Build a better mousetrap, the saying goes, and the world will beat a path to your door. Build a better market index, and perhaps investors will do the same.
Until recently, there has been a consensus in the investment community that the traditional broad market indices like the S&P 500 and the Russell 1000 in the US and the FTSE 350 in the UK give investors the best exposure to the market and therefore the best returns.
The view has been that these traditional indices are near-optimal equity portfolios, and the nearest the investor can get to the so-called market portfolio. The market portfolio is the optimal risky portfolio, the portfolio of all risky assets proposed by the capital asset pricing model (CAPM).
The CAPM has provided a theoretical basis for the construction of the leading indices, and in particular for their method of weighting the stocks they include.
There are a number of ways of weighting an index. Indexes may be price weighted, as in the Dow Jones Industrial Average. Here the weight of each stock in the index depends on the price of the stock. The weight of each stock is the ratio of its price to the sum of the prices of all the stocks that are included in the index.
Indexes can be equal weighted, as in the Russell 1000 in this method, each company is weighted equally. Thus if the index consists of 100 stocks; the weight of each stock is 1%.
Alternatively, indices can be capitalisation weighted. In this case, the weights depend on the capitalisation, or the size of the company. The greater the market caps of the stock, the greater its weight.
Market capitalisation has become the most widely used method of weighting. With a few exceptions, notably the Dow, most indices are now capitalisation weighted. These provide the benchmarks for asset managers, who will own stocks on a market capitalisation basis.
Capitalisation weighting has a number of attractions. It provides a convenient way for investors to participate in the broad market. It is a passive strategy that requires little trading, so it incurs lower trading costs and fees than active management. It is highly correlated with trading liquidity, and therefore concentrates on the more liquid stocks. This reduces portfolio transaction costs.
Yet the primacy of this method of measurement has now been challenged. Robert Arnott and his colleagues at Research Affiliates in the US have developed, tested and built a new way of weighting stocks that they say produces better returns than traditional capitalisation weighted indices.
In their paper ‘Redefining Indexation’ Arnott and his colleagues, Jason Hsu and Phil Moore, suggest that capitalisation-weighted market indices are not good proxies for the market. More seriously, they say that, because of structural flaws in the capitalisation weighting, indices are producing sub-optimal returns.
“Acceptance of the belief that capitalisation-weighted equity market indices represent the market portfolio in the CAPM sense reduces the complicated problem of optimal portfolio construction to essentially buying and holding a capitalisation-weighted index such as the S&P 500 or Russell 1000.
“Our industry’s faith in this seemingly harmless simplifying assumption may have resulted in mean-variance sub-optimal performances for millions of investors.”
Their objection to capitalisation as a weighting metric is that it distorts stock valuations. They say if share price fluctuations are ‘noisy’ - that is, they are nothing to do with changes in fundamental values - capitalisation weighting will ‘oversteer’. It will overweight stocks that are overvalued and underweight stocks that are undervalued.
They say that this oversteer creates a drag on performance and diminishes returns. If investors have most of their money in assets that are above fair value, they will have proportionately too little in assets that are below fair value. As a result the cap-weighted indices will produce returns that are below what they should be, and below what would be available in a index that is indifferent to valuations.

The Research Associates team characterises this tendency to oversteer as ‘error seeking’. It suggests that the way to avoid this is to use an alternative weighting measurement that is entirely independent of share prices and valuations.
Equal weighting is a theoretical possibility. This is because equal weighting reduces the error seeking by half. Equity weighting will underweight every large-cap stock, no matter whether it is cheap or expensive. It will also overweight small-cap stock regardless of valuation. This means that the odds are even whether a stock is overvalued or undervalued or overweight or underweight.
However, equal weighting can lead to a high turnover of some of the most liquid companies in the market, and therefore equal weighting cannot be used on an institutional scale.
Instead, Research Affiliates chose a system of measurement or metrics, which reduces error seeking altogether. It constructed a series of market indices weighted by metrics other than market capitalisation as the basis for choosing and weighting of the 1,000 largest companies in the US. It called these fundamentals.
Fundamentals are ways of describing a firm’s size. They could be the book value of assets, income, sales, gross dividend distributions, or even the number of employees working for the firm. The point about them is that they have nothing to do with share prices.
The change of approach is more than a change of methodology. It is a change in the way people look at companies. The financial market will measure a company’s size by its market capitalisation. The commercial market on the other hand, is more interested in the volume of sales.
Arnott and his colleagues characterise the two approaches as ‘Wall Street indexing’ and ‘Main Street indexing’. “The general public of ‘Main Street’ does not typically think of market capitalisation when considering the size of a company. For most of the population, other measures such as sales, income, number of employees, book value and so forth are the intuitive measures of the true size of a company.
“Indeed when the popular press describes mergers and other corporate actions, the size of the companies is generally described in these Main Street measures of size.
They tested this by developing a series of alternative investment metric (AIM) indices. The indices were weighted according to six metrics or measurements of a company’s size - book value, income, revenue, sales, dividend, employment - and a composite of all six.
They weighted all companies by each metric, ranked them by their metric weight, then chose the 1,000 largest. Each of these 1,000 largest was included in the index at its relative metric weight to create the AIM index for that metric.
Like the capitalisation-weighted index they replace, the AIM indices have inherent biases of their own. There is, for example, a bias against growth companies.
This is because none of the six measures of size is linked to share prices; fundamental indexation is indifferent to valuations. As a result, the index will not capture the current market valuation of the perceived growth opportunities of the firms. This means that fast-growing firms are likely to be under-represented in the AIM index. Capitalisation weighted indices, in contrast, have a bias to growth.

This might be expected to depress returns, since growth firms have both higher market risk and higher expected returns. However, the back-tested performance of the AIM indices shows that this did not happen. The AIM indices constructed from book, income and revenue have significantly higher returns, outperform the S&P 500 by an average of 1.65% per annum over the 42-year span tested.
The AIM indices also stand up well against value-oriented indices. AIM indices produce higher available returns than the conventional value-oriented indices. Creating a value-oriented index involves removing, on average, 50% of the stock in an index. However, applying capitalisation weighting to the remaining stock introduces the drag on returns that is a feature of this weighting method.
Research Associates, however, want to avoid throwing the baby out with the bathwater. Capitalisation weighting has many good features, they say, and any alternative should incorporate as many of them as
The AIM indices achieve this, they say. Most of the alternative or fundamental measures of firm size such as book value, income and sales are highly correlated with capitalisation and liquidity. And like the capitalisation-weighted indices, the AIM indices are mainly concentrated in the large-cap shares. This means that the alternative indices can provide the same liquidity as the traditional indices.

Maintaining low turnover is the most challenging part of building alternative market indices, Arnott and his colleague suggest, since the weight in a non-market-cap AIM will need to be rebalanced. However, they have found that the turnover in AIM indices is only slightly greater than the turnover for capitalisation-weighted indices. Costs, too, are only slightly higher, because of the focus on large and liquid stocks.
Research Associates has now developed the AIM indices into the Research Associates Fundamental Index (RAFI) 1000. Back testing by Robert Arnott, chairman of Research Affiliates shows that the RAFI produced nearly 20% higher returns than the classic capitalisation-weighted indices with 4% lower risk since 1962.
In July, Robert Arnott signed an agreement with FTSE Group to develop fundamental indices jointly for the US and international market. Two fundamental indices, FTSE RAFI 1000 for the US and FTSE RAFI Global ex US 1000 indices are being introduced, and other indices will be added in the future. FTSE is also taking over the calculation of the existing RAFI 1000 index.
More recently, FTSE and Research Affiliates have issued a licence to PowerShares Capital Management to use the new FTSE RAFI US 1000 index to create an Exchange Traded Fund (ETF), which will be listed on the New York Stock Exchange. Meanwhile, PIMCO has launched a fundamental weighted index fund called the Fundamental IndexPLUS TR Fund.
Some of the leading pension funds in the US are now showing an
interest in fundamental indexation as an enhancement of the current use of market capitalisation-weighted benchmarks.
CalPERS, for example says it “is intrigued by the concept of fundamental index construction and how this new approach may complement our traditional passive investments in market capitalisation weighted benchmarks.”
Whether it complements or replaces capitalisation-weighted indexation fundamental indexation looks set to change the way indices are managed.