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*For decades, market capitalisation-based indices have been used to benchmark the performance of active equity fund managers. Although such indices are calculated by a number of index providers, the difference in the indices’ performance tends to be small, as long as they represent the same investment universe, such as a country’s equity market or sector.*

This is because the market capitalisation of a company is precise and easy to calculate, so unless there is a disagreement between index providers about the percentage of a company’s shares to use in the index calculation, for example as a result of investability constraints, the weight of a stock in a capitalisation-weighted benchmark is comparable from one index provider to another.

**Factor indices can look very different from one another**

When it comes to factor indices, the same is no longer true. The composition and weight of stocks in such indices, which are designed to capture the premia from value, quality, momentum or low-risk stocks, can differ significantly from one index provider to another. That is because while there is consensus as to which factors can be used to classify a stock, index providers do not necessarily use exactly the same collection of indicators in their factor indices, the same weighting schemes to construct portfolios, or even the same rebalancing frequency. In turn, this leads to significant differences in the portfolios of factor indices and in their performance.

When it comes to the screening methods used to select stocks for factor indices, for example, we could think of over 30 possible indicators that could be used to identify value stocks. We could use the price-to-book ratio, the price-to-earnings ratio based on historical earnings, the price-to-earnings ratio based on analysts’ earnings forecasts, the EBITDA to enterprise value ratio, the free cash flow-to-price ratio, and so on. But in practice, and for simplicity, factor index providers will only use a handful of such indicators. And since not all use the same measures, the list of stocks they retain for their factor indices will differ too.

The second difference comes from the weighting scheme chosen by the index provider for the particular factor index. The simplest approach is to equally weight all the stocks screened for the portfolio of a given index, for example the cheapest stocks, as measured by their price-to-book ratios, for a value index. An alternative is to weight the stocks retained from the screening by their market capitalisation. A more complex approach is to set the weight of the retained stocks such that it is proportional to the product of their market capitalisation by the factors used in the index construction, normalised in some way that renders them comparable. An alternative, popular for the low-risk factor, is to set stock weights in the factor index so that they are inversely proportional to the stock volatility of returns. In fundamental indices, a variant of value indices, the stock weight is typically set to be proportional to the stock factor data, normalised in some way.

All this helps illustrate two important points. First, there is no single representative benchmark for a given factor, merely a range of different factor indices from which to choose. Second, investors should take into consideration the small but important differences in the construction of factor indices that can impact their performance significantly.

**Some factor index families are more cyclical than others**

Here we show how small differences in the construction of factor indices from two providers can lead to significantly different cyclicality in performance and factor exposure. We consider, in particular, the well-known MSCI factor indices and factor indices developed by BNP Paribas.

We consider MSCI’s enhanced value, quality, momentum and low risk (minimum volatility) indices for Europe and for the US, and the equivalent indices from BNP Paribas. Both families of indices use some relatively similar indicators in each factor index, but they also use less comparable indicators. However, the most important difference between the two families of factor indices is the approach to portfolio construction.

For the MSCI factor indices, the indicators are first used to rank stocks and to screen out those to be excluded from the portfolio. The retained stocks are then weighted by the product of their stock market capitalisation and their stock factor values (normalised in some way). This is the case for the value, quality and momentum indices but not for the minimum volatility indices, where MSCI uses an optimiser to minimise the volatility of the portfolio in absolute terms, subject to a number of portfolio constraints.

Unlike MSCI, in its factor indices BNP Paribas imposes sector controls as it aims to invest in stocks from all sectors. An optimiser is used to maximise the exposure to the factors while controlling for the risk of the factor premia in the final portfolio allocation. An additional difference is that the BNP Paribas indices are rebalanced every month, whereas the MSCI indices are rebalanced less frequently.

As we can see below, the differences in the construction of the factor indices of these two families of indices can lead to significant differences in their performance. In figure 1 we show the Jensen alpha of each of the four factor indices considered for the US and Europe, conditional on different US and euro interest-rate regimes, respectively. We look in particular at the Jensen alpha of the indices when interest rates rise in the month, fall in the month, or remain range-bound.

The results show that the MSCI factor indices tend to show either cyclical or anti-cyclical Jensen alpha, with the value indices performing better in rising interest-rate regimes while the quality and low volatility indices perform better in falling interest-rate regimes. The performance of the momentum indices is not consistent in different interest rate environments, with the MSCI Europe Momentum index producing negative alpha when bond yields fall, while the MSCI US Momentum index produced negative alpha when bond yields rise. This is very much consistent with comments found in MSCI’s research papers, where the firm’s index researchers highlight the cyclicality of the performance of their style factor approaches.

In turn, the BNP Paribas indices do not tend to show any apparent cyclicality. With the exception of the low-volatility indices, which perform better in falling and neutral interest-rate regimes, the other factor indices perform equally well irrespective of what happens to interest rates. But even in low-volatility factor indices, the alpha of the BNP Paribas indices remained significantly higher than that found in the MSCI indices during the period under review.

**Cyclical versus all-weather factor indices**

Figure 1 shows that factor indices based on notionally similar indicators can generate significantly different return streams. In our view, it is the fact that MSCI indices can build up sector exposures that is behind the cyclicality observed. This is also likely to explain the lack of consistency in momentum returns. Instead, the BNP Paribas factor indices deliver all-weather factor premiums in particular because the portfolio construction focuses more on achieving a good balance across the representation of all sectors in the indices at all times.

This observation has important consequences for the investor. Clearly, when investing in these factor indices via ETFs or total return swaps, investors choosing the MSCI indices should be concerned about the tactical allocation to them as a function of the business cycle. For those choosing the BNP Paribas indices, however, this is less of a concern since the value, quality and momentum factor indices behave like all-weather factors and thus require no tactical allocation. Investors can add them to the core of their portfolios to earn the factor premiums over the long term.

**Raul Leote de Carvalho** is deputy head of financial engineering at **BNP Paribas Asset**** Management**

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