Changing the temperature-score provider moves a minimum-variance portfolio's reported result more than tightening its weight cap. In 'Implied temperature rise metrics: a compass without direction?', Kathan, Reisser and Utz score a minimum-variance portfolio of 100 large caps using four providers. The same weights produce 1.663°C from MSCI and 3.386°C from Trucost. Tightening the weight cap from none to 2% changes any one provider's figure by at most 0.85°C; changing providers at the same cap moves it by 1.2°C to 1.7°C.
Where the scores come from
An implied temperature rise (ITR) score compares a company's projected emissions with its allotted share of the global carbon budget. The result is converted from a budget overshoot or undershoot into degrees Celsius. There is no agreed way to allot that share, and each vendor makes its own choice. The paper begins there.
The authors gather 2021 scores from Trucost, Bloomberg, Iceberg Data Lab and MSCI. Their main sample has 1,517 firms rated by at least three providers; 785 have scores from all four. The methods differ by design. Bloomberg uses the CDP-WWF (Carbon Disclosure Project and World Wide Fund for Nature) target-based score, assigning a 3.2°C default where it finds no valid target. MSCI's 2021 methodology projects emissions to 2070 against a 2°C budget. Trucost and Iceberg use 2050 pathways. Trucost reports categories rather than point scores, so the authors assign midpoints and acknowledge the measurement error this introduces.
Agreement is scant. Pairwise Pearson correlations range from -0.02 to 0.14, while Krippendorff's Alpha across all four providers is 0.047. The paper cites ESG-rating correlations of 0.38 to 0.71. When the authors take each provider's 100 worst-scoring firms, 245 firms appear on only one list, 52 on two, 17 on three and none on all four.
A mandate asks whether a firm is Paris-aligned. On that binary measure, MSCI puts 69% of covered firms at or below 2°C, compared with 44% for Trucost, 27% for Iceberg and 10% for Bloomberg. That leaves a 59 percentage-point gap over the same question.
Can calibration explain the gap?
Some of the difference comes from score levels.
MSCI's mean company score is 2.14°C; the other three average 2.97 to 3.07. In the unconstrained minimum-variance portfolio, MSCI reports 1.663°C, which is 0.97°C below the next-lowest provider, Bloomberg at 2.630. MSCI therefore accounts for 0.97°C of the 1.72°C spread. The Paris-aligned benchmark (PAB) fund test shows a similar divide. Among 199 Morningstar PAB funds, median portfolio ITR is about 2.8°C under Trucost, Bloomberg and Iceberg, versus close to 1.75°C under MSCI. The median provider spread exceeds 1°C.
For that fund calculation, the authors fill a missing company score with the relevant provider's mean and rescale equity weights to sum to one within the sample. Imputation retains each provider's level, widening the existing gap between them. The authors report that an untabulated run without imputation is qualitatively unchanged.
Sticking with one vendor can contain a level shift. It cannot resolve disagreement about rank: Spearman correlations reach only 0.222, for Iceberg and MSCI. In tercile sorts using market beta estimated from 2020 returns, Trucost's mean ITR falls from 3.287 to 2.601 as beta rises; MSCI's climbs from 1.942 to 2.358. Portfolio weights also change the providers' ordering. With a 2% cap on the minimum-variance portfolio, Trucost moves from highest to below Bloomberg and Iceberg, while Bloomberg rises from 2.630 to 2.996. A uniform calibration shift would leave those rankings intact.
Firm characteristics shed little light on the disagreement. Fundamentals, emission intensities, region and industry yield an adjusted R² of 0.033 to 0.074. Energy has the largest disagreement coefficient, 0.3978 (t = 3.44), despite being the sector where agreement should be easiest. Against the Transition Pathway Initiative's public classification, no provider's binary association exceeds 0.402. Iceberg puts all 31 overlapping Energy firms above 2°C. RepRisk greenwashing flags fare no better: mean disagreement is 0.883 for flagged firms and 0.838 for the rest, with p = 0.109.
Two mechanical features depress the headline correlations. Bloomberg's default holds its standard deviation to 0.58, against 1.35 to 1.59 for the others; Trucost's open-ended bins truncate variation. The authors flag Bloomberg's compression and the mapping error. Connecting those features to the correlations is our reading. Even without Bloomberg, MSCI's 69% and Iceberg Data Lab's 27% remain 42 points apart.
Optimization and concentration
The conclusion says optimization amplifies disagreement "in return-maximizing portfolios, where concentration effects interact with provider-specific climate metrics". The body qualifies the claim as "in some cases, may amplify" and attributes greater dispersion without weight constraints to "the stronger concentration incentives". A narrower spread after capping weights is consistent with that account.
The conclusion's unqualified "It amplifies" goes too far. The finding holds for the unconstrained tangency portfolio: Trucost reports 4.007°C and MSCI 1.821°C, a 2.19°C gap versus 1.72°C for the unconstrained minimum-variance portfolio. With a 2% cap, the tangency spread shrinks to about 1.0°C, between 3.019 and 2.022. The capped minimum-variance spread is wider, at about 1.3°C.
The optimized portfolios draw on one year of in-sample 2020 returns. Their unconstrained tangency Sharpe is 3.985. The authors attribute it to estimation error and present these portfolios as illustrations. They deserve to be read that way.
Mean disagreement stayed at 0.85
For the convergence test, the authors compare 1,249 firms covered in both 2021 and 2022. Mean disagreement stays at 0.85 in both years; the median moves from 0.76 to 0.73, with a one-sided p of 0.56. They use an unpaired Welch test despite having a balanced panel. A paired test would be tighter, though a mean difference of 0.00 leaves it unable to manufacture convergence. The authors acknowledge the short window and that MSCI's 2024 methodology falls outside it.
We could not test any of this ourselves. The comparison requires company-level ITR scores from all four vendors, which we do not hold. The global universe and PAB fund holdings also lie outside our coverage.
The paper says ITR values "cannot be interpreted as objective or provider-neutral measures" and calls them "provider-dependent indicators". If you write a PAB mandate or client alignment report, put the provider beside every temperature you publish. Avoid comparing funds scored by different vendors. The paper runs no test of ITR against returns, so it supplies no evidence for ITR as a return signal. A rerun using post-2024 methodologies, with Pearson correlations near the 0.38 lower bound the paper cites for ESG ratings, would change my mind.