DISCOVER

# The Average Expected Rate of Return

Updated November 22, 2016

Investors use an asset-pricing model such as the Capital Asset Pricing Model (CAPM) to calculate the average expected rate of return on an investment. The average expected rate of return is the total of each possible rate of return on an investment multiplied by the probability of the investment earning each possible rate of return.

## Significance

The average expected rate of return can give investors a range of what they can expect to earn on a single investment. The average expected rate of return is not and should not be confused with the actual rate of return on an investment. Your investment adviser will most likely calculate the expected rate of return based on the CAPM. The probability of your investment returning the expected rate of return using the CAPM is generally going to be the highest. Remember, the average rate of return is a good guess, not a guarantee.

## CAPM

The CAPM has four basic parts: the risk-free rate of return, beta, expected market return and the market risk premium. The risk-free rate of return is the theoretical rate of return of a risk-free investment. Risk-free investments do not exist, so investors use an investment that represents the smallest risk, typically the interest rate on the three-month U.S. Treasury bill. The beta of a security is the risk of a specific security compared to the risk of the overall stock market. The stock market as a whole always has a beta of 1. The expected market return is the expected return on the overall stock market. The market risk premium is the expected market rate of return minus the risk-free rate of return.

## CAPM Calculation

The CAPM formula is as follows: risk-free rate of return + beta (market risk premium- risk-free rate of return) = expected rate of return. Let's say the risk-free rate of return is 3 per cent, the expected market rate of return is 10 per cent, making the market risk premium 7 per cent (10 per cent -- 3 per cent = 7 per cent). You buy a stock that has a beta of 3. First, convert the percentages to decimals, which gives you .03 + 2(.07 - .03). Next, do the math inside the parentheses, .07-.03 = .04. Now, it looks like this: .03 + 2(.04). Then, get rid of the parentheses by multiplying the 2 by .04 which equals .08. Now, your formula looks like this .03 + .08= .11. Finally, change that decimal point back into a percentage or 11 per cent. This means that your expected rate of return for this investment 11 per cent.

## Average Expected Rate of Return

It's always possible that any investment can underperform or outperform the market. To find the average expected rate of return your investment adviser will calculate the probability that the stock will return at different percentages. Probability distribution calculations are complicated, so the following is a simple example of an average expected rate of return. Using the example from the above section, let's say your investment has a 90 per cent probability of earning 11 per cent, a 7 per cent probability of earning 15 per cent and a 3 per cent probability of earning 20 per cent. Here's the math (.90 x .11) + (.07 x .15) + (.03 x .20). Remember, get rid of the parentheses. Now, it looks like this .99 + .0105 + .006 = .115. Change the decimal to a percentage and you have an average expected rate of return of 11.5 per cent.
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