market it is the expected 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. Note that this is an unobservable quantity since no one knows for sure what the expected rate of return on equities is. Nonetheless, most people believe that there is a risk premium built into equities, and this is what encourages investors to place at least some of their money in equities.
• Debt: In terms of bonds, the term "risk premium" is often used imprecisely to refer to the credit spread (the difference between the bond interest rate and the risk-free rate). To see why this is inconsistent with the given definition, imagine that the risk free rate is 3% and XYZ corporate bonds are yielding 10%. Does that mean that the expected return in excess of the risk free rate is 7%? Almost certainly not; after all, there is surely a positive probability of a default. In reality, the risk premium (as defined above) could very well be zero or negative.

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.

See also

• Interest
• Risk
• Minimum acceptable rate of return
• Expected utility hypothesis

External links

• Hussman Funds - Estimating the Long-Term Return on Stocks - June 1998
• equity risk premium and information quality
• Ruben D. Cohen (2002) “The Relationship Between the Equity Risk Premium, Duration and Dividend Yield (download),” Wilmott Magazine, pp 84-97, November issue.
• Ruben D. Cohen “The Long-run Behaviour of the S&P Composite Price Index and its Risk Premium (download).”