expected rate of return

Fin

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

Abbr. ERR

EXAMPLE

It is calculated by the following formula:

E[r]= ΣsP(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.

     The following example illustrates the principle which 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.

See also capital asset pricing model