Bob Litterman, Kent Daniel & Gernot Wagner* CFEM/GRI New York March. 15, 2017 APPLYING ASSET PRICING THEORY TO CALIBRATE THE PRICE OF CLIMATE RISK *Kepos Capital; Columbia Business School & NBER; and Harvard-Paulson School
Bob L i t terman,
Kent Daniel &
Gernot Wagner*
CFEM/GRI
New York
March. 15 , 2017
APPLYING ASSET
PRICING THEORY TO
CALIBRATE THE PRICE
OF CLIMATE RISK
* K e p o s C a p i t a l ; C o l u m b i a B u s i n e s s S c h o o l & N B E R ; a n d H a r v a r d - P a u l s o n S c h o o l
Provides 3 Lessons for addressing Climate Risk
FINANCIAL RISK MANAGEMENT:
2
Risk management requires
consideration of worst case
scenarios
A growing risk is an urgent
priority; time is of the
essence
The purpose of risk
management is not to
minimize risk, it is to price
risk appropriately
JOHNSTOWN, PA, CIRCA 1888
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JOHNSTOWN FLOOD — MAY 31, 1889
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We lay out a (very simple) model that captures the risks and uncertainty surrounding climate change.
The model incorporates a GHG emissions -> Levels->Temperature -> Damage Function that incorporate uncertainty, along with features such as climate tipping points, technological change, and backstop technologies.
We use Epstein-Zin preferences consistent with observed asset-price and consumption dynamics.
Caveat: while we calibrate our cost and damage specifications to the climate science literature, many aspects of these specifications are sti l l very ad-hoc.
With further progress in understanding the uncertainty by climate scientists, this model can be greatly refined.
WHAT WE DO
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What th is model at tempts to capture is the l ink f rom emiss ions ->atmospher ic concentrat ions ->temperature changes ->damages.
We calibrate each of these links to estimates from the climate literature , as I’ll describe .
In th is model , the only way that soc iety can af fect the consumpt ion damages is v ia mit igat ion/abatement .
x t is the fraction of the flow of emissions that are mitigated at time t.
However, mit igat ing is cost ly – i t lowers consumpt ion today.
The agent chooses a leve l of mit igat ion today (and at each point in the future ) not knowing the model l inking emiss ions ->concentrat ions ->∆T ->damages .
The only uncer ta inty in our model is the re lat ion between GHG concentrat ion and future consumpt ion damages.
We characterize the model uncertainty with a latent variable q t ,which the agent learns over time.
Mit igat ing today has a greater marg inal benef i t when the real ized damage funct ion turns out to be bad
The marginal utility of consumption is also higher in these states.
Thus , h igher r isk avers ion resul ts leads to h igher mit igat ion.
THE BASIC MODEL
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With a few notable exceptions, preferences used in climate studies have been standard isoelastic or power utility functions, with low levels of implied risk-aversion.
As is well known in the macroeconomics and finance l iterature, these utility functions have dif ficulty reconciling the behavior of consumption and asset prices.
See, among others, Mehra and Prescott (1985), Weil (1989), and Hansen and Jagannathan (1997).
For example Stern (2007)
selects an IMRS/risk-aversion
coefficient consistent with an
equity premium of 0.12%/year.
* F ig u r e f ro m A n t h o f f , To l , a n d Yo h e ( 2 0 09) .
THE IMPORTANCE OF RISK
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A consistent 475 basis points per year for the last 140 years
THE HISTORICAL EQUITY PREMIUM
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THE HISTORICAL EQUITY PREMIUM
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CRRA (Constant Relative Risk Aversion) utility embeds
the assumption that agents’ willingness to substitute
consumption across states of nature is the same as their
willingness substitute consumption over time.
Thus, an increase in the coefficient of risk aversion (or
stated differently, a decreased elasticity of substitution
across states), is necessarily linked to a decreased EIS
(Elasticity of Intertemporal Substitution).
Given the fact that consumption grows at a rate of about
2%/year, an unwillingness to substitute across time
leads to a (counterfactually) high risk-free discount rate.
PREFERENCES:
CRRA VS. EPSTEIN-ZIN UTILITY
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Since consumption damages occur far into the
future, a CRRA utility function with a high level of
risk-aversion (and a reasonable rate of time
preference) necessarily implies a high discount rate
for these damages, and a low SCC.
PREFERENCES:
CRRA VS. EPSTEIN-ZIN
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The macro-finance literature has come to focus on a
set of preference specifications that de-link the IES
and risk-aversion:
Kreps and Porteus (1978); Epstein and Zin (1989, 1991).
Recent work has made considerable progress in
laying out consistent specifications of asset
price/consumption dynamics and preference
specifications:
Bansal and Yaron (2004); Hansen, Heaton, and Li (2008).
PREFERENCE SPECIFICATIONS & ASSET
PRICES
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Following Coase (1960), we’ll assume a setting where there are no property-rights issues.
Markets are complete – no transaction costs.
Therefore, our model is of a representative agent whose preferences are consistent with observed financial market prices.
Heterogeneity not modeled – it is not important in the
model as we assume complete markets.
However, in more realistic settings it would (clearly) play a role.
BASIC SETUP
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BASIC SETUP
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BASIC SETUP
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In our representative-agent setting, agent internalizes
consumption damages, and sets mitigation x t* > 0 each
period so as to maximize lifetime utility.
for (atomistic) agents, who do not internalize the costs of
climate damage, xt* = 0.
To determine the optimal price of carbon, we’ll first solve
for the (socially optimal) level of mitigation the
representative agent would choose (for each state).
We then back out the price of carbon that would induce
(atomistic) agents to choose to mitigate at this level.
BASIC SETUP – CALCULATING THE SCC
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CALIBRATING THE COST FUNCTION
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We use cost estimates from McKinsey ( 2009)—scaled to 2015—fit to a power function.
We assume that all tax revenues are rebated to agents with zero loss (or gain).
Were the revenues used to reduce distortionary taxes, the effective costs would be lower.
Based on the McKinsey study, we construct a
marginal cost curve:
CALIBRATED COST FUNCTION
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However, we also allow for pulling carbon directly out of the atmosphere.
In this illustration the
marginal cost
associated with this
“backstop technology”
is assumed to be $350
for the first ton, rising
to a maximum of
$400/ton.
CALIBRATED COST FUNCTION - WITH
$400 BACKSTOP
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Another governance responsibility
Engagement
International Commercial Aviation Organization ( ICAO) is just now
finalizing a Global Market-Based Measure to reduce emissions in
aviation
This measure will be the first globally harmonized emissions pricing
mechanism
MIT is leading an effort to insure that the incentive created for
airlines appropriately reflects the economic externality created by
emissions
Investors have an interest in getting this right
COST FUNCTION: TECHNOLOGICAL
CHANGE
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21
DAMAGE FUNCTION: UNCERTAINTY
* F r o m R o w l a n d s , e t . a l . S c i e n c e , 2 5 M a r c h 2 0 1 2 .
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DAMAGE FUNCTION:
23
DAMAGE FUNCTION COMPONENTS
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NON-CATASTROPHIC COMPONENT
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NON-CATASTROPHIC COMPONENT:
TEMPERATURE MODEL
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NON-CATASTROPHIC COMPONENT:
DAMAGE MODEL
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CATASTROPHIC COMPONENT:
TIPPING POINTS
As noted earlier, the non-catastrophic damage function is
based on temperature distributions that result from a number
of climate models.
However, there is additional uncertainty related to the
possibility that all of the models share a common error.
We capture this with the tipping-point component.
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CATASTROPHIC COMPONENT:
TIPPING POINTS
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TOTAL DAMAGE FUNCTION
Probability of a tipping point as a function of peakT:
Base case peakT= 9.
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PROBABILITY OF REACHING A
TIPPING POINT
Cumulative Probability distribution for damages, conditional
on reaching a tipping point, for five levels of disaster_tail :
Base case disaster_tail=13.
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TIPPING POINT DAMAGE DISTRIBUTION
For a given emissions pathway Business as Usual => 1000 ppm CO2
58% Mitigation Pathway => 650 ppm
92% Mitigation Pathway => 450 ppm
In each period 2030, 2060, 2100, 2200, 2300, 2400
Draw from a gamma distribution for temperature
Conditional on temperature Draw from a gamma distribution for damages conditional on
temperature
Also check for a tipping point? If yes, then reduce current and all future consumption by a factor drawn from
a gamma distribution
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MONTE CARLO SIMULATION
Order the outcomes of the Monte Carlo Simulation to create a
distribution of damages at each time, and in each of 32
equally likely states calculate the average damage
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DAMAGES(STATE, TIME, PATHWAY)
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INTERPOLATION:
DAMAGE(STATE,GHG PATHWAY)
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UNCERTAINTY & SOLVING THE MODEL
Base model is 7-periods.
Time between nodes controls rate of information revelation.
note path-dependence; history of mitigation is important.
The representative agent’s preferences are Epstein and Zin
(1989):
36
EZ PREFERENCES
37
RESULTS: CATASTROPHIC DAMAGES
Our calibration yields an
initial price of $40.61/ton.
As new information reveals
that the planet is more/less
fragile, the optimal price
rises/falls
Note also that the price,
after an initial rise, is
expected to fall over time.
38
PRICE
The initial price of $40.61
leads to a mitigation of
42.8%.
The optimal level of future
mitigation is higher if the
climate is found to be more
fragile.
Given this calibration, the
backstop technology is
used in almost all states
after 2100.
Without the availability of
this backstop technology,
the current SCC increases
dramatically. 39
MITIGATION (X t)
Consumption is lower
in the high fragility
state both because
damages are high…
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DAMAGES
…and because the
fraction of consumption
that is dedicated to
mitigation is higher.
Note that the cost of
mitigation is highest
When “good” news
is followed by
“bad” news.
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COST OF MITIGATION
We also examine the effect:
early vs. late resolution of uncertainty
endogenous and exogenous technical change
different backstop technologies
different growth rates
different preference specifications.
costs of delay
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OTHER ANALYSES
One particularly interesting analysis regards the cost of
delay.
In our model we can calculate the cost of a constraint of
not pricing emissions during the first (15 year) period.
This constraint roughly triples the social cost of
emissions–from $40 to $112/ton.
This certainty-equivalent cost to society of this delay is
6% of consumption.
In our alternative “high risk” scenario, the same
constraint similarly causes the SCC to jump from $156 to
$451/ton.
This certainty-equivalent cost to society of the delay, in
this scenario, is 36% of consumption. 43
COST OF DELAY
A n t h o f f , D a v i d , R i c h a r d S J T o l , a n d G a r y W Y o h e , 2 0 0 9 , R i s k a v e r s i o n , t i m e p r e f e r e n c e , a n d t h e s o c i a l c o s t o f c a r b o n , E n v i r o n m e n t a l
R e s e a r c h L e t t e r s 4 , 0 2 4 0 0 2 .
B a n s a l , R a v i , a n d A m i r Y a r o n , 2 0 0 4 , R i s k s f o r t h e l o n g r u n : A p o t e n t i a l r e s o l u t i o n o f a s s e t p r i c i n g p u z z l e s , T h e J o u r n a l o f F i n a n c e 5 9 ,
1 4 8 1 – 1 5 0 9 .
C o a s e , R o n a l d H a r r y , 1 9 6 0 , T h e p r o b l e m o f s o c i a l c o s t , J o u r n a l o f L a w a n d E c o n o m i c s 3 , 1 – 6 9 .
E p s t e i n , L a r r y , a n d S t a n l e y Z i n , 1 9 8 9 , S u b s t i t u t i o n , r i s k a v e r s i o n , a n d t h e t e m p o r a l b e h a v i o r o f c o n s u m p t i o n g r o w t h a n d a s s e t r e t u r n s I : A
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, 1 9 9 1 , S u b s t i t u t i o n , r i s k a v e r s i o n , a n d t h e t e m p o r a l b e h a v i o r o f c o n s u m p t i o n g r o w t h a n d a s s e t r e t u r n s I I : A n e m p i r i c a l a n a l y s i s ,
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H a n s e n , L a r s P . , J o h n C . H e a t o n , a n d N a n L i , 2 0 0 8 , C o n s u m p t i o n s t r i k e s b a c k ? m e a s u r i n g l o n g - r u n r i s k , J o u r n a l o f P o l i t i c a l E c o n o m y 1 1 6 ,
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5 5 7 – 5 9 0 .
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E c o n o m e t r i c S o c i e t y 4 6 , 1 8 5 – 2 0 0 .
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M e h r a , R a j n i s h , a n d E d w a r d C . P r e s c o t t , 1 9 8 5 , T h e e q u i t y p r e m i u m : A p u z z l e , J o u r n a l o f M o n e t a r y E c o n o m i c s 1 5 , 1 4 5 – 1 6 1 .
44
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REFERENCES II