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Asset Management Calculations

Expected Rate of Return

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

What It Measures

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

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Why It Is Important

No self-respecting businessperson or organization should make an investment without first having some understanding of how successful that investment is likely to be. Expected rate of return provides such an understanding, within certain limits.

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How It Works in Practice

The formula for expected rate of return is:

Expected rate of return = ∑i = 1n [P(i) × ri]

where P(i) is the probability that the return ri is achieved, i.e., the sum of the products of all possible returns and their probabilities.

A simple example, as given below, is far easier to grasp, and adequately illustrates the principle which the formula expresses. It will probably be of more practical use to most of those who need to calculate ERR.

The current price of ABC Inc. stock is $10. At the end of the year, ABC shares of stock 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%) + (20% × –5%) = 7.5 + 6 –1 = 12.5%

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 the ERR can be calculated:

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

Another method that can be used to project expected return is the capital asset pricing model (CAPM), which is explained separately.

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Tricks of the Trade

  • The probability totals must always equal 100% for the calculation to be valid.

  • Be sure not to overlook any negative numbers in the calculations, or the results produced will be incorrect.

  • An ERR calculation is only as good as the scenarios considered. Wildly unrealistic scenarios will produce an equally unreliable expected rate of return.

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