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Home > QFINANCE Dictionary > Definition of expected rate of return

Definition of

# expected rate of return

Stockholding & Investments

probable return on investment the projected percentage return on an investment, based on the weighted probability of all possible rates of return.

It is calculated by the following formula:

ERR = ∑ n i=1 (P(i) × ri)

where P(i) is the probability of outcome i and ri is the return for outcome i.

The following example illustrates the principle that the formula expresses:

The current price of ABC, Inc. stock is trading at \$10. At the end of the year, ABC shares are projected to be traded:

25% higher if economic growth exceeds expectations-a probability of 30%;

12% higher if economic growth equals expectations-a probability of 50%;

5% lower if economic growth falls short of expectations-a probability of 20%.

To find the expected rate of return, simply multiply the percentages by their respective probabilities and add the results:

(30% × 25%) + (50% × 12%) + (25% × −5%) = 7.5 + 6 + −1.25 = 12.25% ERR

A second example:

if economic growth remains robust (a 20% probability), investments will return 25%;

if economic growth ebbs, but still performs adequately (a 40% probability), investments will return 15%;

if economic growth slows significantly (a 30% probability), investments will return 5%;

if the economy declines outright (a 10% probability), investments will return 0%.

Therefore:

(20% × 25%) + (40% × 15%) + (30% × 5%) + (10% × 0%) = 5% + 6% + 1.5% + 0% = 12.5% ERR

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• ### Expected Rate of Return

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Expected rate of return (ERR) is a measure conceived and crafted in the spirit of “forewarned is forearmed.”

• ### Rate of Return

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The geometric or compound rate of return is a better yardstick for measuring investments over the long run, and takes into account the effects of compounding. As one might expect, this formula is more complex and technical, and beyond the scope of this article.

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Definitions of ’expected rate of return’ and meaning of ’expected rate of return’ are from the book publication, QFINANCE – The Ultimate Resource, © 2009 Bloomsbury Information Ltd. Find definitions for ’expected rate of return’ and other financial terms with our online QFINANCE Financial Dictionary.