Equally weighted portfolios outperform their market capitalisation counterparts over the long term and over almost all short term periods. The evidence to support this is cited in the References and is demonstrated in Figure 1, which shows the performance of Australia's standard equal weighted index, the MVIS Australia Equal Weight Index, against Australia's standard market capitalisation weighted index, the S&P/ASX 200.
Various explanations have been offered since this phenomenon was first observed, such as the effect of selling high and buying low when rebalancing the portfolio. There hasn't however been a lot of mathematical analysis. This paper presents the data on individual stock returns to show why equal weighting has outperformed market capitalisation.
Equal weighting outperforming market capitalisation weighting can be explained by the statistical distribution of individual stock returns being skewed, which is contrary to the assumption that researchers generally make.
Figure 1. Cumulative performance since inception of MVIS Australia Equal Weight Index
Source: VanEck, FactSet, as at 31 December 2017. Results are calculated to the last business day of the month and assume immediate reinvestment of all dividends and exclude costs associated with investing in the VanEck Vectors Australian Equal Weight ETF (MVW). You cannot invest directly in an index. Past performance of the Index is not a reliable indicator of future performance of MVW.
To get the maths right you have to start at the right point. The distribution of individual stock returns is not normal. That is, the distribution is not Gaussian.
It is now widely accepted that a normal distribution is a flawed way to explain financial markets because markets have 'fat tails' that normal distributions don't have. This is embodied in the delightful metaphor of a black swan. This is however only one way in which the actual distribution of stock returns differs from a normal distribution. It is time to discard the use of normal distributions.
The consensus description used for the distribution of individual stock returns that can be seen in the data is 'skewed'. Primarily this description indicates that the distribution is not symmetrical, as a normal distribution is. Rather, the actual distribution is pushed to one side, as can be seen in the histograms throughout this paper. There are however more differences than that.