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Ahead of the curve: Introducing the concept of a carbon risk-free curve

Our CEO Giuseppe Amitrano recently talked to Investment & Pensions Europe (IPE), introducing a new Paradigm in Fixed Income Markets: the CO2e Risk-Free Curve.

As global investors and companies progress towards their net-zero emissions targets, the concept of a carbon risk-free curve becomes increasingly relevant within the fixed-income market. In our view, this curve should provide a reference for evaluating the risk levels of bonds in relation to their issuers’ CO₂-equivalent (CO₂e) emissions and can therefore help investors to assess the impact of changes in CO₂e emissions on the yield spread of fixed-income bonds.

A carbon risk-free curve can be derived by applying some of the key concepts of bond investing – spread, volatility and modified duration – to a bond issuer’s CO₂e emissions.

Just as the spread of a bond on a risk-free security is affected by the bond’s terms, the issuer’s creditworthiness and the general economic situation, a breach of CO₂e emission targets can also have a significant impact.

This is because a bond issuer that fails to meet its emission targets may be seen as a higher risk issuer, as it may face penalties or regulatory action. Investors may demand a higher yield to compensate for the increased risk, leading to a decrease of the bond’s price or an increase in its coupon. A change in nominal price will, in turn, impact the bond’s volatility and risk.

“The carbon risk-free curve is a representation of all points in time that are associated with the lowest possible CO₂e emission risk”

Guiseppe Amitrano

The failure to meet CO₂e emission regulatory targets will also increase the default risk and reduce the bond’s appeal to investors, increasing volatility.

A bond’s modified duration – the measure of a bond’s sensitivity to changes in interest rates, expressed in years and derived by weighted average of the present value of the cash flows of a bond – can be used to introduce the concept of carbon modified duration. This would measure the sensitivity of a bond to fluctuations in an issuer’s regulatory compliance probability requirements and meet its carbon emission-reduction targets according to the set timeline.

If two bonds have the same maturity, the one issued by the company with lower carbon emissions will be less volatile and present a lower sensitivity. Conversely, if two bonds are linked to similar carbon-emission patterns, the bond with longer maturity will be more volatile. The carbon-modified duration represents the average length of time it takes to reach the present value target level of carbon emissions.

Therefore, we can now compare bonds with varying maturities and levels of carbon emissions. The carbon-modified duration would be calculated as the average time needed to reach the present value target of carbon emissions. As for the bonds, the calculation will take into account the time-weighted present value of each unit of carbon emissions; not just the time-weighted amount of emissions.

Crucial new risk

The definition of bond yield spread must then reflect this crucial new risk related to the bond issuer. The bond yield spread will thus incorporate both the traditional elements of the spread along with the carbon or CO₂e yield spread, plus or minus additional basis points based on the negative or positive impact of changes in CO₂e emissions.

Modelling the impact of changes in CO₂e emissions and the resulting total yield spread of fixed-income bonds is a complex task that requires a thorough analysis of multiple factors. However, this can be achieved by using a combination of statistical models and economic theories to estimate the potential impact of changes in CO₂e emissions on the resulting yield spread of bonds.

We would use a range of machine-learning algorithms, including ridge and lasso-regression models, and multi-layered deep neural networks to estimate the relationship between the yield spread and explanatory variables such as Scope 1, 2, and 3 CO₂e emissions, GDP growth, inflation, and interest rates. This model can help estimate the impact of CO₂e emissions changes on the yield spread, while holding other factors constant. The estimated impact is known as the carbon or CO₂e DV01, which represents the dollar value change for a one percentage point deviation from an issuer’s 2050 net-zero alignment targets.

Multiple scenario analysis could be used to estimate the potential impact of different CO₂e emissions scenarios on the yield spread of bonds. For example, a scenario where CO₂e emissions decrease rapidly towards the 2050 net-zero target could be compared to a scenario where CO₂e emissions continue to increase. Similarly to the Institutional Investors Group on Climate Change’s (IIGCC) proposed framework stress scenarios, scenario analysis can give an idea of how different CO₂e emissions paths might affect the yield spread of bonds.

We should not assume a linear relationship between the level of carbon emissions and bond yield spreads, given the varying levels of tolerance to CO₂e emissions across different sectors, countries and companies. As a result, we need to incorporate more granularity into the model to accurately capture these nuances.

A bond whose issuer is aligned with the 2050 Paris Agreement target is expected to exhibit lower volatility compared with a bond of an issuer that is not aligned. This is because the bond’s performance is tied to the goals set by the Paris Agreement, which helps to reduce the risk of unexpected fluctuations in CO₂e emissions and the risk of default. As a result, this issuer’s curve can be considered a carbon risk-free curve, providing a reference for evaluating the risk levels of other bonds in relation to CO₂e emissions.

Our definition of the carbon risk-free curve is a representation of all points in time that are associated with the lowest possible CO₂e emission risk. We expect the carbon risk-free curve to become a crucial concept in the field of fixed-income investing. It will represent the standard against which the risk levels of other bonds in relation to CO₂e emissions can be evaluated.

Overall, as companies and countries demonstrate their commitment to meeting their 2050 net-zero targets for CO₂e emissions and actual emissions decrease, the carbon spread of their bonds is expected to decrease and converge towards the CO₂e risk-free curve. This alignment with established net-zero patterns will likely lead to a reduction in the perceived risk of CO₂e emissions and make the bond more appealing to investors.

More research is required to understand the nuances of the non-linear relationship between CO₂e emissions and yield spreads. We propose a methodology based on a shifted Exponentially Weighted Moving Average (EWMA). This statistical method, employed in time series analysis for forecasting, assigns greater significance to more recent observations, while diminishing the importance of older data points. This can be used to assess the impact of CO₂e emission volatility more accurately on the pricing of both sovereign and corporate debt securities.

The carbon risk-free curve should provide the investment community with a basis for evaluating the risk levels of other bonds in relation to CO₂e emissions, and thus will help drive the transition towards a more sustainable financial system.

Giuseppe Amitrano is founder and CEO at Wieldmore Investment Management


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