The 62.3% breach rate needs a benchmark: Féron and Haalebos set the penalty so a fully informed investor breaches the carbon budget on half the simulated paths. Every exceedance probability in the paper is measured against that chosen coin flip.
The paper follows a small, price-taking investor who learns from prices and periodic noisy disclosures. She must infer the climate-transition state, a common driver of expected returns, along with its long-run mean and firms' carbon intensities. Her objective counts financed emissions accumulated over years, so today's holdings draw on the whole-horizon budget. Per-date carbon constraints, common in earlier work, play no role. There is no alpha source here. The question is what information does to welfare and budget breaches.
All results come from the authors' calibrated Monte Carlo model: three stylized assets plus cash, 5,000 monthly paths over 25 years, and no real data. With correct priors, learning costs little. Bias in either direction changes breach odds, though the directions differ.
The carbon bill on terminal wealth
The investor has exponential utility over terminal wealth minus λ times cumulative financed emissions. Under the ownership accounting used here, each holding's dollar value is multiplied by the firm's carbon intensity, its emissions divided by enterprise value including cash (EVIC). Those products accumulate over a 25-year horizon. λ converts a unit of cumulative emissions into wealth; the authors call it a shadow valuation inside the mandate.
The brown asset starts at intensity 100 and reverts toward 70. The decarbonizing asset starts at 75 and reverts toward 35; green starts at 20 and reverts toward 10. Expected returns depend on a common transition factor, an Ornstein-Uhlenbeck process with mean reversion 0.15 and volatility 0.02. The assets' exposures are -0.05, 0.04 and 0.02. The factor's unknown long-run mean also shifts their long-run intensity targets. Cash has an intensity too: 25, decaying at 0.1 a year. Green therefore starts cleaner than the risk-free asset.
The authors solve for three information sets. One investor sees everything. Another observes intensities while filtering the transition state and its long-run mean. The third sees continuous prices and a noisy intensity disclosure once a year, with noise variance 20 per asset; her Kalman filter jumps when a disclosure arrives. Across all three, optimal weights contain a Merton term, a climate tilt to expected returns, an intensity penalty measured against cash, and hedging demands. For full information, hedging reflects the correlation between return and intensity shocks. For the two learners, posterior uncertainty adds another source. The authors simulate monthly over 5,000 paths, using common random numbers across specifications.
Why is the benchmark a coin flip?
The authors set λ so the full-information investor exceeds the budget with probability ε = 0.5. Separately, the budget calls for a 50% cut in cumulative financed emissions. The cut's size is 50%; the chance of missing it is 0.5.
They describe ε = 0.5 as "a median-based calibration convention rather than as a normative tolerance for missing the emissions target," allowing information effects to show in either direction. They hold it at 0.5 throughout. They also cap the target at 50%, approximately consistent, they say, with the NGFS Below 2°C scenario. Beyond that cut, short positions contribute more materially to measured reductions. Their accounting treats shorts as negative emissions, whereas PCAF counts only longs.
For an investor with a hard budget, the median calibration leaves a practical question open. The paper does not show the λ or welfare loss needed for a 95% chance of staying within budget.
Biased beliefs and the cost of learning
With correct priors, the investor who sees intensities has welfare "only slightly lower" than the fully informed investor, and exceedance rises "only slightly". We found no exact figures for either comparison. To test bias, the authors shift the prior means of both the current transition state and its long-run mean by the same amount b. The true process stays fixed.
For the disclosure-based investor, certainty-equivalent loss relative to full information is roughly U-shaped in b. It reaches about 3.0% across the bias and disclosure-frequency grid, and grows when disclosures are less frequent. Pessimists hold more brown and reach a 62.3% exceedance probability in the grid's worst cell, versus about 50% under full information. Optimists favor cleaner assets and breach less often than the full-information investor, yet still lose welfare.
For optimists, welfare falls as budget performance improves.
We did not find the magnitudes of b in the text. Without them, the 3.0% loss and 62.3% breach rate are hard to relate to actual disagreements over climate policy.
When disclosure raises emissions
More frequent disclosure can increase financed emissions in this model. Even with full information, the penalty initially leaves the investor underweight the decarbonizing asset relative to the unpenalized benchmark. As its intensity falls, she adds to it until the position exceeds green. A pessimist expects a worse path and holds less. Each disclosure arrives better than she feared, prompting her to buy more of an asset that starts at intensity 75, well above green's 20. Frequent disclosures bring that adjustment forward. Exceedance rises for pessimists and falls for optimists. As the authors put it, better information "does not necessarily lead to lower realized financed emissions."
The size of that effect depends on the setup. Expected returns of 0.0584, 0.0524 and 0.0411 were backed out to produce initial unpenalized weights of 0.36, 0.34 and 0.25. The decarbonizing asset's large place in the portfolio is therefore partly an input. Transaction costs are absent, and the authors flag sizeable reallocations at each disclosure under a five-year cycle. They also say the framework suits passive footprint reduction; an investor seeking to accelerate real decarbonization would need another model.
Synthetic paths, no trading backtest
These are model-implied allocations on synthetic paths, with no trading backtest. We did not build a trading construction from the paper. Our data lacks firm-level greenhouse-gas emissions histories and disclosure dates. Our enterprise-value fields also fall short of a point-in-time EVIC series, so we cannot rebuild the intensities the investor would have seen. The authors say their parameters were chosen rather than estimated and leave estimation for later. Estimation would change my view if the gap between pessimists' 62.3% exceedance and optimists' sub-50% exceedance survived real disclosure lags, with b sized to observed forecast dispersion.