Why Market-Valuation-Indifferent Indexing Works

Using market values for indexing gives more portfolio weight to the stocks with positive price errors and less portfolio weight to the stocks with negative price errors. Market-valuation-indifferent indexing—such as equal weighting or weighting by number of employees, number of customers, or sales—relies on averaging over hundreds of stocks to give equal weight to the two groups. Stock markets price stocks imperfectly, but the mispricings are always relative. Because overpriced stocks are counterbalanced by underpriced stocks, the distribution of error at any point in time is symmetrical. One can picture this distribution as a bell-shaped curve with “error” on the horizontal axis and some measure of “frequency” on the vertical axis. Because it reflects both the number of companies in the market and their size, aggregate value is the appropriate measure of frequency, but which measure of aggregate value—true value or market value?Large positive errors increase the market value of the stocks with those errors, and large negative errors reduce the market value of stocks with those errors. Unlike a distribution of the pricing error based on true value, the error distribution for market values will be skewed to the right. This lack of symmetry is the problem with capitalization weighting: By using market values to determine its weights, a cap-weighted index fund will invest more money in overpriced stocks than in underpriced stocks.Market-value-indifferent (MVI) indexing avoids this problem. An example is an equally weighted (or constant-weight) portfolio. The problem with equal weighting is that it will have a strong small-cap bias. Other weighting schemes reduce or even reverse the bias.