Equal weighting beat the ESG-constrained ensemble in European large caps: 0.681 Sharpe against 0.363 from July 2020 to December 2025. Both portfolios held the same 46 names. That gap puts pressure on the claim in Dadzie-Dennis and Wirjanto's abstract that the ensemble "provides the best performance". Their conclusion makes a narrower case for competitive performance and stability across models and ESG specifications.

What goes into the average?

The authors fix their universes at June 2020. They use the S&P 500 Top 50, comprising 50 stocks, and the EU STOXX 50, reduced to 46 stocks after dropping Prosus, Linde, Amadeus and Adyen for insufficient data. Expected returns and the covariance matrix come from weekly Yahoo Finance prices covering January 2015 to June 2020. Each stock receives a Sustainalytics ESG risk score. Lower scores mean less risk.

The first three optimizers are long-only, with two constraints. The portfolio's weighted score cannot exceed a target θp, which the authors vary from 0 to 20. Stocks scoring below the universe average must receive at least 50% of the weight. The authors name this the UNPRI constraint, referring to the PRI signatory rule covering more than half of assets.

Four optimizers contribute to the ensemble:

To form the ensemble, the authors average the first three optimizers' weights across every feasible θp and include the constrained two-stage portfolio. They set the weights once and hold through December 2025, without rebalancing. Estimation error supplies the economic rationale. The optimizers make different mistakes with the same noisy inputs. Averaging should cancel some of those mistakes if their errors are imperfectly correlated.

The full headline sentence is: "Although no single strategy dominates across all settings, the proposed ensemble approach provides the best performance by balancing sustainability objectives with diversification and risk-adjusted returns across regions." Its opening clause supplies the hedge. The rest makes the claim.

No objective for the claimed balance

The paper supplies no ranking criterion that weighs return against volatility and portfolio ESG score. Without such a criterion, calling a strategy best at balancing these objectives can only mean dominance. We checked that claim.

In Europe, the ensemble earned 7.32% with 19.44% volatility, a Sharpe of 0.363 and an ESG score of 9.00. The constrained two-stage portfolio earned 18.56%, with a Sharpe of 0.802 and an ESG score of 7.36. It wins on return, Sharpe and greenness. Its only loss is on volatility, at 21.23%. Equal weighting, the 1/N portfolio, returned 11.33% at 15.75% volatility, though its ESG score of 16.56 makes it browner.

One of the ensemble's own inputs therefore beats it in three of four columns. The benchmark beats it in every financial column. The authors acknowledge this: "The equally weighted benchmark, however, outperforms both ensembles."

Stability is their main defence. As the ESG target changes, individual optimizers can jump between allocations. Averaging across targets and frameworks smooths those jumps and makes the result less dependent on a particular specification.

There is a genuine advantage here. The single-target winners, including θp = 8.9 in Europe (Sharpe 0.520) and 11.2 in the US (1.078), are picked from out-of-sample tables. By averaging every feasible target, the ensemble avoids making that selection.

The comparison with the unconstrained ensemble also favours the constrained version. The unconstrained average returned 2.09% with a Sharpe of 0.104; the constrained average is both better and greener. That claim holds, though it falls well short of the abstract's. Nor would we crown the two-stage portfolio. It owns three stocks (ISP.MI, VNA.DE, SU.PA), while its US counterpart delivered a Sharpe of 0.530.

NVIDIA carries weight in the US ensemble's 0.929 Sharpe

NVIDIA does much of the work in the US case for the ensemble. The unconstrained max-return optimizer allocates 100% to NVDA, earning 72.61% at 46.95% volatility. Unconstrained Black-Litterman puts 51% in AMZN and 49% in NVDA.

The averages inherit those bets. DHR accounts for 24.4% of the constrained ensemble and NVDA for 22.1%; the top five holdings together represent about 70% of the book. In the unconstrained ensemble, NVDA receives 37.3%, AMZN 23.3% and AAPL 15.0%.

The constrained ensemble earned 21.40% and a Sharpe of 0.929. Against the 1/N portfolio's 0.892, its Sharpe lead is 0.037. The unconstrained ensemble reached 1.050. Imposing the ESG constraint therefore cost 0.121 of Sharpe, leaving the ensemble with a small advantage over equal weighting. Both figures describe one path. We found no significance test.

The authors acknowledge that sector exposure explains at least part of the US ESG-return relationship. The High and Severe buckets each contain one firm, both placed by the paper in Energy. Their in-sample returns were -9.58% and -0.60%. By comparison, the 33 Low-risk firms earned 16.9%. The authors propose future controls for size, value and momentum, writing that these "would further clarify whether ESG-related performance persists beyond known return drivers".

We draw a stronger inference. The authors describe the lower-risk US firms as "predominantly large-cap growth-oriented companies". Until those controls are run, the US result cannot be separated from a large-cap growth tilt.

A single formation date, with a survivor filter

All the evidence comes from a June 2020 formation date and the subsequent 5.5-year buy-and-hold path. The authors deliberately chose a single date: "Any performance difference reflects the quality of the initial allocation, not active management skill." Fair enough. It remains a single draw from a single allocation.

The setup raises two validation issues. On sample selection, the paper says: "We retain only those companies with complete historical return data over the full sample period." The period ends in December 2025. Eligibility at June 2020 thus depends on data unavailable at formation. Insufficient data also explains the four EU exclusions. We suspect the effect is small among 46 to 50 mega-caps, but the construction introduces look-ahead.

Then there are the ESG scores. The investor is described as holding "yearly ESG data" during the in-sample period, and the paper uses scores as at the June 2020 formation date. We could not find whether these were the scores Sustainalytics published then or values revised later. The distinction matters given the fine-grained feasibility cutoffs: θp of 6.4 in Europe and 9.0 in the US.

We could not test these issues ourselves. Our data lacks company-level ESG risk scores, preventing us from building either the target constraint or the 50% rule. We also have no European equity coverage for the STOXX side.

The same ensemble beating 1/N in Europe across rolling formation dates would change our view.