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Performance Metrics

# Average Return

When describing the performance of a security, it is common to refer to the Return on Investment (ROI), but a simple ROI calculation only applies to a single investment for an arbitrary period of time. The average ROI simply computes the mean of the gains and losses to produce the “average.”

Here’s the formula: $$\overline{R} = \frac{\sum_{i=1}^{n} R_i}{n}$$

where $n$ is the total number of Returns to be averaged, and $R_i$ is the $i^{th}$ ROI to be averaged, and $\overline{R}$ is the average ROI of the data.

It is important to note that the average return will be in the same units as

While the average ROI can be over any number of investments and any time period, it is common to use this methodology to compute an Average annual Return (AAR) by using the ROI of a group of investments made during a single calendar year. This group can be individual stocks, bonds, or other securities held during the year, or it can be a group of ROIs from small, individual trades made during the year.

Example In this example, we will use the following table of annual returns of the S&P 500 from 2000 to 2010 to compute the average Return from January 1, 2000 to December 31, 2010.

Year ROI Year ROI
2000 -9.10% 2006 15.79%
2001 -11.89% 2007 5.49%
2002 -22.10% 2008 -37.00%
2003 28.68% 2009 26.46%
2004 10.88% 2010 15.06%
2005 4.91%

The average return is computed as follows: $$\overline{R} = \frac{-9.10 + (-11.89) + (-22.10) + 28.68 + 10.88 + 4.91 + 15.79 + 5.49 + (-37.00) + 26.46 + 15.06}{11}$$ $$= \frac{27.18}{11}$$ $$= 2.47 %$$

So the average return in this example is approximately 2.47%. This also happens to be an average annual return (AAR), since the inividual returns being averaged were annual returns.

PROS Perhaps the biggest advantage of computing an average ROI is it’s simplicity. The above example is a common method for comparing different investments over a long period of time. Often the scope of the average return will be limited to a fixed number of years (e.g. 3, 5, 10, etc).

CONS The average return actually provides very little information about an investment. Depending on the volatility of an investment, it is possible to have a positive average return and still lose money over the same time frame. It is for this reason that the MCI team prefers to use Compounded Annual Growth Rate (CAGR) instead of an average return whenever possible.