# Calculating Expected Rate of Return

Wise investors calculate the return they expect, based on the weighted probability of all possible rates of return, before parting with their money.

Indeed, no company or individual *should* invest without first arriving at some estimate of how successful their investment is likely to be. This exercise will, within limits, put such expectations in perspective.

The formula to use to make an educated estimate of an investment's potential return is:

*E*[

*r*]=S

*sP*(

*s*)

*rs*

where *E*[*r*] is the expected return, *P*(*s*) is the probability that the rate *rs* occurs, and *rs* is the return at *s* level.

This can be more easily illustrated by considering the case of an investment in stock in J. Smith Inc., presently trading at $10. This stock is expected to be trading at $12.50, 25% higher, within a year if economic growth exceeds expectations—a probability of 30%; at $11.20, 12% higher, if economic growth equals expectations—a probability of 50%; and, at $9.50, 5% lower, if economic growth falls short of expectations—a probability of 20%.

The expected rate of return is found by multiplying the percentages by their respective probabilities and adding the results:

Alternatively, if economic growth remains stable (a 20% probability), investments will return 25%; if economic growth eases, but still performs satisfactorily (a 40% probability), investments will return 15%; if economic growth slows significantly (a 30 per cent probability), investments will return 5%; and, if the economy weakens (a 10% probability), there will be no return. Therefore:

These calculations will be invalid if the probability totals do not always equal 100%. They will also be invalid if negative numbers have not been included. A calculated expected rate of return is only as good as the scenarios considered. Wildly unrealistic scenarios will produce equally unrealistic results.

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