investment viewpoints

A tale of two risks: building robust portfolios aligned to net-zero

A tale of two risks: building robust portfolios aligned to net-zero
Alexey Medvedev, PhD - Portfolio Manager

Alexey Medvedev, PhD

Portfolio Manager
Maxime Kirgo - Quant Analyst

Maxime Kirgo

Quant Analyst

Building climate-aligned portfolios requires a forward-looking approach to maximise opportunities and reduce risks associated with the climate transition. Instead of focusing solely on historical levels of carbon emissions, our TargetNetZero strategies identify the potential leaders and laggards of the climate transition in all sectors of the economy by evaluating companies’ current policies and commitments to decarbonisation. 

Need to know:

  • Building climate-aligned portfolios requires a forward-looking assessment, which is a challenging task due to model uncertainty
  • This uncertainty is evident from the apparent disagreement between data vendors about the alignment of individual companies to the climate transition
  • The standard toolkit of systematic equity is not enough to address model uncertainty in a satisfactory way. In our view, it is important to quantify model error and incorporate it into the investment process to ensure credible climate-aligned portfolios

Challenges of forward-looking approach

The key forward-looking metric is the Implied temperature rise (ITR) that quantifies the alignment of companies and portfolios to climate scenarios in an economically transparent way1. For example, an ITR of 2°C means that, according to our analysis, the company will be meeting its emission budget in a manner which is consistent with a 2°C rise in global temperatures by 2100.

The main difficulty with building portfolios around ITR is the inherent dependence on the modelling framework and assumptions. Depending on their views on how quickly a company must decarbonise, some analysts may believe that the company’s commitments are ambitious, while the others might argue exactly the opposite. 

In comparison, low-carbon investing2 involves much less disagreement. Even if the reporting of carbon emissions is not perfectly harmonised across companies, we more or less agree which ones are high emitters. Interestingly, ESG3 has been criticised for being a highly ambiguous measure, given the correlation of ESG scores between different data providers reach as low as 0.44. ITR sets new records, since the correlation between vendors is twice as low5.

Implementing model-based metrics is nothing new to those of us in systematic equities, with equity factors being most obvious example. Even if practitioners agree on the choice of factors, the difference in their interpretation is generally quite substantial. That being said, it is possible to validate factor definitions at least by backtesting their performance. 

This is not an option for ITR. Firstly, past performance is not necessary a good criterion to judge the quality of the assessment of future transformations. Additionally, while we can gather some supportive evidence on strategy performance, it is not enough to validate the particular implementation6.   

The key element of our TargetNetZero approach is reducing ITR of portfolios or aligning them to a faster pace of decarbonisation. The bulk of carbon emissions is produced by a limited number of companies, meaning the accuracy of portfolio ITR is sensitive to the quality of our assessment of those key players. It is standard practice in systematic investment to use data transformations to mitigate such a concentration and ensure the robustness of portfolios. We cannot apply similar transformations here since carbon emissions have an important economic interpretation, and their concentration is a feature, and not a ‘bug’.  

In our view, building robust equity portfolios aligned to the climate transition requires incorporating the ITR model uncertainty into the investment process. This means that we need to quantify the model error and modify our standard portfolio optimisation procedure to account for both financial risk, in the form of tracking error, and model risk through a measure of uncertainty in true portfolio alignment. 

It is not what it looks like

Essentially, the model uncertainty means that model-based metrics are only approximations of ‘true’ unobservable ones. To understand the implications of the uncertainty in ITR on characteristics of climate-aligned portfolios, we performed a numerical simulation. 

For the sake of the experiment, we assumed that the model-based ITR for companies in our investment universe are the true ones. We then generated multiple perturbations of these values using volatilities provided by our sustainability research team7, which we interpreted as approximations of ITR. For each generated set of ITR, we built a hypothetical portfolio by minimising its tracking error relative to the MSCI World Index8 while targeting portfolio ITR of 2°C based on these approximations9. Figure 1 shows the distribution of the true ITR of those portfolios based on 10,000 simulations. 

This distribution gives us an idea of what is the actual alignment of our portfolios might look like. Unsurprisingly, the true ITR is not constant simply because we built portfolios using only approximated values. What catches our attention is that the whole distribution is shifted above the target. Even though we built a 2°C portfolio, its true ITR will almost certainly be above the target, and with 50% probability in the range between 2.3°C and 2.4°C. 

Figure 1. Distribution of true ITR of a hypothetical portfolio with 2°C target

Source: LOIM. For illustrative purposes only.

Using the statistical terminology, the distribution of true ITR exhibits an upward bias of 0.3°C – the difference between its expected value and the 2°C target. The source of this bias is the direct use of approximate ITR in the portfolio construction process. We tend to overweight companies with erroneously low ITR and underweight companies with erroneously high ITR, thus introducing a correlation between portfolio active weights and model errors. Clearly, such a portfolio is not aligned to 2°C as advertised. While we can accept an inevitable variation in the ITR, the magnitude of the optimisation bias suggests that we will certainly end up with an overly-optimistic portfolio.

A straightforward way to reduce the portfolio bias is to push the ITR target sufficiently below 2°C to make sure that the true one will be around the desirable level. A quick calculation suggests that we should probably target as low as 1.7°C to neutralise the observed bias of 0.3°C10. This does not seem to be a viable solution as only 4% of companies in the MSCI World index are aligned with this scenario, and even fewer are among high-emitters. As a result, the portfolio active risk will be concentrated in a few companies outside of high-carbon sectors, leading to a high tracking error. In our view, a more practical solution is to integrate the uncertainty in ITR directly into the portfolio construction.

Introducing model risk

In the academic community, the phenomenon behind the optimisation bias is known as the “error maximisation”. It first appeared in the context of mean-variance optimisation with uncertain expected returns11. The standard way to address this phenomenon is to anchor estimates of expected returns using certain prior beliefs (the Black-Litterman approach12). Analytically, this amounts to a modification of the original program through tilting estimates of expected returns towards the priors. The less certain we are about our estimates, the more they are modified.

In this context, the approach appears problematic as we do not have reasonable prior for ITR. It is most likely the case that we have no prior at all or, using statistical terminology, the prior is not informative. In this case, the original estimates are not modified and therefore we end up ignoring their uncertainty. These considerations led us to adopt a different approach where instead of modifying the estimates of ITR, we modify the objective function of the optimisation problem by integrating the ITR model risk. 

Figure 2. Portfolios with expected ITR of 2.0°C

Source: LOIM. For illustrative purposes only. 

The naive approach to building climate-aligned portfolios consists of minimising the portfolio financial risk13 subject to an ITR constraint, which results in a bias as illustrated in figure 1. This process can be enhanced by adopting a double objective of minimising both financial risk and ITR model risk, where the latter is naturally defined as the variance of portfolio ITR14. Integrating the model risk will essentially tilt the portfolio in the direction of a better diversification of individual contributions to the ITR volatility, and also towards stocks with lower uncertainty in their individual ITR. This will drive the volatility of portfolio ITR down, and, more importantly, will reduce the optimisation bias.

As both financial and model risk cannot be minimised at the same time, we are facing an obvious trade-off. To visualise this trade-off, we calculated the costs of fully neutralising the ITR bias expressed in terms of tracking error. Figure 2a shows the tracking errors of a number of climate-aligned portfolios that all have the same expected ITR of 2.0°C but which have been built using different compositions of the objective function. Due to the optimisation bias discussed in the previous section, we need to place the portfolio ITR target below 2.0°C to compensate for it. The exact choice of this target, of course, will depend on the weighting between two objectives15.    

The portfolio corresponding to zero weight of the model risk is the one where the ITR bias is the largest. According to figure 2b, we have to set the target as low as 1.6°C to compensate for a 0.4°C bias. This is clearly not the most efficient solution. The other extreme choice is not optimal as well, since incorporating only the model risk amplifies the tracking error. The optimal solution is clearly in between the two extremes. According to figure 2, the portfolio with minimal tracking error has a bias of only 0.15°C, which is mitigated by setting a 1.85°C target.

Focus on ‘ice cubes’

The true climate alignment of a portfolio should be gauged by its expected ITR rather than the measured one, which is not the same for optimised portfolios. We demonstrated that integrating model risk into the portfolio construction helps achieve the desirable climate alignment in a more efficient way. To understand the other implications of this evolution, we will now provide a more detailed comparison between the lowest tracking error portfolio in figure 2 (the efficient portfolio) and the one that fully ignores the model risk (the naïve portfolio). 

Figure 3 shows the contributions of individual positions to the overall ITR for both portfolios. For greater clarity, we partitioned the universe of stocks in the MSCI World index into nine quadrants along the dimension of ITR and carbon footprint. The size of the bubble in each quadrant indicates the total contribution of stocks inside the quadrant to the portfolio’s ITR. 

Figure 3. Contributions to portfolio ITR

Carbon footprint is measured in tonnes CO2e per 1 m. USD invested. Source: LOIM. For illustrative purposes only.

When comparing the two graphs, we can see that the focus of the naïve portfolio is shifted towards companies with lower carbon emissions. This is due to its overly ambitious target of 1.6°C that is necessary to compensate for the optimisation bias. As there are not enough high-carbon companies aligned to this optimistic scenario, the portfolio optimiser looks for such companies elsewhere. 

In contrast to the naïve portfolio, the climate alignment of the efficient portfolio is mainly driven by high-carbon companies with low ITR. We call such companies ‘ice cubes’, in recognition of their leading role in decarbonisation. Ice cubes are key companies for our TargetNetZero strategies, and the integration of model risk helps maintain this focus. 


Measuring climate alignment, one temperature at a time | Lombard Odier
2  The strategy that prioritizes companies with low carbon emissions.
3  Environmental, social, and corporate governance
Berg, F., J. F. Kölbel, and R. Rigobon (2019). Aggregate Confusion: The Divergence of ESG Ratings, Forthcoming Review of Finance.
5  LOIM estimates.
Finding the value in high-carbon sectors | Lombard Odier
7  These volatilities were estimated by varying model assumptions and observing the impact on ITR. 
8  Any benchmarks/indices cited herein are provided for information purposes only. No benchmark/index is directly comparable to the investment objectives, strategy or universe of a fund. The performance of a benchmark shall not be indicative of past or future performance of any fund. It should not be assumed that the relevant fund will invest in any specific securities that comprise any index, nor should it be understood to mean that there is a correlation between such fund’s returns and any index returns.
9  We assumed that the uncertainty is ITR stems from the errors in forecasting companies’ future emission, and not their emission budgets corresponding to different global warming scenarios.
10  As we will see it later, we would have to set the target even lower since the bias gets bigger with a more ambitious target.
11 Michaud, R. 1989. The Markowitz Optimization Enigma: Is ’Optimized’ Optimal?. Financial Analysts Journal, 45(1), pp. 31–42
12  Black, F. and R. Litterman. 1992. Global portfolio optimization. Financial Analysts Journal, 48(5), pp.28-43
13  Tracking error relative to the benchmark.
14  The variance of portfolio ITR can be conveniently approximated by a quadratic function of portfolio active weights allowing its interpretation as the model risk.
15  The ITR target levels were derived using numerical experiments as described in the previous section.


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