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

14

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:

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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.

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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.

41

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

42

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

t h e o r e t i c a l f r a m e w o r k , E c o n o m e t r i c a 5 7 , 9 3 7 – 9 6 9 .

, 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 ,

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 9 9 , 2 6 3 – 2 8 6 .

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 ,

2 6 0 – 3 0 2 .

H a n s e n , L a r s P . , a n d R a v i J a g a n n a t h a n , 1 9 9 7 , A s s e s s i n g s p e c i f i c a t i o n e r r o r s i n s t o c h a s t i c d i s c o u n t f a c t o r m o d e l s , J o u r n a l o f F i n a n c e 5 2 ,

5 5 7 – 5 9 0 .

K r e p s , D a v i d M . , a n d E v a n L . P o r t e u s , 1 9 7 8 , T e m p o r a l r e s o l u t i o n o f u n c e r t a i n t y a n d d y n a m i c c h o i c e t h e o r y , E c o n o m e t r i c a : j o u r n a l o f t h e

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 .

M c K i n s e y , 2 0 0 9 , P a t h w a y s t o a l o w - c a r b o n e c o n o m y : V e r s i o n 2 o f t h e g l o b a l g r e e n h o u s e g a s a b a t e m e n t c o s t c u r v e , D i s c u s s i o n p a p e r

M c K i n s e y a n d C o m p a n y . a v a i l a b l e a t h t t p : / / w w w . m c k i n s e y . c o m / c l i e n t s e r v i c e / c c s i / p a t h w a y s _ l o w _ c a r b o n _ e c o n o m y . a s p .

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

REFERENCES I

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E n v i r o n m e n t a l E c o n o m i c s a n d

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l a r g e c l i m a t e m o d e l

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E c o n o m i c s 2 4 , 4 0 1 – 4 2 1 .

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REFERENCES II