**Please note that this article may contain technical language. For this reason, it is not recommended to readers without professional investment experience.**

#### Market capitalisation indices look much the same

Market capitalisation indices have been used for benchmarking the performance of equity fund managers for decades. There are a number of index providers we can chose from. However, the difference in the performance of market capitalisation-weighted indices tends to be tiny, as long as they apply to the same investment universe, e.g. country or sector. The market capitalisation of a company is a precise and known metric, so the weight of a stock in a benchmark index derived from its stock market capitalisation is comparable from one index provider to another.

#### But factor indices can look very different from one another

When it comes to factor investing, the same is no longer true. The composition and weight of stocks in factor indices designed to capture the premiums 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 – such as value, quality, momentum or low risk – can be used to classify a stock, the fact is that index providers do not necessarily use exactly the same collection of indicators in their factor indices, or the same weighting schemes to construct portfolios, or even the same rebalancing frequency. And, indeed, this can lead to significant differences in the portfolios of factor indices and in their performance.

For example, when it comes to value investing we can 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, or the price-to-earnings ratio based on analyst earnings forecasts, or the EBITDA-to-enterprise-value ratio, or 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, the list of stocks they retain for their factor indices is not exactly the same.

The second difference comes from the weighting scheme chosen to set the weight of a given stock in a style factor index. The simplest approach is to equally-weight all the stocks screened for the portfolio of a given factor index, e.g. the cheapest stocks as measured by price-to-book for a value index. An alternative is to weight the retained stocks by their market capitalisation weight. 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. And 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 means that not only are there no single benchmarks for the different styles in factor investing, but also that 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 cyclical, others are not

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

From MSCI we consider their enhanced value, quality, momentum and low risk (minimum volatility) indices for Europe and for the US, and from BNP Paribas we consider the equivalent indices. 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 screen out those to be retained in the portfolio. The stocks are then weighted by the product of the stock market capitalisation weight with the stock factor values (normalised in some way). This is the case for value, quality and momentum 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, the BNP Paribas family of factor indices imposes sector controls as it aims at investing in stocks from all sectors. An optimiser is used to maximise the exposure to the factors while controlling for the risk of the factor premiums 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 Table 1 we show the __Jensen alpha__ of each of the four factor indices considered for the US and Europe, conditional to 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.

#### Exhibit 1: Jensen alpha generated by the each of the four style factor indices from MSCI and from BNP Paribas for the US and Europe, conditional on US and euro interest-rate monthly changes, respectively. Total returns are gross of management fees, transaction costs and market impact, for the period January 2000 to December 2016*.

Source: MSCI, BNP Paribas Investment Partners and Bloomberg, as of December 2016

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 momentum indices are not consistent, with Europe failing in falling interest rates and the US failing in rising interest rates. This is very much in line with the comments found in __MSCI research papers__ highlighting the cyclicality of performance of their style factor approaches.

In turn, the BNP Paribas indices do not tend to show cyclicality. With the exception of the low-volatility indices that indeed 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, the alpha of the BNP Paribas indices remains significantly higher than that found in the MSCI indices.

#### Cyclical versus all-weather factor indices

Exhibit 1 shows that factor indices based on similar type of indicators can generate significantly different streams of returns. 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 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 equity traded funds (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.

Written on 24 February 2017 in Paris

#### *Exhibit 2: Bloomberg tickers for the above mentioned indices

Source: Bloomberg, BNP Paribas Investment Partners, as of 24 February 2017