Author Details

Abhishek Gupta

Abhishek Gupta

Executive Director, MSCI Research

Ashish Lodh

Ashish Lodh

Executive Director, MSCI Research

Subhajit Barman

Subhajit Barman

Vice President, MSCI Research

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How Portfolio-Weighting Schemes Affected Factor Exposures


  • As investors perform due diligence on single-factor products, one area of focus is the exposure to target and non-target factors in a portfolio.
  • Security-weighting schemes used in factor portfolio construction impacted levels of target factor capture and exposure to unintended factors, as well as portfolio efficiency, concentration and investability.
  • Score-tilt weighting efficiently captured target factors and limited unintended exposure. Equal- and inverse-volatility weightings resulted in implicit exposure to size and low-volatility, regardless of the targeted factor.


Investors often use single-factor portfolios to take advantage of factor cyclicality or to correct the factor bias of an existing allocation. In such implementations, a desirable characteristic of a single-factor portfolio is high exposure to the target factor and limited exposure to non-target factors. While most long-only single-factor portfolios historically had incidental exposures, investors’ due diligence can include an assessment of whether those exposures are significant and if they overwhelm the target factor.

In this blog, we discuss the weighting schemes commonly applied in the construction of heuristic-based single-factor portfolios and the impact they had on target and non-target factor exposures, as well as portfolio efficiency, concentration and investability.


Score-Tilt Weighting Provided Efficient Capture of the Target Factor

We constructed a set of value-, quality- and momentum-factor portfolios following rank-select-weight algorithms for each of the three target factors. That is, we ranked MSCI World Index constituents based on their exposure to each factor defined by multiple descriptors and selected the top 30% of the stocks from the underlying universe and applied six different portfolio weighting schemes independently to the selected stocks.1 The chosen weighting schemes, outlined below, reflect a range of portfolio objectives and are commonly used to construct factor portfolios.


Single-Factor Weighting Schemes

Weighting Scheme Definition
Market-Cap Weighted Stocks weighted in proportion to their free-float market cap
Score-Tilt Weighted Stocks weighted in proportion to the product of their market cap and factor score
Score Weighted Stocks weighted in proportion to their target-factor scores
Equal Weighted Stocks equally weighted
Inverse Volatility Weighted Stocks weighted in proportion to the inverse of their historical volatility
Minimum-Correlation Weighted Optimized weighting scheme to obtain a portfolio with minimum volatility under the assumption that all stocks have identical volatilities


We first compared the intensity of target-factor exposures achieved by the other weighting schemes compared to market-cap weighting, from December 2000 to April 2020, using MSCI FaCSTM.2 For value portfolios, score weighting and score-tilt weighting provided higher value exposure than other weighting schemes. However, across value-, quality- and momentum-factor portfolios, score-tilt weighting consistently improved target-factor exposure relative to market-cap weighting, while other weighting schemes were inconsistent and resulted in lowering factor exposures on average.


Improvement in Target-Factor Exposure with Respect to Market-Cap Weighting

Factor exposures from December 2000 to April 2020 using MSCI FaCS.


Next, we computed the transfer coefficient (TC) to assess the efficiency with which factor insights were transferred into portfolio weighting.3 A positive TC meant the weighting scheme was more efficient in reflecting a factor signal in the portfolio compared to market-cap weighting, and a negative TC meant the weighting scheme was less efficient in doing so. Score-tilt weighting provided the highest TC.


Transfer Coefficient of Single-Factor-Portfolio Weighting Schemes

Transfer Coefficient Benchmark: 30% Market Cap
  Value Quality Momentum
Market-Cap Weighted - - -
Score-Tilt Weighted 0.45 0.46 0.51
Score Weighted 0.28 0.03 0.18
Equal Weighted 0.10 -0.03 0.04
Inverse Volatility Weighted 0.8 -0.04 0.03
Minimum-Correlation Weighted 0.07 -0.03 0.06

To isolate the impact of weighting schemes from stock selection, we used the market-cap-weighted portfolio of the top 30% stocks selected via target-factor scores as the benchmark.


Selection of Weighting Scheme Could Bring Implicit Factor Exposures

Detailed factor analysis showed that equal, inverse-volatility and minimum-correlation weighting schemes introduced exposure to the low-size and, to some extent, low-volatility factors, regardless of the factor being targeted. Score weighting also picked up unintended factor exposures, while market-cap and score-tilt weighting showed only small exposures to non-target factors. In the exhibit below, we show the analysis for quality-factor portfolios as an example.

Constructing quality factor portfolios using equal, inverse-volatility or minimum-correlation weighting has historically resulted in a multi-factor portfolio. This could be beneficial to performance in some periods but exposes the portfolio to potential cyclicality in size and volatility factors that may not be intentional and may not align with the objectives of investors who sought high exposure to a single factor.


Quality Portfolio Factor Exposures Under Different Weighting Schemes

Data from December 2000 to April 2020. Benchmark: MSCI World Index


Investability Challenges

Some weighting schemes resulted in lower capacity and investability relative to others. To assess the capacity profile of the different weighting methods, we compared the average weight multiplier (AWM) and the percentage of stock ownership across the quality-factor portfolios.4 The AWM for score-tilt weighting remained quite close to market-cap weighting, suggesting that smaller stocks were not disproportionately overweighted. Other schemes had AWM figures that were four to five times higher than market-cap weighting.

Since quality scores have historically been relatively stable, the turnover incurred from rebalancing a top-30%-selection quality portfolio was not significantly high for the market-cap-weighted portfolio turnover (29.2%) or the score-tilt-weighted portfolio (28.7%). Other weighting schemes, however, had a much higher turnover, as seen in the exhibit below. The exhibit also shows the maximum days to trade (DTT) figures for a USD 10 billion portfolio.5 For some weighting schemes, trading all positions could take 30 to 100 days, which may pose an issue for funds that track such strategies. It could become even more challenging when implementing weighting schemes with low-size tilts in less-liquid markets.


Capacity and Investability for Different Weighting Schemes

  Market-Cap Weighted Score-Tilt Weighted Score Weighted Equal Weighted Inverse-Volatility Weighted Minimum-Correlation Weighted
AWM  3.5 3.5 17.6 17.4 16.1 24.1
Maximum Stock Ownership (% float) 0.1 0.1 1.6 1.8 1.8 5.5
Turnover (%) 29.2 28.7 46.7 47.8 46.0 73.4

95% DTT

(10 bn$)

1 1 6 6 6 16


(10 bn$)

4 3 30 34 36 98


Seeking Balance Between Factor Exposure, Purity and Investability

Our research showed that when constructing single-factor portfolios based on a rank-select-weight algorithm, using equal- and inverse-volatility weighting resulted in low-capacity portfolios with unintended exposures, while score-tilt weighting guarded against unintended factor exposures and provided a balanced trade-off between factor exposure, factor purity and investability. Given the rise in factor investing and the launch of many factor products, the systematic assessment process could be of assistance to asset owners and wealth managers when performing their due diligence to identify products that match their needs.


1We looked for funds with “growth” but not “value,” “income,” “dividend” or “yield” in their names. The holding data of these funds was as of July 31, 2020.

2MSCI FaCS provides a framework to measure portfolio exposure to eight factor groups (i.e., value, size, momentum, volatility, quality, yield, growth and liquidity).

3Transfer coefficient is measured as the cross-sectional correlation between a security’s target-factor exposure and its active weight relative to the benchmark.

4The proportion of the free-float market capitalization of a stock held in a fund perfectly replicating an index, relative to the free-float market capitalization of the stock.

5Days-to-trade (DTT) is the number of days required to trade a change in a stock position for periodic index review given its average trading volume (ATV). We assume USD 10 billion AUM and 10% ATV limit for the purposes of the calculation. 95% DTT is the 95th percentile of the cross section of stocks.


Further Reading 

Building Single-Factor Portfolios

How to Describe a Factor

MSCI Perspectives Podcast: Single-Factor Portfolio Construction

Single-Factor Portfolio Construction Video