Felix Goltz reports on a recent EDHEC study* into characteristics-based indices versus market cap-weighted indices

The standard practice of using a capitalisation-weighting scheme for the construction of stock market indices has come in for harsh criticism. It has been argued that capitalisation weighting leads to indices that underperform those constructed with other weighting mechanisms and that they provide an inefficient risk/return trade-off.

In response to this criticism, equity indices with other weighting schemes have been created. One particular system, characteristics-based indexing, weights the component stocks by firm characteristics. The idea behind this system is that market capitalisation does not actually convey much information about a stock, and that it would be preferable to use other indicators of company size, such as book value, sales, dividends, or the number of employees.

In recent years, the market for characteristics-based indices has grown tremendously, with more providers launching offers. Our recent study assesses the performance of these indices. The return data for US indices from several providers are used to analyse the properties of these indices and compare them with firmly established indices, such as capitalisation and equal-weighted indices for the total stock market and for the S&P500 universe.

Outperformance of standard indices

The study shows that all characteristics-based indices have higher returns than the capitalisation-weighted S&P500 index, although the difference is not statistically significant for most indices. However, most characteristics-based indices actually have lower returns than do equal-weighted indices. In addition, outperformance of the value-weighted S&P500 depends on market conditions and all characteristics-based indices go through lengthy periods during which they underperform the S&P500.

Return differences with standard indices

Figure 1 indicates annualised return differences for seven characteristics-based indices with respect to four standard indices. The standard indices are the value-weighted and equal-weighted portfolios of S&P500 components (S&P500) or the total market index (TMI) of NYSE-listed stocks. The data are monthly total returns (including reinvested dividends) for the time period from January 1998 to December 2006. The return differences correspond to the annualised returns of a long-short strategy that goes long the characteristics-based index and short the standard index with equal amounts.

 

 Alpha of characteristics-based indices

When the systematic risk factor exposure of characteristics-based indices is adjusted for - and the market factor alone is taken into account - the abnormal returns generated by these indices are tremendous. In the static single-factor model, the alpha of all characteristics-based indices is positive, although in most instances it is not significantly different from zero. However, when the four-factor model is used to account for small-cap, value, and momentum risk as well, the magnitude of alpha is greatly reduced and is in most cases not significantly different from zero. The median annualised alpha across different characteristics-based indices computed from the single-factor model is 3.8% and 1.1% with the four-factor model. However, the seven indices are by no means alike; after all, the alpha with respect to the four-factor model takes on values ranging from an annual 0% to an annual 2.7%.

Overview of alpha with different factor models

The estimated alpha from different factor models is annualised and only the maximum, median, and minimum value across the seven characteristics-based indices is shown. The alpha is based on factor models estimated with monthly total return data (including reinvested dividends) for the time period January 1998 to December 2006. The upper panel of figure 2 shows annualised alpha for three different specifications of a static factor model. The lower panel shows annualised alpha for dynamic factor models.

The positive and significant exposure of all indices to the value premium may account for these findings and for the outperformance of these indices. This value bias is confirmed in an analysis of industry exposures, as typical value sectors (eg utilities) are overweighted and growth sectors (eg technology) are underweighted.

The static analysis is limited by the assumption that the factor exposures remain constant over the entire time period. In fact, the characteristics-based indices may change their factor exposures over time, although one may expect the systematic construction method of these indices to lead to a factor exposure that is more stable than that of actively managed portfolios which may be subject to sudden style or factor drifts. In order to take these shifts into account, we use a Kalman filter combined with a Kalman smoother to estimate time-varying factor exposures. 

The results in terms of alpha from the dynamic analysis are consistent with those from the static analysis. In particular, the annual percentage values are roughly equal to those for the static models. Also, alpha is considerably reduced when the multi-factor rather than the one-factor model is used. However, for a range of indices, alpha is significantly different from zero with the dynamic model specification. Furthermore, the factor exposures of the characteristics-based indices show great variation - in the order of 10-30%. So investors holding one of these characteristics-based indices must be prepared to deal with relatively great changes to their allocation to, say, value and small-cap stocks.

In addition, management fees, transaction costs, and out-of-sample performance may, in practice, reduce the value added of characteristics-based indices. First, the management fees charged by funds that track capitalisation-weighted indices are typically lower than those charged
by funds that track characteristics-based indices. To compensate for these higher fees, characteristics-based indices must deliver a certain level of positive alpha.

Second, the index returns do not include the transaction costs incur-red by investors or asset managers trying to replicate these indices. While transactions are limited to constituent changes for value-weighted indices, a portfolio tracking characteristics-based index will incur transaction costs when it readjusts asset holdings to their characteristics-based weight. Finally, it is necessary to recall that we are dealing with ex post track records, which are susceptible to data snooping.

Are the factor tilts of characteristics-based indices optimal?

The fact that the outperformance of characteristics-based indices may disappear when the systematic risk-factor exposure is adjusted for, and when practical considerations are taken into account, says nothing about whether the choice of risk factors is optimal. Also, given the fluctuations of factor exposures, evident from the dynamic analysis, it is only natural to wonder whether the factor exposures implicit in the characteristics-based indices actually provide investors with an optimal risk/return trade-off.

To deal with this question, we use an optimisation procedure to construct efficient portfolios from the different factors. We consider an optimal allocation to both style factors (the market portfolio, small-cap factor, value factor, and momentum factor) and sector indices. In particular, we implement one out-of-sample minimum variance portfolio that invests in the market, small-cap, value, and momentum factor, and another that invests in sector indices. The Sharpe ratios of these two strategies are higher than those of the characteristics-based indices and the difference is significantly different from zero in most cases.

Characteristics-based indices: a revolution, or old wine in new bottles?

One can conclude that the characteristics-based indices are value-tilted investment strategies. When this tilt is properly adjusted for, most characteristics-based indices do not post significant outperformance. The benefits of value investing are of course well known. In addition, if one recognises the possibility to make bets across factors or industry sectors, it is possible to construct portfolios whose mean-variance efficiency is greater than that of the characteristics-based indices.

*Noël Amenc, Felix Goltz, and Véronique Le Sourd, 2008, The Performance of Fundamentally Weighted Indices, EDHEC Working Paper

Felix Goltz is senior research engineer with the EDHEC Risk and Asset Management Research Centre in Nice