health economics series no. 2017-01 - bfi · 2. fda binary options in this section, we consider...

Health Economics Series

No. 2017-01

Sharing R&D Risk in Healthcare via FDA Hedges

Adam Jørring, Andrew W. Lo, Tomas J. Philipson, Manita Singh, and Richard T. Thakor

March 28, 2017

JEL Codes: G11, G12, G13, G22, G23, G31, I18, K23, L65, O32

Keywords: Healthcare Finance, R&D Investments, Drug Development, FDA Approval, Idiosyncratic Risk, Risk Sharing, Hedging

Becker Friedman Institute for Research in Economics

Contact:

773.702.5599 [email protected] bfi.uchicago.edu

SharingR&DRiskinHealthcareviaFDAHedges∗

AdamJørring,1AndrewW.Lo,2TomasJ.Philipson,3

ManitaSingh,4andRichardT.Thakor5

ThisDraft:28March2017

Abstract

Thehighcostofcapitalforfirmsconductingmedicalresearchanddevelopment(R&D)hasbeenpartlyattributedtothegovernmentriskfacinginvestorsinmedicalinnovation.Thisrisk slows downmedical innovation because investors must be compensated for it. Weproposenewandsimplefinancialinstruments,FoodandDrugAdministration(FDA)hedges,to allow medical R&D investors to better share the pipeline risk associated with FDAapprovalwithbroadercapitalmarkets.UsinghistoricalFDAapprovaldata,wediscussthepricingofFDAhedgesandmechanismsunderwhichtheycanbetradedandestimateissuerreturnsfromofferingthem.Usingvariousuniquedatasources,wefindthatFDAapprovalriskhasalowcorrelationacrossdrugclassesaswellaswithotherassetsandtheoverallmarket.Wearguethatthiszero-betapropertyofscientificFDAriskcouldbeamainsourceofgainsfromtradebetweenissuersofFDAhedgeslookingfordiversifiedinvestmentsanddevelopers looking to offload the FDA approval risk. We offer proof of concept of thefeasibilityoftradingthistypeofpipelineriskbyexaminingrelatedsecuritiesissuedaroundmergers and acquisitions activity in the drug industry. Overall, our argument is that, byallowing better risk sharing between those investing in medical innovation and capitalmarketsmoregenerally,FDAhedgescouldultimatelyspurmedicalinnovationandimprovethehealthofpatients.Keywords: Healthcare Finance, R&D Investments, Drug Development, FDA Approval,IdiosyncraticRisk,Risksharing,HedgingJELClassification:G11,G12,G13,G22,G23,G31,I18,K23,L65,O32

∗ We would like to thank Frederico Belo, Mark Egan, Ralph Koijen, Colin Ward, and seminar participants at the Milken Institute for helpful comments and discussions. Any errors are our own. 1UniversityofChicago,BoothSchoolofBusiness2MITSloanSchoolofManagement,CSAIL,andNBER3UniversityofChicago,HarrisSchoolofPublicPolicyandNBER4GoldmanSachsandMITLaboratoryforFinancialEngineering5UniversityofMinnesota,CarlsonSchoolofManagement

15March2017 FDAHedges Page2of41

1. Introduction

Biopharmaceuticalandmedicaldevicecompaniestypicallyinvestverylargeamountsof

moneyinordertodevelopatreatment.Forexample,recentestimatessuggestthatthecost

of developing a single new drug in the biopharmaceutical sector is $2.6 billion (DiMasi,

Grabowski,&Hansen,2014).However,thisdevelopmentprocessisalsoquiterisky,notonly

duetotheinherentscientificriskofdevelopingnewcompoundsforhumans,butduetothe

risk involved in regulatory approval processes as well. Companies undertaking drug

developmentintheU.S.aresubjecttotheFoodandDrugAdministration’s(FDA)approval

process.Asaresult,giventhehighcostofdevelopment, failureduetoeitherscientificor

regulatoryriskduringanypartoftheFDAapprovalprocesscanhaveahighlyadverseimpact

on a company undertaking drug research. Significantly, this risk is borne only by those

investingintheparticulartreatmentunderconsiderationbytheFDAandcannoteasilybe

sharedbyotherinvestorsinthegeneralcapitalmarket.Somehavearguedmoregenerally

thatgovernmentuncertaintyultimately slowsdownmedical innovationandhurts future

patients(Koijen,Philipson,&Uhlig,2016).

To overcome this problem, Philipson (2015a,b) suggested financial instruments that

allow those investing in medical innovation to better share scientific and policy-related

developmentriskswithoutsideinvestors.Wecallthesetypesofinstruments“FDAhedges.”

Inthispaper,wediscussthepricingofFDAhedgesandmechanismsunderwhichtheycan

betradedandestimateissuerreturnsfromofferingthem.Inaddition,weexaminetheirrisk

characteristicsandevaluatesomeuniqueevidencesuggestingaproofofconceptthatthese

riskscanbetradedincapitalmarkets.


If FDA hedges were exchange-traded, there would be direct risk-sharing benefits to

developerswhoareabletolayoffsomedevelopmentriskstootherpartsofcapitalmarkets.

Wethereforeconsiderexchange-tradedFDAbinaryoptions,whichpaya fixedamountof

money in the event of a trigger. Binary options arewell-known and regularly traded on

variousexchanges.6InthecaseofanFDAbinaryoption,thetriggeringeventwouldbethe

failureofaspecificdrug in theFDAapprovalprocess. Weprovidedetailsofhowsucha

binaryoptionwouldbepricedandusehistoricaldataondrugdevelopmentsuccessratesby

phaseanddrugtypetocalculatewhatthetypicalpriceofanFDAbinaryoptionwouldbefor

adrugineachtherapeuticarea.

While the insurance value of FDA hedges is clear to drug developers, the question

remains ofwhat the valuewill be to the issuer. In the absence of exchange-traded FDA

hedges, we consider over-the-counter (OTC) issuers whomight offer a portfolio of FDA

contracts across developers. We simulate the return distribution of such portfolios by

calibratingthedatatohistoricalFDAapprovalratesandestimatetherisk/rewardprofiles

that they imply and how they vary depending on different assumptions related to the

underlyingcontracts.

ApotentialadvantageofFDAhedgestoissuersisthattheyonlydependonpurescientific

riskanddonotaimtoinsurepost-approvalmarketriskofacompound.Thismakesassessing

theriskoftheseoptionseasierandreducestheircorrelationtotraditionalassetclassessuch

asstocksandbonds.ToinvestigatethecorrelationpatternsofFDAoptions,wemakeuseof

a novel dataset of project-level time-series estimates of the likelihood of eventual FDA

6OnedifferencebetweenbondandFDAoptionmarketsinthatoptionsdonotneedtoberated.Thisfacilitatesmarket-makingandtradingrelativetoothertypesofstructures.


approvalforthousandsofdrugsandbiologics.Weusethesedatatoconstructapaneldataset

of the implied prices and returns of FDA options if they were priced as predicted. We

examinethenatureoftheriskofthesesyntheticFDAoptionsandfindthattheriskislargely

idiosyncratic and unrelated to systematic factors. Since the prices of these hedges are

uncorrelatedwiththebroadermarketorotherfactors,wearguethattheriskassociatedwith

FDAhedgesmayappealtoinvestorsandissuersinterestedindiversification.

Indeed,thiszero-betapropertycouldbethemainsourceofgainsfromtradebetween

issuerslookingfordiversifiedinvestmentsanddeveloperslookingtooffloadtheapproval

risk.Itmaygenerallyholdiftheinherentscientificriskofmoleculesworkinginhumansthat

drive the FDA approval risk were not correlated with other asset classes. A broader

implication of our empirical findings is that the risk of R&D projects is, in general,

idiosyncratic,sincethevalueofFDAoptionsisdirectlytiedtotheunderlyingR&Dprojects.

Toourknowledge,ourpaperisthefirsttoprovideproject-levelevidenceofthispoint,which

hasbeenpositedbyanumberofpapers(e.g.PastorandVeronesi(2009),Fernandez,Stein,

andLo(2012),ThakorandLo(2015)).

Giventheseriskpatterns,weexaminehowwellissuersmaybeabletohedgetheriskof

offeringFDAoptions.Weconsider thehedgeofshorting thestockof theunderlying firm

whosedrug isgoingthroughtheFDAapprovalprocessandexaminethe impliedvalueof

suchhedgesgiventhepricesofthesyntheticFDAhedgesandtheunderlyingstocks.

Finally,weconsidersomeevidencethatFDAriskcanbetraded,andproposeanindirect

measureof thecovarianceof this typeof riskwith thebroadermarket. Inparticular,we

arguethatseveralexchange-tradedContingentValuationRights(CVRs)issuedinconnection

with pharmaceuticalmergers implicitly offer evidence about themarket acceptance and


covariancepropertiesofFDAhedges.Thefactthatsimilarriskshavebeentradedwithgreat

liquidityisusefulevidencebecauseitnegatespotentialtheoreticalargumentsthattrademay

beinfeasibleduetoasymmetricinformationbetweendevelopersandissuers.Weconsider

thepriceandvolumedata for theseCVRsandexamine their risk.Weshowthat theCVR

contracts have no significant exposure to the overall market and other factors, which

providesfurtherevidencethatFDAhedgeswouldbeattractiveaszero-betaassetstoissuers

interestedindiversification.

Ourpaperrelatesmostcloselytotheemergingliteratureonmeasuringandanalyzingthe

economic implications of policy uncertainty on economic activity (Davis (2015)). It also

relatestoanemergingliteratureontheinteractionbetweenreal-andfinancialhealthcare

marketsandtheimportanceofgovernmentriskinslowingdownmedicalinnovation(Koijen,

Philipson, & Uhlig, 2016; Thakor, Anaya, Zhang, Vilanilam, & Lo, 2016). We extend the

existing literature by suggesting new financial innovations to try to limit the economic

distortions imposedbypolicyuncertainty.Ourwork is also related to the literature that

argues that alternative innovations are needed to mitigate underinvestment in medical

innovation(Fernandez,Stein,&Lo,2012;Thakor&Lo,2017).

WestartinSection2withadiscussionofthepricingofFDAbinaryoptionsandsimulate

theirpricesgivenhistoricalFDAapprovalratesandthetimetheyremainineachFDAphase.

InSection3,weexaminethereturndistributionsofpoolsofFDAhedgesofferedbypotential

over-the-counter issuers. InSection4,weexaminetheriskcharacteristicsofFDAhedges

usingapaneldatasetofFDAapprovalprobabilitiesandexplorehowthisriskmaybehedged

byissuers.InSection5,weprovidetheproofofconceptofmarketacceptanceofFDAhedges


throughCVRcontractsandanalyzethecorrelationoftheFDAriskwiththebroadermarket.

WeconcludeinSection6withasummaryofourfindingsanddiscussfutureresearch.

2.FDABinaryOptions

In this section, we consider exchange-traded FDA binary options andwe derive and

calibratepricesfortheseoptionsinvarioustherapeuticareas.

2.1BinaryFDAOptions

Binaryoptionsaresimplecontractsthatarecurrentlytradedonseveralexchanges.Using

thisconceptasatemplate,wedefineanFDAbinaryoptionasafinancialcontractthatissold

foracertainprice,entitlingtheholdertobepaidapre-specifiedamountintheeventthata

certaindrugfailsagivenphaseoftheFDAapprovalprocess(ortheentireFDAprocess),and

nothingintheeventthatitsucceeds.AnFDAoptionmaybeissuedatthestartofagiven

phasefortheapprovaloutcomeofthatphase.Withoutlossofgenerality,weassumeitpays

onedollarifthedrugisnotapproved,andzeroifitis.

Throughout, our pricing formulas will use actual probability estimates to compute

expected valueswhich are then discounted at the risk-free rate. Themotivation for this

approachisthefactthattheriskassociatedwithFDAapprovalisunlikelytobecorrelated

withpricedfactorssuchasstockmarketreturnsoraggregateconsumption.Therefore,the

risk inherent in FDA option payoffs should be solely idiosyncratic, in which case the

equilibriumpriceshouldbegivenbytheexpecteddiscountedvalueofthepayoff,discounted

attherisk-freerateofreturn.WeshalltestandconfirmthiskeypropertyexplicitlyinSection

4.


Assumingthatapprovalriskispurelyidiosyncratic,thepriceofabinaryFDAoptionis

simply thepresentvalueof theprobabilityofnon-approval.The twouncertainties is the

outcomeoftheapprovaldecisionitselfaswellastimewhentheapprovaldecisionismade.

Iftheapprovaltimeisdistributedaccordingthefrequencyf(t),andtheprobabilityofnon-

approvalisp,thepriceatthestartofthephaseisgivenby:7

P= e-rtpf t dt,

where r is the risk-free rate.Clearly, the sooner thedecision ismade, and the larger the

chanceofnon-approval,thehigheristheprice.

2.2CalibratedPricesofFDAOptions

WeestimatethepricesforbinaryFDAoptionsusingrecentevidenceonFDAapproval

rates.Table1belowreportstheaveragehistoricalphasefailureratesfordifferentdisease

groups.8

7Thisassumesthatthereisnocorrelationbetweenthetimeoftheapprovaldecisionandthechanceofnon-approval.Ifthereisadependence,wewouldmodeltheprobabilityasanon-constantfunctionp(t)oftime.8ThesefailureratesarefromThomasetal.(2016),basedupondatafrom2006-2015.


Table1:ProbabilitiesofPhaseFailurebyDiseaseGroupThetableshowstheaverageprobabilityoffailingeachphaseoftheFDAdrugdevelopmentprocess,brokendownbydiseasegroups.Thesefailureratesarefromdatafrom2006-2015,andaretakenfromThomaset.al.(2016).

ProbabilityofFailingPhaseConditional

onReachingIt

DiseaseGroup Phase1 Phase2 Phase3

NDA/BLAApprovalPhase

OverallProbabilityofFailure

Hematology 27% 43% 25% 16% 74%InfectiousDisease 31% 57% 27% 11% 81%Ophthalmology 15% 55% 42% 23% 83%OtherDiseaseGroups 33% 60% 30% 12% 84%Metabolic 39% 55% 29% 22% 85%Gastroenterology 24% 64% 39% 8% 85%Allergy 32% 68% 29% 6% 85%Endocrine 41% 60% 35% 14% 87%Respiratory 35% 71% 29% 5% 87%Urology 43% 67% 29% 14% 89%Autoimmune/immunology 34% 68% 38% 14% 89%Neurology 41% 70% 43% 17% 92%Cardiovascular 41% 76% 45% 16% 93%Psychiatry 46% 76% 44% 12% 94%Oncology 37% 75% 60% 18% 95%

Giventheseprobabilitiesoffailure,wecalibratethepricesoftheFDAbinaryoptionsthat

payoffonemillionafteragivenphaseifthedrugfailsthatphase.Wecomputetheseprices

forcontractsstructuredassingle-phaseandmultiple-phaseoptions.Forourcalculations,we

assumeanannualrisk-freeinterestrateof1%.

InordertocalibratethetimingofFDAdecisions(f),wereport inTable2 theaverage

duration of each phase of the FDA approval process, taken from DiMasi and Grabowski

(2007).Theestimatesforthephaselengthsaredifferentforbiotechfirmsandpharmafirms.

Wethereforeusetheaveragephaselengthforbiotechandpharmafirmsinourcalculations.

Table2:FDAApprovalProcessPhaseLengths


ThistableshowstheaveragelengthofeachphaseintheFDAapprovalprocessforthebiotechandpharmasectors.Phaselengthisinmonths(yearsinparentheses).EstimatescomefromDiMasiandGrabowski(2007). AverageLengthoftimeinmonths(years)

Sector Phase1 Phase2 Phase3

NDA/BLAApprovalPhase

TotalLengthofTime

Biotech 19.5(1.6) 29.3(2.4) 32.9(2.7) 16.0(1.3) 97.7(8.1)Pharma 12.3(1.0) 26.0(2.2) 33.8(2.8) 18.2(1.5) 90.3(7.5) Average 15.9(1.3) 27.65(2.3) 33.35(2.8) 17.10(1.4) 94.0(7.8)

CombiningthedataonapprovalratesandthetimingofFDAdecisions,Table3reports

the impliedprices(ifpurchasedat thebeginningof the indicatedphase) forsingle-phase

FDAbinaryoptions—optionsthatpayoff$1millionifthereisfailureintheindicatedphase,

andnothingotherwise.For thepurposeofsimplifyingourcalculationsandmoredirectly

conveying the intuition behind the prices of these FDA options, we do not make

distributional assumptions on f and treat the phase length as deterministic by using the

averagephaselengthsfromTable2directlyindiscountingthepayoffsoftheoptions.Inother

words,thepayoffofasingle-phaseFDAoptioninTable3isgivenbythefollowingformula:

P=e-rTpX,

whereXisthepromisedpayoffoftheoption,pistheprobabilityofnon-approval,andTis

theaveragephaselengthtakenfromTable2.Weusearisk-freeinterestrateof1%inour

calculations.Inoursimulationresultslaterinthepaper,wewillmakeexplicitdistributional

assumptionsonfinourpricing.

Table3:PriceofSingle-PhaseFDABinaryOptionsThetableshowsthepricesofsingle-phaseFDAbinaryoptions,whichareissuedatthestartofeachphaseandpayoffintheeventoffailureinthatphase.Pricesareinthousandsofdollars.


PriceofFDAOptionthatPays$1minaGivenPhase

($thousands)

DiseaseGroup Phase1 Phase2 Phase3NDA/BLAApproval

Hematology $263 $424 $243 $158InfectiousDisease $301 $560 $266 $111Ophthalmology $150 $541 $406 $222OtherDiseaseGroups $329 $589 $296 $114Metabolic $384 $536 $278 $219Gastroenterology $241 $628 $383 $76Allergy $320 $660 $278 $61Endocrine $406 $585 $340 $138Respiratory $342 $693 $281 $53Urology $423 $658 $278 $141Autoimmune/immunology $338 $667 $368 $138Neurology $404 $687 $414 $166Cardiovascular $406 $742 $433 $156Psychiatry $455 $746 $431 $119Oncology $367 $737 $583 $174

For example, in Hematology it would cost $243,000 to buy insurance for a $1 million insurance

policy. Thepricesofthesingle-phaseoptionscorresponddirectlytothefailureratesineach

phase.Inparticular,thepricetopurchaseanoptionatthebeginningofphase2toinsure

against phase 2 failure is significantly higher than the price to purchase options at the

beginningoftheotherphases.Thisreflectsthefactthatthefailureratesinthedevelopment

processforthevariousdiseasegroupsarethehighestinphase2.Bycontrast,thepricesare

muchlowerinthefinalFDAapprovalphase,wherethefailureratesarethelowest.

Wenextcalculatethepricesofmultiple-phaseFDAbinaryoptions,whichpayoffifthere

isfailureinanysubsequentphaseoftheFDAprocess.Wediscussthepricingoftheseoptions


intheAppendix.Table4reportsthepricesoftheseoptionsifpurchasedatthebeginningof

agivenphase,therebyprovidinginsuranceagainstfailureinanyoftheremainingphases.9

Table4:ThePriceofMultiple-PhaseFDABinaryOptions,forPayoffineachanySubsequentPhase

Thistableshowsthepricesofmultiple-phaseFDAbinaryoptions,whichareissuedatthestartofeachphaseandpayoff intheeventoffailureinanysubsequentphase.Pricesareinthousandsofdollars.

PriceofFDAOptionthatPays$1mforFailureinSubsequent

Phases($thousands)

DiseaseGroup Phase1 Phase2 Phase3NDA/BLAApproval

Hematology $714 $622 $358 $158InfectiousDisease $784 $704 $344 $111Ophthalmology $797 $773 $531 $222OtherDiseaseGroups $812 $734 $373 $114Metabolic $821 $726 $430 $219Gastroenterology $821 $778 $428 $76Allergy $828 $761 $321 $61Endocrine $843 $753 $428 $138Respiratory $847 $783 $318 $53Urology $862 $778 $376 $141Autoimmune/immunology $862 $807 $451 $138Neurology $890 $834 $507 $166Cardiovascular $907 $863 $517 $156Psychiatry $913 $860 $495 $119Oncology $921 $893 $650 $174

There are a few noteworthy patterns in the table. First, naturally the price to insure

againstany phase riseswith non-approval rates. Second, the price of themultiple-phase

optiongoesdownasoneadvancestosubsequentphases,sincetheconditionalprobability

ofthedrugfailinginthefuturegoesdownovertime.However,thepricethatonewouldpay

9ThedetailsofhowthesepricesarecalculatedareprovidedintheAppendix.


for themultiple-phaseoptiononlygoesdownslightly fromphase1 tophase2,dropping

muchmoresignificantlyfromphase2tophase3,duetothehighfailureratesinphase2.

Sincethefailurerateismuchhigherinphase2relativetoallotherphases,mostofthecost

oftheoptioninphases1and2willbetoinsureagainstfailureinphase2.Oncefailurein

phase2hasbeenaverted,thepriceoftheoptiondropssignificantly,sincefailureisrelatively

lesslikelygoingforward.

3.Risk/RewardProfileofFDAHedgesviaOTCIssuers

TheinsurancevalueofFDAhedgesiscleartodrugdevelopers,butthequestionremains

ofwhatthevaluewillbetothoseholdingtheothersideofthetrade,i.e.,theissuers.Inthis

section,wethereforeconsiderthevaluetoover-the-counter(OTC)issuersthatofferFDA

contracts to investors. Inorder todoso,wesimulate theriskandreturndistributionsof

poolsofFDAhedgesofferedbyissuers.

3.1Risk/RewardProfileofPoolsofFDAOptions

We first empirically investigate the risk and return tradeoff of a pool of FDA option

contracts.WeexamineaportfolioofNcontracts,eachlinkedtoaparticularFDAapplication.

IftheFDArejectstheapplicationatanytpriortothecontractmaturitydateT,theissuer

paystheinsurancebuyer$1.TheprecisetimingoftheFDA’sapprovaldecisionfisunknown;

wemodelthetimeuntilanFDAdecisionasanexponentialdistributionwithrateparameter

λ. When the FDA reaches a decision before the contract expires, we assume that the

applicationiisrejectedwithprobabilitypi,andinourbasecalculationsweassumethatthere

isnocorrelationbetweentherejectionprobabilitiesoftwodifferentapplications,piandpj.


Inotherwords,ifeachcontractrepresentsanFDAoptionbasedonthefailure/successofa

different drug, the probabilities of failure of each drug are independent. A priori, this

assumptionofnocorrelationacrosscontractswillholdifalargerprobabilityofonemolecule

working inhumansdoesnot increase the chanceof another.Thiswill likelybe the case,

exceptwhenmoleculesworkwithinthesameindicationormechanismofaction,inwhich

caseacorrelationmayoccur.10InSection5,weprovideevidencethatseemstosuggestthat

theassumptionofnocorrelationbetweenthecontractswouldholdinpractice.

Inourbenchmarksimulationresults,wevarythenumberofcontractswhilefixingother

parameters, inorder toexplore thepotentialdiversificationbenefitsofaddingadditional

contractstotheissuer’sportfolio.Morespecifically,wesimulateportfoliosofN=1,N=10,

N=50,andN=100contracts.WeassumeacontractmaturityofT=5years,andpi=30%.

Wechoosearateparameterofλ=1/3forthetimeuntilanFDAdecisionismade,inorderto

matchameanFDAdecisiontimeofthreeyears.Forrobustness,inTableA1intheappendix,

weprovidetheportfoliopayoutdistributioncharacteristicsforalternativechoicesforthe

sizeoftheportfolioN,therejectionprobabilitypi,thecorrelationacrossdrawsρ,andthe

arrivalrateλ.

Weexaminetherisk-returntradeoffthattheissuerfacesbycalculatingtheSharperatios

of the portfolios. Consider an issuerwho has issuedN contracts priced at price $Pwith

expectedpayoutsX1,…,XN.Heinvests$NPattherisk-freeratewiththereturn:

R=[NP(1+r)-∑Xi]

NP= 1+r -

XP

10AcorrelationwouldalsooccuriftheFDAdecision-makingprocessacrossmoleculesistiedtogetherduetoregulatorybehavior.IntheAppendix,weexplorehowourresultsareaffectedwhenthisassumptionisrelaxedandweallowforcorrelationbetweendrugapplications.


whereX=( 1N)∑Xi.TheSharperatio iscalculatedbydividing themarkupby thestandard

deviationoftheportfolio:

SR=E R -rσ(R) =

P-E[X]σ(X)

InordertocalculatetheSharperatiosinthissetting,weassumecontractfeesof2%ofthe

expected payout of the portfolio, and a risk-free rate equivalent to the current five-year

Treasury yield. We vary the portfolio markup, up to a maximum markup of 50% over

expectedportfolioreturn.

Figure1belowpresentsthevaluesoftheSharperatioforvariousvaluesofNasafunction

oftheportfoliomarkup.Forexample,foraportfolioofN=10contracts,theexpectedpayout

isestimatedtobe$2.04,andthestandarddeviationoftheportfolioisestimatedtobe0.449.

Withapricegivenbya35%markupovertheexpectedpayout,contractfeesof2%,andrisk-

freerateof1.22%,theSharperatioiscalculatedtobe1.5546.Asthefigureshows,theSharpe

ratio intuitively improves as the markup increases, but an increase in the number of

contracts also consistently improves the Sharpe ratio. Thus, in the case of independent

payoffsamongstthecontracts,a largernumberofcontracts improvethe issuer’sreturns.

Theunderlyingintuitionisthesameasthatofportfoliodiversification.Withanyportfolioof

assets, introducing uncorrelated assetswill reduce the volatility of the portfolio through

diversification.11

Figure1:SharpeRatios

11InSectionA.2oftheAppendix,weprovidetheresultsfortheSharperatiosassumingacorrelationbetweenthecontracts.


This figure plots the Sharpe ratios of dealer returns as a function of the portfoliomarkup% forvarious values ofN, the number of contracts offered in the pool. These calculations assume nocorrelationbetweenthepayoutsofthecontracts.

3.2Risk-ReturnDistributionsforDiseaseGroups

Theresultsaboveshowtherisk-returntradeofffacedbyissuersforgeneralpoolsofFDA

option contracts. It is informative to examine in more detail how this tradeoff varies

dependingontheparticulardiseasegrouptheFDAOptionsarebasedupon,sincedifferent

diseasegroupscanhaveverydifferentsuccessprobabilities.Table5providestheexpected

payout,variance,andSharperatioforaportfolioofFDAoptionsbasedonadrugprojectin

eachrespectivediseasegroup(assumingN=50contracts inthepool),usingtheaverage

probabilitiesoffailureinPhase3foreachgroupthatwereshowninTable1.


Table5:ExpectedPayoutsofPortfoliosofN=50ContractsThistableprovidesthesimulationresultsforthemeanportfoliopayoutandvarianceofpayoutfordifferentdiseasegroups,assumingN=50contracts.

DiseaseGroupProbabilityofApprovalinPhaseIII

ExpectedPayout Variance SharpeRatio

Hematology 75% $0.51 0.003 2.39InfectiousDisease 73% 0.50 0.003 2.22Ophthalmology 58% 0.40 0.003 1.91OtherDiseaseGroups 70% 0.48 0.003 2.33Metabolic 71% 0.64 0.004 2.99Gastroenterology 61% 0.42 0.003 2.08Allergy 71% 0.48 0.003 3.16Endocrine 65% 0.44 0.003 2.19Respiratory 71% 0.48 0.003 2.86Urology 71% 0.48 0.003 2.36Autoimmune/immunology 62% 0.42 0.003 2.11Neurology 57% 0.39 0.003 1.98Cardiovascular 55% 0.38 0.003 1.94Psychiatry 56% 0.38 0.003 1.96Oncology 40% 0.27 0.002 1.51

As can be seen from the table, the portfolio payouts vary between disease groups,

dependingontheprobabilityofapproval.Inparticular,theexpectedpayoutsbytheissuer

arehigheriftheprobabilityofapprovalislower(i.e.theprobabilitythattheoptionwillpay

out is higher), with the highest expected payout being in oncology. The variance of the

payouts also increasesas theprobabilityof approvaldecreases.TheSharpe ratio for the

issuerisalsogenerallyhigherfordiseasegroupswithahigherprobabilityofsuccess.For

example,issuerswillfindthatissuingpoolsofFDAoptionsaremoreattractivefordrugsin

HematologythanfordrugsinOncology,sincedrugsinOncologyaremorelikelytofailand

thereforenecessitatepayoutsbytheissuer.Overall,therelativelyhighSharperatiosforall

ofthediseaseclassreinforcethenotionthatFDAoptionsmaybeattractiveforissuers.For


example,theSharperatiooftheS&P500SPDRETFoverthepastfiveyearswas1.32,which

issubstantiallylowerthantheSharperatiospresentedabove.

Whiletheanalysisaboveprovidesaviewintotherisk-returntradeofffacedbyissuersof

FDAoptions,theriskthattheseissuersareexposedtomaybefurtherreducedifissuersare

abletohedgetheriskoftheseoptions.Weexplorethisissuefurtherinthenextsection.

4.TheRiskofFDAOptions

Inthissection,wereturntotheissueofthenatureoftheriskofFDAhedgesthatissuers

face.FDAhedgesmayhavediversificationappealtoinvestorsandissuersifthereturnsto

thesesecuritiesareuncorrelatedwiththebroadermarketorotherfactors,thatis,iftherisk

ofthehedgeisidiosyncraticandnotsystematic.Weexplorewhetherthisisempiricallythe

caseusinganoveldatasetoftheapprovalprocessofdrugs.Giventhisrisk,wethenexamine

thecircumstancesunderwhichissuersmaybeabletohedgetheriskofFDAoptions.

4.1DatasetDescription

WeuseanoveldatasetonthedrugapprovalprocessfromtheBioMedTrackerPharma

Intelligencedatabase.Thisdatabasecontainsdetaileddrugtrialinformationforpharmaand

biotech companies, including historical approval success rates, development milestone

events,progressupdates,and,mostimportantly,estimatesofthelikelihoodoffutureFDA

approval for individual drugs in development by each company. The database provides

information on 11,587 drugs across 2,893 different companies. Although the dataset

containsinformationonahandfulofdevelopmenteventspriorto2000,ithasfullcoverage

from2000to2016,andwethereforefocusonthisperiodforouranalysis.


More specifically,weuse the reported likelihoodof futureFDAapprovalprovidedby

BioMedTrackerinordertoconstructhypotheticalpricesforFDAoptionsonawidevariety

ofdrugs.Foreachdrugand foragivendate,BioMedTrackerprovidesanestimateof the

probability that thedrugwillultimatelybeapprovedby theFDA.Theseprobabilitiesare

updatedeachtimethereisanyannouncementorotherdevelopment-relatedeventrelated

totheparticulardrug.12 Inordertodetermine likelihoodofapproval(LOA)probabilities,

BioMedTracker uses a combination of historical approval rates and analyst adjustments

basedondevelopmentevents.Morespecifically,whenadrugdevelopmentprojectisinitially

started,BioMedTrackerassignsanLOAprobability to itbasedon thehistorical approval

ratesofdrugsintheparticulardiseasegroupthatthedrugbelongsto.BioMedTrackerthen

adjuststheLOAprobabilityforthedrugeachtimeadevelopmenteventoccurs.Iftheevent

conveysnorelevantinformationastotheeventualdevelopmentsuccessofthedrug,then

theLOAisunchanged.However,iftheeventcontainsrelevantinformation(forexample,trial

results), then the LOA is adjusted either up or down by BioMedTracker depending on

whether the information is positive or negative. Themagnitude of the change in LOA is

determined by analysts,who evaluate the information content of the event and assign a

changesizebaseduponpre-specifiedcriteria.

Asanexample,accordingtoBioMedTracker,aneventinPhaseIIIthat“[m]etprimary

endpoint,butwithmarginalefficacyornoquantitativedetails;failedprimaryendpointbut

strongpotentialinsubgroup;someconcernwithefficacyvs.safetybalance”willcausean

increaseintheLOAbetween1%and5%.Incontrast,aneventwhichposted“[m]odestPhase

12 These include a wide variety of events broadly related to the company and drug under development,includingtrialresultsandprogressupdates,regulatorychanges,litigation,andcompanynews.


IIIresultsorpositiveresultsinnon-standardsubgroup;metprimaryendpointbutconcerns

over safety profile or study design” causes a decrease in the LOA between 1% and 5%.

BioMedTrackerprovidesevidencethatitsLOAestimateshavepredictiveabilityintermsof

the eventual success/failure of the drug under development. More specifically,

BioMedTrackernotesthat,from2000-2015,87%ofdrugsthatwereeventuallyapproved

hadbeenclassifiedashavinganabove-average(relativetothediseasegroup)LOA.Similarly,

75%ofthedrugsthateventuallymovedfromPhaseIItoPhaseIIIfrom2000-2015hadbeen

assignedanabove-averageLOA.80%ofthedrugsthatwereeventuallysuspendedduring

thesameperiodhadabelow-averageLOA.

4.2RiskExposureofFDAOptions

Weuse this time series data onprobabilities of future approval (LOA) to empirically

verifywhethertheriskofFDAoptionsisidiosyncratic—andthusrelatedonlytoscientific

risk—or systematic and related to the broadermarket or other factors. Specifically, we

construct a time-series of synthetic FDAmulti-phase binary optionprices using the LOA

probabilitiesdescribedintheprevioussection.Atanygiventimet,wesetthepriceFi(t)of

thesyntheticFDAoptiononagivendrugprojectiwhichpaysoff$1iftheprojectfailsas:

Fi(t)=exp(-rt(T-t)) 1-LOAi,t

whereLOAtistheLOAprobabilityattimet,rtistherisk-freeinterestrateattimet,andT-t

is the expected duration of the contract. For simplicity, we use the expected remaining

development time of the drug as a proxy for the expected duration of the contract.We

estimatethisusingtheaveragedevelopmenttimesforeachphasefromTable2.13Asbefore,

13Forexample,foracontractcurrentlyinPhase3,wesetT-t=4.204years.


weuseactualprobabilitiestocomputeexpectationsandthendiscounttheexpectedvalueby

therisk-freeratebecausetheriskisassumedtobepurelyidiosyncratic.Welaterprovide

evidence that justifies this assumption. Using this time-series of constructed prices, we

computethereturnsforthesesyntheticoptionsforalldrugsintheBioMedTrackerdatabase.

WeexcludeLOAprobabilitiesthatareeither0(thedrughasbeensuspended)or1(thedrug

hasbeenapproved),sincethereisnofuturedevelopmentuncertaintyforthedrugatthose

timepoints.

Withthesereturns,werunregressionstoestimateCAPMandFamaandFrench(1993)

3-factor betas over the period from 2000-2016, and examine whether these betas are

significant.We run these regressionsat theoption level, aswell as theportfolio levelby

combiningtheoptionsintoanequally-weightedportfolio.Wefirstusedailydatatoestimate

thebetas.Whileusingdailydatahasthepotentialadvantageofincreasingtheprecisionof

thebetapointestimate,onepossibleconcernwithusingdailydatainthissettingisthatthere

istypicallynoinformationoneachdrugbetweeneventdays,andthusthereturnfortheFDA

optionwillbezeroforthosedays.Whilethelackofcorrelationduetofeweventsmayindeed

bevaluabletoanissuer,forrobustnesswealsoprovidethebetaestimatesusingmonthly

data.

Table6belowprovidestheresultsofthesefactorregressions.Ascanbeseenfromthe

table,thecoefficients(betas)areinsignificantlydifferentfromzerofortheCAPMandFama-

Frenchfactors,usingbothdailyandmonthlydataaswellasrunningtheregressionsatboth

the option and portfolio levels. Moreover, the intercept (alpha) estimates are also

insignificant.Thisprovidesevidence that theriskofFDAoptions is idiosyncraticandnot

related to systematic factors, and thus issuing themmay be valuable for diversification


purposes.Atabroaderlevel,sincethevalueofFDAoptionsaredirectlytiedtotheunderlying

R&Dprojects,thisprovidesevidencethatisconsistentwiththeriskofR&Dprojectsbeing

idiosyncratic,apointthathasbeenpositedbyanumberofpapers(e.g.PastorandVeronesi

(2009)).

Table6:SystematicRiskofFDAOptions

ThistablegivestheresultsofCAPMandFama-French3-factorregressionsoftheexcessreturnofFDAoptionsonthemarket,size,andvaluefactors.Regressionsarerunattheoptionlevelorportfoliolevelusingeitherdailyormonthlyreturndata from2000 to2016,as indicated.Robuststandarderrors are in parentheses, and are clustered by date when run at the option level. * indicatessignificanceatthe10%level,**indicatessignificanceatthe5%level,and***indicatessignificanceatthe1%level.

DependentVariable:Ri,t–rft

(1) (2) (3) (4) (5) (6) (7) (8) (Mkt–rf)t -0.0003 0.010 -0.0007 0.010 -0.059 -0.0003 -0.061 -0.029 (0.0069) (0.008) (0.008) (0.008) (0.051) (0.059) (0.055) (0.059) SMBt -0.0003 0.015 0.074 0.130 (0.012) (0.025) (0.062) (0.091) HMLt 0.002 -0.026 -0.077 -0.102 (0.019) (0.021) (0.076) (0.111) Constant(α) 0.00003 0.00003 0.00003 0.00003 0.0008 0.0001 0.0007 0.0001 (0.00008) (0.0001) (0.00008) (0.0001) (0.0018) (0.0022) (0.0018) (0.0021) RegressionLevel

Option Portfolio Option Portfolio Option Portfolio Option Portfolio

Data Daily Daily Daily Daily Monthly Monthly Monthly Monthly Obs 20,690,864 3,918 20,690,864 3,918 1,008,291 192 1,008,291 192 R2 0.0000 0.0003 0.000 0.0012 0.0003 0.0000 0.0006 0.0460

4.3ADirectTestofIdiosyncraticRisk

Apotential concernwith our factor regressions is that the lack of significance of the

factorsmaybeduetohowwediscountthepayoffsoftheoptions.Inparticular,iftheriskof

FDAapprovalis,infact,notpurelyidiosyncratic,thenouroptionpricingformulaisincorrect.

Insuchcases,weshouldbeusingthestochasticdiscountfactortocomputeoptionprices,


which amounts to discounting option payoffs using risk-neutral probabilities instead of

actual probabilities to compute expectations. It is therefore possible thatwedonot find

significantcorrelationwithpricedfactorsbecausewearenotproperlyaccountingforthe

pricingkernel.

To address this concern, we examinewhether themarket return has any significant

predictivepoweron the successor failureofdrugs.The ideabehind this test is thatany

correlationbetweenFDAoptionreturnsandfactorssuchasthemarketshouldalsomanifest

itselfinwhetherdrugsultimatelysucceedorfail(andthustheFDAoptionexpiresworthless

orpaysoff).Sincethesuccessorfailureissimplyabinaryoutcome,examiningwhetherthe

marketreturnisafactorinpredictingthisoutcomeisthereforeawaytotesttherobustness

ofourresultsabovewithouthavingtodiscountorrelyonestimationofthepricingkernel.

Specifically,weruna logitregressionatthedruglevelwherethedependentvariable isa

binaryvariablewhichequalstooneifthedrugsucceeded(passedU.S.regulatoryapproval)

onthegivendayandequalstozeroifthedrugfailed(developmentsuspension)onthegiven

day.Werunthissuccess/failurevariableonthecontemporaneousmarketreturn,aswellas

thelaggedandforward20-,60-,and90-daycumulativemarketreturns.

TheresultsoftheseregressionsaregivenbelowinTable7.Ascanbeseenfromthetable,

themarketreturnisinsignificantateveryhorizon,indicatingthatthemarketreturndoes

nothavepredictivepoweronthesuccessorfailureoutcomesofdrugs.Thisprovidesfurther

evidencethattheriskofFDAapprovalispurelyidiosyncratic.

Table7:DrugSuccess/FailureOutcomesandtheMarketReturnThistablegivestheresultsoflogitregressionsofdrugsuccessorfailureoutcomesonmarketreturnsoverdifferenttimeperiods.Thedependentvariableisequaltooneifthedrugsucceededonthegivendayandzeroifthedrugfailedonthatday.Themarketreturnsarecumulativereturnsbetweentheindicatedlaggedorforwarddateandthedayt.Regressionsarerunatthedruglevelusingdailydatafrom2000to2016.Robuststandarderrorsareinparentheses,andareclusteredbydate.*indicates


significanceatthe10%level,**indicatessignificanceatthe5%level,and***indicatessignificanceatthe1%level.

DependentVariable:DrugSuccess/Failure

MarketReturnWindow:

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Contemporaneous,t -5.201 (4.272) Lagged,t–1tot 1.656 (3.182) Lagged,t–20tot -0.214 (1.066) Lagged,t–60tot -0.314 (0.717) Lagged,t–90tot -0.626 (0.510) Forward,ttot+1 -1.765 (3.002) Forward,ttot+20 0.338 (1.235) Forward,ttot+60 -0.127 (0.770) Forward,ttot+90 -0.464 (0.626) Obs 9,678 9,678 9,678 9,678 9,678 9,676 9,628 9,553 9,474 Pseudo-R2 0.0007 0.0001 0.0000 0.0001 0.0008 0.0002 0.0000 0.0000 0.0003

4.4HedgingtheRiskofFDAOptions

Inthissection,weoutlinetheextenttowhichanissuerofFDAriskcanhedgebytrading

thestockoftheunderlyingdrugdeveloper.Theideaisthatanysignificantmovementsinthe

valueoftheunderlyingprojectthatanFDAoptionisbaseduponwillalsoaffectthestock

priceofthedevelopingfirm.Toillustrateinasimplemanner,considerasingleFDAoption

thattheissuerhedgesbyshortingtheunderlyingfirm.LetthevalueofthefirmbeVbefore


theapprovaldecisionismade,andV1ifapprovedandV0ifnotapproved.Theseapproval-

contingentvaluesmaybewrittenas:

V1=X1+A

V0=X0+0

where(X0,X1)arethevalueoftheassetsofthefirmduetootherfactorsthanthedrugunder

consideration,andA isthevalueofthedrugunderconsiderationconditionalonapproval

(andthusequaltozeroafternon-approval).IfX0andX1differ,thereisacorrelationbetween

theapprovaldecisionandthevalueofthefirmsduetootherfactors.Beforetheapproval

decision,thevalueofthefirmis:14

V=pV1+ 1-p V0

Thisequationimpliesthatthepriceincreaseduetoapprovalislargerwhentheprobability

ofnon-approvalislarger.Likewise,pricedropsduetonon-approvalaresmallerwhenthe

probabilityofnon-approvalissmaller.

ConsiderwhentheissueroftheFDAoptionshortstheunderlyingdevelopertohedgethe

FDAoption.Considerthecasewhenthereisindependencebetweentheapprovaldecision

andtheotherfactorsdrivingfirmvalue:,X1=X0.Thepayoffoftheissuerhedgeafternon-

approvalisthen:

V-V0+P-1

The first term is positive because the firm loses value and the second term is negative

because thepayouton theoption is larger than thepricecharged for it.Thepayoffafter

approvalis:

V-V1+P

14Thisignoresthepossibilitythatthestochasticdiscountfactormaydifferacrossthetwoapprovalstates.


The first term is negative because the firm gains value, and the second term is positive

becauseoftherevenuefromsellingtheoptioncomeswithoutapayout.

Asanillustrativeexampleofhowthisissuerhedgingmayworkinpractice,considerthe

case of Poniard Pharmaceuticals, a firm with a lead drug known as Picoplatin under

development, which is designed to tackle platinum resistance in chemotherapy. While

Picoplatinwasunderdevelopment for a number of different indications, one of itsmain

indicationswassmallcelllungcancer.AccordingtodrugtrialdatafromtheBioMedTracker,

PicoplatinforsmallcelllungcancerwasinphaseIIIoftheFDAapprovalprocessasoflate

2009,whenithadaprobabilityofeventualFDAapprovalof35%.Supposethatanissuerhad

soldamulti-phaseFDAbinaryoptionasofthispointintime,whichpaysoffintheeventthat

thedrugfailsanysubsequentstageofthedevelopmentprocessorisnotapproved.Ignoring

discounting for simplicity, the price of an FDA option with a $100 face value will be

approximately$100× 1-0.35 =$65.

Now, phase III trial data for Picoplatin for small cell lung cancer was released on

11/16/2009,andtheresultsprecipitatedadropinthelikelihoodofapprovalforthedrugof

20%,from35%to15%.Sincethedrugwasthenlesslikelytobeapproved,thiswouldin

turnimplyanincreaseinthepriceoftheFDAoptionfrom$65to$100× 1-0.15 =$85,or

areturnof-30.7%fromtheperspectiveoftheissuer’sposition.However,supposethatthe

issueralsohadashortpositionintheunderlyingPoniardstock.Inthe10dayssurrounding

thetrialdatareleasedate,Poniard’sstockpostedareturnof-70.8%,thusyieldingareturn

oftheshortpositionof70.8%.15Asaresult,onaone-for-onebasis,theshortpositioninthe

15 One could alternatively examine abnormal returns for the stock, i.e. returns that are attributed to theidiosyncraticmovement of the stock (related to the stock’s fundamentals) and not to themarket or other


stockmorethanoffsetstheincreasedliabilityfromtheFDAoptionfromtheperspectiveof

theissuer.Afullhedgeinthiscasewouldthereforeinvolveaportfoliowitharoughly50%

weightintheshortstockanda50%weightinrisk-freeassets.

Moregenerally,wecanusethetime-seriesofapprovalprobabilitydataaswellasstock

returndatainordertoestimatetheoptimalnumberofunderlyingstocksneededfor

issuerstohedgetheriskofFDAoptions.LetF(t)bethepriceoftheFDAoptionatdatet

thatisgivenbyourpreviousformulas.DenotetheunderlyingstockpricereturnbyS(t)and

letnbethenumberofsharesoftheunderlyingstockthatissuersholdinordertohedgethe

FDAoption.Theoptimalnumberofsharesthatminimizestheoverallvarianceoftheissuer

satisfiesthewell-knownformula:

n*=𝜎$σS

ρF,S

whereσFisthestandarddeviationoftheFDAoptionprice,σSisthestandarddeviationof

theunderlyingstockprice,andρF,SisthecorrelationbetweenthepricesoftheFDAoption

andtheunderlyingstock.

Inordertomoreclearlyillustratehowthishedgingmayworkinpractice,weobtainthe

approval probability data for the30 companies in theBioMedTrackerdatabasewith the

lowestmarketcapitalizations,sincethesecompaniesarelikelytohavethefewestnumberof

drugs or indications in development. We then obtain daily stock price data for these

companies.Weeliminatecompaniesforwhichthereareeithernodrugtrialeventsorfor

systematicfactors.Doingsobycalculatingabnormalreturnsrelativetothemarketfactoryieldsanevenlargerdropof74.8%.Thevery largedropmayindicatethat investorsviewedthedisappointingtrialresultsasanindicationthatPicoplatinmayfailsomeofitstrialsforotherindications.Asaresult,inthiscaseitislikelythatthedrugunderconsiderationiscorrelatedwiththeotherassetsofthecompany.


whichthereisaninsufficientamountofdrugtrialorstockdata.Thisleaves19companies

forwhichwerunourestimationresultsfor.

Using the time-seriesdataon changes in approvalprobabilities fordifferentdrugs to

estimatethepricesofmultiple-phaseFDAbinaryoptionswrittenonthosedrugs,aswellas

stock price data for the underlying company stocks, belowwe estimate the parameters

neededtodeterminetheoptimalhedgeandtheamountofvariancereductionitimpliesfor

differentdrugs.ThepricesoftheFDAoptionsarecalculatedinthewaydescribedinSection

4.2.Table8belowpresents theoptimalhedge forvariousdrugs.The first threecolumns

correspondtothethreeparametersabove,andthefourthcolumntotheoptimalnumberof

shorted stocks. The fifth column calculates the reduction in variance enabledby optimal

hedging.16

Table8:OptimalIssuerHedgesforFDAOptionsonDifferentDrugs

Thistablegives, forvariousdrugs,thestandarddeviationofthepriceofanFDAbinaryoptionσFbased upon that drug, the standard deviation of the researching company’s stock price σS, the

16Variancesandcorrelationsarecalculatedbasedonthesampleperiodforwhichthereisdataforeachdrug.Forsimplicity,weassumearisk-freeinterestrateof0andweignorethefactthatthetimingoftheFDAapprovaldecisionisuncertain.Accountingforthisuncertaintywillrequireadditionaldistributionalassumptions.


correlationbetween thesepricesρF,S, theoptimalnumberof underlying stocks topurchasen* in

ordertohedgetheoptionrisk,andthereductioninvarianceimpliedbythehedge.CompanyName Drug σF σS ρF,S n*

VarianceReduction

AcusphereInc. AI-128forAsthma 14.13 26.78 -0.42 -0.22 17%AcusphereInc. CEP-33222forBreastCancer 15.02 26.78 -0.37 -0.21 13%AdvancedLifeSciencesHoldings ALS-357forMelanoma 2.96 38.63 -0.54 -0.04 10%AdvancedLifeSciencesHoldings RestanzaforRespiratoryTractInfections 4.07 38.63 -0.93 -0.10 82%ARYxTherapeutics ATI-9242forSchizophrenia 4.32 2.27 -0.74 -1.42 53%ARYxTherapeutics NaronaprideforChronicIdiopathicConstipation 12.29 2.27 -0.84 -4.53 70%ARYxTherapeutics NaronaprideforGastroesophagealRefluxDisease 12.23 2.27 -0.84 -4.51 69%BoneMedicalLtd CapsitoninforOsteoporosis/Osteopenia 2.75 84.04 -0.61 -0.02 4%BostonTherapeutics BTI-320forDiabetesMellitus,TypeII 0.63 84.04 -0.24 0.00 0%TaxusCardium GenerxforAngina 0.72 84.04 -0.25 0.00 0%diaDexus AIDSVAXforHIVPrevention 1.70 0.34 0.00 -0.02 1%diaDexus PreviThraxforAnthraxInfection(Antibacterial) 10.01 20.40 -0.81 -0.40 65%EntiaBiosciences ErgoD2forRenalDisease/RenalFailure 5.10 20.40 -0.73 -0.18 53%MultiCellTechnologies MCT-125forMultipleSclerosis(MS) 0.27 108.04 0.57 0.00 8%Neuro-Hitech HuperzineAforAlzheimer'sDisease(AD) 9.48 108.04 -0.51 -0.04 23%NeurobiologicalTechnologies XereceptforCerebralEdema 1.13 0.37 0.24 0.75 0%NuoTherapeutics ALD-201forCoronaryArteryDisease 11.87 0.65 -0.76 -13.86 20%NuoTherapeutics ALD-401forIschemicStroke 10.21 2.74 -0.94 -3.51 88%NuoTherapeutics ALD-451forBrainCancer 4.54 1.03 -0.69 -3.02 41%OrePharmaceuticalHoldings ORE10002forInflammatoryDisorders 1.03 1.10 0.13 0.13 1%OrePharmaceuticalHoldings ORE1001forUlcerativeColitis(UC) 0.31 1.10 0.01 0.00 0%OncoVistaInnovativeTherapies OVI-237forBreastCancer 0.54 1.10 -0.10 -0.05 0%OncoVistaInnovativeTherapies OVI-237forGastricCancer 7.01 0.37 -0.80 -15.10 64%OncoVistaInnovativeTherapies P-AATforAcuteCoronarySyndrome(ACS) 0.54 10.67 0.29 0.01 0%OncoVistaInnovativeTherapies P-AATforDiabetesMellitus,TypeI 2.09 10.67 0.50 0.10 1%PoniardPharmaceuticals PicoplatinforColorectalCancer(CRC) 7.39 0.55 -0.83 -11.07 60%PoniardPharmaceuticals PicoplatinforOvarianCancer 8.50 0.55 -0.78 -11.96 45%PoniardPharmaceuticals PicoplatinforProstateCancer 0.84 0.55 0.20 0.31 1%PoniardPharmaceuticals PicoplatinforSmallCellLungCancer(SCLC) 10.46 1094.51 -0.71 -0.01 8%PoniardPharmaceuticals SkeletalTargetedRadiotherapyforBreastCancer 13.53 1094.51 -0.81 -0.01 11%

PoniardPharmaceuticals SkeletalTargetedRadiotherapyforMultipleMyeloma 13.30 1094.51 -0.35 0.00 5%

Stromacel UMK-121forLiverFailure/Cirrhosis 13.44 1094.51 -0.81 -0.01 11%Proteo ElafinforCoronaryArteryBypassGraft(CABG) 12.66 1094.51 -0.74 -0.01 12%RockCreekPharmaceuticals AnatabinecitrateforAlzheimer'sDisease(AD) 0.98 1094.51 0.78 0.00 12%RockCreekPharmaceuticals AnatabinecitrateforAutoimmuneDisorders 2.66 1094.51 0.52 0.00 6%RockCreekPharmaceuticals AnatabinecitrateforMultipleSclerosis(MS) 0.67 352.99 0.10 0.00 0%RockCreekPharmaceuticals AnatabinecitrateforTraumaticBrainInjury(TBI) 2.19 2.39 -0.21 -0.19 1%VioQuestPharmaceuticals LenoctaforAnti-ParasiticandAnti-Protozoal 0.87 2.39 -0.29 -0.11 2%VioQuestPharmaceuticals LenoctaforSolidTumors 0.77 2.39 -0.29 -0.09 2%VioQuestPharmaceuticals VQD-002forMultipleMyeloma(MM) 14.63 2.39 -0.31 -1.88 3%


VioQuestPharmaceuticals VQD-002forSolidTumors 0.59 41.71 0.10 0.00 1%

However, in a number of the other cases, the variance reduction is low—on the

magnitudeof5%orless.Thereareafewreasonsforthis.Onereasonisthat,forsomedrug

indications,thereareonlyafewdateswithanynews,andmoreoverthereisnochangein

theprobabilityofsuccessformanyofthesedates.Becauseofthis,thepriceoftheFDAoption

will remain constant (ignoringdiscounting) formanydates, and thevarianceof theFDA

optionwillbesmallbecausethepriceonlychangeswhenthereisanevent.Thismayleadto

impreciseinputsintotheoptimalhedgecalculation,andthereforealowvariancereduction.

Thesecondreasonisthatcertaindrugsorindicationsmakeuparelativelysmallproportion

ofthevalueofacompany’soveralldrugportfolio.Forexample,acompanymaytestacertain

compoundforefficacyintreatmentareasthataredifferentfromthedrug’sprimarytarget,

and expect a very low likelihood of success. The company’s overall valuewill therefore

relativelyunaffectedbyclinicalnewsaboutthisindication.Asaresult,fortheseparticular

typesofdrugsorindicationsindevelopment,theunderlyingstockofthecompanymaynot

offer an ideal hedge against an FDA option issued on that drug. But as noted, for other

drugs/indications which make up a substantial portion of the company’s portfolio, the

reductioninvariancecanbesubstantialfortheissuer.

6.ProofofConceptviaCVRContracts


Thereareseveralpotential theoreticalargumentsagainst the liquidityofFDAhedges.

For example, one may argue that trading FDA hedges is infeasible due to asymmetric

informationbetweensellersandbuyers,preventingthemarketfromfunctioning.

Becauseof thesepotentialobjections, in this sectionwediscussan interesting traded

instrumentthatprovidesa“proofofconcept”oftheliquidityinmarketstradingFDArisks.

It is similar in many respects to FDA hedges, and the instrument is liquid and follows

predicted pricing and volume patterns. This instrument is a particular version of an

exchange traded contingent valuation rights (CVR) issued in mergers and acquisitions

(M&A)deals,whichpaysinvestorspre-specifiedamountswhencertainmilestonesaremet

as part of aM&A deal structure. As thesemilestonesmany times include FDA approval

decisions,thesetradedcontractscontainimplicitFDAoptions.

However,oneprovisoshouldbekeptinmind.AlmostallcurrentbiopharmaCVR’sare

“impure”with respect to FDA approval decisions, as they often include non-FDA related

milestonesinadditiontoFDAapprovals.Forexample,thesemilestonesmayincludesalesor

marketingtargets.Duetotheseadditionalnon-FDAmilestones,thedailypricemovements

oftheCVR’smaybedrivenbyotherfactorsnotrelatedtoFDAapproval.However,thisalso

suggeststhattheCVRitself isnotanadequatehedgeagainstFDAapprovalrisk,andthus

thereisneedformorepureFDAhedges.

6.1ContingentValuationRightswithFDAOptions

The contingentvaluation right (CVR) is a shareholder right, oftengiven to the selling

shareholdersduringamergeroranacquisition,whichgivestheholderacashpaymentif

certainmilestones are achieved. Just as listed companies can be traded on the NYSE or

NASDAQ,CVRscanalsobetradedontheseexchanges.AnexampleofaCVRthatwastraded


ontheNASDAQistheCVRissuedbyCelgeneonitsacquisitionofAbraxis.Celgeneissuedthe

Celgene CVR contract, with the holder of the contract entitled to milestone and sales

payments.Forthemilestonepayments,theholderoftheCVRwasentitledtoafixedsumof

money($250milliondividedbythenumberofCVRsoutstanding)uponFDAapprovalofthe

drugAbraxaneforuseinthetreatmentofnon-smallcelllungcancerbyacertaindate.In

addition,theholderoftheCVRwasentitledtoanothersumofmoney($400milliondivided

by the total number of outstanding CVR contracts) if the drug Abraxane achieved FDA

approval foruse inthetreatmentofpancreaticcancer.Thesemilestonepaymentscanbe

viewedasbinaryFDAoptions.

Figure2belowshowsthevolumedataoftheCelgeneCVRcontract,whileFigure3shows

thepricedata.Inbothfigures,thetopgraphsshowthevolumeandpriceoftheCVRcontract,

while the bottom graphs show the volume and price normalized as a percentage of the

underlyingCelgenestockvolume/price.NoticethejumpinpricearoundOctober2012,when

theFDAapprovedAbraxanefornon-smallcelllungcancer,andsimilarlyinNovember,after

atrialthatshowedpromiseforpancreaticcancer.

EventhoughthepriceofthisCVR,byandlarge,hasfollowedtheFDA’sdecisions,itisstill

an“impure”FDAhedge.Forexample,itisanunsecuredobligationofCelgene,andisjunior

toallotherclaims.ItisalsocallablebyCelgene,sothereisoptionalityembeddedintoit.The

CVRalsohassalestargetpaymentsinadditiontomilestonepayments,whichmayinturn

carry with it additional risk correlated to the overall market but not FDA risk. These

additional features generate price movements that are orthogonal to any change in the


probabilityofFDAapproval,andthuscounteracttheabilityofthecontracttoactasahedge

againstFDArisk.17

Figure2:CelgeneCVRTradedVolumeThisfigureplotsthedailytradingvolumeoftheCelgeneCVRcontract,CELGZ,innumberofshares(top figure) and as apercentageof thenumberof shares traded in theunderlyingCelgene stock(bottomfigure).

17ForthisparticularCVR,therewerealsomechanicalpricechanges,suchasalargepricedropoccurringinOctober2013duetothepricegoingex-dividend.

0.0%5.0%10.0%15.0%20.0%25.0%30.0%35.0%40.0%

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CELGZDailyVolume,as%ofCelgeneVolume


Figure3:CelgeneCVRStockPriceThisfigureplotsthestockpriceoftheCelgeneCVRcontract,CELGZ,pershare(topfigure)andasapercentageofthestockpriceoftheunderlyingCelgenestock(bottomfigure).

AnadditionalexampleistheCVRissuedbyAstraZenecaafteritsacquisitionofOmthera

Pharmaceuticals,Inc.inMay2013.ThisCVRensuredapaymentforshareholdersof$1.18

pershare,providedthatspecificFDAapprovalsforinvestigationalcholesteroldrugEpanova

$0.00$1.00$2.00$3.00$4.00$5.00$6.00$7.00$8.00$9.00$10.00

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CelgeneCorporation(CELGZ)- StockPrice

0.0%2.0%4.0%6.0%8.0%

10.0%12.0%14.0%16.0%18.0%20.0%

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CELGZPrice,as%ofCelgenePrice


werereceivedbyJuly31,2014andanexclusivitydeterminationwasreceivedbySeptember

30,2014.Anadditionalpaymentof$3.52pershareistobepaidifadditionalpre-specified

FDAregulatoryapprovalsarereceivedbyMarch31,2016.

6.2CorrelationsandBetasforContingentValuationRights

InSection5.3,weshowedthattheriskinsyntheticFDAhedgeswasidiosyncratic.We

nowexplorewhetherthisisalsothecaseforCVRcontractsthatareactuallytraded.Below

inTable9,wereport theCAPMandFama-Frenchbetasof threeCVRcontracts—Celgene

(CELGZ), Sanofi (GCVRZ), andWrightMedical Group (WMGIZ).We calculate these betas

usingbothdailyandmonthlydata,inordertoensurethattheresultsarenotduesimplyto

asmalltime-seriessamplesize.Ingeneral,thebetasofthecontractsareinsignificant,even

withfeaturessuchassalestargetsthatmayincludesomesystematicrisk.

For the Celgene CVR contract (Panel A), themarket betas (columns (1) and (3)) are

insignificant using both daily and monthly data. When incorporating the Fama-French

factors, themarketbetabecomesnegativeandsignificantusingdailydata,butnotwhen

using monthly data. Thus there is weak evidence that the Celgene CVR carries some

(negative)marketrisk.ThebetasoftheSanofiCVRcontract(PanelB)areallinsignificant

using both daily andmonthly data. Finally, the betas of theWright Medical Group CVR

contract(PanelC)areallinsignificantwhenusingdailydata;whenusingmonthlydata,the

HMLbetabecomessignificant.However,thereareonly37monthsofdataavailableforthe

WMGIZcontract,andthusthesignificantbetaincolumn(4)maybeanartifactofthesmall

sample size.Overall, the regression results show that thebetas of theCVR contracts are

largelyinsignificant,whichprovidesadditionalevidencethatFDAhedgesarealsolikelyto


beuncorrelatedwiththemarketiftradedinthemarket,andthusmayhavediversification

appealtoinvestors.

Table9:CVRFactorRegressionsThis table provides CAPM and Fama-French 3-factor regressions of the excess return of CVRcontractsonthemarket,size,andvaluefactors.Regressionsarerunusingeitherdailyormonthlyreturn data for the Celgene-Abraxane CVR contract (CELGZ) in Panel A, the Sanofi CVR contract(GCVRZ)inPanelB,andtheWrightMedicalGroupCVRcontract(WMGIZ)inPanelC.Standarderrorsareinparentheses.Allregressionsincludeaconstantterm(notreported).*indicatessignificanceatthe10%level,**indicatessignificanceatthe5%level,and***indicatessignificanceatthe1%level.

PanelA:CELGZContractDependentVariable:Ri,t–rft

(1) (2) (3) (4) (Mkt–rf)t -0.209 -0.282* 0.808 0.801

(0.133) (0.145) (0.673) (0.735) SMBt 0.350 -0.092 (0.281) (1.224)

HMLt 0.154 0.388 (0.307) (1.367)

Data Daily Daily Monthly Monthly Obs 1,379 1,379 66 66 R2 0.002 0.003 0.022 0.023

PanelB:GCVRZContractDependentVariable:Ri,t–rft

(1) (2) (3) (4) (Mkt–rf)t -0.330 -0.270 -0.283 -0.568

(0.220) (0.238) (0.820) (0.888) SMBt -0.345 1.068 (0.468) (1.534)

HMLt 0.020 1.582 (0.508) (1.677)

Data Daily Daily Monthly Monthly Obs 1,257 1,257 61 61 R2 0.002 0.002 0.002 0.026

PanelC:WMGIZContract


DependentVariable:Ri,t–rft (1) (2) (3) (4)

(Mkt–rf)t 0.757 0.771 0.332 0.386 (0.786) (0.798) (1.720) (1.673)

SMBt -0.205 0.206 (1.400) (2.305)

HMLt -0.186 6.723** (1.591) (2.800)

Data Daily Daily Monthly Monthly Obs 774 774 37 37 R2 0.001 0.001 0.001 0.150

WhilethebetasoftheCVRcontractsgenerallyarenotsignificantlydifferentfromzero,it

ispossiblethatsomeothertypeofriskiscommontoallthesecontracts.Forexample,there

maybe a systematic factorother than themarketorFama-French factors that affect the

pricesandreturnsof thesecontracts.Onepossibility isregulatoryrisk,affectingmultiple

drugs simultaneously (Koijen, Philipson, & Uhlig, 2016). Another possibility is that CVR

contractsmaybebasedoncompaniesworkinginsimilartherapeuticareas,inwhichcase

thesuccessofadrugspecifictoonecompanymaybecorrelatedwiththesuccessofasimilar

drugunderdevelopmentbyanothercompany.

To explore these possibilities, we examine the correlations of the daily andmonthly

returnsfortheCVRcontracts.ThiscorrelationmatrixisshowninTable10below.Thetable

showsthatthecorrelationsbetweenthedifferentcontractsareverylowandinsignificantly

different from zero, suggesting that there is no other common factor is that driving the

returnsoftheCVRs.ThisprovidesfurtherevidencethattheriskembeddedinFDAhedgesis

likelyidiosyncratic,relatedtothesuccessoftheunderlyingdrugs.


Table10:CorrelationmatrixofCVRReturnsThistableprovidescorrelationsbetweendaily(PanelA)andmonthly(PanelB)stockreturnsfortheCelgene-AbraxaneCVRcontract(CELGZ),theWrightMedicalGroupCVRcontract(WMGIZ),andtheSanofiCVRcontract(GCVRZ).*indicatessignificanceatthe10%level,**indicatessignificanceatthe5%level,and***indicatessignificanceatthe1%level.

PanelA:DailyReturns CELGZ GCVRZ ObservationsCELGZ 1,379GCVRZ 0.015 1,257WMGIZ 0.009 0.001 774

PanelB:MonthlyReturns CELGZ GCVRZ ObservationsCELGZ 66GCVRZ -0.134 61WMGIZ -0.009 0.107 37

The insignificant betas and low correlation between contracts also underscore an

importantpointrelatedtotheappealofFDAhedgestoOTCissuers.Inparticular,theSharpe

ratiostoOTCissuersofpoolsofFDAhedgesaresubstantiallylowerwhenthepayoffsofthe

contracts are correlated. These results provide evidence that the assumption of no

correlationbetweenthepayoffsofcontractsmaybemoreapplicable,andthatthehigher

SharperatiospresentedinSection3.1withuncorrelatedcontractsapplies.

OnealternateexplanationforthelowbetasandcovariancesoftheseCVRcontractsisthat

theyhavealowtradingvolume,andthereforetheyhavezerocovariancewithanything,since

thecontractsarenottraded.However,evenif lowtradingvolumeisthecauseofthelow

correlation, thecorrelation is still lowwhich isvaluable to issuers.That reasoningaside,

Table11belowgivestheyearlysummarystatisticsforthetradingvolumeofthethreeCVR

contractsdiscussedabove.


Table11:CVRDailyTradingVolumeSummaryStatisticsThistableprovidessummarystatisticsforthedailytradingvolumefortheCelgene-AbraxaneCVRcontract (CELGZ), theWrightMedicalGroupCVRcontract (WMGIZ), and theSanofiCVRcontract(GCVRZ).Allnumbersrepresentthenumberofsharestraded.

PanelA:CelgeneCVR(CELGZ) Mean Std.Dev. p25 Median p75

2015 17,012.6 20,114.9 3,875 10,950 20,8502014 21,906.0 44,141.3 5,800 11,600 23,6002013 67,625.4 216,749.9 4,225 18,000 68,0752012 52,040.8 182,213.2 3,050 14,900 38,7502011 35,493.7 140,553.7 2,325 8,950 28,0002010 70,990.2 85,968.6 22,650 49,500 94,500

PanelB:SanofiCVR(GCVRZ) Mean Std.Dev. p25 Median p75

2015 664,032.1 2,055,218.4 110,900 235,250 516,2752014 850,199.2 1,699,940.0 147,225 348,950 777,4502013 1,177,137.3 4,337,753.0 74,150 237,050 624,7002012 609,218.0 1,003,581.5 109,400 207,600 588,1502011 2,321,230.4 4,181,025.7 529,300 1,054,800 2,424,800

PanelC:WrightMedicalGroupCVR(WMGIZ) Mean Std.Dev. p25 Median p75

2015 18,037.3 47,647.4 1,100 4,300 17,7002014 43,925.8 91,923.1 6,900 17,400 47,4502013 108,033.8 335,577.3 10,900 33,800 88,625

Ascanbeseenfromthetable,themeantradingvolumeeachyearissignificantforallof

thecontracts.WhilethevolumeforCELGZandWMGIZaresomewhatsimilar,thetrading

volumeeachyearforGCVRZislarge,andsignificantlyhigherthantheothertwo.Thistable

shows that there is significant trading volume for the CVR contracts, and thus the

correlationsandbetasshownabovearelikelynotduetoilliquidityofthecontracts.


7.Conclusion

ThehighcostofcapitalforfirmsconductingmedicalR&Dhasbeenpartlyattributedto

theriskoftheregulatoryapprovalprocessthatinvestorsmustfaceinmedicalinnovation

(Koijen,Philipson,&Uhlig,2016).Weproposednewfinancialinstruments,FDAhedges,to

allow medical R&D investors to better share the pipeline risk associated with the FDA

approval process with broader capital markets. Using FDA approval data, we discussed

pricingofFDAhedgesandmechanismsunderwhichtheycanbetradedandsimulatedtheir

risk and return distributions. We then used a novel panel data set of FDA approval

probabilities toempiricallyexplorethenatureof therisk inherent in thesecontractsand

showed how issuers may effectively hedge this risk. We found evidence that the risk

associatedwithofferingFDAhedgesfacedbyanissuerwaslargelyuncorrelatedwithother

asset classes. Finally,weofferedproof of concept that this typeof risk canbe tradedby

examiningrelatedsecuritiesissuedaroundM&Aactivityinthedrugindustry.

Webelievethetypeofanalysisconductedinthispaperisafirststepindemonstrating

that FDA hedges would enable better risk sharing between those investing in medical

innovationandcapitalmarketsmoregenerally.Byallowingsuchrisksharing,FDAhedges

wouldultimatelyhelpacceleratethedevelopmentofnewmedicalproductsandimprovethe

healthofcountless futurepatients.Therefore, financial innovations like thesemaybetter

spurmedicalinnovation.


References

Davis,StevenJ."Regulatorycomplexityandpolicyuncertainty:headwindsofourown

making."BeckerFriedmanInstituteforResearchinEconomicsWorkingPaper(2015).DiMasi,JosephA.,andGrabowski,HenryG."ThecostofbiopharmaceuticalR&D:isbiotech

different?"ManagerialandDecisionEconomics28,no.4-5(2007):469-479.DiMasi,J.A.,Grabowski,H.G.,andHansen,R.W."Innovationinthepharmaceutical

industry:newestimatesofR&Dcosts."Medford,MA:TuftsCenterfortheStudyofDrugDevelopment(2014).

DiMasi,JosephA.,Hansen,RonaldW.,Grabowski,HenryG.,andLasagna,Louis."Costof

innovationinthepharmaceuticalindustry."JournalofHealthEconomics10,no.2(1991):107-142.

DiMasi,JosephA.,Reichert,JaniceM.,Feldman,Lanna,andMalins,Ashley."Clinical

approvalsuccessratesforinvestigationalcancerdrugs."ClinicalPharmacology&Therapeutics94,no.3(2013):329-335.

Fama,EugeneF.,andFrench,KennethR."Commonriskfactorsinthereturnsonstocksand

bonds."JournalofFinancialEconomics33,no.1(1993):3-56.Fernandez,Jose-Maria,Stein,RogerM.,andLo,AndrewW."Commercializingbiomedical

researchthroughsecuritizationtechniques."NatureBiotechnology30,no.10(2012):964-975.

Koijen,R.,Philipson,T.,andUhlig,H.(2016),“FinancialHealthEconomics”,Econometrica84,no11:195–242

Philipson,Tomas,“HedgingPipelineRiskinPharma:FDASwapsandAnnuities.”Milken

Institute(March2015a).Philipson,Tomas.“SavingLivesthroughFinancialInnovation:FDASwapsandAnnuities”Forbes,(March2015b).

Thakor,RichardT.,Anaya,Nicholas,Zhang,Yuwei,Vilanilam,Christian,andLo,AndrewW.

“FinancialRiskandReturnintheBiotechandPharmaceuticalIndustriesfrom1930to2015”.WorkingPaper,SloanSchoolofManagement,MassachusettsInstituteofTechnology,2016.

Thakor,RichardT.,andAndrewW.Lo.“CompetitionandR&Dfinancingdecisions:Theory

andevidencefromthebiopharmaceuticalindustry.”No.w20903.NationalBureauofEconomicResearch,2015.


Thakor,RichardT.,andLo,AndrewW.“OptimalFinancingforR&D-intensiveFirms”.

WorkingPaper,2017.Thomas,DavidW.,Burns,Justin,Audette,John,Carroll,Adam,Dow-Hygelund,Corey,and

Hay,Michael.“ClinicalDevelopmentSuccessRates”.BiotechnologyInnovationOrganization(BIO),2016.

15March2017 Appendix:FDAHedges PageA–1of9

AppendixA:AdditionalResults

A.1Multiple-PhaseOptions

AnFDAoptionmaybestructuredtocovermultiplephasesofapproval,sothatitpaysoff

if there is failure inany subsequentphaseof thedrugdevelopmentprocess.Asa simple

example,considerthecasewheretherearefourdiscretedatesintheapprovalprocess:t=1

(phase1), t=2 (phase2), t=3 (phase3), and t=4 (final FDAapproval of aNewDrug

Application orBiologics LicenseApplication). In order to demonstrate the conceptmore

simply,inthefollowingweassumethateachphaseisthesamelengthoftime,thusremoving

theuncertaintyrelatedtothetimewhentheapprovaldecisionismade.Asbefore,weuse

actualprobabilitiestocomputeexpectedvalueswhicharethendiscountedattherisk-free

rateduetotheidiosyncraticnatureofapprovalrisk.IfptistheprobabilitythattheFDAwill

approvethedrugattimet,thenthepriceoftheFDAoptionatt=3willbe:

P3= exp -rt (1-p4)X

Theoptionwillbepricedrecursivelyateachstage.Therefore,theFDAoptionwhichhas

thepayoffindicatedbyFigureA-1below,wouldbepricedatthestartt=0by:

P0= exp -4r p1p2p3(1-p4)X + exp -3r p1p2(1-p3)X + exp -2r p1(1-p2)X

+ exp -r (1-p1)X

Togiveanexample,supposethatabinaryoptionisstructuredsothatitpaysoff$1,000

wheneverthedrugfailstheapprovalprocess.Assumethattherisklessinterestrateis1%

peryear,andthattheprobabilityofsuccessforeachphaseofthedevelopmentprocessisthe

same at 60%. Then purchasing this contract at t = 3 will cost

exp(-0.01) (1-0.60)×1000 =$396.02.Purchasingthiscontractatt=0,however,willcost


$854.10. The high price relative to payoff reflects the fact that the contract offers full

insurance:itwillpayoffifthedrugdevelopmentfailsduringanyphase.Alternatively,one

couldpurchaseacontractofferinginsuranceagainstfailureinaspecificphase,whichwould

thusbevaluedatalowerprice.Thislattercontractmaybevaluableiftherisksoffailurefor

aparticulartypeofdrugareconcentratedinaspecificphase.Forexample,theprobability

ofsuccessforrespiratorydrugsissignificantlylowerinphase2thanitisinanyoftheother

phasesofthedrugdevelopmentprocess(seeThomasetal.(2016)). Asaresult,abinary

optionthatpaysoffintheeventoffailureonlyinphase2maybeparticularlyvaluabletoa

companyoraninvestorthatisfundingsuchadrug.

FigureA1:PayoffDiagramofaFDABinaryOptionattheStartofMultiplePhasesThisfigureshowsthepayoffstructureofamultiple-phaseFDAbinaryoption,whenviewedatthebeginningoftheR&Dprocess.Ineachbranch,ptindicatestheprobabilityofsuccess.

A.2CorrelatedPayoffCalculationsandResults


IntheanalysisinSection3ofthepaper,thepayoffsoftheindividualcontractsinthepool

areassumedtobeindependent.However,asdiscussedpreviously,itispossiblethatthereis

somecorrelationbetween theoutcomesof thevariouscontracts. In thissection,we thus

examinetheresultswhenrelaxingtheassumptionofindependentoutcomes,andintroduce

acorrelationof0.3betweenthepayoutsoftheNcontracts.

Toexplorethis,wesimulatetheX1,…,X50contractsasBernoullirandomvariables,and

weallowforpairwisedependencebetweenallcontractsbyassociatingeachcontractwitha

randomvariableZithatisnormallydistributedwithmean0andvariance1.Ziisassociated

withXiasfollows:

Xi=1ifZi<αi0ifZi≥αi

Here,lettingZ1,…,Z50bedistributedaccordingtoamultivariatestandardnormaldistribution

withcovariancematrix∑allowsthepairwisecorrelationamongX1,…,X50tobecapturedby

thepairwisecorrelationamongtheZi's.

FigureA2presentstheSharperatiosforvariousvaluesofNasafunctionoftheportfolio

markupwiththiscorrelationassumption.Inthiscase,theSharperatiosarelowerthanthe

casewith independent contracts. Moreover, the improvement in the Sharpe ratio is not

monotonic as the number of contracts increase. In particular, while there is a large

improvementintheSharperatiofromN=1toN=10,theSharperatiosareverysimilar

betweenN=50andN=100.ThecorrelationbetweenthecontractsreducestheSharperatio

becausethecorrelationincreasesthestandarddeviationoftheportfolio.Sincethestandard

deviationentersintothedenominatoroftheSharperatio,alargercorrelationwillcausethe

Sharpe ratio to decrease. In this case, introducing correlated assets reduces the

diversificationoftheissuer’sportfolio,thusreducingtheSharperatio.Thisanalysisshows


thatthebenefittotheissuerofholdingcontractscriticallydependsonboththenumberof

contracts, and on the correlation of the payouts between the contracts. However, aswe

previously discussed, a substantial correlation between contracts is not likely to hold in

practice.

FigureA2:SharpeRatios,EquicorrelatedContractsThis figure plots the Sharpe ratios of dealer returns as a function of the portfoliomarkup% forvarious values of N, the number of contracts offered in the pool. These calculations assume acorrelationof30%betweenthepayoutsofthecontracts.

A.3PortfolioPayoffSimulationResultsAcrossVariedParameters


TableA1 belowprovides theportfoliopayoutmean,variance, andstandarddeviation

whenvaryingtheparametersforthenumberofcontractsN,theFDAdecisionarriverateλ,

probabilityofpayoutp,andcorrelationbetweencontractsρ.TableA2providestheportfolio

payoutmean,variance,andstandarddeviationforvariousnumbersofcontractsNacross

thedifferentdiseasegroups.

TableA1:PortfolioDistributionAttributes

This tableprovides the simulation results for themeanportfoliopayout, varianceofpayout, andstandard deviation of payout for various numbers of contractsN, arrival rate parameters λ, forvariousdiseasegroups,andforprobability,andvaryingcorrelationparameters.

NumberofContracts λ Mean Variance StdDev

N=1

0.20 0.15 0.105 0.320.25 0.18 0.117 0.340.33 0.20 0.132 0.360.50 0.24 0.152 0.391.00 0.27 0.176 0.421.50 0.28 0.185 0.432.00 0.29 0.191 0.44

N=10

0.20 0.16 0.011 0.100.25 0.18 0.012 0.110.33 0.20 0.013 0.120.50 0.24 0.015 0.121.00 0.27 0.018 0.131.50 0.28 0.019 0.142.00 0.29 0.019 0.14

N=50

0.20 0.16 0.002 0.050.25 0.18 0.002 0.050.33 0.20 0.003 0.050.50 0.24 0.003 0.061.00 0.27 0.004 0.061.50 0.28 0.004 0.062.00 0.29 0.004 0.06

N=100 0.20 0.16 0.001 0.03


0.25 0.18 0.001 0.030.33 0.20 0.001 0.040.50 0.24 0.002 0.041.00 0.27 0.002 0.041.50 0.28 0.002 0.042.00 0.29 0.002 0.04

NumberofContracts Correlation Mean Variance StdDev

N=1 0.00 0.20 0.133 0.36

NumberofContracts Probability Mean Variance StdDev

N=1

p=0.2 0.14 0.097 0.31p=0.3 0.20 0.133 0.36p=0.4 0.27 0.158 0.40p=0.5 0.34 0.175 0.42p=0.6 0.41 0.182 0.43p=0.7 0.48 0.180 0.42p=0.8 0.54 0.169 0.41

N=10

p=0.2 0.14 0.010 0.10p=0.3 0.21 0.013 0.12p=0.4 0.27 0.016 0.13p=0.5 0.34 0.018 0.13p=0.6 0.41 0.018 0.14p=0.7 0.48 0.018 0.13p=0.8 0.55 0.017 0.13

N=50

p=0.2 0.14 0.002 0.04p=0.3 0.20 0.003 0.05p=0.4 0.27 0.003 0.06p=0.5 0.34 0.003 0.06p=0.6 0.41 0.004 0.06p=0.7 0.48 0.004 0.06p=0.8 0.55 0.003 0.06

N=100

p=0.2 0.14 0.001 0.03p=0.3 0.20 0.001 0.04p=0.4 0.27 0.002 0.04p=0.5 0.34 0.002 0.04p=0.6 0.41 0.002 0.04p=0.7 0.48 0.002 0.04p=0.8 0.55 0.002 0.04


0.05 0.20 0.133 0.360.10 0.21 0.133 0.370.15 0.21 0.133 0.370.20 0.20 0.132 0.36

N=10

0.00 0.20 0.013 0.120.05 0.20 0.019 0.140.10 0.21 0.025 0.160.15 0.20 0.031 0.180.20 0.20 0.037 0.19

N=50

0.00 0.20 0.003 0.050.05 0.20 0.009 0.100.10 0.20 0.016 0.130.15 0.21 0.022 0.150.20 0.20 0.029 0.17

N=100

0.00 0.20 0.001 0.040.05 0.20 0.008 0.090.10 0.20 0.014 0.120.15 0.20 0.021 0.150.20 0.20 0.028 0.17

TableA2:PortfolioDistributionAttributesAcrossDiseaseGroups

This tableprovides the simulation results for themeanportfoliopayout, varianceofpayout, andstandarddeviationofpayoutforvariousnumbersofcontractsN,acrossdifferentdiseasegroups.

NumberofContracts DiseaseGroup Mean Variance StdDev

N=1

Hematology 0.51 0.176 0.42InfectiousDiseases 0.50 0.178 0.42Opthamology 0.40 0.181 0.43OtherDiseaseGroups 0.48 0.180 0.42Metabolic 0.64 0.177 0.42Gastroenterology 0.42 0.182 0.43Allergy 0.48 0.179 0.42Endocrine 0.44 0.182 0.43Respiratory 0.49 0.179 0.42Urology 0.48 0.179 0.42


Autoimmune 0.42 0.182 0.43Neurology 0.39 0.181 0.43Cardiovascular 0.37 0.180 0.42Psychiatry 0.38 0.180 0.43Oncology 0.27 0.158 0.40

N=10

Hematology 0.51 0.018 0.13InfectiousDiseases 0.50 0.018 0.13Opthamology 0.39 0.018 0.14OtherDiseaseGroups 0.48 0.018 0.13Metabolic 0.64 0.018 0.13Gastroenterology 0.42 0.018 0.14Allergy 0.48 0.018 0.13Endocrine 0.44 0.018 0.14Respiratory 0.48 0.018 0.13Urology 0.48 0.018 0.13Autoimmune 0.42 0.018 0.14Neurology 0.39 0.018 0.13Cardiovascular 0.37 0.018 0.13Psychiatry 0.38 0.018 0.13Oncology 0.27 0.016 0.13

N=50

Hematology 0.51 0.003 0.05InfectiousDiseases 0.50 0.003 0.05Opthamology 0.40 0.003 0.05OtherDiseaseGroups 0.48 0.003 0.05Metabolic 0.64 0.004 0.06Gastroenterology 0.42 0.003 0.05Allergy 0.48 0.003 0.05Endocrine 0.44 0.003 0.05Respiratory 0.48 0.003 0.05Urology 0.48 0.003 0.05Autoimmune 0.42 0.003 0.05Neurology 0.39 0.003 0.05Cardiovascular 0.38 0.003 0.05Psychiatry 0.38 0.003 0.05Oncology 0.27 0.002 0.04

N=100

Hematology 0.51 0.002 0.04InfectiousDiseases 0.50 0.002 0.04Opthamology 0.40 0.002 0.04OtherDiseaseGroups 0.48 0.002 0.04


Metabolic 0.64 0.002 0.04Gastroenterology 0.42 0.002 0.04Allergy 0.48 0.002 0.04Endocrine 0.44 0.002 0.04Respiratory 0.48 0.002 0.04Urology 0.48 0.002 0.04Autoimmune 0.42 0.002 0.04Neurology 0.39 0.002 0.04Cardiovascular 0.38 0.002 0.04Psychiatry 0.38 0.002 0.04Oncology 0.27 0.002 0.04

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