Eduardo Schwartz KBL 12 Slides

8/10/2019 Eduardo Schwartz KBL 12 Slides

1/89

ChallengesandOpportunities

UCLA

Anderson

SchoolKarlBorch Lecture:May2012


2/89

MinesandOilDeposits

ForestryResources

ExpropriationRisk

in

Natural

Resources

Internet

Companies InformationTechnology


3/89

BasicideasaboutRealOptionsValuation

Naturalresourceinvestmentsandthe

stoc astic

e avioro

commo ity

prices

ResearchandDevelo mentInvestments


4/89

BasicIdeasaboutRealOptions


5/89

financialoptionstheorytooptionsonreal(non

financial

assets

Optionsarecontingentdecisions Give the o ortunit to make a decision after ou see

howevents

unfold

Payoffisusuallynotlinear

RealOptionvaluationsarealignedwithfinancial

marketvaluations

Ifpossibleusefinancialmarketinputandconcepts


6/89

respondtoit(flexibility)arethesourceof

Whennottouserealoptions:

en

t ere

are

no

opt ons

at

aWhenthereislittleuncertainty

Whenconsequencesofuncertaintycanbe

ignored Mostprojectsaresubjecttooptions

valuation


7/89

1.Optiontoexpandaproject:

theoptiontodevelopanewproject.

2.

Optionto

postpone

investment:

,

mightnotbeoptimaltoexercisetheoption

,

informationinthefuture(valuationof

mines).


8/89

3. Optiontoabandon:

,

alwayshavetheoptiontoabandonitifweare

.4. Optiontotemporarilysuspendproduction:

openandclosefacility.


9/89

Tra t ona

Va uat onToo s

D F

Requireforecasts

generallyused

rate

when

options

(e.g.,

exit

option)

are

Futuredecisionsarefixedattheoutset

no ex y or a ng ec s ons ur ng ecourseoftheinvestmentproject


10/89

Letsfirstlookatoneaspectofthenew

a roach Traditionalvs.CertaintyEquivalentapproach

Optionsalittlelater


11/89

Riskadjusteddiscountrate

N

tCCNPV

t k1 )1(

expected

cash

flow

in

period

ttCk riskadjusteddiscountrate


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N tCEQ

tt

fr10

)1(

exchanged

for

risky

cash

flow

(market

based)

t


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ConsiderasimplifiedvaluationofaMineor

OilDe osit

Themainuncertaintyisinthecommodity

exist(copper,gold,oil)

BrennanandSchwartz(1985)


14/89

.

TraditionalValuation:

N

t

tttN

t

tt CostSqCCostv

CNPV 00Re

N CostF

tt

fr10

)1(


15/89

CoxandRoss(1976),HarrisonandKreps(1979)and

Harrisonand

Pliska

(1981)

show

that

the

absence

ofarbitrageimplytheexistenceofaprobability

distributionsuchthatsecuritiesarepricedattheir

discounted(at

the

risk

free

rate)

expected

cash

flows

underthisriskneutralorriskadjustedprobabilities

(Equivalent

Martingale

Measure).

Adjustmentfor

risk

is

in

the

probability

distribution

of

cashflowsinsteadofthediscountrate(Certainty

EquivalentApproach).


16/89

hedged)theseprobabilitiesareunique.

mar etsarenotcomp etet eyarenot

necessarilyunique

(any

of

them

will

eterminet esamemar etva ue .

Futures ricesareex ectedfutures ot

pricesunder

this

risk

neutral

distribution.

.

T

][ 00 T

ttrQ

XeEVf


17/89

OptionPricingTheoryintroducedthe

conceptof

pricing

by

arbitrage

methods.

Forthepurposeofvaluingoptionsitcanbe

assumedthatthe

ex ected

rate

of

return

on

thestockistheriskfreerateofinterest. Then,

(underthe

new

distribution)

can

be

.

the

market

is

complete

and

the

EMM

is

unique.


18/89


19/89

UsingtheRiskNeutralFrameworktovalue

projectsallows

us

to

Usealltheinformationcontainedinfutures

riceswhen

these

rices

exist

Takeintoaccountalltheflexibilities(options)

Usethepowerfulanalyticaltoolsdevelopedin

contingentclaimsanalysis


20/89

BlackScholesworld

, ,ofthisworld

F =S 1+r T,


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Trueandriskneutralstochastic

processfor

Gold

prices

dS

0 dtNdz

zS

~

~zdrdtS

,


22/89

Ris neutra istri utioncan eo taine rom

futuresprices

or

other

traded

assets

Coppermine,oildeposits

Futureprices

are

available

only

for

short

time

Copperminescanlast50years!

Themodelsfitpricesanddynamicsverywell

formaturitiesofavailablefutures rices


23/89

Nee anequi i riummo e CAPM too tain

riskneutral

distribution

because

there

are

no

futuresprices

R&Dprojects

Internetcompanies

Informationtechnolo


24/89

ummary:

ea

p ons

a ua on Formanyprojects,flexibilitycanbeanimportant

componentof

value

Theoptionpricingframeworkgivesusapowerfultooltoanalyzethoseflexibilities

Thereal

options

approach

to

valuation

is

being

appliedinpractice

Theapproachisbeingextendedtotakeintoaccountcompetitiveinteractions(impactofcompe on

on

exerc se

s ra eg es


25/89

SolutionProcedures


26/89

DynamicProgrammingapproach

aysoutposs e utureoutcomesan o s

backthevalueoftheoptimalfuturestrategy

binomialmethod

widelyusedofpricingsimpleoptions

goodforpricingAmericantypeoptions

notso

good

when

there

are

many

state

variables

or

therearepathdependencies

Needtousetheriskneutraldistribution


27/89

Partia i erentia equation PDE

hasclosed

form

solution

in

very

few

cases

BSequationforEuropeancalls

generallysolvedbynumericalmethods

veryflexible

goodforAmericanoptions

forpathdependenciesneedtoaddvariables

notgoodforproblemswithmorethanthreefactors

technicallymoresophisticated(needtoapproximateboundaryconditions)


28/89

mu a onapproac averagesthevalueoftheoptimalstrategyatthe

decision date for thousands of ossible outcomes

verypowerfulapproach easilyappliedtomultifactormodels

rec yapp ca e opa epen en pro ems

canbe

used

with

general

stochastic

processes

intuitive,transparent,flexibleandeasilyimplemented

Butitisforwardlooking,whereasoptimalexerciseof

Americano tions

has

features

of

d namic

programming


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ValuingAmericanOptionsbySimulation:A

simpleleast

squares

approach

Thisconditionalexpectationisthekeytobeingable

tomake

o timal

exercise

decisions.

Mainideaoftheapproachisthattheconditionalex ectedvalueofcontinuationcanbeestimated

fromthe

cross

sectional

information

from

the

simulationbyleastsquares.

30


31/89

ValuingAmericanOptionsbySimulation:A

simpleleast

squares

approach

eest matet econ t ona expectat on unct on yregressingdiscountedexpostcashflowsfrom

valuesofthestatevariables.

isan

efficient

estimator

of

the

conditional

.estimatetheoptimalstoppingrulefortheoption,

andhence

its

current

value.


32/89

NaturalResourceInvestments


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Firstpaperoncommodities1982:ThePricingof

Commodity

Linked

Bonds,

bonds

in

which

the

payout(couponand/orprincipal)islinkedtothe

priceofacommodity(oil,copper,gold)

In1985,

Evaluating

Natural

Resource

Investments

(withM.Brennan),mineandoildepositscouldbe

interpretedandvaluedascomplexoptionsonthe

underlying

commodities.

One

of

the

first

papers

on

RealOptions.


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Assumedstochasticprocessforcommodityprices

.

forgoldbutnotforothercommodities.

Assumptionnotsatis actory ecausesupp yan

demandadjustmentsinducemeanreversionincommo ty

pr ces


35/89

Inthenext30yearsIwrote(aloneandwith

coauthors)

many

articles

trying

to

make

more

realisticassumptionsabouttheprocessfollowedby

commodityprices.Includingaboutelectricityprices

where

seasonality

is

important PresidentialaddresstotheAFA(1997)onThe

StochasticBehaviorofCommodityPrices:

Implications

for

Valuation

and

Hedging


36/89

ThreeFactorModel:Actual

(Cortazarand

Schwartz

(2003))

SdzSdtdS

33 za


37/89

111

222 z

*

333 zta

We need to make assumptions about the functional

orm o e mar e pr ces o r s s


38/89

Oil Futures 01/08/99

Three-Factor Model30.00

25.00

15.00

20.00

e(US$)

Observed

Model

10.00

Pri

0.00

5.00

0 1 2 3 4 5 6 7 8 9 10

Maturity (Years)


39/89

Oil Futures 10/12/00

Three-Factor Model

35

25

30

)

Observed

Model

15

20

Price

(US

10

0

0 1 2 3 4 5 6 7 8 9 10

a ur y ears


40/89

Acceptthemodelpredictionsformaturities

wherethere

are

no

futures

rices?

Maybeafewyearsonly?

Assume at uturesprices

Assumefutures ricesincreaseatafixedrate

(inflation?)?

nce

ere

smore

uncer a n y

n

sarea,

whatdiscountratetouse(riskfreerate?)?


41/89

TworecentpaperswithAndersTrolle

Unspanned stochasticvolatilityandthepricingof

commodit derivatives 2009

Pricingexpropriation

risk

in

natural

resource


42/89

Extenttowhichvolatilityisspannedbyfutures

Arecommodityoptionsredundantsecurities?

Critical

for

pricing,

hedging

and

risk

management

of

commodityoptionsandrealoptions

Weanalyzetheseissuesinthecrudeoilmarketand

develop

a

new

model

for

pricing

commodity

derivativesinthepresenceofunspannedstochastic

volatility


43/89

marketintheworld

arges rangeo ma ur esan s r epr ces,w c varysignificantlyduringthesampleperiod

DailydatafromJan2,1990toMay18,2006

Wechoosethe12mostliquidcontractsforthe

analysis M1,M2,M3,M4,M5,M6(first6monthly

contracts)

Q1,

Q2

(next

two

quarterly

contracts

expiringinMar,Jun,SeporDec) Y1,Y2,Y3,Y4(next

fouryearlycontractsexpiringinDec)


44/89


45/89


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Ifweregresschangesinvolatilityonthereturnsof

futures

contracts

(or

its

PC),

the

R2

will

indicate

the

extenttowhichvolatilityisspanned

Butvolatilityisnotdirectlyobservable

Returnon

Straddles:

Call

+Put

with

the

same

strike

closesttoATM lowdeltasandhi hve as.

Modelindependent

expectedvolatilityoverthelifeoftheoption


47/89

Wefactoranalyzethecovariancematrixofthe

futuresreturnsandretainthefirstthreeprincipal

components

(PCs) Regressstraddlereturns(changesinimplied

volatilities onPCsandPCss uared

WefindthattheR2aretypicallyverylow,especiallyfortheimpliedvolatilityregressions(between0and

21%)


48/89

Thus,factorsthatexplainfuturesreturnscannot

explain

changes

in

volatility Wethenfactoranalyzethecovariancematrixofthe

residualsfromtheseregressions.Ifthereis

unspanned

stochastic

volatility

in

the

data

we

should

seelargecommonvariationintheresiduals

WefindthattypicallythefirsttwoPCexplainover

80%of

the

variation

in

the

residuals


49/89


50/89

Pricing expropriation risk in natural


51/89

Pricingexpropriationriskinnatural

resourcecontracts

ConferenceonTheNaturalResourcesTrap,Private

InvestmentwithoutPublicCommitment(Kennedy

School,Harvard)

Therearemanydimensionstothestudyof

expropriation

risk

in

natural

resource

investments:

political,environmental,sociological,economic

Inourapproachweabstractfrommanyofthese

issuesand

we

concentrate

on

some

of

the

im ortant

economictradeoffsthatarisefromagovernment

havin ano tiontoex ro riatetheresource


52/89

xpropr a on

p on Wevalueanaturalresourceproject,inparticularan

oilfield

ex osed

to

ex ro riation

risk

Weviewthegovernmentasholdinganoptionto


53/89


54/89

Weabstract

from

the

various

o erational

o tions

thataretypicallyembeddedinnaturalresource

ro ectsandconcentrateontheex ro riationo tion

Spotprices,

futures

prices

and

volatilities

are


55/89

Expropriationoptioncanbeexercisedatanytimeduringthe

lifeoftheoption:Americanstyle(LSM)

everypo n

n

me

egovernmen

mus

compare

e

valueofimmediateexercisewiththeconditionalexpected

Outcomeis

the

optimal

exercise

time

for

each

simulated

path

whichcanbeusedtovaluetheex ro riationo tion

Wecanalsoestimatethevalueoftheoilfieldtothe

governmentandthefirmbothinthepresenceandabsenceof

expropriationrisk

Main Results


56/89

MainResults For

agiven

contractual

arrangement

the

value

of

the

expropriationoptionincreaseswith

Thespotprice

Theslope

of

the

futures

curve

(contango,

backwardation)

Thevolatilityofthespot(futures)price

Foragivensetofstatevariablesthevalueofthe

expropriationoptiondecreaseswiththe

Taxrate

Variousexpropriationcosts

Theincreaseinthefieldsvaluetothegovernmentdueto

expropriationriskisalwayssmallerthanthedecreaseinthefieldvaluetothefirms,sincetherearedeadweightlosses

assoc a e w expropr a on pro uc on ne c encyan

reputationalcosts)


57/89


58/89

ep armaceut ca n ustry as ecomearesearc orientedsectorthatmakesamajorcontributionto

.

Thesuccessoftheindustryingeneratingastreamof

createdan

intense

public

policy

debate

over

issues

thefinancingofthecostofresearch

the

rices

char ed

for

its

roducts

thesociallyoptimaldegreeofpatentprotection


59/89

Thereis

atrade

off

between

promoting

marketoutcomes.

duringthelifeofthepatentcompensatetheinnovatorforitsrisk investment.

Theonset

of

competition

after

the

expiration

of

the atentlimitsthedeadwei htlossestosociet thatarisefrommonopolypricingunderthepatent.

Regulationhashadimportanteffectsonthecostofinnovationinthepharmaceuticalindustry.

AnalysisofR&Dprojectsisaverydifficult


60/89

investmentproblem

a esa ongt metocomp ete

Uncertaintyaboutcostsofdevelopmentandtimetocomp et on

Highprobabilityoffailure(fortechnicaloreconomicreasons

Drugrequires

approval

by

the

FDA

Uncertaintyaboutlevelanddurationoffuturecashflows

Abandonmentoption

is

very

valuable


61/89


62/89

Research Spending Per New Drug

Total R&D

-Company Ticker

drugs approved

Per Drug ($Mil)

2011 ($Mil)

AstraZeneca AZN 5 11,790.93 58,955

GlaxoSmithKline GSK 10 8,170.81 81,708

Sano i SNY 8 7,909.26 63,274

RocheHoldingAG RHHBY 11 7,803.77 85,841

Pfizer Inc. PFE 14 7,727.03 108,178

Johnson &

Johnson JNJ 15 5,885.65 88,285Eli Lilly & Co. LLY 11 4,577.04 50,347

oLaboratories ABT 8 4,496.21 35,970

Merck & Co Inc MRK 16 4,209.99 67,360

Bristol-MyersSquibb Co. BMY 11 4,152.26 45,675

Novartis AG NVS 21 3,983.13 83,646

Amgen Inc. AMGN 9 3,692.14 33,229

ources: nno n en er or esearc n ome ca nnova on; omsonReuters Fundamentals via FactSet Research Systems

PfizerYouthPillAteUp$71MillionBefore


63/89

ItFlopped

: ay ,

Theexperimentaldrugaimedtoreversethephysicalec ne

t at

comes

w t

ag ng.

Nearlyadecadeofresearch.

Patientstakingthefrailtydrughadgainedsomemuscle

mass

but

less

than

3%

more

than

the

p ace ogroup w c a soexper ence musc eincrease.

rugappeare

ne ect ve.

Medivation,Pfizerendworkon


64/89

AlzheimersDrug

WSJ January18,2012

upfront andupto$500millionifsuccessful

.

Some5.4

million

in

the

US

and

18

million

worldwideareestimatedtohaveAlzheimers

reach$25billionperyear


65/89

MostprescribednamebrandintheUSwith

3.5

million

eo le

takin

it

ever

da Enterthemarketin1997andlosspatent

.

salesof

$81

billion

But(WSJMay2,2112),Pfizer'sfirstquarter

rofit declined 19% as sales of its to roduct

Lipitor,tumbled71%intheU.S.amid

.


66/89

1. EvaluationofResearchandDevelopment

Investments(withM.Moon,2000)

2. PatentsandR&DasRealOptions(2004)

3. R&D Investments with Com etitive Interactions

(withK.

Miltersen,

2004)

.

ResearchIncentives(withJ.Hsu,2008)


67/89

Patentsand

R&D

as

Real

Options

MethodologyforthevaluationofasingleR&D

Orequivalently,fordeterminingthevalueofapatent


68/89

TreatthepatentprotectedR&Dprojectorthepatentasacomplexoptiononthevariablesunderlyingthevalueoftheproject

expectedcoststocompletion

anticipatedcashflows

Uncertainty

is

introduced

in

the

analysis

by

allowing

thesevariablestofollowstochasticprocessesthroughtime

Theriskadjustedprocessforthecashflowsisobtained

using

the

beta

of

traded

pharmaceutical

companies


69/89

pro ec a es me ocomp e e

Maximumrateofinvestment

Totalcosttocompletionisrandomvariable

Probabilit of failure catastro hic events

Optionto

abandon

the

project

en,an ,pro ec scomp e e cas ows

starttobegenerated

Cashflows

are

uncertain

(level

and

duration)

ProjectispatentprotecteduntiltimeT


70/89

-

Receive C

Invest K at rate ITerminal value

0 T


71/89

Expectedcosttocompletionfollows(technicaluncertainty):

dzIKIdtdK 2)(

Varianceof

cost

to

completion:

2

22

2

)~

(

K

KVar


72/89

CashflowratefollowsGeometricBrownianmotionwhich

CdwCdtdC

Riskadjustedprocessusedforvaluation:

CdwCdtCdwCdtdC *

ValueofProjectonceInvestmenthas


73/89

beenCompleted:

V(C,t)

0*

1 22

CrVVCVVC

CTCV

Hassolution:

**C

*,

r

oc as c process or e rue re urn on e


74/89

oc as cprocess or e rue re urnon e

projectonce

investment

is

completed

dwdtrV

)(

Volatilityand

risk

premium

are

the

same

as

for

cash

flows.

m

ValueoftheInvestment


75/89

Opportunity:F(C,K,t)

*)()(

11

[

2

1

222 CFFIKCFIKFCMax

CCKKKCCI 0])( IFrFIF tK

Subjectto

boundary

condition

at

completion

of

investment:

),(),0,( CVCF

Problem with this is that time of com letion is random.

Simulated Paths of Cost to Completion and Quarterly Cash Flow


76/89

Simulated Paths of Cost to Completion and Quarterly Cash Flow

120 9

1007

8

Investment is completed

and Cash Flows start

Ant icipated Cash Flows

80

5

6

40 3

4

Realized Cash Flows

201

2Cost to Completion

0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0

Cost to Completion Distribut ion


77/89

Cost to Completion Distribut ion

9000

7000

8000

5000

6000

3000

40002.3% reach

patent expiration

1000

2000

35 55 75 95 115 135 155 175 195

Cost to Completion

Figure 4:

Critical Values for Investment


78/89

18.00

16.00

17.00

13.00

14.00

.

FlowR

ate Invest at Maximum Rate

11.00

12.00

C

ash

Do not Invest

Pro ect Value E ual 0

9.00

10.00

.80.00 85.00 90.00 95.00 100.00 105.00 110.00 115.00 120.00

Cost to Completion

R&DInvestmentswithCompetitiveInteractions


79/89

(joint

with

K.

Miltersen) oncen ra esoncompe ve n erac onsan e

effectithasonvaluationandoptimalinvestment

Realoptionsframeworkisextendedtoincorporategametheoreticalconcepts

TwofirmsinvestinginR&Dfordifferentdrugsbothtargeted

to

cure

the

same

disease

Ifbothfirmssuccessful:Duopolyprofitsinmarketingphase. Butitcanaffectdecisionsindevelopment

.outcomeinmarketingphase


80/89


81/89


82/89

Competition ringsa out

Higherproductionatlowerprices

Higherprobabilityofsuccess

Shorteravera edevelo menttime

Butwith

higher

total

development

costs

and


83/89


84/89


85/89


86/89

Whats new in this paper?

QualityoftheR&Doutputismodeledexplicitly

thequality

thefirmspricing(andquantity)strategy

Marketdemand

Firmspriceandquantitystrategycoulddependon

Monopolypower


87/89

us on rac s:

Fulldiscretionaryresearchgrant

Sponsorcopayment

Pull Contracts:

Extendedpatent

protection

xe pr cepurc asecomm men

Variablepricepurchasecommitment

on rac pec cs


88/89

Developerretainsright,suppliesmonopolyquantity

Fulldiscretionaryresearchgrant

Sponsorcopayment

Patentextension

Sponsor

can

contract

the

socially

optimal

quantity

tobe roduced

Purchasecommitmentcontracts

asymmetricinformationbetweenvaccinedevelo erands onsor andfromcontractin issues


89/89

at st erequ re eve o monetary ncent vetoinducethefirmtoundertakethevaccineR&D?

atare

t e

expecte

pr ce,

quant ty

supp e

an

efficacyofthedevelopedvaccine?

at st epro a tyt atav a evacc new e

developed? at st econsumersurp usgenerate

Whatistheexpectedcostperindividualsuccessfully

vacc nate

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Eduardo Schwartz KBL 12 Slides

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