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Wize University Introduction to Finance Textbook > Risk, Return & Portfolio Theory

Average Returns and Standard Deviation

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Average Returns

Average returns can be measured in two ways:

1. Arithmetic mean (AM)

The numerical average of the returns.

2. Geometric mean (GM)

The geometric mean is the average compounding growth rate over n periods.

GM=[(1+r1)(1+r2)(1+r3)...(1+rn)]1n−1GM=\left[\left(1+r_1\right)\left(1+r_2\right)\left(1+r_3\right)...\left(1+r_n\right)\right]^{\frac{1}{n}}-1

Wize Concept
In finance, we use the geometric mean when evaluating an investment. The arithmetic mean tends to overstate average returns because it does not considering the compounding effect.

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Example: Average Returns

Estimate the arithmetic mean (AM) and geometric mean (GM) for the following returns: 5.4%, 6.2%, 4.5%, -7.8% and 10.1%.

Practice: Average Returns

Your portfolio earned the following returns over the last 5 months: 10%, -2%, 12%, -4%, 15%

What is the arithmetic average monthly return and the geometric average monthly return. Round your final answers to 2 decimal places.

Arithmetic average monthly return
%
Geometric average monthly return
%
Extra Practice
You purchased a stock for $34 three years ago. The price of the stock increased by $1.88 in the first year, then decreased by $2.89 in the second year, and today is trading at $43.90.
You received a dividend of $0.15 in year 1, $0.20 in year 2 and $0.25 in year 3.
What is the arithmetic average annual return?
You purchased a stock for $34 three years ago. The price of the stock increased by $1.88 in the first year, then decreased by $2.89 in the second year, and today is trading at $43.90.
You received a dividend of $0.15 in year 1, $0.20 in year 2 and $0.25 in year 3.
What is the standard deviation of the annual return?
You purchased a stock for $34 three years ago. The price of the stock increased by $1.88 in the first year, then decreased by $2.89 in the second year, and today is trading at $43.90.
You received a dividend of $0.15 in year 1, $0.20 in year 2 and $0.25 in year 3.
What is the geometric average annual return?
The following table shows the closing prices and monthly returns of JOK Inc. in the first 6 months of this year:
What is the return in June if the geometric average monthly return is 8.22% and wha it the closing price of the stock in June?
The following table shows the closing prices and monthly returns of ACME Inc. in the first 6 months of last year:
Calculate the monthly geometric and arithmetic average returns.
The annual returns for XYZ Inc. for the past five years were: 5%, 10%, -6%, -8.5%, and 14%. What are the arithmetic and geometric average annual returns for XYZ Inc. over the five-year period?