Building Fama–French and ESG Factors to Compare Sustainable Indices
Summary
The document outlines a proposed factor analysis comparing sustainable equity indices with conventional benchmarks across several regions. The author has compared performance using Sharpe ratios and Jensen’s alpha, and wants to explain return differences with a Fama–French three-factor model plus an ESG premium labeled Good Minus Bad. They ask how to construct size and value factors for these indices and whether the paired indices should be combined to form them.
For the ESG factor, the proposed idea is to take the return difference between high- and low-ESG portfolios, but the author is unsure what universe or portfolio construction to use. The document presents these as research questions rather than offering an answer or validated factor methodology. It gives no regression results beyond noting that the estimated intercepts are not significant, and does not explain how to form, rebalance, or test the proposed factors.
Key ideas
- The proposed analysis compares sustainable equity indices with conventional benchmarks using factor regressions.
- The author seeks to construct size and value factors for the regional index comparisons.
- Good Minus Bad is proposed as the return spread between high- and low-ESG portfolios.
- The document raises questions about factor universes and portfolio construction but does not resolve them.
- The reported Jensen’s alpha estimates are not statistically significant, according to the author.
Tags
Full text
# How to build Fama-French model factors SMB and HML to compare sustainable index to conventional benchmark? # How to build Fama-French model factors SMB and HML to compare sustainable index to conventional benchmark? My goal is to analyze and compare the performance between socially responsible indices and conventional ones. I am comparing for each region (Europe, UK, World, US) a sustainable index to a conventional one (Eurostoxx Sustainability 40 Index vs Eurostoxx 50 Index, FTSE4GOOD UK vs FTSE 100, MSCI World ESG Leaders Index vs MSCI World Index, Dow Jones Sustainable Index vs Dow Jones Industrial Average). I looked at the performance of each one over the period 2016-2021 using Sharpe ratio and Jensen's alpha. None of my intercept(Jensen's alpha) for the linear regression is significant, however, there are some sustainable indices that overperform their benchmark. Therefore, I would like to explain these excess return by using the Fama-French 3 factor model + an additional factor that I would call Good Minus Bad taking into account the ESG scores. I know there is data available on Fama-French website but it is not calculated for the indices I am looking at. Therefore, I would like to know the procedure to calculate the size and value factors using my indices. The doubt I have is the following : - a single portfolio composed of both indices combined should be used to calculate SMB and HML factors? The regression I would like to do is the following : E(R)_i - R_f = α_i + β_iM * [ E(R)M )- R(f )]+ β_SMB* E(R)_SMB)+ β_HML* E(R)_HML+ β_GMB * E(R)_GMB Where : E(R〗_i) = Expected return of the asset R_f = Risk-free rate α_i = Intercept of the equation β_iM = Beta [E(R)M ) - R(f )] = Excess expected return of the market portfolio β_SMB = Beta with respect to size premium SMB = Small Minus Big, size premium β_HML = Beta with respect to value premium HML = High Minus Low, value premium β_GMB = Beta with respect to ESG premium GMB = Good Minus Bad, ESG premium Then, the following question I have is related to the following : - Does it make sense to build the GMB factor as follows= High ESG Score - Low ESG Score Then, the question is with which index I am going to calculate this factor ? With a combined portfolio of both indices for each region ? or something else ? Thank you in advance for your help,
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