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Two suggestions are offered to address growing criticism of the ESG-based investing. First, socially responsible investors need to use portfolio performance measure that is explicitly sensitive to the portfolio ESG value. Second, since the corporate ESG ratings are not regulated and are vaguely defined, the ratings agencies should provide detailed information on how their ratings are calculated and allow their clients to implement the customized ratings of their choice.

I call myself outsider because I don’t make living in the ESG space. I’m an educator and research scientist, most recently in quantitative finance. My interest in ESG has been an offshoot of my research of the optimal portfolio theory, specifically, the problem of portfolio diversification. This problem per se, as I indicate further, is very important for ESG.

Recently, the ESG-based investing has come under criticism on two fronts. First, it is relationship between the corporate ESG ratings and market performance. Even though positive correlations between these two factors can sometimes be found, the causality of this effect remains questionable: are the ‘good’ companies more profitable or more profitable companies can afford to look good (Damodaran, 2021; Pucker, 2021)? Another issue is that the very popularity of some ESG investments may drive their price up (van der Beck, 2021).

Then, there is a problem with the choice of the ESG ratings for individual companies that may differ significantly (sometimes dramatically) among their providers (Berg et al., 2019; Christensen at al., 2021; Dimson et al., 2021; Schmidt & Zhang, 2021).

Moreover, absence of regulation has led to well-publicized instances of “greenwashing” (Fancy, 2021; Eccles, 2021b; Plucker, 2021). Still, the ESG-based investing has influential advocates who offer their own remedies to its current problems (see, e.g., Eccles, 2021a, 2021b; Edmans, 2021; Lukomnik & Hawley, 2021). And I agree with them, up to a point: no matter how messy is the current situation with ESG, growing public interest exerts a pressure on corporations to take socially responsible actions. Nevertheless, the ESG conundrum I mentioned above should be addressed. So, let me offer two suggestions in this regard.

I start with the ESG-based investing performance problem by relying on the optimal portfolio theory. The classical mean-variance paradigm pioneered by Markowitz is based on

minimization of the objective function that is the difference between portfolio risk (characterized by portfolio variance) and expected portfolio return. Unfortunately, such an approach yields highly concentrated portfolios. Namely, the minimization protocol leaves in the portfolio only a few best past performers and drops the rest. One way to increase portfolio diversity is to add the Herfindahl–Hirschman index to the minimizing objective function (Bouchaud et al., 1997; Schmidt, 2018). This index is used as a measure of concentration of firms within industry. When it becomes the dominant term in the minimizing objective function, all portfolio constituents become equally weighted.

Similarly, if portfolio’s ESG value (PESGV) is a true priority for socially responsible investors, it should be added to the minimizing objective function (Pedersen et al., 2019; Schmidt, 2020). A natural PESGV measure is the sum of the weighted ESG ratings of portfolio constituents. Then, portfolio can be optimized simultaneously in terms of its return, risk, and PESGV.

As far as ESG-based investing is concerned, practitioners prefer ESG-enhanced (or ESG-tilted) equity indexes and related ETFs. An evidence that these investments outperform their ESG-neutral siblings is mixed at best (cf., e.g., Kumar, 2019 and La Torre et al., 2020, with Clark & Lalit, 2020). In my opinion, practitioners’ investment performance reports often lack statistical rigor. In particular, they neglect the entry point bias. Specifically, the data samples in these reports start at the beginning of a year and end at the end of another year. However, investors may put their money in the market and withdraw them on any day. Then what? Remember, those who invested in NASDAQ at the top of the internet boom in March 2000 and experienced later the dot-com crash recovered their principal capital only in 2015. The correct way to test performance of investing strategy is to use rolling windows of a chosen holding period (e.g., one year or five years) that start on each day within the given data sample (e.g., the last 10 years) and collect performance statistics for all windows. Then, one can compare different investing strategies using statistical hypothesis testing (see, e.g., Cai & Schmidt, 2020; Schmidt, 2021). So, let’s leave the discussion of outperformance for another day.

A more generic problem is that for some ESG optimal portfolios, the classical performance measure, the Sharpe ratio (Sh) that has the sense of risk-adjusted return, may actually monotonically decline with growing PESGV. This happens because of low correlations between the corporate ESG scores and stock returns. Moreover, portfolio diversity decreases when PESGV rises (Schmidt, 2020; Schmidt & Zhang, 2021). Therefore, I suggest that socially responsible investors use a portfolio performance measure that is determined not only with portfolio return and risk but also with PESGV. I offer such a measure that I call the ESG tilted Sharpe ratio:

ESG tilted Sharpe Ratio

Sh_ESG = Sh(1 + PESGV)  

Sh_ESG has a maximum at intermediate PESGVs, which may serve as a criterion for choosing an optimal ESG portfolio. Similar ESG-dependent performance measures were proposed by Chen & Mussalli (2020) and Alessandrini & Jondeau (2021).

Investors should be able to define their own ESG priorities.
Dr. Anatoly Schmidt

All these and other ESG considerations make sense only if the ESG ratings can be trusted. And that is where the problem is: as the famous data science GIGO adage states: “garbage in, garbage out.” From what can be found on the ratings agencies’ websites, the ESG ratings are the (almost) equally-weighted sum of their E (environmental), S (social), and G (corporate growth) components. Really? Let’s start with G. If it is not highly correlated with the stock return, I do not know what it is. In other words, the G component, if it is really relevant to the company’ performance, may be redundant as far as optimal ESG portfolios are concerned (see also Pedersen et al., 2019; Lioui & Tarelli, 2021). Then there is S. Should we treat it as equally important to E provided that mankind faces the climate crisis? And another problem is that it is really difficult (if even possible) to find out in public domain how exactly the E, S, and G components themselves are calculated.

I do not have a strong opinion on how the ESG ratings should be defined and I am not sure that regulation would be helpful, though the expert recommendations won’t hurt. But I do have a suggestion. Namely, since it is investors’ choice how to invest their money, they should be able to define their own ESG priorities. As for the ratings agencies, they need to be fully transparent on what factors they include into the E, S, and G components and let their clients to mix these factors into the ESG components and then combine them into the ESG ratings according to their own vision. This will not preclude the ratings agencies to offer some default ESG ratings to less sophisticated investors.


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Electronic copy available at:

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