Weighting isn’t the only factor that affects an index’s results. The return an equal-weighted index reports is determined by the way that the average is calculated.
To calculate an average, you add the price changes in each stock together and divide by the appropriate number. What that gives you is an arithmetic average, or mean. The problem with this approach is that because of the way the result is calculated an arithmetic average tends to produce a higher return than the actual return on a typical stock portfolio. It’s the same kind of overstatement that can result if you average stock returns over several years rather than finding the compound return. A straight average doesn’t take into account the full impact of changing values over a number of years.
Here
are six hypothetical sets of investment returns
totaling 27% over three years. The average
annual return is 9% in each case, but the compound
annual returns vary.
Investment
1
2
3
4
5
6
Year 1
9%
5%
0%
0%
-1%
-5%
Year 2
9%
10%
7%
0%
-1%
8%
Year 3
9%
12%
20%
27%
29%
40%
Average return
9.00%
9.00%
9.00%
9.00%
9.00%
9.00%
Compound
return
9.00%
8.96%
8.69%
8.29%
8.13%
6.96%
The alternative to using an arithmetic average is calculating the geometric mean, or average, which is the standard practice when looking at historical results. Because it takes compounding into account, a geometric mean tends to be more accurate about what the actual rate of return was over the period being considered. And in most cases, the result will be lower than the arithmetic average.
The solution is not abandoning all indexes as misleading, but rather being aware of the biases any particular index may introduce and letting that knowledge guide your use of the index.
