This document discusses the concept of a "carbon bubble" where fossil fuel companies may be overvalued because climate policies have not accounted for the need to limit carbon emissions to avoid dangerous global warming. The document estimates that to have a 50% chance of staying below 2°C of warming, only around 270-350 gigatons of carbon can still be emitted, yet worldwide fossil fuel reserves approved for development total around 760 gigatons. If strong climate policies are adopted, most reserved fossil fuels would be "stranded assets" that cannot be burned, potentially popping this carbon bubble and lowering stock prices in high-carbon industries.

1. Popping the Carbon Bubble
Michael Diamond
Teaching Assistant, EES 201
November 13, 2013
Contents
1 Introduction 1
2 Staying below the 2◦C target 2
2.1 BaU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 UN-H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 UN-M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.4 UN-L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Other targets 5
4 Carbon capture & storage 6
5 Stranded assets 6
6 Conditions for a carbon bubble 7
7 TL;DR 8
1 Introduction
In the Copenhagen Accord of 2009 and the Cancun Agreements of 2010,
the majority of the world’s governments agreed to set a target limiting an-
thropogenic warming to 2◦C from preindustrial times. Meeting this target
implies setting an upper limit on the amount of fossil fuels that can be
burnt — this limit can be thought of as a “carbon budget.” In the past few
years a number of estimates have been made about the size of the world’s
carbon budget, making different assumptions about the growth of non-CO2
1

2. greenhouse gas emissions and the climate sensitivity. One of the first or-
ganizations to try quantifying the carbon budget was the Carbon Tracker
Institute, a UK-based non-profit dedicated to aligning capital markets with
a climate change policy agenda. Its most recent report,1 released in 2013
in collaboration with the Grantham Research Institute on Climate Change
and the Environment at the London School of Economics and Politics, is
referenced here. Additionally, the latest version of the Intergovernmental
Panel on Climate Change’s (IPCC) report2 on the state of climate science
also includes estimates of the remaining carbon budget, which has brought
more mainstream attention to carbon budgeting and the idea of the “carbon
bubble.”
The idea behind the carbon bubble is that fossil fuel companies and other
carbon-intensive industries may currently be overvalued in capital markets
because the impact of climate policy has not been adequately priced. Staying
within any of the carbon budget scenarios calculated by institutions like the
IPCC require that a large portion of coal, oil, and gas reserves that are
already on the books will need to stay in the ground. Those worried about
a carbon bubble fear that once investors at large realize that much of what is
currently listed as assets will never be burned, fossil fuel stocks will plummet
in an event reminiscent of the 2008 financial crisis.
How likely is it that the carbon bubble exists, and if it does exist, when
will it pop? No one knows the exact answer to these questions, but we can
start thinking about the problem using the concepts and techniques we have
already learned in this course.
2 Staying below the 2◦
C target
In this section, we will explore how long it would take to exhaust the car-
bon budget if emissions were to grow as the EIA predicts in its reference
case.3 The parameters P, G, E, F, g, e, and f are the same as those used in
the Decarbonization Project Assignment. We will additionally define three
1
Carbon Tracker & The Grantham Research Institute, LSE, Unburnable Carbon 2013:
Wasted capital and stranded assets., 2013
2
IPCC Fifth Assessment Report, Climate Change 2013: The Physical Science Basis
Summary for Policymakers, September 27, 2013.
3
U.S. Energy Information Administration, International Energy Outlook 2013. Choose
“Kaya Identity Components” under Subject Filter and “World population by region”
under Table.
2

3. random4 variables: X, Y, and Z. Let X be the total amount of warming,
measured in ◦C, since the preindustrial era; let Y be year; and let Z be the
carbon budget. Z is measured in GtC (gigatons of carbon) in the IPCC
report and GtCO2 (gigatons of carbon dioxide) in the EIA and Carbon
Tracker reports. The conversion between GtC and GtCO2 is 1 GtC = 12
44
GtCO2.
From the IPCC report, we can see that to keep warming below 2◦C with
a 33% likelihood of success, the carbon budget would have to be set at 350
GtC. For a 50% probability of success, the budget would have to fall to 310
GtC, and for a 67% probability, to 270 GtC. We can consider these chances
to be high-risk, medium-risk, and low-risk, respectively.
Now let’s define a few scenarios for different values of Z (this is similar
to having different emissions scenarios). Let BaU be the Business-as-Usual
scenario, UN-H be a scenario following the IPCC’s high-risk carbon budget,
UN-M be a scenario following the IPCC’s medium-risk carbon budget, and
UN-L be a scenario following the IPCC’s low-risk carbon budget.
2.1 BaU
For BaU, let’s assume that no action is taken to meet the 2◦C target. Thus,
there is no limit on the carbon that can be burned and no chance of a
carbon bubble, or at least a policy-fueled bubble. Although carbon-intensive
industries would be fine in this scenario, climate-sensitive industries could
suffer.
Using the EIA’s Kaya identity parameters, we can calculate the pre-
dicted growth rates of carbon dioxide emissions that we’ll need for the rest
of the scenarios:
F(2011) = P(2011) x g(2011) x e(2011) x f(2011)
F(2011) = 6,957 x 106 people x 10,515 2005$ per person x 7.33 x 103 BTU
per 2005$ x 59.7 x 10−18 GtCO2 per BTU
F(2011) = 32.035 GtCO2 = 8.737 GtC
rF = rP + rg + re + rf
rF = .008 + .028 - .020 - .002
rF = .014
4
In probability theory, random means “subject to chance or uncertainty” rather than
“arbitrary.”
3

4. 2.2 UN-H
In the formal language of probability theory, we could express “the prob-
ability that warming stays below the 2◦C target given a carbon budget of
350 GtC is 33%” as:
Pr(X ≤ 2|Z = 350) = .33
In order to find out when the carbon budget would run out given the
EIA estimates, we need to add each year’s emissions past 2011 (the latest
year for which the EIA has data) until the cumulative sum is equal to Z.
This can be done using methods we learned in class by plugging the formulae
into an Excel spreadsheet. It also possible to find the answer using a simple
integral:
Y
2011
F(2011)erF (Y −2011)
dy = Z
Which becomes:
F(2011)
rF
(erF (Y −2011)
− 1) = Z
Solving this using Z = 350 GtC and the values of F(2011) in GtC and
rF , we get:
8.737
.014
(e.014(Y −2011)
− 1) = 350
Y = 2043
This means that if we were to set a carbon budget of 350 GtC and
did not implement effective climate policies, we would burn through all the
allowable fuel by the year 2043.
2.3 UN-M
Repeating the procedure from UN-H, we get:
Pr(X ≤ 2|Z = 310) = .50
8.737
.014
(e.014(Y −2011)
− 1) = 310
4

5. Y = 2040
To keep warming below 2◦C with a 50% probability, all the fuel that
could be burned under the necessary carbon budget would only last us until
2040 at predicted growth rates.
2.4 UN-L
Repeating the procedure from UN-H and UN-M, we get:
Pr(X ≤ 2|Z = 270) = .67
8.737
.014
(e.014(Y −2011)
− 1) = 270
Y = 2037
To keep warming below 2◦C with a 67% probability, all the fuel that
could be burned under the necessary carbon budget would only last us until
2037 at predicted growth rates.
These numbers show that unless the rate of emissions growth is slowed
dramatically, warming of greater than 2◦C will be inevitable by mid-century.
Decreasing the value of rF would extend the timeframe we have to continue
burning fossil fuels, but would require greater cuts in fossil fuel use in the
near-term.
3 Other targets
Of course, not everyone agrees that 2◦C is a feasible, or even a desirable,
target. In his new book The Climate Casino, William Nordhaus argues that
a better target would be 2.3◦C if mitigation were accomplished through a
Pigouvian tax and up to 4◦C if accomplished through command-and-control
regulations.5 Even if the target warming were higher, however, the basic
logic of a finite carbon budget would not change.
Going in the other direction, there is a strong case that carbon budgets
should be even lower than the IPCC and Carbon Tracker estimates once
non-CO2 factors are taken into account. In a recent letter to the journal
5
Paul Krugman, “Gambling with Civilization,” The New York Review of Books, Vol.
60, No. 17, November 7, 2013.
5

6. Nature,6 a group of climate researchers argue that taking into account the
need to mitigate not only global warming but also impacts such as ocean
acidification and biodiversity loss, more stringent carbon budgets would be
needed to meet multiple goals simultaneously.
Finally, the longer we wait to take action on climate change, the fewer
options we will actually have available. Certain warming targets become
unattainable over time because emissions would need to be reduced by more
than 100% to achieve them. In one study7 published earlier this year on
this topic, the climate scientist Thomas Stocker finds that the 2◦C target
becomes impossible after the year 2044, which is consistent with our calcula-
tions above. When taking into account the economic reality that emissions
reductions above 5% per year are virtually impossible, the 2◦C target is lost
by 2027 barring implementation of a serious mitigation policy.
4 Carbon capture & storage
One way to limit warming while still being able to burn more fossil fuels is
the widespread deployment of carbon capture and storage (CCS) technology
to take CO2 out of the atmosphere directly. Unfortunately, even under the
most optimistic scenarios, CCS cannot make more than a minor impact.
When Carbon Tracker modeled how the carbon budget would expand under
the International Energy Agency’s most optimistic projections, CCS still
only increased the budget by 12-14%.
5 Stranded assets
Now that we’ve seen over what timeframes the carbon budgets would be
exhausted, the next question becomes how these budgets compare with our
reserves of fossil fuels. If the budgets were larger than the reserves we
currently plan to burn, there would be no problem. Unfortunately, the
proven reserves of carbon owned by private companies and governments far
exceeds all of the carbon budgets we have analyzed. Using Carbon Tracker’s
estimates, listed reserves of coal, oil, and gas total total 762 GtCO2 and
listed resources total 1,541 GtCO2. Reserves are economically recoverable
now, whereas resources are expected to be economically recoverable in the
6
Marco Steinacher, Fortunat Joos, and Thomas Stocker, “Allowable carbon emissions
lowered by multiple climate targets,” Nature, Vol. 499, pp. 197-201, July 11, 2013.
7
Thomas Stocker, “The Closing Door of Climate Targets,” Science, Vol. 339, pp.
280-282, January 18, 2013.
6

7. future. In comparison to these numbers, Carbon Tracker calculates that the
carbon budget needed to have a 50% chance of avoiding 2◦C is 269 GtCO2
and 3◦C is 356 GtCO2. Thus, there is already three times as much carbon
in listed reserves as it would take to blow through the 2◦C target, and
there is six times as much carbon in listed resources. Even when using the
more lenient 3◦C target, there is twice as much carbon in reserves and more
than four times as much carbon in resources than can be burned. Making
matters worse, the figures above only include reserves held by publicly listed
companies. Governments (think Venezuela and Saudi Arabia) own about
75% of all reserves, bringing the real total to 2,860 GtCO2, or more than
ten times the carbon budget for 2◦C.
Not only do current reserves exceed the allowable amount that can be
burned, but fossil fuel companies are spending on the order of $6-7 trillion
each year in capital expenditures exploring for new reserves. Traditionally,
fossil fuel companies have been evaluated based on their reserves replacement
ratio (RRR), which is basically a measure of whether reserves are growing
or shrinking. Companies have financial incentives to maintain RRRs over
100%, meaning their reserves will grow. However, if a carbon budget is
enforced, most of those new reserves will become stranded assets — an
economic term meaning that assets that the companies were developing on
the assumption they would have future value turn out to be worthless. Thus,
if emissions reductions are achieved, most of the capital investment that has
went into exploring for new reserves will have been wasted.
6 Conditions for a carbon bubble
The mere existence of stranded assets, however, does not mean that there
will necessarily be a carbon bubble. The Bank of England has identified
three necessary conditions for there to be a true “carbon bubble”:
1. Financial institutions must have a large exposure to the affected stocks
of carbon-intensive industries relative to their total assets.
2. The risk of climate policy stranding carbon-intensive assets must not
be properly priced by the market already, either through lower expected
returns or higher risk premiums.
3. The transition away from fossil fuels must happen so quickly that
companies do not have enough time to adapt and alter their business plans
and institutions do not have enough time to adjust their portfolios.
Arguments could be made for or against the plausibility of any of those
three conditions. Additionally, it is far from certain that a binding treaty
7

8. will emerge from the Paris Climate Conference in 2015 to replace the Kyoto
Protocol or that any other concerted international action will be successful
in limiting global greenhouse gas emissions, potentially making the whole
issue of a carbon bubble a moot point.
Nevertheless, the impacts of a carbon bubble, if one were to burst, should
not be taken lightly. According to one report by the bank HSBC, between
40 and 60% of the market capitalization of certain fossil fuel companies
could be at risk if a stringent carbon budget is adapted.8 Additionally, the
HSBC report casts doubt on the idea that this risk has been sufficiently
priced already, perhaps because it is a long-term risk in a market that tends
toward myopia.
Moreover, the lessons of the financial crash of 2008 do not bode well for a
carbon bubble. The risk posed by subprime mortgage assets seems obvious
in retrospect, and was obvious to a few Cassandras beforehand, but most
market participants were taken by complete surprise. It seems possible,
at the very least, that history could repeat itself with the carbon bubble.
Although it is still too early to say with any confidence when, and whether,
the carbon bubble will pop, in any event the logic of carbon budgeting poses
a real challenge to business-as-usual in resource exploration and extraction
in the fossil fuel industry.
7 TL;DR
If we are to limit global warming to within 2◦C, only a certain amount
of fossil fuel reserves can be burnt. This limit is referred to as a carbon
budget. Based on figures from the latest IPCC report and expected growth
in emissions from the EIA, this budget would be exhausted sometime around
2040 barring ambitious climate policy at the international level. The amount
of carbon fossil fuel companies and resource-rich governments have in reserve
vastly exceeds the carbon budget for 2◦C, meaning these companies could
take a large hit in their stock prices if a carbon budget is enforced. This
could result in the popping of a carbon bubble, hurting investors across
the economy. Although the probability of the carbon bubble popping is
unknown, it is a real risk that should be taken into account by investors and
policymakers.
8
Paul Spedding, Kirtan Mehta, and Nick Robins, “Oil & carbon revisited: Value at
risk from ‘unburnable’ reserves,” HSBC Global Research, January 25, 2013.
8