expected return
   HOME

TheInfoList



OR:

The expected return (or expected gain) on a financial investment is the
expected value In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informa ...
of its return (of the profit on the investment). It is a measure of the center of the distribution of the
random variable A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathema ...
that is the return. It is calculated by using the following formula: :E \sum_^R_P_ where :: R_ is the return in scenario i; ::P_ is the probability for the return R_ in scenario i; and ::n is the number of scenarios. The expected
rate of return In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment over a specified time period, such as i ...
is the expected return per currency unit (e.g., dollar) invested. It is computed as the expected return divided by the amount invested. The
required rate of return The discounted cash flow (DCF) analysis, in financial analysis, is a method used Valuation (finance), to value a security (finance), security, project, company, or financial asset, asset, that incorporates the time value of money. Discounted cas ...
is what an investor would require to be compensated for the risk borne by holding the asset; "expected return" is often used in this sense, as opposed to the more formal, mathematical, sense above.


Application

Although the above represents what one expects the return to be, it only refers to the long-term average. In the short term, any of the various scenarios could occur. For example, if one knew a given investment had a 50% chance of earning a return of $10, a 25% chance of earning $20 and a 25% chance of earning $–10 (losing $10), the expected return would be $7.5: :E R_P_ + R_P_ + R_P_ = 10*0.5 + 20*0.25 + (-10)*0.25 = 7.5.


Discrete scenarios

In
gambling Gambling (also known as betting or gaming) is the wagering of something of Value (economics), value ("the stakes") on a Event (probability theory), random event with the intent of winning something else of value, where instances of strategy (ga ...
and
probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
, 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 : E = \frac \cdot 1 - \frac \cdot 0.5 = 0. When we calculate the expected return of an investment it allows us to compare it with other opportunities. For example, suppose we have the option of choosing between three mutually exclusive investments: One has a 60% chance of success and if it succeeds it will give a 70% ROR (rate of return). The second investment has a 45% chance of success with a 20% ROR. The third opportunity has an 80% chance of success with a 50% ROR. For each investment, if it is not successful the investor will lose his entire initial investment. * The expected rate of return for the first investment is (.6 * .7) + (.4 * -1) = 2% * The expected rate of return for the second investment is (.45 * .2) + (.55 * -1) = -46% * The expected rate of return for the third investment is (.8 * .5) + (.2 * -1) = 20% These calculations show that in our scenario the third investment is expected to be the most profitable of the three. The second one even has a negative ROR. This means that if that investment was done an infinite number of times one could expect to lose 46% of the money invested on the average occasion. The formula of expected value is very straightforward, but its value depends on the inputs. The more alternative outcome scenarios that could occur, the more terms are in the equation. As Ilmanen stated, "The foremost need for multi-dimensional thinking is on inputs. When investors make judgments on the various returns on investments, they should guard against being blinded by past performance and must ensure that they take all or most of the following considerations into account". * Historical average returns * Financial and behavioral theories * Forward looking market indicators such as bond yields; and * Discretionary views


Continuous scenarios

In
economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...
and
finance Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Admin ...
, it is more likely that the set of possible outcomes is continuous (any numerical value between 0 and infinity). In this case, simplifying assumptions are made about the continuous distribution of possible outcomes.


See also

*
Abnormal return In finance, an abnormal return is the difference between the actual return of a security and the expected return. Abnormal returns are sometimes triggered by "events." Events can include mergers, dividend announcements, company earning announceme ...
*
Expected value In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informa ...
*
Rate of return In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment over a specified time period, such as i ...


Notes


External links


Using Expected Return to Maximize Growth


{{DEFAULTSORT:Expected Return Theory of probability distributions Financial risk