Implications of firm-level carbon emissions on risk implied
by option prices
June 29, 2020
Bachelor Thesis
Author: Frederik Burmester (11841915) Supervisor: Stan Olijslagers
Bachelor’s Economics and Business Economics Major Economics
Statement of Originality
This document is written by student Frederik Rolf Per Burmester who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
Scientific studies almost unanimously agree that climate change is manmade and that strong reg-ulatory action is needed to prevent permanent damage. Uncertainty about whether new policies will be adopted and when, induced by short-term policy considerations, means that the stock of carbon intense firms should theoretically have a more volatile and heavy tailed return. Event studies of the Paris agreement and the election of US president Trump fail to provide statistical evidence for the pricing of such increased return risks in the US option market.
1
Introduction
The earth’s climate is warming and scientific publications almost unanimously attribute much of the warming to mankind (Cook et al.,2016). Strong change to human behaviour will be necessary to counter the developments but how regulation may look like, when it will be adopted, and how strong it will be, on the other hand, is highly uncertain. The uncertainty may have consequences on factors that both policymakers and investors should take into account.
One approach to counter climate change is investment into funds which specifically target sustainable firms. ESG (Environmental, Social and Governance) investing is becoming increas-ingly popular and, to the the surprise of some, can actually outperform traditional funds (Riding,
2020). A failure of traditional funds to correctly assess a stocks risk due to uncertainty about climate regulation may be able to explain the good performance of ESG funds. A failure of mar-kets to price risks associated with emission regulation may also have interesting consequences for the ongoing discussion around the efficiency of markets.
From a policy standpoint it is interesting to assess consequences of uncertainty on welfare. Higher uncertainty about regulation and thus returns in the economy may be utility decreasing among risk-averse investors, at least in the short-term where consequences of climate change are mild. Further, as a risk-averse market will decrease funding for risky firms, the mere potential of the introduction of climate policy may already reduce investment into carbon intensive firms, potentially leading to a reduction of emissions. The reverse may be interesting for managers: if markets correctly price the risk of new climate regulation, managers may use prices to make inferences about the probability of new policy, allowing them to make better decisions.
There already is some empirical evidence for a pricing of regulatory risks associated with carbon intensities in the options market, specifically effects on volatility and left side tail risk. However, other studies have analysed the more general question of whether carbon intensity causes a risk premium or have focused on aggregated carbon intensities. This thesis tries to replicate earlier results and to determine whether effects of uncertainty about climate regulation associated with firm-level carbon emissions on firms’ volatility and tail risk are priced in the option market.
To do so, the methodology developed by Kelly, P´astor, and Veronesi (2016) is adapted to perform two event studies using options for US American firms: one event study on the Paris agreement and one for the Trump election. The Paris agreement is taken as a signal of a probability increase that environmental policy will become stricter in the near future. The Trump election, on the other hand, is assumed to have lowered the probability of coming regulation.
This thesis is structured as follows. Section 2 provides a literature review of publications analysing the pricing of economic policy uncertainty, literature into the pricing of climate policy uncertainty, and findings about the ability of investors to correctly assess risks associated with climate change. The following section3introduces the model byHsu, Li, and Tsou(2018) about climate regulation uncertainty and derives theoretical implications for the two event studies. Section4describes the methodology used and tested for the Paris agreement in section5and for
the Trump election in section6. Finally, section7discusses the analyses and section8concludes.
2
Literature Review
Global warming and measures against it have become a big part of today’s policy discussions. Many scientists have warned about the dangers of increasing temperatures and pollution, but governments are hesitant to introduce strict regulation because other factors also play a role in their decision process. Uncertainty about the true objective function of a government results in uncertainty about what policy will be adopted and how it is going to affect the economy.
P´astor and Veronesi (2012) model uncertainty both about whether a new policy will be adopted and analyse the stock market response at the time of announcement. The government, who decides at a given point in time whether to make a policy change, cares not only about investors terminal wealth but also incurs a political cost (or benefit) when changing policy. If this cost is neutral, the government will act as a social planner and change policy in case of a low performing current policy. If there is a cost (benefit) associated with changing the policy, however, a badly (well) performing policy may be retained (changed). Since investor and government preferences are misaligned, a policy change is likely to cause a negative response by the stock market. While the higher expected profitability increases prices, the higher uncertainty about the new policy’s impact increases the discount factor which, P´astor and Veronesi find, usually outweighs the price increase.
In their subsequent paper (P´astor & Veronesi, 2013), they extend the model by agents’ learning over time about the political costs of potential policies. This introduces a new type of shock to the economy which increases volatility and correlation among stock returns and requires an additional risk premium which they name political risk premium. Their model predicts that in times of higher uncertainty about government policy the risk premium for political risk should be higher. The risk should manifest itself along three dimensions: a higher volatility of returns, increased probability of changes in return volatility, and increased tail risk.
To test the predictions about a political risk premium, Kelly et al. (2016) analyse a large number of elections and summits using option price measures and the assumption that elections and summits present uncertainty about future policy decisions that will be reduced once the outcome is known. They find that options spanning political events result in higher values for all of the three risk measures (volatility, variance risk, tail risk) than their neighbouring options. There is an alternative approach to assuming political uncertainty around elections and sum-mits. Baker, Bloom, and Davis(2016) develop an economic policy uncertainty index by counting frequencies of terms related to economic policy uncertainty in newspaper articles. They find that stock prices are more volatile in times of larger economic policy uncertainty.
Uncertainty about future carbon regulation is a specific part of economic policy that firms are differently exposed to. While carbon-neutral firms may only be affected indirectly by policy changes, firms reliant on emissions may encounter severe changes to profitability. Hsu et al.(2018)
extend the model byP´astor and Veronesi(2013) to capture this kind of regulation (discussed in detail in section3). In contrast to the original model, exposure to policy changes is heterogeneous in the extension. In their empirical analysis,Hsu et al.find that toxic chemical emissions, scaled by book-value of equity, and excess return are positively correlated, indicating a positive pollution risk premium that increases with the level of emissions.
Ilhan, Sautner, and Vilkov (2019) set out to empirically test the model of Hsu et al.(2018) for the case of regulation against carbon emissions via option prices. Although they use similar measures to the ones introduced byKelly et al. (2016), they regress measures for left tail risk, volatility, variance risk premia, and skewed return distribution on the carbon intensity and controls using panel data. While they find support for the predicted increased left-tail risk, volatility, and variance risk premium for more carbon-intensive firms, they only do so at the sector level. In their analysis, firm-level carbon intensity does not appear to have a significant effect on the risk-measures beyond the sector intensity. Ilhan et al.also implement a difference-in-differences model for the election of US president Donald Trump. They find that left-side tail-risk decreased for firms with higher carbon-emissions following the election.
The subject of this thesis is closely related to the publications ofHsu et al.(2018) andIlhan et al. (2019), but has a different goal in mind and uses a different methodology; one that much closer resembles the one ofKelly et al.(2016). Hsu et al.(2018) try to determine whether there is a risk premium for carbon intensive firms. This thesis emphasises specifically effects on the risk of extreme outcomes and expected future volatility. Ilhan et al. (2019) look for an effect of industry carbon intensity, while this thesis focuses on individual emissions. Further, except for a case study on the Trump election,Ilhan et al.perform a panel data analysis. Next to the analysis of firm-level emissions, this thesis tries to replicate their results for the Trump election and, additionally, the Paris agreement.
There is a growing literature into the effects of climate risk perception on asset prices. Engle, Giglio, Kelly, Lee, and Stroebel (2020) develop a dynamic hedging strategy to hedge against negative climate change news, indiscriminate of regulatory risks and real effects, while keeping the same exposure to other types of risks. Choi, Gao, and Jiang (2020) find that in times of extraordinary warm weather, local non-institutional investors invest away from carbon-intensive firms. Complementing that finding, Alok, Kumar, and Wermers(2020) conclude that institu-tional investors overreact more to natural disasters if they are based geographically close to the location of the disaster but lose this bias over time.
Another strand of literature deals with the implications of global warming and increasing flood risk on real estate prices. Evidence in this area is mixed: Bernstein, Gustafson, and Lewis(2019) find that houses projected to be flooded trade at a discount, while rental prices in those areas do not reflect such a risk. Baldauf, Garlappi, and Yannelis(2020) conclude that the pricing of flood-risk depends on whether residents in the neighbourhood deny climate change. If they do, prices do not seem to be discounted, while they are if the neighbourhood believes in climate change. In line with that, a field survey byBakkensen and Barrage (2017) found significant heterogeneity
on flood risk perception. Using their theoretical model, the authors estimate that house prices in coastal regions are overvalued by 10%. Murfin and Spiegel(2020) exploit differences in vertical land movement among houses with similar elevation to find variation in the time until the houses will be flooded. They do not find an effect of this variation on house prices.
3
Theoretical Framework
This section first discusses the theoretical model developed byHsu et al.(2018) as an adaption of the model developed byP´astor and Veronesi(2013), and then implications of the model specific to the event study approach of this thesis.
3.1
Hsu et al. model
Hsu et al. (2018) develop a model where profitability depends on environmental policy and exposure to such policy. The version discussed here only considers equity financing as debt considerations do not add to the usefulness of the model in the context of this thesis.
In the model, a continuum of risk-averse households invests into a continuum of firms. Ini-tially, all firms are equally capitalised but their value will diverge as their profitability follows a stochastic process influenced by an average profitability and exposure to climate policy, as well as both systemic and an idiosyncratic stochastic variation.
dΠit= (µ + ξig)dt + σdZt+ σIdZti (1) g = gW if t ≤ τ
gW if t > τ and there was no policy change gS if t > τ and the policy changed
(2)
where ξi and Zi
t are firm-specific exposure to climate policy and Brownian motion of firm i at
time t while µ, g, and Zt are average profitability, average climate change policy impact, and
systemic Brownian motion, independent of the individual Brownian motion. Parameters µ, σ, and σI are observable and constant while g can change at a pre-determined time τ ∈ (0, T ): it
either maintains the current, positive, impact of the initially weak policy (in which case g = gW),
or it jumps to the negative average impact of a strong policy on firms’ profitability (in which case g = gS). Note that, as the exposure ξi may also be negative, a stronger climate policy may also have a positive effect on some firms. The exposure of firms’ profitability to climate policy is assumed to follow a uniform distribution centred around one.
The firms are owned by a continuum of households with constant relative risk-aversion who derive utility only from terminal wealth provided by the liquidating dividends at time T . The government maximises total utility but also faces a cost of retaining the initial weak climate
policy. It maximises max τ >t n Eτ (1 + C)WT1−γ 1 − γ Weak Policy , Eτ WT1−γ 1 − γ Strong Policy o (3)
where Eτ is the expectation at time τ and C is the environmental cost of retaining the old
policy. WT is the sum of terminal profit and γ > 1 is the coefficient of relative risk-aversion.
Since 1−γ < 0, the government is maximising a negative which is decreased by the environmental cost function for costs larger than 1.
The true value of the environmental cost is unknown until time τ , when the true value of the cost is first revealed to all agents and then used by the government to make the decision whether to adopt the stronger policy. The prior distribution of the cost is log-normal and centred around one. Prior to any information about the realisation of the environmental cost, the distribution of agents’ belief equals the distribution of the cost before it was drawn.
c ≡ log(C) ∼ N−1 2σ 2 c, σ 2 c (4)
where N is the normal distribution. Hsu et al. refer to σc as regime shifts uncertainty, as this
parameter drives uncertainty about the probability of an unfavourable regime shift (adoption of the stronger policy).
While agents do not know the true value of c, they receive noisy signals dst about c which
follow
dst= cdt + ηdZtc. (5)
Using those signals, agents learn in a Bayesian way about the true value. At any time t < τ , the posterior distribution of c is given by the agents’ belief ˆctabout the cost and its uncertainty
ˆ σ2 c,t, such that c ∼ N (ˆct, ˆσ2c,t), where (6) dˆct= ˆσc,t2 d ˆZc t η , and (7) ˆ σc,t2 = 1 1 σ2 c + t η2 (8)
The uncertainty about the environmental costs, thus, increases with the regime shifts uncertainty and the weight η of noise in the signals, but decreases with time. The posterior mean is driven by shocks due to the stochastic element of the signals and fluctuates more if agents just started to learn about the environmental cost, in cases of more noise in the signals, and if the regime shifts uncertainty is higher.
The authors then derive the threshold environmental cost above which the stronger climate policy is adopted. The threshold c(τ ) at time τ and the probability pτ that the cost is indeed
above that threshold are
c(τ ) = loge(γ−1)(gW−gS)(T −τ )
− 1
(9) pτ = 1 − Φ(c(τ ); ˆcτ, ˆσ2c,τ) (10)
where Φ(c(τ ); ˆct, ˆσ2c,t) is the cumulative normal distribution function with mean ˆctand variance
ˆ
σc,t2 evaluated at c(τ ). Since the expectation at time t of ˆcτ is ˆct and the variance of c based on
information at time t is ˆσ2
t, the probability pτ |tthat the government adopts the strong policy at
time τ , given all information at time t is
pτ |t= 1 − Φ(c(τ ); ˆct, ˆσc,t2 ). (11)
Equation (8) shows that the threshold value for the policy change inducing environmental cost depends on the coefficient of relative risk-aversion, the difference in profitability impact between the weak and strong policy, and the time left after the policy change until firms are liquidated. Since environmental damage is not part of the households utility (they only care about terminal wealth), higher risk-aversion increases the threshold cost, meaning that in an environment of very risk-averse households, the environmental cost has to be higher to induce adoption of the stronger policy. Similarly, a higher difference between the policy impact on profitability will result in a higher threshold. Finally, having more time left with the policy after time τ also implies a larger threshold value.
From the above setup,Hsu et al.derive that, before time τ , each firms’ realised stock returns follow the process
dMti Mi t = Et dMi t Mi t + σdZt+ σIdZti+ βM,ti d ˆZtc (12) where Mi
t is firm i’s valuation at time t, σ its exposure to systemic shocks, σI its exposure to
idiosyncratic shocks to its return, and βi
M,t the exposure to policy regime shift shocks, where
βM,ti is given by βiM,t= 1 Θit ∂Θi t ∂ˆct ˆ σc,t2 η < 0. (13) Θi
treflects firm i’s market to book ratio. Firm i’s exposure to policy regime shift shocks is, thus,
larger when that ratio is more sensitive to signals, when uncertainty about the environmental cost is higher, and when there is less noise in the signals. Negativity of βi
M,t indicates that
positive shocks to the enviornmental costs decrease returns.
Shifting towards the question of this thesis, it is relevant to understand both how a firm’s exposure to regime shift shocks is affected by its emissions and whether this commands a risk premium. First, Hsu et al. show that if a firm’s profitability is more sensitive to its emissions (higher ξi), then its return is more sensitive to regime shift shocks (more negative βi
other words, the emission elasticity of the cost-shock exposure of the realised return is positive. ∂βiM,t ∂ξi < 0 (14) ∂βi M,t/βiM,t ∂ξi/ξi > 0, assuming positive ξ i (15)
This indicates that the realised stock return of firms with higher emissions is affected more by regime shift shocks, which should result in a risk premium for those firms. Hsu et al.decompose the risk premium into two parts, one for systemic risk, and one for the exposure to climate policy risk. As the model does not incorporate debt financing, leaving the interest rate at zero, the risk premium in equilibrium equals the expected return. For t < τ this is
RP = Et dMi t Mi t = σ2γdt − βM,ti λc,tdt (16)
where λc,t is the price of risk for regime shift shocks in the stochastic discount factor. Thus,
the first term indicates that there is a risk premium for systemic shocks which is higher if either the relative risk-aversion is higher, or if the volatility of profitability due to systemic shocks is higher. The second term shows that stocks more vulnerable to climate regulation (higher ξi and as a result more negative βi
M,t) require a higher risk premium.
When going beyond time τ , there is an additional term for the jump at time τ + just after τ . Realised returns thus follow the process
dMi t Mi t = Et dMi t Mi t + σdZt+ σIdZti+ β i M,td ˆZ c t+ J i M,τ +It=τ (17) where Ji
M,τ + is the jump of firm i’s stock at time τ + and It=τ is an indicator function which
is always 0, except when t = τ . The jump, of course, depends on whether the weak policy is retained, in which case JM,τ +W,i > 0 or the strong policy is adopted (JM,τ +S,i < 0). The two jumps are given by JM,τ +S,i = (1 − φt)(1 − e ξi(gW−gS)(T −τ ) ) φτ+ (1 − φτ)eξ i(gW−gS)(T −τ ) (18) JM,τ +W,i = −φt(1 − e ξi(gW−gS)(T −τ ) ) φτ+ (1 − φτ)eξi(gW−gS)(T −τ ) (19) φt≡ pτ |t pτ |t+ (1 − pτ |t)e−γ(g W−gS)(T −τ ). (20)
Most interesting here is to see that the size of the jump is larger for firms with higher ξi.
The jump in case the initial, weak, policy is retained is positive as long as ξi is positive, while
3.2
Implications of the Theoretical Framework
The model from Hsu et al. (2018) allows several predictions about the riskiness from stock returns. First, consider the variation of the stock returns. The variance at time t < τ of the realised returns of a stock is given by
Vit dMi t Mi t = Et dMi t Mi t − Et dMi t Mi t 2 (21) = Et σdZt+ σIdZti+ β i M,td ˆZ c t 2 (22) = (σ2+ σI2+ (βM,ti )2)dt. (23)
Thus, the variance of an individual firms stock increases with the exposure to systemic profitabil-ity shocks, with the exposure to individual profitabilprofitabil-ity shocks, and, crucially, with the exposure to policy regime shift shocks. Since the elasticity of the exposure βM,ti with respect to emissions ξiis positive, the stock returns of firms with higher emissions are more volatile in a cross-section,
all else equal.
Further, a positive regime shift shock, so new information indicating a higher environmental cost than expected (an increase in ˆct), increases cross-sectional volatility differences caused by
different emission levels. The sign of the particular change of variance due to an increase in the belief about the environmental cost is ambiguous and depends on the parameters of the model. To get an intuition, however, consider a particular instance of the model, using the parameters listed in table 1. The choice of parameters is mostly in line with Hsu et al. (2018), who set parameters that also appeared inP´astor and Veronesi(2013) equal to their value. Three choices depart from the parameters chosen by Hsu et al. (2018). First, the point in time t considered here is set to 2.5, which is at the half-way mark between the start of the model and the time of a possible policy change at time τ . Second, the variance over one year is considered (dt = 1). Third, the average impact of the weak and strong environmental policies was adapted. Hsu et al. (2018) set gW = 0.02 and gS = −0.06, which, given the other parameters, results in a
threshold environmental cost c of -0.71, even though Hsu et al. ruled out negative thresholds. This threshold, however, is not problematic itself as it represents the logarithm of the actual cost and still translates to a positive environmental cost C of around 0.49. Nevertheless, the parameters were changed to be symmetric around zero at gW = 0.1 and gS= −0.1, resulting in
a threshold c of around 0.54 and an actual cost C of 1.716. Given the other parameter choices, this means that the government will adopt the strong policy if the aggregate terminal wealth under the weak policy is at most 2.716 times as large as the aggregate terminal wealth under the strong policy, which may seem excessive but the change does not affect the interpretation and a realistic range for the environmental cost of not adopting the stronger regulation depends on many factors, starting with the difference in emissions induced by the regulation and beyond strategic implications for international cooperation.
Table 1: Parameter choices to illustrate dynamics in the model. µ, σ, and σI are parameters
from equation (1), γ is the coefficient of relative risk-aversion of households from equation (3), η is the noise in the signals form equation (5), gW and gS are the average policy impacts for
the weak and strong policy, respectively, given in equation (2), T is the terminal time in the model, τ < T is the time at which a decision about adopting a new policy is made, t is the time considered, and dt is the size of the time step. All parameters, except for γ, η, T, τ , and t, are interpreted to be annual.
µ σ σI σc γ η gW gS T τ t dt
0.2 0.1 0.05 0.95 2 0.6 0.1 -0.1 10 5 2.5 1
simulated for different states of the belief about the log-environmental cost ˆct. The result is
plotted in figure 1. First, as was already derived by Hsu et al. (2018), a higher emission level ξi results in a higher variance of the returns, as long as the policy decision is uncertain (ˆc
t is
close to c). Second, the more uncertain the policy decision is, the higher the variance for firms whose profit is affected by climate change regulation. Third, and crucially, higher uncertainty, translating to ˆct closer to c (which is 0.54 in the simulation), leads to a larger increase of the
variance for firms with higher emissions.
Finally, the probability density function of a firm with carbon emissions’ return is, in this model, bimodal. There is a high-return peak for the case in which the weak policy is retained, and a low-return peak for when the stronger policy is adopted. How far the peaks are away from each other depends on the size of the jump at time τ . Since JM,τ +S,i < 0, ∂J
S,i M,τ + ∂ξi < 0, J W,i M,τ +> 0, and ∂JM,τ +W,i
∂ξi > 0, higher emissions increase this difference. In the scenario of a positive political cost
shock, the probability distribution shifts weight from the upward jump towards the downward one, resulting in a heavier left tail.
To illustrate this dynamic, take two firms, one with a profitability independent of environmen-tal regulation (i.e. ξi= 0) and one with positive exposure to such regulation. The distribution of
the return of the former firm is normal around the expected return, while the latter firms return is bimodal. This illustrates that the return probability distribution of a firm’s stock with posi-tive exposure to regulation should have heavier tails than a firm which is environmental policy neutral. Extending this, a higher probability of stronger environmental regulation corresponds to a higher probability of a negative jump, which increases the area underneath the left side of the distribution for the firm exposed to regulation, while it does not affect the distribution of the regulation independent firm. Therefore, following a positive cost shock, and, thus, increased probability of stronger regulation, the downward tail risk increases for the carbon-intensive firm while it does not change for the neutral one.
4
Methodology
The rest of this thesis tries to find empirical evidence for the theoretical implications put for-ward in the previous section, using an event study based approach. To do so, this section first
Figure 1: An illustration of how the belief at time t about environmental costs ˆct and firm
i’s profit exposure to climate policy ξi influence the variance implied by the model, using the
parameters from table1.
i
0.0 0.2
0.4 0.6
0.8
c
t
0.50
0.25
0.00
0.25
0.50
0.75
1.00
1.25
1.50
Variance
0.013
0.014
0.015
0.016
0.017
0.018
0.019
0.020
introduces two measures adapted fromKelly et al.(2016) (KPV in the hereafter): a measure for expectations about volatility, and a measure for the tail risk.
4.1
Risk measures
The approach of this thesis differs slightly from the one chosen by KPV. While they use elections and summits where regulation is agreed upon and in place shortly after, climate regulation usually works somewhat different. Instead of deciding what policy should be adopted (or retained) on a fixed date, events mostly affect the probability with which regulation will be increased. Governments pledge to implement stricter policy, thereby increasing the probability that strict regulation will be adopted in the future and increasing the cost of retaining the old policy. Thus, this thesis interprets points in time significant for emission regulation as environmental cost shocks (changes to ˆct in the model by Hsu et al. (2018)) affecting the probability that stricter
policy is adopted in the foreseeable future, and not events τ , as in KPV. The time of the cost shocks is denoted by t0. In this interpretation the date τ is assumed to be at some point in the
future and shocks to the environmental cost are used for identification.
The two measures used for expectations about future volatility and tail risk rely on the Black-Scholes model. The model allows the calculation of a theoretical price for a European option, using the risk-free rate, the underlying stock’s volatility and price, as well as the options time to expiration and strike-price. At the same time, if option prices are given, the model implies expectations about the future volatility of the underlying stock. Since option prices are determined in a market, the implied volatility by option prices allows inferences about the markets expectations about future volatility, given that the model holds. This is used for the IVD measure introduced in the next subsection.
To measure tail-risk, the assumptions of constant volatility and normal returns of the Black-Scholes model are exploited. If the return distribution is normal, the volatility implied by the model should be constant across different levels of returns. Heavier than normal tails, on the other hand, result in implied volatilities that are higher the further away from the current stock price the option’s strike price is, which results in the volatility smile. To measure how far current stock price and strike price of the option are from each other, the Black-Scholes delta can be used. The delta indicates the change in the theoretical price of an option following an increase in the price of the underlying stock. For example, put options have negative deltas because an increase of the price of the underlying decreases the probability that a put option ends up in-the-money at the time of expiration.
Using the delta instead of, for example, strike-price over underlying stock price, has the advantage that the delta takes into account other characteristics of the option contract as well, such as time to maturity and the historic volatility. All else equal, delta moves in the opposite direction of the value of underlying stock price minus option strike price, i.e. an out-of-the-money put option (strike price < stock price) has a higher delta than an in-the-money put option. This means that a higher probability of extreme outcomes than under a normal distribution results in a positive correlation of delta and implied volatility.
4.1.1 Implied Volatility
Following KPV, let IVt,m denote the volatility implied at time t by an at-the-money (ATM)
option expiring at time m, where ATM refers to options with absolute deltas between 0.4 and 0.5. To filter out random daily variation, the average over a 20 day period is computed and defined as IVt where t = a if the period averaged over is before the cost shock and t = b if
the period is after the cost shock. Further, to avoid inaccurate implied volatilities from options with ultra-short maturities, the averaging period ends 5 days before the expiration date. To summarise
IVa = Mean{IVa−s,a: s ∈ [5, 25]} (24)
where a is the last expiration date ahead of the cost shock at time t0, and
where b is the first expiration date after t0 for which b − s > t0 for all s.
Using the above, the implied volatility difference for the cost shock at time t0is denoted as
IVDt0 = IVb− IVa, (26)
such that a volatility increase at t0 results in a positive difference. What this measure does not
account for is a slow moving volatility time trend. However, first, a strong trend would only be mis-attributed to the cost shock if it was significantly more relevant to firms with high emissions, and second, keeping the sample period close around the date of interest minimises the impact of a slow moving time trend. Taking the difference between two sample periods is an attempt to filter out factors affecting the level of the implied volatility, e.g. the size of a firm, which, thus, do not have to be controlled for.
4.1.2 Volatility Slope
The implied volatility slope is a one-sided measure to quantify departure from a normal prob-ability distribution. Since a higher delta of a put option translates to a deeper OTM (out-of-the-money) option, a positive value for the volatility slope implies a heavier tail, i.e. higher probability of lower than expected returns.
Following KPV, options used are OTM put options, defined as those options with −0.5 < ∆ < −0.1, thereby excluding very far OTM options which may give inaccurate implied volatilities. To calculate a slope there need to be at least two options with open interest, but to filter out some of the noise, only day-firm combinations with at least three data points are used1. The Slopet,m,
volatility slope for time t and expiration date m, is then estimated using OLS and averaged for each day in the interval.
Slopeθ= Mean{Slopeθ−s,θ: s ∈ [5, 25]}, where θ ∈ {a, b} (27)
and
SlopeD = Slopeb− Slopea. (28)
A positive value for SlopeD indicates that the cost shock at time t0 increased the tail risk for a
firm.
4.2
Hypotheses
Throughout the rest of this section, it will be assumed that the current belief about the environ-mental cost used by the government to decide whether to adopt stronger environenviron-mental policy is lower than the threshold value for which it is welfare improving, or in other words, an increase in the probability that environmental policy will be made stricter, makes it more uncertain what
policy will be implemented. Obviously, this is not a given and yet it is likely as follows from the discussion around what policy to adopt and its implications.
Using the measures introduced above, the implications discussed in section3.2can be trans-lated into empirically verifiable hypotheses. First, the theoretical model showed that the variance of stock returns for firms with higher emissions should be higher, at least for parameter choices such as the ones used byHsu et al. (2018) andP´astor and Veronesi(2013), if there is a positive shock to the estimated environmental cost which brings the belief closer to the threshold cost. If this is the case also in reality, then a positive cost shock will increase IVD.
Hypothesis 1: Cost shocks (i.e. the probability of stricter regulation) and IVD move in the same direction. IVD changes more if firm-level emissions are higher.
Second, the model predicted that a positive cost shock will lead to heavier tailed distributions for stock returns of firms with higher emission levels. Using the SlopeD measure introduced above, this translates into the following hypothesis.
Hypothesis 2: Cost shocks (i.e. the probability of stricter regulation) and SlopeD move in the same direction. SlopeD changes more if firm-level emissions are higher.
4.3
Data
Both measures use option prices as a proxy for risk perceived by the market. The source of the option data used is OptionMetrics IvyDB database for US American firms. Data for the firms’ carbon emissions are accessed via DataStream from the Asset4 database. Summary statistics for the two event studies can be found in the appendix in tablesA1andA2, respectively.
There are three different ways how to measure emissions defined by the Greenhouse Gas Protocol. Scope 1 emissions are emissions that are directly caused and controlled by the operation of a firm. This includes emissions from stationary combustion, such as running machinery, but emissions from sources such as company vehicles are also counted if the firm owns or controls the activities. Scope 2 indirect emissions are caused by the operation of a company but do not occur at the hands of the firm. For example, some firms may be energy intensive but still have low direct emissions. Their scope 1 score be very low, but if the energy the company bought to run the electric motors is not from renewable energy sources, scope 2 would capture carbon dioxide emitted in the process of extraction. Finally, scope 3 emissions are caused by the firms operations, without them being controlled or owned by the firm.
The data acquired via Datastream divide the emissions into two different categories. Direct CO2emissions relate to scope 1, while indirect CO2emissions relate to scope 2 and scope 3. It is
not immediately clear whether indirect emissions should be included. While indirect emissions are neither owned nor controlled by firms, carbon regulation may significantly hinder a firms business model. For example, producing biofuel may emit little carbon dioxide and, yet, using those fuels results in carbon emissions. If there was a ban on carbon emissions, the biofuel producer would
lose customers and go bankrupt. Because it is unclear whether to include indirect emissions, both will be used to run the analysis.
Large companies may have high absolute carbon emissions by nature of being large, but their profitability should be less affected by regulation than a small firm with the same absolute carbon emissions. Thus, in line withIlhan et al.(2019), carbon emissions are scaled by the firm’s market value of equity.
Emission data in the United States are collected via surveys, which leads to missing data and a potential selection problem, at least thats howIlhan et al.(2019) argue. Publishing data on emissions may be more desirable for firms with lower carbon intensities than competitors or if there is peer-pressure for firms in the industry to publish carbon emissions. Tables A1 and
A2 show that data for reported carbon emissions are scarce, only about 15% of the firms in the sample are reporting. To account for the missing variables,Ilhan et al.employ a Heckman selection model which is surprising as the problem is one of a missing independent (and not dependent) variable.
While it is easy to intuitively explain why emission observations may be missing, it is non-trivial to intuitively reason whether this should result in biased estimates. According to
Wooldridge (2016, Ch. 17-5), if whether an observation is missing depends entirely on the ex-planatory variables and a random term that is independent of both the exex-planatory variables and the population residual, OLS is still consistent and unbiased. Under the zero mean assumption of the population residuals, controlling for the industry a firm is in should result in unbiased and consistent estimates.
There is, however, another option available. The DataStream Asset4 dataset contains not only data for reported emissions, but also for emissions estimated (estimated are total CO2
emissions) using one of four methods (“Reported/CO2/Energy/Median”). Estimated data is available for a much larger part of the sample, about half of all firms in the sample and most of the firms for which IVD and SlopeD are observable (For the Paris agreement, estimated emissions are available for 75% of firms with observed IVD and 90% of observed SlopeD. In the case of the Trump agreement, availability is 95% and 99%, respectively). The estimated emissions are used next to the reported direct and total emissions.
There may be another source of selection bias which has not been considered byIlhan et al.
(2019). If there is a higher regulatory risk associated with firms that are more carbon intensive, this may increase hedging and/or speculation on the security and result in higher liquidity in the option market. Following this line of reasoning, more carbon intensive firms would be more likely to have been traded enough to allow calculation of IVD and SlopeD. However, as the risk of climate regulation among the total risk of a firm should be relatively small, meaning that variation in the data availability due to emission intensity should be low, unbiasedness of estimators is assumed for the rest of the thesis.
5
Paris Agreement
The Paris agreement is one of the major pieces of information that comes to mind when thinking about climate change regulation. It was agreed upon at the 2015 United Nations Climate Change Conference (UNCCC) in Le Bourget, a suburb of Paris. The conference started on November 30th, 2015, and concluded on December 12th, 2015 and made signees of the agreement, among them the United States, pledge to put measures in place to slow climate change by reducing carbon emission with the goal of keeping global warming below 1.5°C, although no country is forced to implement any measures beyond planning and reporting efforts regularly.
Since signing countries pledged to reduce emissions, the agreement should signal an increase in the cost of retaining weak regulation, i.e. increase the probability that stricter policy will be adopted. The value of this signal is difficult to measure as it is a mere pledge without requirement to implement new regulation and depends on the credibility of the intention to implement regulation. Further, Donald Trump famously withdrew from the agreement in June 2017 which may suggest that the pledge was, indeed, not very credible. Nevertheless, results indicating the expected change to risk assessments, under the assumption of a cost increase, may be interpreted as evidence in favour of the hypotheses. A lack of a significant change, on the other hand, does not necessarily indicate a lack of the pricing of regulatory risk, as a non-credible pledge would be able to explain non-significant results.
5.1
Implied Volatility
Assuming the Paris signalled an increase of the cost for retaining weak policies as a government, hypothesis 1 says that the IVD measure should be more positive for firms with more carbon emissions.
Table2shows the results of the analysis for the change in the implied volatility. Column (1) shows results for OLS estimation of the effect of direct CO2 intensity on the change in implied
volatilities. It is noticeable that the constant is positive and significant at the 5% significance level. This is consistent with the theory since the average exposure to regulation is positive. The coefficient for the direct carbon intensity, however, is not significantly different from zero. The negative sign of the coefficient is surprising, as the increase of regulatory risk should be larger for firms with high carbon emissions. If the estimate was to be believed, it would imply that a firm with a carbon emission intensity that is one standard deviation (0.027) larger saw their implied volatility increase by 0.0069, or 0.037 standard deviations, less than the same firm without the higher intensity, which would, if it was carbon neutral, only experience the 0.72 standard deviations increase of the ATM implied volatility.
Further, the coefficient of determination is very low for all four regressions, suggesting that there is a lot of noise in the estimation. Column (2) uses total emissions, instead of the direct emissions of column (1). The constant is, again, significantly positive but carbon intensity is positive although very close to zero. Column (3) uses estimated total carbon intensities and
Table 2: IVD results for the United Nations Climate Change Conference (UNCCC), where the Paris agreement was agreed upon.
Dependent variable: IVD (1) (2) (3) (4) CO2 Intensity – Direct −0.254 (0.215) CO2 Intensity – Total 0.008 (0.216) CO2 Intensity – Estimated −0.009 (0.007) CO2 Intensity – Industry 0.382 (0.423) Constant 0.131∗∗∗ 0.097∗∗ 0.104∗∗∗ 0.045 (0.033) (0.039) (0.005) (0.064) Observations 309 370 1,167 1,335 R2 0.005 0.00000 0.002 0.001 Adjusted R2 0.001 −0.003 0.001 −0.0001 Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01 Standard errors in parentheses
produces results similar to columns (1) and (2) in that the constant is significantly positive while the carbon intensity is not significantly different from zero. Standard errors, however, are much smaller due to the larger sample size. While this may point towards a negative effect of carbon intensity, it may also be the estimation technique driving the results if, for example, the estimated intensities are derived from some kind of average.
Finally, column (4) uses the industry average direct carbon intensity, instead of firm-level data. This analysis is replicated fromIlhan et al.(2019) who find significant effects of industry carbon intensity. While the coefficient of carbon intensity in column (4) is positive, as was expected, the effect is not significant and therefore does not allow the conclusions ofIlhan et al..
As such, the results do not constitute evidence in favour of hypothesis 1.
5.2
Volatility Slope
According to hypothesis2, a positive cost shock (i.e. policy change probability increase) should result in a SlopeD that is higher for firms with a higher carbon intensity. Again, assuming that the Paris agreement represented a significant positive cost shock, this translates into a positive
Table 3: SlopeD results for the United Nations Climate Change Conference (UNCCC), where the Paris Agreement was agreed upon.
Dependent variable: slopeD (1) (2) (3) (4) CO2Intensity – Direct 0.254 (0.412) CO2Intensity – Total 0.225 (0.378) CO2Intensity – Estimated −0.001 (0.101) CO2Intensity – Industry 0.141 (1.316) Constant 0.034 0.037 0.069 0.045 (0.063) (0.068) (0.049) (0.200) Observations 169 187 408 416 R2 0.002 0.002 0.00000 0.00003 Adjusted R2 −0.004 −0.003 −0.002 −0.002 Note: ∗p<0.1; ∗∗p<0.05;∗∗∗p<0.01 Standard errors in parentheses
SlopeD measure.
Results can be seen in table3. Column (1) shows estimates for the effect of the direct carbon intensity on the value of SlopeD. Different from the results for the implied volatility, the average volatility slopes do not appear to be significantly steeper after the agreement than before. The coefficient for carbon intensity, on the other hand, has the expected positive sign, albeit non significant. Results for the total carbon intensity in column (2) align with those of column (1) in that estimates are similar in value and also non-significant, indicating that for the slope indirect emissions play only a small role.
Column (3) shows the effect of the estimated emission intensity on the volatility slope. The carbon intensity coefficient is again insignificant and very close to zero. Finally, column (4) presents the estimates when using the average industry carbon intensity. Results resemble those of columns (1) and (2). The fact that estimates of different measures of carbon intensities all suggest positive or zero effects on the volatility slope could be due to a small effect that is not significant because missing observations lead to a loss of power. If emission data for more firms was available, the effect may turn out to be significant.
Coefficients for carbon intensity in columns (1), (2), and (4) of table 3 have the expected positive sign, but are not significant, while the coefficient in column (3) is very close to zero and insignificant. To try an alternative approach, the methodology of Ilhan et al. (2019) is replicated. They test a very similar hypothesis in an event study of the volatility slope around the Trump election. In the DiD approach, the volatility slope is regressed on a dummy for whether the firm’s industry is among the ten most carbon intensive industries in the sample, a dummy indicating whether the agreement was already signed and the interaction of the two dummies. The regression model for firm i on day t is
Slopei,t= α+β1High Emissions/Market Value Industryi,t× Post Agreementt
+β2High Emissions/Market Value Industryi,t
+β3Post Agreementt+ γXi+ εi,t
where Xi is a vector of controls. Controls are share price, price over earnings, dividend yield,
market value, price-to-book ratio, debt over total capital, the beta, historical volatility, and capital investment per total assets. Results of the analysis can be found in table B1 of the appendix. While point estimates somewhat differ from column (4) of table 3, the sign of the estimate for carbon intensity is still positive and non significant. Thus, also for hypothesis2, the implemented methodologies for the Paris agreement do not provide conclusive evidence.
6
Trump Election
President Trump was elected on November 8th, 2016. Since he advocated for policies in quite stark contrast to the other candidate, Hillary Clinton, there was political uncertainty about future environmental policy around that time. The election has already been subject to a case study inIlhan et al.(2019) who found evidence for both hypothesis1 and2.
6.1
Implied Volatility
Donald Trump made it very clear that his interests were to strengthen the economy by retaining the status quo, characterised by a lack of regulation against carbon emissions. Translating this to hypothesis 1, the election should have signalled a decrease the environmental costs to the government and thus a decrease in the probability that stricter emission regulation would be introduced soon. The IVD measure, therefore should be negative and even more so for firms exposed to climate policy.
Results of the analysis can be found in table4. Column (1) tests the effect of direct carbon intensities on implied volatilities. Given thatIlhan et al. (2019) found a significant effect it is surprising that estimates for constant and carbon intensity impact are not significantly different from zero. While the total carbon intensity reported in column (2) does not change the (lack of) conclusion, using the estimated intensities in column (3) results in a non-significant coefficient
Table 4: IVD results for the election of US president Trump. Dependent variable: IVD (1) (2) (3) (4) CO2 Intensity – Direct 0.005 (0.141) CO2 Intensity – Total −0.106 (0.125) CO2 Intensity – Estimated −0.002 (0.006) CO2 Intensity – Industry 0.184 (0.362) Constant 0.006 0.028 0.019∗∗∗ −0.007 (0.022) (0.023) (0.005) (0.055) Observations 350 409 1,462 1,340 R2 0.00000 0.002 0.0001 0.0002 Adjusted R2 −0.003 −0.001 −0.001 −0.001 Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01 Standard errors in parentheses
for the carbon intensity but the constant is positive and significant at the 5% significance level, suggesting that the election of president Trump raised expectations of return volatilities in the economy. Finally, column (4) uses the industry average intensities to arrive at similar results.
The estimates for the coefficients of carbon intensity in table4are small and switch signs for no obvious reason. This suggests a lack of an effect and, while this may be the case, it may also be due to other factors in the election that are not accounted for. Possible confounding factors are discussed in section7.
6.2
Volatility Slope
Hypothesis2 implies that a negative cost shock (decrease of the probability of the adoption of strong climate regulation) should decrease the volatility slope and do so more for more carbon intensive firms. Thus, the measure of SlopeD should be negative on average and even more negative for more carbon intensive firms.
Table 5 shows the results of the analyses of the impact of carbon intensity on the volatility slope. The analysis is again characterised by a lack of significant estimates. In columns (1) and
Table 5: SlopeD results for the election of US president Trump. Dependent variable: slopeD (1) (2) (3) (4) CO2 Intensity – Direct −1.464 (2.086) CO2 Intensity – Total −0.825 (1.708) CO2 Intensity – Estimated 1.333 (1.777) CO2 Intensity – Industry 13.847 (21.652) Constant 0.125 0.063 −0.535 −1.885 (0.315) (0.305) (0.951) (3.289) Observations 166 185 416 382 R2 0.003 0.001 0.001 0.001 Adjusted R2 −0.003 −0.004 −0.001 −0.002 Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01 Standard errors in parentheses
(2) the sign of the intensity coefficient is negative while using estimates (3) and industry average emissions (4) results in a positive sign.
Since Ilhan et al. (2019) find seemingly robust evidence for a significant impact of carbon intensity on the volatility slope, their methodology is replicated. To do so, the implied volatility slope for each company i and date t combination for which there is data is regressed on a dummy indicating whether the firm’s industry is one of the top ten carbon intensive industries in the sample, a dummy for whether Trump was elected before (1) or after (0) the date, the interaction of the two, and a vector Xiwith controls. Controls are share price, price over earnings, dividend
yield, market value, price-to-book ratio, debt over total capital, the beta, historical volatility, and capital investment per total assets.
Slopei,t= α+β1High Emissions/Market Value Industryi,t× Post Electiont
+β2High Emissions/Market Value Industryi,t
+β3Post Electiont+ γXi+ εi,t
from table5, do not allow any conclusions as estimates are not significantly different from zero. The interaction has the same unexpectedly positive sign as the intensity in column (4) of table5. Thus, using the methodology and data of this thesis does not allow to make conclusions about hypotheses1 and2.
7
Discussion
Both event studies do not allow to make conclusions about the hypotheses, which said that positive cost shocks should have a more positive effect on the implied volatility and left-side tail-risk for firms which are more carbon intensive. This is surprising, as previous studies (i.e.
Ilhan et al.,2019;Hsu et al.,2018) did find evidence for similar relationships. There are at least four reasons that can explain this lack of significant results.
First, the risk environmental regulation poses for carbon intensive firms may just not be priced in the option market (yet). Studies about related pricing questions where climate change plays a role in, such as in the market for coastal houses mentioned above, have found mixed evidence, suggesting that markets do sometimes struggle with correctly pricing climate change risk. However, the question at hand does not relate as much to expectations about climate change as it does to expectations about regulation. While the two are intertwined, Ilhan et al.(2019) and Hsu et al.(2018) were able to find empirical evidence for risk premia related to climate change risk andKelly et al.(2016) found evidence for the pricing of risks related to policy uncertainty in general.
Second, the events selected for the event studies may not have had the assumed signalling effect on the market or other, confounding, events may have happened at the same time. There aren’t many substantial events for climate change regulation which lie in recent history where data is available and most importantly, significant regulation to target climate change has not yet been introduced. Next to the Trump election and the Paris agreement, other noticeable events that may be studied but will likely run into data issues are the 1992 Rio Earth Summit, the adoption of the Kyoto protocol in 1995, and the Cancun agreements from 2010. Analysing the effect of the United States’ withdrawal from the Paris agreement in 2017 may be worth a study where at least some base-level of data should be available. Analysing the 2020 Coronavirus pandemic may offer another opportunity, as one could argue that the regulators focus shifted from climate change to containing the disease.
Specific to the adoption of the Paris agreement, two confounding pieces of information may explain a lack of results: in September 2015, three months before the Paris conference, the Volkswagen emissions scandal started. The EPA’s notice of the violation of the clean air act may have temporarily increased investors assessment of the US government’s intention to fight climate change, meaning that implied volatilities and volatility slopes were at high levels already when the sampling period for this thesis started. Further, there is some evidence for an increase in the perception of climate risk in times of extraordinary warm weather (Choi et al., 2020).
2015 was the warmest year on record (at the time) with various wildfires around the world. This may have contributed to a higher assessed probability of stronger emissions regulation, but have subsided until the second sampling period, as there were no large climate related events in early 2016.
Confounding factors can also be found for the election of Donald Trump. Retaining the current status of climate policy was certainly not the only campaign promise made. Ilhan et al. (2019) argue that the promised tax cuts and repealment of Obamacare may confound the analysis. It may also be that farsighted investors understand a lack of timely regulation to slow climate change as an indication of even stricter regulation in the future. Such a line of argument, even though not part of the theoretical model, would be able to explain offsetting changes to the risk assessment of carbon intensive firms.
Third, there may be problems with the data. As mentioned before, data on carbon emissions is sparse and may be biased, mostly because collection and submission of emissions data is done via survey and on a voluntary basis. This problem may be ameliorated by analysing other countries which may have a higher proportion of reporting firms. The downside of analysing other countries is that this would be trading one missing data problem for another as the United States has the largest stock market in the world and, crucially, the most liquid option market, which even for the US appears to be somewhat of a bottleneck. The options of many firms have not been traded at all on at least some days in the sample, let alone have been traded enough to estimate a volatility slope. Calculating the slope based on only very few observations, however, results in noisy and unreliable estimates, which may be another factor explaining why results of the event studies in this thesis are insignificant. Averaging the implied volatilities over 20 days is an attempt to smooth estimation errors, but such smoothing only works if there are estimates for multiple days in the period.
Fourth, there may be shortcomings of the methodology chosen. Estimating volatility slopes using OLS an averaging over some period of days may be inferior to more sophisticated models of estimating volatility slopes. Ilhan et al. (2019), for example, rely on IvyDB OptionMetrics Volatility Surface file, which uses a kernel smoother to interpolate existing data points. Ulrich and Walther (2020) find that option implied information is sensitive to the way the volatility surface is constructed. Consequently, one of the reasons for the divergence of results of this paper and the event study in Ilhan et al.(2019), may be the way the volatility slope is created. But other differences exist. Ilhan et al.use a couple of different controls and sample over 250 days in each direction of the Trump election, while the analysis in this thesis only uses 25 days. Further theIlhan et al.paper uses control data of the previous year, while this analysis is using data of the year the Paris agreement was signed and Trump was elected, respectively.
Finally, a linear relationship of carbon intensity and the change in volatility and tail risk was assumed, which may not be correct2. Misspecification may cause larger errors, reducing the
power of the procedure.
8
Conclusion
The goal of this thesis was to determine whether firm-level carbon emissions affect the expected volatility and left-side tail risk of firms via uncertainty about environmental regulation and whether this is priced in the option market. The model developed by Hsu et al.(2018) implies that both volatilities and tail risks are larger for firms which are more exposed to environmental regulation. The predictions were tested using an event study methodology on data for US American firms for the 2015 UNCCC, where the Paris agreement was struck, and the election of US president Donald Trump in 2016.
Even though previous studies have found empirical evidence for the predictions made by the model, results obtained via the analyses of this thesis do not allow the conclusion that firm-level carbon intensity affects the expected volatility and tail risk implied by option prices. While there is some evidence for a general increase of implied volatilities following the Paris agreement, as was predicted by the model, the carbon intensity does not appear to have a statistically significant effect on the change in volatility. For the tail-risk, statistically significant evidence is lacking but signs of coefficients, at least, are consistent. Results for the Trump election are less indicative as for both volatility and tail risk estimated signs depend on the carbon intensity measure chosen and are not significant. Findings of an event study byIlhan et al.(2019), which found evidence for a tail-risk decrease following the Trump election, could not be replicated.
Several confounding factors may have caused the results, the most obvious of which is data availability. First, only few companies reported their carbon emissions for the years studied. This, however, may change over time as global warming becomes an increasingly large problem and regulation may force firms to report emissions. Second, relatively few options used in the analysis were traded frequently enough to allow inferences about the risk measures, especially about the tail risk. Further, the approach to smooth inference errors by averaging may be inferior to other techniques of interpolation. One issue with using an event study approach may be that it is difficult to isolate a timeframe where only an event relating to climate regulation happened. Future studies may either heavily increase the number of events studied, which may be difficult as important events for climate regulation are scarce, or use a panel data approach. If discussion about climate change becomes more prevalent in the future, more such events, as well as more emission reporting, may make the analysis more feasible.
Given that results are mostly non-significant it can not be concluded that the theoretical prediction of a higher expected volatility and left-side tail risk with higher exposure to climate regulation is priced in the option market. However, given limitations and uncertainties, the lack of significance should not be interpreted as a lack of an effect. Further research is necessary to arrive at a conclusion.
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A
Descriptive Statistics
Table A1: Descriptive statistics for the dataset around the Paris climate conference. SlopeD and IVD are the only variables that are measured using the difference of averages over a 20 day period before and after the conference, as described in section4. Other variables are collected on an annual basis, with their values for 2015 being presented below. There are N = 2555 firms in the sample.
Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) Max
IVD 1,571 0.105 0.183 −1.072 0.029 0.163 2.376 SlopeD 455 0.077 0.387 −2.502 0.012 0.139 2.813 CO2direct 312 1,555.920 249.762 1.000 1,513.750 1,686.500 1,768.000 CO2Indirect 306 1,467.748 299.603 35.000 1,453.250 1,619.500 1,705.000 CO2Total 373 1,842.013 263.703 102.000 1,783.000 1,982.000 2,086.000 EstimatedCO2 1,188 4,743.379 650.901 43.000 4,442.500 5,166.750 5,526.000 CO2 per Revenue 373 1,763.013 328.631 30.000 1,728.000 1,932.000 2,031.000 ESGscore 1,188 2,572.973 1,155.072 23.000 1,667.500 3,514.250 3,812.000 EmissionsScore 1,188 2,638.520 1,134.157 8.000 1,829.500 3,494.250 3,810.000 Price - Trade 1,533 4,918.208 2,321.016 48.000 2,829.000 6,839.000 7,266.000 Dividend Yield 1,533 150.865 208.765 1.000 1.000 225.000 877.000 Price-Earnings 1,238 312.689 311.368 2.000 108.000 427.750 1,191.000 Market Value 1,533 10,291.000 1,069.131 238.000 9,813.000 10,940.000 11,475.000 Price-To-Book 1,522 581.241 481.187 19.000 214.250 764.750 1,682.000 Debt Per Total Capital 1,569 3,688.604 2,436.390 16.000 1,236.000 6,156.000 6,723.000 Beta 1,528 6,803.954 2,517.446 35.000 5,578.000 8,494.250 9,009.000 Volatility 1,321 1,826.486 1,219.063 1.000 612.000 2,987.000 3,802.000 Capital Inves. Per Total Assets 1,509 668.409 612.342 1.000 152.000 1,063.000 2,209.000 Industry Avg CO2/Market Value 1,335 0.152 0.012 0.055 0.149 0.158 0.184
Table A2: Descriptive statistics for the dataset around the Trump election. SlopeD and IVD are the only variables that are measured using the difference of averages over a 20 day period before and after the election, as described in section4. Other variables are collected on an annual basis, with their values for 2016 being presented below. There are N = 2555 firms in the sample.
Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) Max
IVD 1,551 0.020 0.162 −1.664 −0.022 0.051 2.598 SlopeD 421 0.143 5.659 −11.347 −0.099 0.055 114.317 CO2direct 276 1,883.986 290.707 31.000 1,837.750 2,031.500 2,124.000 CO2Indirect 268 1,819.907 288.631 155.000 1,779.750 1,963.250 2,052.000 CO2Total 324 2,247.133 318.259 218.000 2,181.500 2,410.250 2,524.000 EstimatedCO2 1,009 6,390.063 965.029 80.000 5,961.000 7,017.000 7,559.000 CO2 per Revenue 324 2,080.336 464.205 36.000 2,082.750 2,323.250 2,429.000 ESGscore 1,009 2,913.478 1,421.668 45.000 1,728.000 4,189.000 4,573.000 EmissionsScore 1,009 3,140.448 1,565.400 4.000 1,800.000 4,449.000 4,860.000 Price - Trade 1,037 5,100.189 2,776.566 40.000 2,381.000 7,650.000 8,100.000 Dividend Yield 1,037 193.275 248.919 1.000 1.000 287.000 976.000 Price-Earnings 805 299.088 310.984 1.000 92.000 438.000 1,268.000 Market Value 1,037 12,479.120 1,126.968 223.000 12,001.000 13,136.000 13,704.000 Price-To-Book 1,031 525.333 533.705 4.000 173.500 685.000 1,887.000
Debt Per Total Capital 1,043 3,845.859 2,651.032 16 1,163.5 6,760 7,379 Beta 1,036 7,699.916 3,015.401 229.000 5,620.750 9,847.250 10,341.000 Volatility 923 1,830.658 1,237.808 20.000 587.000 2,945.000 3,977.000 Capital Inves. Per Total Assets 1,000 627.671 617.317 1.000 138.000 892.250 2,306.000 Industry Avg CO2/Market Value 928 0.152 0.012 0.066 0.150 0.157 0.182
B
Ilhan Methodology
Table B1: Ilhan methodology for the Paris agreement. The dummy variable top10 indicates whether the underlying firm’s industry is among the ten most carbon intense industries in the sample. Post Agreement is another dummy variable that indicates whether the datapoint is taken before (0) or after (1) the agreement was signed. Standard errors are two-way clustered by firm and date.
Dependent variable: slope
top10 × Post Agreement 0.083
(0.086) top10 −0.277 (0.106) Post Agreement −0.016 (0.081) ‘Price - Trade‘ −0.0001 (0.00002) ‘Dividend Yield‘ −0.0001 (0.0001) ‘Price-Earnings‘ 0.00000 (0.0001) ‘Market Value‘ −0.00004 (0.00004) ‘Price-To-Book‘ −0.0001 (0.0001)
‘Debt Per Total Capital‘ −0.00002
(0.00001)
Beta 0.00002
(0.00001)
Volatility −0.00002
(0.00004) ‘Capital Inves. Per Total Assets‘ −0.00003 (0.0001) Constant 1.391 (0.464) Observations 10,967 R2 0.004 Adjusted R2 0.003 Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
Table B2: Ilhan methodology for the Trump election. The dummy variable top10 indicates whether the underlying firm’s industry is among the ten most carbon intense industries in the sample. Post Election is another dummy variable that indicates whether the datapoint is taken before (0) or after (1) president Trump was elected. Standard errors are two-way clustered by firm and date.
Dependent variable: slope
top10 × Post Election 2.672
(2.601) top10 −1.312 (1.529) Post Election −2.538 (2.127) ‘Price - Trade‘ 0.00002 (0.0002) ‘Dividend Yield‘ 0.007 (0.007) ‘Price-Earnings‘ −0.001 (0.002) ‘Market Value‘ −0.0001 (0.0002) ‘Price-To-Book‘ −0.0001 (0.0004)
‘Debt Per Total Capital‘ −0.001
(0.0005)
Beta 0.0002
(0.0002)
Volatility −0.001
(0.001) ‘Capital Inves. Per Total Assets‘ −0.001 (0.002) Constant 6.985 (3.074) Observations 9,520 R2 0.001 Adjusted R2 −0.0003 Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01 Standard errors in parentheses
