Expected return
Encyclopedia
The expected return is the weighted-average outcome in gambling
, probability theory
, economics
or finance
.
It is
the average of a probability distribution of possible returns, calculated by using the following formula:
E(R)= Sum: probability (in scenario i) * the return (in scenario i)
How do you calculate the average of a probability distribution? As denoted by the above formula, simply take the probability of each possible return outcome and multiply it by the return outcome itself. For example, if you knew a given investment had a 50% chance of earning a 10% return, a 25% chance of earning 20% and a 25% chance of earning -10%, the expected return would be equal to 7.5%:
Although this is what you expect the return to be, there is no guarantee that it will be the actual return.
and probability theory
, there is usually a discrete set of possible outcomes. In this case, expected return is a measure of the relative balance of win or loss weighted by their chances of occurring.
For example, if a fair die is thrown and numbers 1 and 2 win 1, but 3-6 lose 0.5, then the expected gain per throw is
Because the expected return is 0, the game is called a fair game.
and finance
, it is more likely that the set of possible outcomes is continuous (a numerical or currency value between 0 and infinity). In this case, simplifying assumptions are made about the distribution of possible outcomes. Either a continuous probability function is constructed, or a discrete probability distribution is assumed
Gambling
Gambling is the wagering of money or something of material value on an event with an uncertain outcome with the primary intent of winning additional money and/or material goods...
, probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
or finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
.
It is
the average of a probability distribution of possible returns, calculated by using the following formula:
E(R)= Sum: probability (in scenario i) * the return (in scenario i)
How do you calculate the average of a probability distribution? As denoted by the above formula, simply take the probability of each possible return outcome and multiply it by the return outcome itself. For example, if you knew a given investment had a 50% chance of earning a 10% return, a 25% chance of earning 20% and a 25% chance of earning -10%, the expected return would be equal to 7.5%:
- = (0.5) (0.1) + (0.25) (0.2) + (0.25) (-0.1) = 0.075 = 7.5%
Although this is what you expect the return to be, there is no guarantee that it will be the actual return.
Discrete scenarios
In gamblingGambling
Gambling is the wagering of money or something of material value on an event with an uncertain outcome with the primary intent of winning additional money and/or material goods...
and probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, there is usually a discrete set of possible outcomes. In this case, expected return is a measure of the relative balance of win or loss weighted by their chances of occurring.
For example, if a fair die is thrown and numbers 1 and 2 win 1, but 3-6 lose 0.5, then the expected gain per throw is
- 1 × 1/3 - 0.5 × 2/3 = 0
Because the expected return is 0, the game is called a fair game.
Continuous scenarios
In economicsEconomics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
and finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, it is more likely that the set of possible outcomes is continuous (a numerical or currency value between 0 and infinity). In this case, simplifying assumptions are made about the distribution of possible outcomes. Either a continuous probability function is constructed, or a discrete probability distribution is assumed
Alternate definition
In finance, expected return can also mean the return of a bond if the bond pays out. This will always be higher than the expected return in the other sense presented in this article because the bond paying out is the highest payout scenario, and failure is always possible.See also
- Abnormal return
- Expected gainExpected gainThe expected gain is the weighted-average most likely outcome in gambling, probability theory, economics or finance.-Discrete scenarios:In gambling and probability theory, there is usually a discrete set of possible outcomes...
- Expected valueExpected valueIn probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...