In the last post, we saw how market cap weighting systematically over-weights “expensive” stocks and underweights “cheap” stocks.
Non-market cap weighting is a potential solution.
Non-Market Capitalization Weighting
Let’s look at a few studies regarding the effects of different indexing methods.
The availability of historical returns databases, and modern computing power, have made it feasible for researches to look at historical stock return data and study what would have been the effects of a variety of index weighting schemes.
A particularly interesting set of results to such studies is reported in two papers by Clare, Motson and Thomas.[1]
In their first paper, the trio tested a variety of weighting formulas, including what they called:
- Equal weights – each stock is weighted the same as every other in the index
- Diversity weights – because some stocks are illiquid, the illiquid stocks have a smaller weight, and the remaining stocks are all equally weighted
- Inverse volatility – each weight is assigned based on the inverse of the stock’s historical standard deviation (more weight is assigned to lower volatility stocks)
- Equal risk – each stock is weighted to provide (approximately) the same amount of risk to the overall portfolio. This depends on the stock’s volatility, but also the correlation of the stock’s returns to the returns on the rest of the portfolio, thus it can only be approximated.
- Risk clustering – this approach assumes that “similar” stocks will have similar risk characteristics (e.g. it may treat “financials” or “consumer durables” as a cluster), and seeks to spread the portfolio risk evenly among these clusters.
They also examined several more weighting approaches, each based on some version of mean/variance optimization.
The researchers defined these various portfolios, then tested them using data from the Center of Research for Security Prices from the period 1968 to 2011. Note that they limited the data set to 1000 largest companies by market cap in the database. In standard terminology then, they included mostly mid-cap and large-cap stocks, with relatively few “small” cap stocks. (There is no universal agreement regarding exactly how to define these size categories of stocks.)
Their results are shown in the following table:
Remarkably, this table finds that a market capitalization weighted portfolio was the worst performing of all the reported portfolios.
Random Weightings
Having thrown into doubt the conventional wisdom of market-capitalization based weighting of indexes, the authors then borrow a trope from the efficient markets literature. That trope probably originated with Burton Malkiel’s 1973 Random Walk book.
In the book, he suggests:
“A blindfolded monkey throwing darts at a newspaper’s financial pages could select a portfolio that would do just as well as one carefully selected by experts.”
Clare, Motson and Thomas simulate these imaginary monkeys using a statistical technique called Monte Carlo analysis. They ran 10 million simulations of stock portfolios, based on the actual historical returns. In each run of the simulation, the weights to each stock were assigned randomly, as Malkiel expected his imaginary monkey’s stock selections to be random.
They report, “The vast majority of the monkeys produced a better result than was achieved by the Market-cap index.”
These portfolios and index weightings were all simulated using a computer and historical data. Is any of this achievable in the real world? Could random weightings of an index do better than market cap weighting?
Empirical Results – Equal Weighting
Most of the empirical work studying whether investors can consistently “beat the market” has focused on active stock selection, as opposed to a different form of indexing.
But active selection isn’t the only alternative to market-cap weighting.
Another simple index approach is to use an index that’s equally weighted among its various components.
Though the math is significantly more involved, if we truly believe we know nothing about future performance (except that we have a general idea of the expected return and risk) of each specific stock, equal weighting, not market cap weighting, can be shown to be superior.
And, indeed, we have real world evidence that tends to support this theoretical claim.
There is an ETF – ticker symbol RSP — that tracks the equally weighted S&P500. It has been around for over 20 years, and over that period it has outperformed the market capitalization weighted S&P 500. In recent periods, however, RSP has underperformed the cap weighted S&P 500.
This is not intended as a recommendation of RSP or any other fund. Rather, the point is that at least in this one instance, over a long time period, and in the real world, a weighting system other than market capitalization has been shown to deliver higher returns.
Before we leave the discussion of RSP, please note that most funds that pursue a non-market-cap weighting strategy will have to trade more than the market cap weighted index. This trading might result in material tax consequences, and could generate higher costs compared to the market cap weighting. Investors would want to consider these other factors if making a decision between funds.
In the US, much focus is on the S&P 500. But that selection of stocks is not necessarily representative of the relevant market for all investors.
That topic, “What is the relevant market?” will be the topic of a future post.
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[1] An evaluation of alternative equity indices, Professor Andrew Clare, Dr Nick Motson and Professor Stephen Thomas, Cass Business School, City University London, 2013, and An Evaluation of Alternative Equity Indices – Part 2: Fundamental Weighting Schemes
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