**How does the EU carbon market work?**

**This research aims to analyze the dynamics of carbon price in the European carbon market. **

###### Theoretical phase diagram of carbon, which shows the state of matter for varying temperatures and pressures. The hatched regions indicate conditions under which one phase is metastable, so that two phases can coexist. The source reference says that the phase diagram is well established only up to around 100 GPa. More recent work shows that the melting point does not go as high as 10,000 K. Accurate illustration but not a pixel-exact plot. Also note that a considerable disagreement exists between theory and experiment, e.g., for the triple point doi:10.1016/0008-6223(76)90010-5

The study begins with an analysis of the supply and demand mechanism of the carbon market, including the factors that drive carbon price. Data is then collected from various markets, including energy, stock, bond, and carbon, to provide a comprehensive analysis of the interplay between these markets and the carbon market. Next, variable selection and modeling techniques are employed to analyze the carbon return, with the goal of developing a robust model for the construction of trading signals.

Finally, the performance of trading signals becomes analyzed, providing insights into the effectiveness of the carbon market and its potential for sustainable investment strategies. This study contributes to a better understanding of the dynamics of the EU carbon market, with implications for investors and other stakeholders.

**Introduction **

Climate change has been one of the most serious issues governments around the world have been trying to fight for decades. This issue is serious as it has shown that it has effects on human health, animals, and species. Rising heat is a problem humans have been facing, rising temperature causes glaciers to melt and as a result causes sea level to rise. The final result is an increase in the number of hurricanes. Dry weather has a direct link to the increase in wildfires around the globe (noaa.gov, Aug, 2021).

The European Union realized the issue in the 1990s, as the leaders tried to stabilize the greenhouse gas emissions of the European countries by the year 2000; in 2000, the European Climate Change Program was launched (www.climatepolicyinfohub.eu, 2020). The EU Emissions Trading System “is a cornerstone of the EU’s policy to combat climate change and its key tool for reducing greenhouse gas emissions cost-effectively. It is the world’s first major carbon market and remains the biggest one.”( climate.ec.europa.eu, 2019). The EU ETS uses a cap and trade system, where a cap is the number of greenhouse gasses that can be emitted by a corporation; the plan is to have this cap decrease by phases, which would cause an overall decrease of emissions.

Corporations could buy or receive carbon allowance, this allowance can be traded to other corporations as well. The limitation of the allowances makes the value of the Carbon Credits, and therefore the ’price’ of Carbon increase. If a corporation emits greenhouse gasses over a period of time, it must provide a number of allowances to cover the cost of emission by a certain deadline, otherwise this corporation will be fined (climate.ec.europa.eu, 2019). Similar Schemes are also present in the USA and the UK.

Due to the trade-able nature of these Carbon Credits, in addition to offsetting carbon, Carbon Credits can also be used by investors for hedging, speculation and arbitrage. The majority of the traded volume of Carbon Credits is done through ICE (Intercontinental Exchange Inc). Carbon Credits are traded by way of Carbon Futures, a futures contract which delivers Carbon Credits at expiry.

This work has two main objectives. The first objective is to gain an understanding on what key factors drive EU Carbon prices. Using this information, we then try to complete our second objective, which is to build Carbon Trading Strategies in an attempt to outperform just holding Carbon.

1.1 EU ETS Phases

The strategy to reduce gas emission was segmented into phases. Phase One was from 2005-2007, in this phase allowances were given for free, penalty for non-compliant companies was $40 per ton, and the cap was only on CO2. Phase 2, was from 2008-2012, this phase imposed a stricter restriction on emission, where the cap was lowered by 6%, moreover, the cap included Nitrous oxide alongside with CO2, the non-compliance penalty increased to $100, the amount of free allowances decreased by 10%. It is worth noting that the 2008 financial crisis caused a surplus in allowances, this explains the stability in the price of carbon when phase two launched in 2008, figure 1 shows the price of carbon over time.

Phase three, was from 2013-2020, this phases put a cap on more gasses and more sectors, and it reserve an allowance of 300 million to the development of the renewable energy technology (climate.ec.europa.eu, 2019).Phase 4, started in 2021, emphasize on the reduction of the allowances given by 2.2% each year, also promotes a stronger the Market Stability Reserve (MSR) policy. The Market Stability Reserve launched in 2017, that declares a removal volume of allowance supply of around 400 Mt CO2 by 2019, figure 5 shows the impact on carbon price for such policy. The carbon price started an upward trend since the policy was first introduced in 2017, the estimated price impact on carbon is roughly 220% (Azlen, Gostlow, Child,2022).

**Figure 1: European Carbon Spot Price **

1.2 The Carbon Market

As limitation on carbon increases, the value of carbon increases in the market, hence the importance of the allowances. The trading volume of the allowances also increased, in phase one the volume reached $2.1 billion by 2007, $3.1 billion by 2008, $6.3 billion by 2009, and $7.9 billion by 2012 (climate.ec.europa.eu, 2019). Figure 3, shows the proportion of the allowances that were auctioned, traded over the counter, or traded in an exchange.

**Figure 2: Carbon Market Trading Segments **

1.3 Literature Review

The first paper we referred to in our analysis was written by Michael Azlen, Glen Gostlow, and Alex Child, titled ’The Carbon Risk Premium’ this paper was important for us because it illustrates the economic fundamentals of carbon price changes. The first thing it outlines is that supply and demand, alongside the expectations of future changes in prices, are the factors that shift the price of carbons up and down. The authors shed light on the concept of the abatement costs.

As Investopedia defines it, abatement costs ‘are the costs firms pay that are associated with removing negative byproducts created during production’ (Will Kenton, 2020, Investopedia). Companies need carbon allowances for carbon emission during production; Azlen, Gostllow, and Child, state that companies with the lowest abatement costs will reduce their emissions first, since it doesn’t cost them as much to do so. Then, Firms will produce at the level such that: Marginal Abatement Cost = Equilibrium carbon price (Azlen, Gostlow, Child,2022).

The second paper we utilized titles ’Modeling of carbon credit prices using regime switching approach”Modeling of carbon credit prices using regime switching approach’, by Anakoglu, Adıyeke, Agrali, this paper analyzes price dynamics of EU ETS prices using several models incorporating structural changes, including econometric time series, regime switching, and multivariate Vector Autoregression models. The model also investigates under a frame of joint relations among carbon, electricity, and oil prices. This paper first analyzes the structural breaks in the period between 2009 and 2017. Then, the paper uses various models to represent the structural changes in the carbon price.Main model used: (i) pure econometric models, which fit both univariate and Vector Autoregressive models (ii) structural models, which use the relationship between carbon prices and other commodities (iii) stochastic models, which use Markov processes to model price series. (Anakoglu, Adıyeke, Agrali, 2018).

2 Mechanism

In this part we will analyze the fundamental drivers of the carbon price.

The primary factors that influence carbon prices are the interplay of supply and demand, as well as predictions about how these factors may change in the future. As a result, carbon markets function much like other commodity markets, where prices are determined by the unique supply and demand conditions of the market, as well as broader global economic factors. In this section, we will delve into how changes in supply and demand can affect carbon prices at a fundamental level.

The supply of carbon in the EU ETS is determined by the European Commission, and there is a predetermined upper bound on the total quantity of greenhouse gas emissions allowed each year. To comply with EU climate targets, this cap is gradually reduced over time. Consequently, the Commission’s decision on the cap plays a crucial role in shaping the carbon market.

Current research indicates that the factors that significantly impact carbon demand can be classified into two categories: energy sector factors and macroeconomic factors. Energy consumption is crucial to support the production activities of companies, and the price of energy affects the energy demand and structure. Since energy consumption generates carbon emissions, companies must purchase carbon allowances. As a result, any changes in the energy market will inevitably impact the carbon market. On the other hand, macroeconomic factors impact carbon demand indirectly but significantly.

These factors are indicative of the level of economic development, and as companies adjust their production activities at different stages of development, carbon prices may be impacted. In our study, we will examine the role of the energy market by examining oil, coal, and gas prices. Macroeconomic factors will be represented by the stock and bond market, which can provide insight into industry performance and investor risk preference.

It is important to note that in the energy sector, the prices of coal and gas are interrelated with carbon prices through a combined effect. The substitution effect between coal and gas needs to be considered as coal is generally cheaper than gas, but gas is more efficient and generates fewer carbon emissions. Coal power generation produces around twice the amount of GHGs per kilowatt-hour compared to natural gas power generation. Therefore, after the introduction of EU ETS, companies are encouraged to switch to more efficient energy sources as the cost of carbon increases.

Moreover, companies make this decision by considering the cost of switching fuel. In section 3.2, we will quantify this fuel-switching cost as the relative price of gas compared to coal. Previous studies have shown that the economics of fuel-switching in power producers has been a primary driver of carbon prices (Bai et al., 2019). Theoretically, carbon prices should be positively correlated with fuel-switching prices. This means that when the relative price of gas increases compared to coal, fuel-switching becomes more costly, and carbon demand increases as coal power generation becomes more desirable.

Figure 3 provides an overview of the supply and demand factors that drive the EU allowance market. The next section involves conducting an empirical analysis to examine the underlying mechanism in greater detail.

**Figure 3: Supply and demand dynamics of EU Allowance **

3 Data Description

3.1 Data source

Our data is obtained from the Bloomberg terminal and we collect daily price series for all assets measured in USD. The assets are sourced from various markets, including the carbon, energy, commodity, stock, and bond markets. The time period of data is 2014/01/01 *∼ *2022/09/30. Table 1 shows the asset name and description.

Bloomberg Code | Description | Market classification |

ICEEUA Index | EUA Futures Contracts | Carbon market |

CO1 | Brent Crude Oil | Energy market |

TTFGCY1 | Netherlands TTF Natural Gas Forward | Energy market |

API2YR1 | European Steam Coal Inclusive | Energy market |

ELUB1MON Index | 1-month forward price for electricity | Energy market |

CRB CMDT Index | Indicator of global commodity markets, measures the aggregated price of various commodity sector | Commodity market |

DAX Index | German Stock Exchange Index | Stock market |

EURSA Spread | 10 Year EURO Yield – 3 month EURO Yield | Bond market |

Credit Spread | Moody BAA Average Yield – AAA Average Yield | Bond market |

ICECCA Index | California Carbon Allowance Futures | Carbon market |

ICERGGI Index | Regional Greenhouse Gas Initiative Futures Contracts | Carbon market |

3/6/12 Month Momentum Factors | 3/6/12 months return of EU Carbon | Carbon market |

Table 1: Table of data source

3.2 Fuel-switching measurement

Section 2 demonstrates that the cost of switching fuels is connected to the carbon price, and it is determined by the relative prices of gas and coal. Companies can choose to switch from using coal to using gas when more efficient energy becomes available at a lower cost. This decision incurs fuel-switching costs.

To determine whether it is economical for a company to switch from coal to a gas power plant, we will evaluate the average cost (AC) of generating 1 MWh of power. The costs of the power plant before and after the implementation of carbon pricing are:

*Before *: *AC *= *F C/η *

*Af ter *: *AC *= *F C/η *+ *EF/η ∗ EC *

whereas FC is the fuel price, *η *defines the fuel’s efficiency, EC is the carbon price. And EF, the quantity of emission produced by the fuel.

The critical point that companies will switch from coal to gas should satisfy: *AC** _{gas }*=

*AC*

_{coal}

So the carbon price that satisfies factories should be indifferent between coal and gas should be: *⇒ EC*_{switch }_{=}*η*_{coal}*F C*_{gas }*− η*_{gas}*F C*_{coal}

*η*_{gas }*EF*_{coal }*− η*_{coal}*EF*_{gas}

If the market carbon price is lower than the *EC** _{switch }*calculated above, generating electricity from coal is more profitable than gas, and vice versa. So these fuel-switching settings provide a reference for carbon prices, and can well reflect companies’ demand for carbon.

Input for calculation becomes given by: efficiency of the coal plant is 40% and efficiency of a gas plant is 50%; The emissions factor of a coal plant is 0.364 tCO2e/MWh and that of a gas plant is 0.21 tCO2e/MWh. Fuel costs become calculated from the TTF contract (TTFGCY1 OECM Index) for gas and ARA coal (API2YR1 OECM Index) for coal (converted to a unit of $/MWh).

3.3 Factors correlation

Figure 4 displays the correlation between the weekly returns of different assets. Several observations can become made from this matrix:

• The EU carbon return exhibits a strong correlation with the DAX Index, which suggests that stock returns are significant macroeconomic factors. Additionally, the EU carbon return demonstrates strong momentum, particularly in its 3-month momentum.

• The correlation between factors within the energy sector is approximately 0.2, indicating that they are part of the same production line but perform different functions.

• Different carbon markets have varying levels of correlation with one another. Specifically, the EUA has a negative correlation with the CCA and RGGI indices, while the CCA and RGGI indices have a positive correlation. This suggests that the dynamics of different carbon markets are not synchronized.

To avoid potential multi-collinearity, we will conduct feature selection prior to implementing carbon pricing.

**Figure 4: Heatmap of asset return correlation **

3.4 Quota cap event study

As demonstrated in Section 2, the EU carbon supply is established through the decisions of European commissions, which means that the disclosure of carbon policies is critical to the market. In this subsection, we will examine the effects of significant announcements regarding carbon supply on the carbon market.

Starting from 2017, the European Commission started to publish the Total Number of Allowance in Circulation (TNAC) for the first time, and this report has been published on a yearly basis since then. TNAC is the inventory of carbon since the launch of EU ETS. It is calculated by:

*T NAC *= *Supply − Demand − allowances in MSR *

The Market Stability Reserve (MSR) is a mechanism launched in 2019 and is designed to manage the supply of allowances in EU ETS. MSR dynamically adjusts the supply of allowances based on market conditions, reducing the supply when the carbon price is lower than expected and increasing it when the price is higher, helping to stabilize the market and reduce price volatility.

The European Commission’s publishing of TNAC has had a significant influence on the carbon market, particularly the price of carbon. TNAC represented a significant tightening of the cap on carbon emissions in the EU Emissions Trading System (EU ETS), which led to a reduction in the supply of allowances available for trading. Figure 5 shows the historical price of EU carbon with a time of TNAC publications labeled. It can be seen that when TNAC was published in 2017 for the first time, it gave an estimation of 400 MtCO2 will be put in MSR in 2019.

And since then carbon price has had over 50% growth in the next half year. Also from the plot in the years 2018 and 2020, the carbon price seems to react positively to the publications. So in this subsection, we will use the method of event study to see the effect of TNAC publications on the carbon price.

**Figure 5: Plots of Historical Carbon Price with Policies labeled **

We collect the history of TNAC reports from the European Commission website. ^{1 }The reports are published in mid-May and record TNAC at the end of last year. The number that will be put into MSR is calculated based on the rule that: if TNAC is larger than 833 million, then 24% * TNAC will be put into MSR; otherwise, 12% of TNAC will be deducted. And the deduction will be performed from the publication year’s September to next year’s August. We calculate both the total return and the abnormal return after the yearly publication of TNAC. The abnormal return is modeled by regressing carbon return on DAX Index return and fuel-switching return:

*carbon return ∼ DAX Index return *+ *fuel switching return *

^{1}see Communication from the Commission, available at: https://eur-lex.europa.eu/homepage.html

Furthermore, calculate the abnormal return as the pricing error. Table 2 displays the total and abnormal returns following the release of each TNAC report, with returns being calculated over different time horizons (1, 5, 20, 40, and 60 days). The data suggest that it takes 20-40 days for the effects of a TNAC report to become apparent.

Thus, theoretically, changes in TNAC are supposed to have an impact on carbon prices: if TNAC is higher than last year, prices should decrease, and if TNAC is lower, prices should increase. However, this mechanism is influenced by people’s expectations. The empirical result shows that the market responds positively to the TNAC results from 2017-2020 but not the most recent 2 years. To sum up, the impact of carbon supply on the market is not evident due to the influence of investor expectations. One potential avenue for future investigation is to explore the precise disclosure dates of each individual item in TNAC and gain insight into how investor expectations regarding carbon supply are formed.

Total Return | Abnormal Return | ||||||||||

Date | TNAC | 1 | 5 | 20 | 40 | 60 | 1 | 5 | 20 | 40 | 60 |

5/12/17 | 1693904897 | 0.025 | 0.092 | 0.154 | 0.226 | 0.205 | 0.018 | 0.078 | 0.117 | 0.147 | 0.149 |

5/15/18 | 1654574598 | -0.022 | 0.063 | 0.042 | 0.119 | 0.185 | -0.020 | 0.048 | 0.055 | 0.068 | 0.142 |

5/14/19 | 1654909824 | 0.034 | 0.008 | 0.003 | 0.128 | 0.135 | 0.026 | -0.007 | -0.034 | -0.004 | 0.087 |

5/08/20 | 1385496166 | -0.01 | -0.036 | 0.181 | 0.438 | 0.321 | -0.018 | -0.020 | 0.014 | 0.207 | 0.109 |

5/12/21 | 1578772426 | 0.043 | 0.004 | 0.019 | 0.001 | 0.073 | 0.042 | -0.007 | -0.053 | -0.055 | -0.090 |

5/13/22 | 1449214182 | 0.002 | -0.056 | -0.066 | -0.03 | -0.033 | -0.005 | -0.064 | -0.144 | -0.150 | -0.236 |

**Table 2: Table of total and abnormal return after TNAC publication **

4 Methodology and empirical results

4.1 Variable Selection

Based on the factor correlation analysis, we initially conducted regressions according to groups/univariate and gained some insights on potential factor selection. Some variables may show significance in all the regressions, while others can show a different pattern. For example, the Commodity Index (CMDT Index) variable is not significant when running univariate regression, but significant when running with all the other factors. Also, predictive regression mostly showed non-significant results. The results may further prove the existence of multicollinearity if we include all the variables. Also, it suggests that contemporary regression would be more appropriate to be further studied.

Subsequently, we performed feature selection using LASSO regression. We determined the optimal Lasso regularization parameter through grid search and cross-validation with the scoring parameter set as the cross-validation score in LassoCV. After hyperparameter tuning, we obtained the optimal value of alpha and identified a list of selected features, including fuel switching, CO1 Comdty, DAX Index, EUSRA Spread, ICECCA Index, ICEEUA Index 3momentum, and ICEEUA Index 12momentum.

###### methane hydrocarbon

USGS images (public domain) see their policy – https://soundwaves.usgs.gov/2012/06/

We also plot the LASSO coefficient decay with an increasing penalty parameter *α *in each factor category in Figure 6. The plot reveals that certain variables in each category experience a faster reduction in their coefficients towards zero compared to others, while the chosen features generally maintain their coefficient level. This can be attributed to the strong correlation present within each feature category, whereby the impact of insignificant factors is replaced by the more meaningful ones.

**Figure 6: Plots of Coefficient decay with alpha parameter **

4.2 Contemporary regression

The contemporary regression method involves conducting a regression analysis of weekly carbon returns using selected independent variables that have been identified through feature selection, with a focus on the contemporaneous values. The analysis tends to prove the importance of variables in explaining the current return.

For each selected variable, we conduct regressions for univariate, grouped multivariate, and all multivariate settings. The regression results concluded in Table 3 where the value in the parentheses indicates the P-value of the variable.

Univariate | Multivariate(group) | Multivariate(all) | Class | |

fuel switching price | 0.146(0.0) | 0.129(0.0) | 0.081(0.007) | commodity factors |

CO1 Comdty | 0.16(0.001) | 0.115(0.021) | 0.063(0.18) | commodity factors |

DAX Index | 0.646(0.0) | 0.674(0.0) | 0.513(0.0) | macro factors |

EUSRA Spread | 0.066(0.05) | 0.089(0.006) | 0.061(0.044) | macro factors |

ICECCA Index | 0.592(0.0) | 0.592(0.0) | 0.315(0.006) | other market factors |

3m momentum | 0.131(0.0) | 0.127(0.0) | 0.109(0.0) | momentum factors |

12m momentum | 0.03(0.0) | 0.003(0.743) | 0.002(0.757) | momentum factors |

Table 3: Table of coefficients, univariate/multivariate (within groups) / multivariate (all factors), P-values in bracket

The regression analysis provided valuable insights into the significance of various variables in explaining the returns on carbon futures. Within the commodity factors, the fuel-switching factor is significant in all regressions, showing it’s a pivoting factor driving the carbon return. The CO1 commodity variable also performs well in both univariate and grouped multivariate regressions. Its explanatory capacity shrinks when including all the factors, which may be caused by its correlation with other exogenous variables. The macro factors, the DAX index as a representative of the stock market performance and the EUSRA as a proxy for the treasury term structure, are significant in all regressions. Finally, the three-month momentum dominated over the long-term momentum even though the twelve-month momentum shows its significance in univariate regression.

To summarize, we can derive that carbon prices are highly influenced by three types of main drivers. The fuel-switching and the Brent oil price are fundamental factors, explaining the return by the basic supply and demand balance. The general market environment, both stock and fixed-income markets, also interacts with carbon prices implicitly. Lastly, the return exhibits a noticeable short-term momentum characteristic, referred from the importance of the three-month momentum factor.

4.3 Rolling coefficients analysis

We also plot the regression coefficients of the variables using rolling contemporary regression, which are shown in 7. Particularly, in order to facilitate a clearer comparison within each group, the variables belonging to the same category were plotted together.

The graphs present meaningful insights into the dynamics of the relationship between carbon return and independent variables over time.

(1) Trend: By examining the slope of the rolling regression line, we can determine the trend in the strength or weakness of the relationship over time. In the case of commodity factors, the coefficients of fuel switching and crude oil commodity appeared to exhibit an opposite pattern, suggesting that the fundamental influencer had a contemporaneous effect. The coefficient of fuel switching price displayed a positive trend since 2018, reaching its peak in the middle of 2019, whereas the trend for Brent oil was the opposite trend.

It became observed that the coefficient of Brent oil dropped sharply from 2022, possibly due to the ongoing war. As for macro factors, the coefficient of the stock market index experienced a sharp strike in early 2018 and fluctuated until 2022 when it experienced a sudden decline. On the other hand, the treasury spread did not exhibit significant changes during the test period. For momentum factors, the 3-month momentum factor oscillated around 0.1 while the twelve month momentum factor remained almost constant throughout most periods. Finally, the coefficient of the ICECCA index exhibited an extreme decrease in early 2016 and spiked in 2019.

(2) Volatility: By examining the variability of the rolling regression coefficients, we are able to identify periods of high and low volatility in the data. The analysis suggests that there are several intervals where instability arises, namely, the beginning of the year 2016, the period between 2017 and 2018, the start of 2019, and the start of 2022.

**Figure 7: Plots of Rolling Coefficients of the selected factors **

The temporal variation of regression coefficients implies the feasibility of implementing dynamic models to account for the transitions between different time periods. Therefore, in the latter section, we applied regime-switching models to explore this characteristic further.

4.4 Regime switching model

4.4.1 Introduction

The regime-switching models are a family of models that exhibit different dynamics across unobserved states using state-dependent parameters to accommodate structural breaks or other multiple-state phenomena. These models are known as Markov-switching models because the transitions between the unobserved states follow a Markov chain.

Following the analysis of the rolling regression, we have identified some time-varying properties of the model. In addition to the factors we already included, the demand and supply-related factors that may influence carbon are hard to be observed. However, such fluctuations can be modeled by switching between high variance /low variance, so that the unobservable or unquantifiable factors can be captivated by the state variables. Thus we have tried to use the regime-switching models to incorporate these stochastic state changes.

4.4.2 Models specification

We have implemented two models and ran regressions on weekly returns on all the relevant factors. A brief introduction of the models is as follows:

1. Markov switching dynamic regression

*y** _{t }*=

*µ*

*+*

_{s }*x*

_{t}*α*+ +

*z*

_{t}*β*

*+*

_{s }*ϵ*

*(1)*

_{s }The dependent variable is determined by the exogenous variables *x** _{t }*and

*z*

*, with state-invariant coefficients*

_{t}*α*and state-dependent coefficients

*β*

*respectively.*

_{s }2. Markov switching autoregression

*y** _{t }*=

*µ*

_{s}*+*

_{t }*x*

_{t}*α*+ +

*z*

_{t}*β*

_{s}

_{t }_{+}X

^{p}*i*=1

*ϕ*_{i,s}* _{t}*(

*y*

_{t−i }*− µ*

_{s}

_{t−i }*− x*

_{t−i}*α − z*

_{t−i}*β*

_{s}*) +*

_{t−i}*ϵ*

_{s}*(2)*

_{t}The MSAR model includes a term with coefficient *ϕ *which scale the error term of the previous state. The demeaned, lagged errors cause a dependence on the state previously occupied by the process, which is not present in the dynamic regression model.

Both models are estimated by the Maximal likelihood implemented by python.

4.4.3 Empirical Results

For both models, we started with models with two regimes and retrieved the outputted smoothed marginal probabilities of each time step. The probabilities represent the probability of being on each regime conditional on all information. By setting thresholds to the smoothed marginal probabilities, we can get the dominant regime for each time step and observe the switching pattern of the dominant regime.

1. Markov dynamic regression

The dominant regime in the Markov dynamic regression with filtered variables implies the low predictability of the regime-switching pattern: The regimes jumped with scarcely any order or stayed in the same regime. The significance of the variables was also checked, which once again proves the effectiveness of the factors, especially fuel switching, DAX index, and short-term momentum.

2. Markov autoregression

We have tried the regression in running both rolling and non-rolling weekly returns.

The result for rolling returns is showing a relatively clear switching path of distinct regimes. The majority of the regime has low volatility while the P-value of the model coefficients indicates a strong statistical significance. Despite this fact, the result is only based on the auto-dependence of the rolling return series.

**Figure 8: Dominant regime for weekly rolling return **

For weekly non-rolling univariate regression, the dominant regime retains mainly in the low volatility regime, which is regime 1 in figure 4. While adding variables selected from the LASSO regression, the result is similar, indicating the switching between regimes is led by the auto correlation between the y variables. However, we also noticed in different regimes, the significance of the variables may vary. In a few periods with less volatility, EUSRA Spread and ICECCA Index may appear more important, while in most cases, the fuel switching factor and mid-term momentum have positive effects.

**Figure 9: Dominant regime for weekly non-rolling return **

3. Comparable results

The variables are more significant in non-rolling return prediction. In rolling return regression, the 3-month momentum has positive coefficients while the 12-month’s is always negative. For both returns, the regimes have no significant switching pattern.

For the Markov Autoregression, there was a less volatile period between 2015-2016. There was a more volatile period between 2016-2017, the start of 2020, and the start of 2022. The general conclusions are similar for rolling/non-rolling return, but the significance of variables are higher for rolling returns. Many variables have significant explanatory power to the endogenous variable, with a p-value smaller than 0.01. For all Markov switching models, the Markov switching shows a clear pattern only when we add the lag 1 term of the return.

Markov AR model with explanatory variables performs better than Markov switching regression model when predicting non-rolling return.

In summary, although the Markov switching models indicate a similar result for identifying volatile/non-volatile periods, it is difficult to extract the switching characteristics for independent variables.

5 Trading Strategy

Using the insights we gained in the previous section, we aim to build trading strategies to profit from Carbon. Our objective is to try and outperform simply holding Carbon over the long run. The returns and summary statistics of holding EUA Carbon shown below:

**Figure 10: Long EUA Carbon P&L **

**Figure 11: Long EUA Carbon Summary Statistics **

It should be noted that in this section, in *P*&*L *plots it is assumed that profits are not re-invested in the strategy.

5.1 Trend Signal

Our contemporary regression indicated that the momentum of Carbon is a significant factor affecting returns. This motivated us to try and build a simple Momentum based Trading Strategy. Our Trading Signal is as follows, and is of Daily Frequency:

_{Signal = }*ewm** _{m}*(

*λ*= 20 Days)

*− ewm*

*(*

_{m}*λ*= 120 Days)

*ewm*_{std}_{(}_{λ }_{= 252 Days) }(3)

Where *ewm _{m }*refers to an exponentially weighted moving average of carbon price,

*ewm*refers to exponentially weighted Standard Deviation of Carbon Price, and

_{std }*λ*refers to the half-life of the moving average. The Signal became given a daily trading frequency, with a trading delay of two days. Additionally, as Carbon is an asset class that has so far seen mostly positive long term returns, we decided not to make the trend signal a pure long/short signal. Instead we developed a timed-long only signal. Whenever the signal predicted negative returns, the strategy simply went to a trading weight of zero. This trading strategy therefore can become considered a direct alternative to just holding carbon. The strategy also became leveraged to match the volatility of holding Carbon. The Results of the strategy shown below:

**Figure 12: P&L and Trading Weight of Trend Signal Strategy **

**Figure 13: Summary Statistics of of Trend Signal Strategy **

We can see that the strategy is profitable, and has a slightly higher Sharpe ratio and returns than just holding carbon. However one strong benefit of the strategy is the relatively lower draw-downs, which is desirable. To obtain a similar volatility to Long Carbon, we can see that 2x long only leverage becomes required at certain times in the strategy, which is high, but not excessive.

5.2 Contemporary regression

This signal utilizes the modeling result from section 4.2. And the construction is performed by: 1. running contemporary regression using past 1 year data

2. for the next half year repeating the following process:

• At the end of each week, calculate the residual *δ*, which is the true return minus the predicted return.

• starting next week, hold carbon with weight *−δ*.

• adjust the holding weight at end of the week

3. Roll the timeframe half a year ahead and perform 1&2 again.

As opposed to the previous trend following strategy, this strategy is trading on the mean-reversing features of carbon returns. When a large prediction error occurs during a particular week, it is probable that the pricing error will be corrected in the following week, leading to a decrease in prices. Therefore, this signal involves trading in the opposite direction to the residuals. Additionally, a higher probability of a significant pricing error being corrected exists when the absolute value of the residual is larger. The Residual is also smoothed using an exponentially weighted moving average with a half life of 4 weeks. As opposed to the trend based signal, the mean-reversion contemporaneous signal is of weekly frequency.

The reason for the rolling contemporary regressions is due to the regime switching nature of Carbon. As discussed, the exposure of Carbon to different factors could change significantly in different regimes. The results of the Contemporary Trading Strategy are shown below. As Before, the strategy was Leveraged in order to obtain a similar volatility to pure Long Carbon.

**Figure 14: P&L and Trading Weight of Contemporaneous Regression Strategy **

**Figure 15: Summary Statistics of Contemporaneous Regression Strategy **

We can see from the results, results are initially poor, however they significantly improve from 2018. Despite being a long/short signal for an asset class that has a high risk-premium, the trading strategy is still able to outperform holding carbon, and has a decent Sharpe ratio of 1.07. As before, 2x leverage is required on both the long and short side to have comparable volatility to Long Carbon. Which is not a small amount of leverage. Another problem is that the maximum drawdown of the strategy is significantly worse than Long Carbon.

Being a Long/Short signal in an asset that is predominately long, it is of interest to us if the model is accurately able to predict when Carbon has negative Returns. To that end we show the confusion matrix below.

**Figure 16: Confusion Matrix of Contemporaneous Regression Strategy **

We can see that it is decent at predicting true positives (ie, predicting positive returns). However, it is not as good at accurately predicting negative returns, more often than not when it predicts a negative return a positive return actually follows.

5.3 Combination Signal

After developing two profitable signals, we wanted to see if we could create a better trading signal by combining the two signals together. We developed two different ways of doing this, a Long Only Combination Strategy, and a Long Short Combination Strategy. The signal is of daily frequency; as the contemporaneous signal is weekly, its values become forward filled to convert it to a daily signal.

5.3.1 Long Only

Where *c *is the Contemporaneous signal, and *t *is the trend signal. This acts as a sort of consensus signal, if both the trend, and mean reversion signal agree, then the trading weight will be positive, otherwise it will be zero. See the results for this signal below:

**Figure 17: P&L and Trading Weight of LO Combination Strategy **

**Figure 18: Summary Statistics of LO Combination Strategy **

We can see through the Sharpe ratio that this trading strategy outperforms both of the previous strategies. Restricting it too long only has also limited its drawdown potential. However before declaring the strategy fully superior to the previous two, there are a couple of points to note. First of all, for the given Long Carbon volatility target, we can see that the strategy requires significant leverage. Secondly, we can see for most time periods, the strategy trades flats, as opposed to the previous strategies, which exhibit more consistent growth.

5.4 Long/Short

We also form a Long/Short signal of the following form:

Combination Long/Short Signal = *c · t *(5)

The results shown below:

**Figure 19: P&L and Trading Weight of L/S Combination Strategy **

**Figure 20: Summary Statistics of L/S Combination Strategy **

The performance of the strategy is effectively the same as the Long Only signal, with the exception that the L/S signal has worse drawdowns.

5.5 Summary

The summary statistics of all trading strategies shown below:

**Figure 21: Summary Statistics of all Strategies **

All the developed trading strategies were able to outperform holding Carbon on its own when considering the metric of Sharpe Ratio. No clear winner stands out from the different developed strategies, all have certain benefits and drawbacks. For instance, although the Long Only Combined strategy had the best Sharpe and lowest maximum drawdown, it was also often trading not trading for much of the time period, which can be undesirable for some investors. Overall, the initial success of these strategies motivates further investigation.

6 Future Work

This work consists of an initial exploration into the analysis, prediction and trading of Carbon Markets. However there are a number of aspects that we were not able to cover due to time-constraints. In this paper we only investigated the prediction and trading of EU Carbon Futures. American and UK Carbon Futures should be investigated in further work. Although cross-correlation was briefly investigated, future work could also consider potential arbitrage opportunities between the Carbon Futures in different Regions.

In this project we only looked at the effective Spot Rate of Carbon. However both from a modeling and a trading perspective, it would be useful to consider Carbon Futures Contracts of varying expiry. Greater opportunities for trading may be present on the Futures Curve, and how the curve changes over time may give us additional insight into carbon prices.

As Carbon is a new asset class, as a result, the practicalities of trading it needs to become looked into. Transaction costs and Bid/Asks Spreads could severely limit the theoretically profitable trading strategies developed in this work. Low liquidity/volume in Carbon Futures may also mean that the trading strategies will not work if any significant capital becomes employed in them.

In this project we only perform a preliminary study on quota cap. Supply is essential to the dynamics of carbon. In our event study, the impact of carbon supply on the market is not evident due to the influence of investor expectations. One potential avenue for future investigation might become exploring the precise disclosure dates of each individual item in TNAC. In addition gain insight into how investor expectations regarding carbon supply become formed.

Finally, additional factors could become considered in the models we developed.

**Conclusion **

In conclusion, this study has provided an overall analysis of the dynamics of the European carbon market. We have demonstrated that the price of carbon is driven by a supply and demand mechanism, with supply determined by policymakers and demand influenced by production activities and the broader macroeconomic environment. Our empirical analysis has also revealed the significance of energy and stock markets in shaping the performance of the carbon market. However, we acknowledge the challenges associated with modeling the regime switch dynamics of the market, which are highly volatile and difficult to capture. Despite this limitation, we have developed a robust model for constructing trading signals and achieved Sharpe ratio over 1, demonstrating the potential for sustainable investment strategies in the carbon market.

How does the EU carbon market work? Written by:

**Keyao Deng, Wenxi Xia, Hakan Serpen, Mohammed Alshowaikhat**

**References for How does the EU carbon market work?**

The Carbon Risk Premium, (Michael Azlen, Glen Gostlow, and Alex Child), The Journal of Alternative Investments Summer 2022, 25.

Ethem Anakoglu, Esra Adıyeke, Semra Agrali,Modeling of carbon credit prices using regime switching approach, JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY. Will Kenton,Abatement Cost 2020,Investopedia, www.investopedia.com/terms/a/abatementcost https://climate.ec.europa.eu/eu-action/eu-emissions-trading-system-eu-ets/development-eu-ets-2005-2020 en http://climatepolicyinfohub.eu/european-climate-policy-history-and-state-play

**How does the EU carbon market work?**