Author Details

Abhishek Gupta

Abhishek Gupta
Executive Director, MSCI Research

Ashish Lodh

Ashish Lodh
Vice President, Equity Solutions Research

Subhajit Barman

Subhajit Barman
Vice President, MSCI Research

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How to Describe a Factor

  • As investors perform due diligence on factor products, one area of focus is how well a factor is defined and captured in a portfolio.
  • Some factors, notably value and quality, are multi-dimensional and may be better captured by combining multiple factor descriptors, each describing one part of the factor.
  • Use of multiple descriptors has provided a more comprehensive definition of factors, generally, and helped mitigate the risk arising from the choice of a single factor descriptor.

How can one define a factor? This has been a challenge for asset owners and wealth managers in evaluating how well factor products meet investment objectives.

Factors may be defined and targeted using single or multiple stock-level characteristics (descriptors). Our research has shown that multiple descriptors of these factors have historically been rewarded with risk premia over long time periods.

While different descriptors can be used to identify stocks with a given factor characteristic, an improved and more robust measure can be formed by combining multiple descriptors. Multiple descriptors also have mitigated the risk arising from the choice of a single descriptor. In this post, we illustrate this using the value factor as an example.


Multiple Value Descriptors Were Rewarded with Risk Premia

The MSCI Enhanced Value Index combines three valuation descriptors: book-to-price (B/P), forward earnings-to-price (E/P) and operating cash flow-to-enterprise value (CFO/EV) to target the value factor.

The three value descriptors have been individually rewarded with risk premia over long time periods. Decile portfolios constructed by sorting on each descriptor (each decile has an equal number of stocks) showed the level and monotonicity of the factor risk premia. The relative underperformance of the ninth and tenth deciles meant that forward E/P and CFO/EV each appeared to be a more robust discriminator of stock performance than B/P.


Annualized Excess Returns of Deciles for Different Value Descriptors

Excess returns of equally weighted decile portfolios over the MSCI World Equal Weighted Index from December 2000 to April 2020. Deciles are constructed using sector relative value scores, rebalanced semi-annually. Decile 1 represents stocks with the highest value characteristics; Decile 10 represents stocks with the lowest value characteristics.


Value Descriptors Exhibited Low Correlations with One Another

We next evaluated whether any of the descriptors were redundant, or if they captured different elements of the factor. We found the three value descriptors had, on average, low return correlations with each other. Notably, B/P exhibited either a negative or low correlation with forward E/P during most of the analysis period.

Low correlations may indicate that the descriptors had different fundamental drivers of returns. It suggests that each descriptor deserved its place in a value-factor definition, as it seemed to capture a different slice of the factor.


Three-Year Rolling Correlations of Decile 1 to Decile 10 Value Returns


Combining Value Descriptors Provided a Potential Hedge

Each value descriptor usually takes a different slice of a firm’s fundamental data often providing different insights. Combining B/P, forward E/P and CFO/EV reflects asset-based, earnings-based and whole-firm valuation approaches. Combining representatives of distinct classes of value descriptors has the potential to provide a more comprehensive view of the valuation of a company.

Additionally, combining multiple descriptors may help mitigate the fact that each descriptor can have limitations, as well as potential advantages, as shown in the exhibit below. For example, while B/P represents a fundamental aspect of value, it employs historical accounting data and does not directly account for intangible assets, such as patents, goodwill or brand value.


Advantages and Disadvantages of Different Value Descriptors

Value Descriptor Fundamental Driver of Risk Premia Advantages Disadvantages
Book-to-price ratio ROE, level of unexpected earnings Stable, low turnover Historical data, sector biases, doesn’t capture intangibles
Forward earnings / price Growth rate of predicted earnings  Forward-looking Subject to distortion, can be volatile, analyst biases
Operating cash flow to enterprise value Growth rate of cash flow Captures all sources of capital If EBITDA is used for cash flow, cash flow is overstated if working capital is growing


To examine the potential benefits of combining descriptors, we looked at different security-selection approaches using B/P and forward E/P. As illustrated below, selecting the top 30% of securities based on B/P (the leftmost chart) could result in the inclusion of companies with poor earnings outlooks — that is, potential value traps. Likewise, selecting securities based on forward E/P (the middle chart) could lead to the inclusion of companies with potentially inflated expectations.

When selecting companies based on the average of the two descriptors, however, (the rightmost chart), some of the potential value traps or companies with inflated expectations may be avoided (highlighted in green).


Security Selection Based on One Versus Multiple Descriptors (Z-scores)

Each circle in the scatter plot represents a constituent of the MSCI World Index, as of November 2019; the size of the circle denotes its index weight. The top right quadrant represents constituents with positive B/P and forward E/P z-scores. Z-scores are computed by standardizing the raw descriptor values such that each descriptor has a market-cap-weighted mean of zero and a unit standard deviation.

Combining B/P, forward E/P and CFO/EV is an extension of this idea. It encourages the selection of securities that have the highest average score based on all three dimensions.


Different Descriptors, Different Perspectives

Investors often ask if there is a “right” descriptor to capture a factor. As corporate business models change in response to dynamic market conditions, e.g., technological advances and shifts in consumer behavior, new descriptors may be rigorously tested to see whether they appropriately capture the factor.

That said, we find it best to use multiple descriptors. Using value as an example, we saw that while different descriptors can be used to define a factor, any single descriptor can have flaws. Using multiple descriptors captured the value factor more comprehensively and helped overcome the shortcomings of each.



1Robustness in factor definition is one of several important evaluation criteria for investors’ due diligence. Other considerations may include purity of factor signal, undue influence from non-target factors, portfolio concentration and investability.

2A detailed index methodology may be found at



Further Reading

Building Single-Factor Portfolios

MSCI Perspectives Podcast: Single-Factor Portfolio Construction

Single-Factor Portfolio Construction Video