A measure of average return which divides the sum of periodic returns by the number of returns:
The periodic returns must have the same periodicity, i.e., all must be of a daily, weekly, monthly, quarterly, or yearly frequency. Calculating an investment return using arithmetic mean particularly fits historical return measurement, but not the projection of the future value of an investment (as it doesn’t take into account the compounding of returns over time).
For example, if we have the following annual returns:
| Year | Return |
|---|---|
| 1 | 11% |
| 2 | 20% |
| 3 | 10% |
| 4 | 9% |
The arithmetic mean return is: [(11%+20%+10%+9%)/4]= 12.5%
However, the compound 4-year return would be [(1.11)x(1.20)x(1.10)x(1.09)-1]x100= 59.7%
Taking the arithmetic return and plugging it in into the the compounding formula will produce a different figure:
[(1.125)x(1.125)x(1.125)x(1.125)-1]x100 = 60.18%
Therefore, using the arithmetic mean return (in reconciling the beginning to end investment value) would overstate the ending value. Accounting for the compounding process between periods would prompt the use of an average rate that is lower than the arithmetic mean return.
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