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A risk premium is the minimum difference a person requires to be willing to take an uncertain bet
Bet

Bet or BET may refer to:* A wager in gambling* Basic Economics Test *Bet , the second letter in many Semitic alphabets, including Aramaic, Hebrew, Phoenician and Syriac...
, 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.)

ose a game show
Game show

A game show is a type of television program in which members of the public or celebrity, sometimes as part of a team, play a game which involves answering questions or solving problems for money and/or prizes....
 participant may choose one of two doors, one that hides $1,000 and one that hides $0.






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A risk premium is the minimum difference a person requires to be willing to take an uncertain bet
Bet

Bet or BET may refer to:* A wager in gambling* Basic Economics Test *Bet , the second letter in many Semitic alphabets, including Aramaic, Hebrew, Phoenician and Syriac...
, 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
Game show

A game show is a type of television program in which members of the public or celebrity, sometimes as part of a team, play a game which involves answering questions or solving problems for money and/or prizes....
 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
Risk aversion

Risk aversion is a concept in economics, finance, and psychology related to the behaviour of consumers and investors under uncertainty. Risk aversion is the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected value....
 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
Minimum acceptable rate of return

In business and engineering, the minimum acceptable rate of return, often abbreviated MARR, is the minimum return on a project a manager is willing to accept before starting a project, given its risk and the opportunity cost of foregoing other projects....
 of $500 or more will likely choose a door instead of accepting the guaranteed $500.

Finance

In finance
Finance

The field of finance refers to the concepts of time, money and risk and how they are interrelated. Banks are the main facilitators of funding through the provision of credit, although private equity, mutual funds, hedge funds, and other organizations have become important....
, the risk premium can be the expected rate of return above the risk-free interest rate
Risk-free interest rate

The risk-free interest rate is the interest rate that it is assumed can be obtained by investment in financial instruments with no default risk....
. 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
    Dividend yield

    The dividend yield on a company stock is the company's annual dividend payments divided by its market cap, or the dividend per share divided by the price per share....
     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
    Bond (finance)

    In finance, a bond is a debt security , in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest and/or to repay the principal at a later date, termed Maturity ....
    , the term "risk premium" is often used imprecisely to refer to the credit spread
    Credit spread (bond)

    In finance, a credit spread is the yield spread, or difference in Yield between different securities, due to different credit quality. The credit spread reflects the additional net yield an investor can earn from a security with more credit risk relative to one with less credit risk....
     (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
Arithmetic mean

In mathematics and statistics, the arithmetic mean of a list of numbers is the sum of all of the list divided by the number of items in the list....
 of historical returns.”

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

The geometric mean, in mathematics, is a type of mean or average, which indicates the central tendency or typical value of a set of numbers. It is similar to the arithmetic mean, which is what most people think of with the word "average," except that instead of adding the set of numbers and then dividing the sum by the count of numbers in the...
 of the periods.

See also

  • Interest
    Interest

    Interest is a fee paid on borrowed assets. It is the price paid for the use of borrowed money , or, money earned by deposited funds .Assets that are sometimes lent with interest include money, shares, consumer goods through hire purchase, major assets such as aircraft finance, and even entire factories in finance lease arrangements....
  • Risk
    Risk

    Risk is a concept that denotes the precise probability of specific eventualities. Technically, the notion of risk is independent from the notion of value and, as such, eventualities may have both beneficial and adverse consequences....
  • Minimum acceptable rate of return
    Minimum acceptable rate of return

    In business and engineering, the minimum acceptable rate of return, often abbreviated MARR, is the minimum return on a project a manager is willing to accept before starting a project, given its risk and the opportunity cost of foregoing other projects....
  • Expected utility hypothesis
    Expected utility hypothesis

    In economics, game theory, and decision theory the expected utility theorem or expected utility hypothesis predicts that the "betting preferences" of people with regard to uncertain outcomes can be described by a mathematical relation which takes into account the size of a payout , the probability of occurrence, risk aversion, and the...


External links

  • Ruben D. Cohen (2002) “The Relationship Between the Equity Risk Premium, Duration and Dividend Yield ,” 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 .”