3D Investing: Jointly Optimizing Return, Risk, and Sustainability

Abstract

Traditional mean-variance portfolio optimization is based on the premise that investors only care about risk and return. However, some investors also have non-financial objectives such as sustainability goals. We show how the traditional approach can readily be extended to mean-variance-sustainability optimization and explain why this 3D investing approach is ex-ante Pareto-optimal. We illustrate its efficacy empirically in several studies, including carbon footprint and sustainable development goal objectives. Importantly, we highlight conditions under which a 3D optimization approach is superior to a naïve 2D approach augmented with sustainability constraints.

Keywords:

• carbon footprint
• ESG
• factor investing
• portfolio optimization
• sustainable development goals (SDG)
• sustainable investing

PL Credits:

• 2.0

Disclosure statement

The authors disclose that they are employed by Robeco, a firm that offers various investment products. The construction of these products may, at times, draw on insights related to this research. The views and results presented in this article were not driven by the views or interests of Robeco and are not a reflection of its points of view.

Acknowledgments

The authors thank two anonymous reviewers as well as participants at the Robeco research seminar and EQDerivatives Europe SRI workshop. The views expressed in this paper are not necessarily shared by Robeco or its subsidiaries.

Notes

1 The reduction of the carbon footprint of a portfolio (as given by CO₂ emissions scaled by some measure of a company’s size) is one of the most common sustainability objectives. For examples, see Andersson, Bolton, and Samama (2016), Hao, Soe, and Tang (2018), Görgen, Jacob, and Nerlinger (2020), Roncalli et al. (2020), Bender et al. (2020), Benz et al. (2020), Bolton and Kacperczyk (2021), Bolton, Kacperczyk, and Samama (2022), and Kolle et al. (2022).

2 This is the transaction cost at which the outperformance of the portfolio would be zero.

3 For practical considerations on the sustainability metric ${\mu }_{\mathit{\text{SI}}},$ see Chen and Mussalli (2020).

4 Prior to 2001, we use constituents of the FTSE Development Markets index as a proxy for MSCI World constituents.

5 In unreported results, we find qualitatively similar results when using raw scope 1 and scope 2 emissions and carbon intensity (scaled by revenue instead of EVIC) and when incorporating scope 3 emissions into carbon footprint.

6 We additionally use the data-simulation approach of Blitz and Hoogteijling (2022) to produce a longer history of carbon footprint data and SDG data. Note that any potential forward information leakage is of little concern as we are comparing two portfolio-construction approaches on the same data. We aim to illustrate the broad application of our methodology on a representative set of sustainability data.

7 Examples can be found at the Robeco SI open-access page: https://www.robeco.com/en-int/sustainable-investing/how-do-companies-and-countries-score-on-sustainability.

8 We use the same benchmark, MSCI World, when constructing portfolios and evaluating financial and sustainability objectives.

9 We define the “risk-return efficient frontier” to be the traditional efficient frontier for a constant level of portfolio sustainability and the “maximum risk-return efficient frontier” to be the risk-return efficient frontier when sustainability considerations are dropped. That is, the maximum risk-return efficient frontier is the efficient frontier in the traditional sense.

10 Similarly, we define the “risk-sustainability efficient frontier” to be the risk versus sustainability efficient frontier for a constant level of expected return and the “maximum risk-sustainability efficient frontier” to be the risk-sustainability efficient frontier when expected return considerations are dropped.

11 For the carbon footprint scenario, we use coefficients of (−0.016 and −0.020) and for the SDG scenario we use coefficients of (2.0 and 1.5) for the 0.5%/1.0% tracking error targets, respectively.

12 For more discussions on the skewed distribution of MSCI ESG scores, see Chen, von Behren, and Mussalli (2021).

13 This approach is not extensively discussed in this paper, as it is common and straightforward.

Additional information

Notes on contributors

David Blitz

David Blitz is Chief Researcher at Robeco, Rotterdam, the Netherlands. Mike Chen is Head of Next Gen Research at Robeco, Rotterdam, the Netherlands. Clint Howard is a Quantitative Researcher at Robeco, Rotterdam, the Netherlands. Harald Lohre is Head of Quant Equity Research at Robeco, Rotterdam, the Netherlands, and an Honorary Researcher at Lancaster University Management School, Lancaster, United Kingdom.

Mike Chen

David Blitz is Chief Researcher at Robeco, Rotterdam, the Netherlands. Mike Chen is Head of Next Gen Research at Robeco, Rotterdam, the Netherlands. Clint Howard is a Quantitative Researcher at Robeco, Rotterdam, the Netherlands. Harald Lohre is Head of Quant Equity Research at Robeco, Rotterdam, the Netherlands, and an Honorary Researcher at Lancaster University Management School, Lancaster, United Kingdom.

Clint Howard

David Blitz is Chief Researcher at Robeco, Rotterdam, the Netherlands. Mike Chen is Head of Next Gen Research at Robeco, Rotterdam, the Netherlands. Clint Howard is a Quantitative Researcher at Robeco, Rotterdam, the Netherlands. Harald Lohre is Head of Quant Equity Research at Robeco, Rotterdam, the Netherlands, and an Honorary Researcher at Lancaster University Management School, Lancaster, United Kingdom.

Harald Lohre

David Blitz is Chief Researcher at Robeco, Rotterdam, the Netherlands. Mike Chen is Head of Next Gen Research at Robeco, Rotterdam, the Netherlands. Clint Howard is a Quantitative Researcher at Robeco, Rotterdam, the Netherlands. Harald Lohre is Head of Quant Equity Research at Robeco, Rotterdam, the Netherlands, and an Honorary Researcher at Lancaster University Management School, Lancaster, United Kingdom.