The expected rate of return is the return an investor anticipates on an investment, computed as the probability-weighted average of every outcome the investor thinks possible, and stated as a percentage of the amount invested. It is an estimate built from assumptions, so it describes the center of a range rather than the number the investment will actually deliver.
Two things follow from that definition, and both are missed often enough to be worth stating up front. The expected rate of return is not a forecast of next year, and it is not the return the investor demands before agreeing to the risk.
How the Expected Rate of Return Is Calculated
Assign a probability to each outcome, multiply each outcome by its probability, and add the products. The probabilities have to sum to one, or the weighting is meaningless.
Say an analyst models one investment across three scenarios.
Scenario Return Probability Weighted
Strong year 18.0% 0.25 4.5%
Normal year 8.0% 0.50 4.0%
Weak year -6.0% 0.25 -1.5%
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1.00 7.0%The expected rate of return is 7.0 percent. Notice that no scenario in the model produces 7.0 percent. That is normal and it is the point: the figure is the center of a distribution, not a prediction of any single year.
Where the probabilities come from is the whole argument. Historical frequencies, a model, or judgment are all defensible inputs, and all three are assumptions. Change the probabilities and the answer changes with them, which is why an expected return quoted without its assumptions is not a usable number.
Expected, Required and Realized Are Three Different Numbers
These get used as synonyms, and they are not.
| Term | What it is | Where it comes from |
|---|---|---|
| Expected return | What the investor thinks the investment will average | Probability-weighted outcomes |
| Required return | The minimum the investor will accept for the risk | A pricing model or a hurdle rate |
| Realized return | What the investment actually delivered | The historical record |
The comparison that matters in practice is expected against required. When the expected return sits above the required return, the investment clears its own hurdle on the analyst’s assumptions. When it sits below, it does not, whatever the historical record says. Realized return settles neither question, because it is a fact about a period that has already finished.
A related but separate measure, the accounting rate of return, works from average annual accounting profit rather than from probability-weighted outcomes, and answers a different question about a project rather than about an investment’s risk.
Where the Phrase Is a Statutory Term
Outside finance, expected return is a defined term in US tax law, and a return preparer meets it on annuity income rather than on a portfolio.
Gross income does not include that part of any amount received as an annuity under an annuity, endowment, or life insurance contract which bears the same ratio to such amount as the investment in the contract, as of the annuity starting date, bears to the expected return under the contract as of that date (26 U.S.C. 72(b)(1)). That ratio is the exclusion ratio, and the expected return is its denominator, which means the whole taxable portion of an annuity payment turns on it.
The statute then says how to compute it. If the expected return under the contract, for the period on and after the annuity starting date, depends in whole or in part on the life expectancy of one or more individuals, the expected return shall be computed with reference to actuarial tables prescribed by the Secretary; if it does not, the expected return is the aggregate of the amounts receivable under the contract as an annuity (26 U.S.C. 72(c)(3)).
Read that against the finance definition and the difference is sharp. The investment version is a probability-weighted estimate the analyst chooses. The statutory version is a computed total with a prescribed method, and there is no probability in it at all. Same phrase, different objects.
What the Number Cannot Do
An expected rate of return carries no information about dispersion. Two investments can share an expected return of 7.0 percent while one of them ranges from 6 to 8 percent and the other from negative 40 to positive 60. The average is identical and the risk is not comparable, which is why the expected return is normally read next to a measure of variability rather than on its own.
It also inherits every weakness of its inputs. Probabilities drawn from a short history, or from a period that did not include a downturn, produce a confident-looking figure resting on a sample that never tested the assumption.
Common Questions
Multiply each possible return by the probability of that outcome and add the results, with the probabilities summing to one. The worked table above runs the calculation on three scenarios. For a portfolio rather than a single holding, the same method applies at the portfolio level, weighting each asset’s expected return by its share of the portfolio’s value.
No. The expected rate of return is what the investor thinks an investment will average; the required rate of return is the minimum the investor will accept given the risk. They are compared, not equated, and an investment is attractive on these terms only when the first exceeds the second.
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