Working Paper Series Adjusted Money s Worth Ratios in Life Annuities. Jaime Casassus; Eduardo Walker.

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1 Working Paper Series Adjusted Money s Worth Ratios in Life Annuities Jaime Casassus; Eduardo Walker Pontificia Universidad Catolica de Chile

2 ADJUSTED(MONEY S(WORTH(RATIOS( IN(LIFE(ANNUITIES( JaimeCasassus * andeduardowalker ** August2013 ABSTRACT TheMoney sworthratio(mwr)measuresanannuity sactuarialfairness. It is calculated as the ratio of the present value of expected future paymentstothecostoftheannuity.wearguethatfromtheperspectiveof annuitants,thismeasuremayoverestimatethevaluejforjmoneyobtained, since it does not adjust for illiquidity and default risk of the insurer. We proposeamultijfactorsolutionforanadjustedmwr(amwr)thataccounts forthesesourcesofrisk.measuringtheseriskadjustments ischallenging, requiringdetailedknowledgeofthejointdistributionofassetsandliabilities of the insurer. We use our model to analyze the competitive Chilean annuity market, which offers MWRs above 1, finding that indeed these ratiosarebiasedupward7percentonaverage.wealsopresentestimates ofdefaultoptionvalues,assetinsufficiencyprobabilitiesandimpliedcredit spreadsforeachannuityproviderinthechileanmarket. KEYWORDS:Money'sworthratios,annuities,insurancecompanies,creditrisk,liquiditypremium, defaultprobability,multicfactorcontinuousctimemodels,emergingmarkets JELClassification:G22,G13,G28 * InstituteofEconomicsandFinanceUC,PontificiaUniversidadCatólicadeChile,jcasassus@uc.cl. ** SchoolofBusiness,FinanceUCandCGCUC,PontificiaUniversidadCatólicadeChile,ewalker@uc.cl. The authors wish to thank the efficient assistance of Andres Mourgues, the generous facilitation of local fixedincomedatabylvaindices,andtheoverallsupportofthesuperintendenciadevaloresyseguros.we also acknowledge financial support from Grupo Security through FinanceUC and from FONDECYT (grant ).WeappreciatethecommentsofDavidBlake,FernandoColoma,PatricioEspinoza,RodrigoFlores, EstelleJames,MarcosJaque,OsvaldoMacías,JorgeMastrangeloandErnestoRios,aswellastheseminar participantsatuc,bancocentraldechile,the4 th WorkshoponRiskManagementandInsurance(Spain),the 3 rd InternationalConferenceoftheFinancialEngineeringandBankingSociety(France)andthe1 st Workshop onquantitativeriskmanagement(chile).naturally,theremainingerrorsareofourexclusiveresponsibility. 1

3 1. Introduction, Longevity is one of the most important risks faced upon retirement by pensioners, and life annuities are the bestjsuited instruments to handle this risk. As explained in Brown, Mitchell, Poterba and Warshawsky (2001), there are many kinds of annuities, but they all share the longevityriskinsuranceattribute.herewefocusonfixedlifeannuities. Animportantissueistomeasurehowgoodadealapensionergetswhenbuyingafixedannuity.In this context, Mitchell, Poterba, Warshawsky and Brown (1999) propose, define and estimate Money s Worth Ratios (MWR) for pension annuities in the US. MWRs are defined as the discounted present value of expected future annuity payments divided by the money (or premium)paidinadvancefortheannuity.expectedvaluesareestimatedusingmortalitytables anddiscountingtakesplaceusingthefulltermstructureofriskjfreeinterestrates.highermoney s worthratiosimplybetterdealsforannuitants. ManystudieshaveusedthismethodologytodeterminethevalueJforJmoneythatpensionersget aroundtheworld.forexample,jamesandsong(2001)aresurprisedtofindmwrsgreaterthan oneinmanycases,amongotherreasonsbecausethereexistoperationalcostswhichmustbepaid by the pension annuity providers, whose present value should be added to that of annuity outflows(e.g.thesameratiofromtheperspectiveoftheproviderislarger).fong,mitchelland Koh (2010, 2011) evaluate MWRs of life annuities and discuss the impact of the government mandatetoannuitizeanditsroleasanannuityproviderontheinsurancemarketinsingapore. CannonandTonks(2009)surveyseveralstudiesforannuitymarketsaroundtheworldandfind thatalthoughmwrsdifferwidelyacrosscountries,theyareconsistentlyveryhigh.theyclaimthat annuities seem remarkably good value for consumers and that it appears that insurance companiesarelosingmoneyontheannuitybusinessthattheywrite.forchile,thecasestudyto which we apply our methodology below, because of detailed data availability, James, Martinez and Iglesias (2006) and Rocha, Morales and Thorburn (2008) find that MWRs are significantly largerthanone. WearguethatMoney sworthratiosofirrevocablelifeannuitiesshouldbeadjustedtoconsider atleasttwofactors:illiquidityandcredit risk.withouttheseadjustments,measuredmwrs are upward biased. Indeed, pension annuities tend to be completely illiquid liabilities from the perspectiveofannuityproviders.therefore,(ignoringlongevityrisk)arisklessannuitymaybepaid withcertaintybyinvestinginaportfolioofcompletelyilliquiddefaultjriskjfreebonds.liquidity spreads can be substantial, so the numerator of MWRs may be overstated simply because expectedflowsarediscountedusinginterestrateswhichare toolow. 1 Also,thereisdefaultrisk, so future flows are not received with certainty. This also rather obviously reduces the present valueoffuturepayments(orthenumeratorofthemwrs). 1 SeeforexamplePfluegerandViceira(2011)whofindaliquidityriskPremiuminTIPSofabout70basis pointsinnormaltimes.fora10jyeardurationannuitythisisanoverstatementof7%. 2

4 Hereweproposeaclosedformsolutionformoney sworthratioswhichconsidersboth,illiquidity anddefaultrisk.wecallittheadjustedmoney sworthratio(amwr).thisadjustmentisdoneby taking as reference an illiquid defaultjriskjfree replicating portfolio of bonds with payments identicaltotheexpectedannuities andthenadjustfordefaultriskusingoptionpricingtheory.as expected,riskissummarizedinthevolatilityoftheannuityprovider sequity,whichdependson leverage, maturity mismatching, illiquidity mismatching and other assets volatilities. These parametersthemselvesdependonthemeanreversionininterestratesandinliquiditypremia, amongotherfactors. WeillustrateourresultswithadataJintensiveapplicationtotheChileanpensionannuityindustry. This market has been considered quite competitive even before the mandatory auction system (namedscomp)wasimplementedin2004.walker(2006,2009)documentsastructuralchangein 2001afterwhichMWRsbecamelargerthanone. 2 Jamesetal(2006)andRochaetal(2006,2008) findthatthechileanmarketseemstobeamongthemostcompetitiveintheworld.theaverage MWRreportedinRochais1.064 for2004,withanupwardtrendsince ThesehighMWR levels may be interpreted as a puzzle, for the reasons discussed in James and Song (2001). However, our results indicate that the high MWRs for Chile indeed reflect lack of liquidity and creditriskadjustments.thismayalsoexplainthepuzzleelsewhere. 4 Naturally, we are not the first to notice that credit risk is an important issue in life annuities. BabbelandMerrill(2007)modelindividualbehaviorunderthepossibilityofdefaultbytheinsurer issuing annuities, finding that even a little default risk can have a very large impact on annuity purchasedecisions. Soitisimportanttomodelandmeasuredefaultriskinthiscontext,focusingonthesupplysideof annuities, which we do. It is perhaps due to practical difficulties that the default or credit risk adjustments have not been implemented in the annuities literature so far, since it requires detailedknowledgeoftheinvestmentportfoliooftheannuityprovider,modelingthebehaviorof theassetclassestheyinvestinandmeasuringeconomicleverage. We model credit risk and illiquidity following two different literature strands: default risk and options associated with life insurance contracts. Structural models of default start with Merton (1974),relatingcapitalstructureandtheliabilities creditrisk.defaultistriggeredwhentheasset value falls below a certain threshold. Some articles determine this threshold endogenously, includingleland(1994),lelandandtoft(1996),goldstein,juandleland(2000)andacharyaand 2 Walker op cit. shows that the annuity IRR that equates expected payments to the annuity premium became larger than the IRR of corresponding riskless bond (with identical payment structures), which is equivalent. 3 ForamorerecentandcomprehensivedescriptionoftheannuityindustryinChile,seeMitchellandRuiz (2011). 4 AsfoundinDoyle,MitchellandPiggott(2004),adverseselectionofannuitiesbylongJlivedindividualsmay also be an important issue from a supply side perspective, but this should bias the measured MWRs downwardandnotviceversa. 3

5 Carpenter (2002). These models are elegant when it comes to interpreting the equity holders option to default, but are difficult to implement. Important practical differences in the case of annuityliabilitiesisthatassetscorrespondtoaportfolioofdifferentkindsofinvestmentsandthat liabilitiesareverylongjtermandcompletelyilliquid. The model is also related with the literature of embedded options in life insurance contracts, which begins with Brennan and Schwartz (1976) and Boyle and Schwartz (1977). Briys and de Varenne (1994), Miltersen and Persson (1998), Grosen and Jorgensen (2000) reconsider these articlestomodellifeinsurancecontractswithassociatedsavingsthathaveguaranteedminimum ratesofreturn.inaddition,brownandwalker(2009)usethisconceptualframeworktostudythe specificproblemofmaturitymismatching,typicalofannuityinsurancecompanies,whichhappens when assets mature before liabilities, allowing an analogy between reinvestment risk and prepaymentrisk. Inourcase,thepossibletriggersfordefaultarethateitherthemarketvalueofliabilitiesgrows beyondtheassets (whichhappenswhenassetsareshorterthanliabilitiesandinterestratesdrop and/orwhenpeopleonaveragelivelongerthanexpected)orwhenassetvaluesfallfasterthan liabilities (whichmayhappenduringacrisis,forexample). Inordertodeterminethetimingofthedefaultoption,whichiscrucialtodetermineitsvalue,itis knownsincemerton(1974)thatequityholderswillpostponeitasmuchaspossible.wetakean eclectic view in this aspect, and assume that the supervisory authority will check the annuity insurancecompany sequityatfixedtimeintervals.whenequityturnsnegative,shareholdersare requiredtoinvestmorecapital.iftheydon t,theyhavetheoptiontowalkaway.thevalueofthis optionispaidbysomeone:theannuityholders,thestate,orsomecombinationthereof. Anotheraspectthatinterestsusisilliquidity.Weconjecturethatwhennegativeequityiscaused byaliquidityshock,implyingadropinthemarketvaluesofrelativelylessliquidassets(suchas duringthe2007j2008crisis;seedemyanykandhemert(2009),forexample)itmaynotbeoptimal to require additional capital, since liquidity premia are mean reverting. In any case, it may be difficult to disentangle liquidity risk from credit risk (Longstaff, Mithal et al. (2005)). We also considerthattheliabilitiesoftheinsurancecompany(i.e.,thelifeannuities)areilliquid,astylized fact that has been recently recognized in the portfolio choice with annuities literature (see for example,browne,milevskyandsalisbury(2003),horneff,maurerandrogalla(2010)andkoijen, NijmanandWerker(2011)). The rest of the paper is organized as follows. Section 2 presents a multijfactor model for the adjusted Money s Worth Ratios. Section 3 develops the methodology used to estimate the marketjvalue balance sheets that are input for our optionjpricing model. Section 4 shows the estimationoftheparametersourmodelandtheempiricalresults.inthissectionwealsodiscuss the regulatory incentives that have driven the Chilean market to an outcome of high MWRs. Finally,section5concludes. 4

6 2. A,Multi1factor,Model,for,Adjusted,Money's,Worth,Ratios, ThissectionfirstderivestheMoney sworthratiosadjustedforliquidityandcreditrisk,andthen presentsamultijfactoroptionpricingapproachforlifeannuities.finally,italsoshowsthelinkage between the default probabilities of the annuity providers (i.e., insurance companies) and the parametersthatdeterminethedefaultoptionvalues. a. Adjusted,Money's,Worth,Ratios,(AMWR), TheMoney sworthratios(mwr)ofanannuityisameasureofactuarialfairnessandiscalculated as: # = (1) where is the discounted present value of expected future annuity payments and is the initialpaymentmadebytheannuitant.astandardpracticeistodiscounttheexpectedpayments withthetreasurytermstructureofinterestrates,therefore: = [] [] (2) Here,[]is the expected payment at timeand []is the price of a zerojcoupon liquid governmentbondmaturingin.theexpectedflow considersthesurvivalprobabilityandalso unexpectedchangesinthemortalitytables,ariskthatisuncorrelatedwiththeinterestraterisk. Wefirstarguethattheexpectedflowsshouldbediscountedusingthetermstructureofilliquid defaultjfree bonds instead of using the Treasury yields. These are the correct discount rates, because an irrevocable life annuity is equivalent to a nonjcallable, nonjputtable illiquid bond issuedbyanannuityprovider. 5 Let bethepresentvalueofexpectedannuityflowsusingthe termstructureofilliquiddefaultjfreebonds: = [] [] (3) where []isthepriceofazerojcoupondefaultjriskjfreeilliquidzerocouponbondmaturingin. Notethat [] []becauseilliquidbondsarediscountedathigherratesthancorresponding liquidbonds,therefore, 1. WealsoproposethatanappropriatemeasureofthevalueJforJmoneyofannuitiesshouldconsider thepossibilitythattheannuityinsurancecompany(aic)maydefaultinthefuture.todothisina 5 Inthetextweusetheterms annuityinsurancecompany(aic) or annuityprovider indistinctively. 5

7 simpleway,wefollowthestructuralmodelofmerton(1974).weassumethatregulatordefines anexogenousregulatoryhorizontafterwhichitwillexaminethemarketjvaluebalancesheetof theannuityprovider.forexample,belowweconsiderregulatoryhorizonsof1,3and5years.if thevalueofassetsisbelowtheliabilities,theaicmayinvestmorecapitalordecidetowalkaway, whichimpliesbankruptcy.exjante,theshareholder sequityhasembeddedtheoptiontodefault, avaluethatisextractedfromtheannuityholders(and/orfromthestate,ifthereisaguarantee). For simplicity we assume that the annuity provider issues only one life annuity, hence, the liabilitiesoftheinsurancecompanyareexactlythatannuity. TheMoney sworthratioadjustingforbothliquidityandcreditriskisthusdefinedas: with #$ = (4) [] = [#[0, ]] (5) where []is the adjusted value of the annuity and[#[0, ]]corresponds to the value of the option to default owned by the AIC. Equation (5) shows that it is also the value extracted from the annuity holders (and/or from the State if guarantees exist). Note also that [] 1because the value of the option is nonjnegative. The following proposition formalizes bothmarketjbasedadjustmentsconsideredforthemwr. Proposition)1:TheMoneyWorth sratioadjustedforilliquidityandcreditriskis: #$ = # [] (6) wheretheliquidityfactor,,andthecreditriskfactor, [],arebothlessthanorequaltoone. Therefore, #$ # (7) ThepropositionshowsthesourcesoftheoverstatementoftheMWR s.first,theliquidityfactor adjuststhemwrforliquidityshocksinthemarket.duringnormaltimesthisfactorisclosetoone, however,ifaliquidityshockoccursitsvaluewilldecrease.second,thecreditriskfactoradjuststhe MWRfortheoptiontodefaultownedbytheAIC.Weknowfromtheoptionsliteraturethatthe 6

8 value of this option is increasing in the leverage ratio,, and in the volatility of the underlying equity,,therefore,thecreditriskfactorisdecreasinginthesetwovariables.finally,notice thatifdefaultoftheaiciscertaininthehorizon,then #$ = # < # (8) b. Determinants,of,the,AMWR,, ToquantifythedeterminantsoftheAdjustedMoney sworthratios(i.e.,theliquidityandcredit riskfactors),wefirstneedtoconsideradynamicmodelofinterestratestoobtainthedefaultjfree zerojcoupon bonds []and [], and the value of the option to default owned by the AIC shareholders. WefollowtheaffinetermstructureliteratureofDuffieandKan(1996),Duffie,PanandSingleton (2000), and Dai and Singleton (2000) and choose a Gaussian threejfactor model for the illiquid defaultjfree yields. The Gaussian nature of our model helps us obtain a simple closedjform solutionfortheoptiontodefaultandtheamwr,whichisoneoftheimportantcontributionsof thiswork.6 The variables that determine the state of the fixed income market are: the shortjterm riskjfree interest rate, ; the longjterm riskjfree interest rate, ; and the shortjterm liquidity spread,. Thesevariableshavethefollowingdynamics: (9) = +, (10) = ( ) +, +, = + + +, +, +, (11) where, are standard Brownian processes independent of each other. We define these processesundertheriskjneutralmeasureq,becauseitisconvenientforvaluationpurposes.later in the paper, we assume a constant riskjpremia structure that will help us clarify if these risk factorsarepricedornotbytheagentsintheeconomy. TheshortJandlongJterminterestratefactorsarededicatedtomatchtheTreasurytermstructure ofinterestrates.thesefactorsfollowmeanjrevertingprocessestowardsalongjtermmean.we assume that the speed of meanjreversions and are positive. However, we validate these assumptions when we estimate the model. For the illiquid term structure we also consider the liquidityspread.thisvariablealsofollowsameanjrevertingprocess.inthiscase,theexpected 6 OfcoursenonJGaussianspecificationscanbeusedinstead,butthiswouldimplytheusageofnumerical techniquestosolvethemodel(seeforexample,duffieetal.(2000)andcasassus,collinjdufresneand Goldstein(2005)). 7

9 change in the spread depends on the shape of the Treasury term structure of interest rates through the parameters and. For example, if > 0 then the spreads will tend to decreasewhentheshortjrateishigh.theonlyrestrictionthatneedstobeimposedisthat > 0, aconstraintthatisalsovalidatedinthedata. LetthezeroJcouponbondsbe: [] = and [] = [ ] (12) Theaffinetermstructuremodelpresentedinequations(9)to(11)providesclosedJformsolutions forthesebonds,andtherefore,fortheannuitiesusingbothsetsofdiscountrates(seeequations (2)and(3)).Inparticular,the(log)priceoftheTreasurybondislinearintheshortJandlongJterm interest rates, and the (log) price of the illiquid bond is linear in the interest rates and in the liquidity spread. These solutions allow us to get closedjform expressions for the liquidity adjustmentmultiplierfortheawmr.thefollowingpropositionshowsthisresult. Proposition) 2: Given the expected annuity payments and the affine term structure model in equations(9)to(11),theliquidityfactorhasthefollowingrepresentation = [] [] [] [] (13) wherethepriceoftheliquidandilliquidzeroccouponbondsaregivenby = # + + (14) = # (15) respectively. Here, and are deterministic functions of the maturity of the bond that dependontheparametersofthemodel. Proof:SeeAppendixA.1. ToobtainthecreditriskadjustmentfortheAMWR,weneedtoderivethedynamicsofbothassets andliabilitiesoftheinsurancecompany.sincetheliabilitiesoftheaicarethelifeannuities,itis straightforwardtoobtainthedynamicsof byapplyingito slemmatoequation(3): 8

10 = + +, +, +, (16) Theexpectedliabilities returnundertheriskjneutralmeasureistheilliquidinterestrate, +, becauseoftheilliquidnatureofthelifeannuities.theparameters dependonthecovariance and persistence of the state variables and on the expected annuity payments. In particular, the sarerepresentedby: = + +, = + wherethe areweightedaverage givenby = and = [][] [] [] [] (17) for =,,. Notethatthemarketvalueofliabilitiesisendogenousandcanbespannedbytheinterestrates andliquidityspreadstatevariables.theunderlyingassumptioninequation(16)isthattheaicwill keep annuities with the same duration and convexity over time. This is, as time goes by, the annuitiesarepaidandnewannuitantswithasimilarprofileenterthecompany.thisalsoimplies thatthevolatilityoftheliabilitiesoftheaicisconstantovertime. An annuity provider should invest most of its funds in fixed income securities, but it may also invest in other asset classes, such as, stocks, real estate and commodities. This means that the assets of the AICs are affected by risks which are unspanned by the term structures of interest rates. For this reason, we assume an exogenous process for the AICs assets that has an extra sourceofuncertainty.fortractability,weassumethattheexpectedreturnoftheassetsunderthe riskjneutral measure is also the illiquid riskjfree rate because many of the assets of the AIC are illiquid.inparticular,weconsiderthefollowinggeometricbrownianmotion: = + +, +, +, +, (18) Here,, isastandardbrownianprocessindependantofthefixedincomebrownianprocesses.it represents the uncertainty from the nonjfixed income investments. The covariance parameters are estimated from an OLS timejseries regression between the asset returns and the fixed incomefactors. Using equations (16) and (18) we can obtain the value of the default option for any regulatory horizont.replacingthevalueoftheoptioninequation(5)yieldsthefollowingexpressionforthe marketjvalueoftheliabilities,i.e.,theadjustedvalueoftheannuity: [] = [ #[0, ]] (19) 9

11 Equation(19)showsthatthevalueoftheoptiontodefaultcorrespondstoaEuropeanexchange option of the liabilities for the assets of the AIC, which matures at the regulatory horizon (see Margrabe, 1978). In the same way, we can obtain the equity market value of the insurance companythatincludestheoptiontodefault: [] = [] = [ (20) #[, 0]] Notethatthemarketvalueoftheequityisgreaterthanvalueoftheequitywithouttheoptionto default,i.e., [].Here, alsorepresentstheequityvalueinthecasethataic shareholders are forced to invest more capital if at the regulatory horizon the company has insufficientassetstocoverliabilities. Our model provides a closedjform solution for the option value to default based on the BlackJ ScholesJMerton formula (see Black and Scholes, 1973, and Merton, 1973), and therefore, the credit risk adjustment factor and the market values of the equity and liabilities of the annuity providercanbeobtainedexplicitly.thefollowingpropositionshowstheseresults. Proposition)3:)IftheliabilitiesandassetsoftheAICfollowthedynamicsinequations(16)and(18), thenthecreditriskadjustmentfactoroftheamwrhasthefollowingsolution: [] = + (1 ) where[]denotes the standard normal cumulative distribution function and = (21) #[ ], = + and = ( ) + ( ) + ( ) +. Moreover, the marketvalueoftheequityconsideringtheoptiontodefaultis: [] = [ ] [ ] (22) Proof:SeeAppendixA.2. AsintheBlackJScholesJMertonformula, and areadjustedprobabilitiesofexcercising the option. In our case, if = = 0, the firm will go banckrupt with probability 1 and [] [] = and [] = 0.If = = 1thefirmwon tdefaultunderanyevent,therefore, = 1and [] =. c. Asset,Insufficiency,Probabilities,, Ourmodelallowsustoobtain,foranyregulatoryhorizont,theprobabilitythatthevalueofassets isbelowtheliabilities,whichisthereforetheassetinsufficiencyordefaultprobabilityoftheaic. Thisprobabilityisdefinedas: 10

12 #$ = (23) where. istheindicatorfunctionsuchthat = 1ifBistrue. 0otherwise Onedifferencewiththepricingapproachusedaboveisthatinthiscaseweareinterestedinthe distribution of the variables under the true probability measure P. For this reason we need to considerthesystematicriskassociatedwitheachriskfactor.weassumethattheriskpremiaare constant,implyingthatbothassetsandliabilitiesalsohaveconstantriskpremia.wedenotethese as and, respectively. This assumption is crucial to obtain a closedjform expression for the defaultprobabilitiesinequation(23).thefollowingpropositionpresentsthisresult. Proposition) 3:) Assume that the liabilities and assets of the AIC have constant risk premium and that they are driven by equations (16) and (18), respectively. Their dynamics under the true probabilitymeasureare: = + + +, +, +, +, = + + +, +, +, (24) (25) Moreover,thebankruptcyprobabilityfortheAICattheregulatoryhorizont,isgivenby: #$ = 1 with = # and = Proof:SeeAppendixA.3. Itisimportanttonoticethatbyassumingconstantriskpremiathereisnopredictabilityinthese markets, because both assets and liabilities have permanent shocks. The predictability in stocks andbondshasbeendiscussedwidelyinthefinancialliteraturewithmixedresults.asarobustness test,weestimatedaversionofthemodelconsideringthattheriskpremiaareaffineonthestate variables,butwefindnoneoftheseestimatestobesignificantlydifferentfromzero. 11

13 3. Data,sources,and,input,elaboration,to,estimate,the,default, option,values, The Annuity Insurance Companies (AICs) regulator, the Superintendencia de Valores y Seguros (SVS)hasgivenusaccesstodetailedinformationregardingassetsandliabilitiesforeachAICasof December2008andDecember2009.Tradedassetsarevaluedatmarketprices.Inpractice,we consider three sources for the valuation of these instruments: LVA Indices, a price provider for localfixedincome;thepricevectorofthesuperintendenceofpensions;andinformationofeach AIC for instruments which are not local fixed income, such as mutual funds, stocks and a few internationalinvestments.itturnsoutthatusingthesuperintendenceofpensionsdataorthelva Indicesdatagivesverysimilarresults,soweadopttheformer,sinceit stheofficialsourceusedby thesvs. TherearetwokindsofnonJtradedlocalfixedincomeinstrumentswhicharemoredifficulttoprice: mortgagesandleasingcontracts.appendicesbandcexplainthemethodologiesusedtoestimate themarketvalueoftheseinstruments.insummary,tovaluemortgages,weempiricallyestimate the relationship between the interest rates of new mortgages in each month with a lagged reference interest rate and the characteristics of the individual mortgage and the debtor. Considering the regression results and the available data for the explanatory variables as of December2008and2009weestimate marketinterestrates forthemortgages,allowingusto estimatethemarketvaluesofthemortgageportfolios.forleasingcontracts,weassumethatthey aresimilartolargemortgagesbutwithhighercreditrisk. a. Present,value,of,annuity,liabilities,assuming,no,default,risk, Assuminginitiallynodefaultrisk,annuitiesarevaluedasthepresentvalueoftheexpectedfuture paymentsdiscountedusingatermjstructureofinterestrateswithnodefaultriskdenominatedin thesamecurrencyunitastheannuityliabilities(uf,thelocalinflationindexedunitofaccount). The annuities expected cash flows are estimated using the most recently available mortality tablesatthetimeofthestudy(2009fortheprincipalsand2006forbeneficiaries).weusedthe SVS official software (SEACSA) to estimate the aggregate expected annuity cash flows for each annuityprovider. Theyieldcurveoflocalgovernmentbondsislikelytoreflectthegreatermarketliquiditythatthese bonds have, so these interest rates are low relative to less liquid but safe bonds. We have arguedthatgiventhatirrevocablelifeannuitiesarecompletelyilliquid,thereplicatingportfoliois composedofilliquidbonds,andthatsuchayieldcurveshouldbeusedtovaluethem. Totakethisilliquidityintoaccount,hereweusealocalAAAJratedbondyieldcurvetoestimatethe present value of liabilities. It is true that AAA bonds have some credit risk, but the additional spreadforcreditriskispresumablysmallcomparedwiththespreadattributabletotheirlower 12

14 liquidity. Still, for completeness, we also estimate the present value of annuity liabilities using governmentandlocalaajratedyieldcurves. ThegovernmentbondyieldcurvewasfittedusingtheNelsonandSiegelmethodology,treating couponbondsasportfoliosofzerojcoupons,usingthelast5tradingdaysin2008and2009.figure 1presentsthefittedcurvesineachperiod. FortheAAAandAAyieldcurveswetriedtofollowthesameprocedure,butthereducednumber oftransactionsimpliedunreliableresults.soinsteadwedidthefollowing:first,foreachannuity provider(oraic)weestimatethepresentvalueofannuityliabilitiesusingthegovernmentyield curve.then,foreachaicweestimatetheinternalrateofreturn(irr)whichequatesthepresent value of the expected flows with the present value using the entire government yield curve. Finally, we add to each AIC s IRR the spread corresponding to AA and AAA bonds. Figure 2 presentsthespreadsforaaandaaabondsovertime.wetakethespreadsattheendof2008and 2009,whicharepresentedinTable1. Table 2, Panel A, shows the present value of annuity liabilities using the methodology just described.usingtheaaacurveweobtainanaverageirrof4.13%(measuredintheindexedunit ofaccount,uf)andapresentvalueofusd27,500million,approximately. 7 Thesamecalculation usingthegovernmentbondyieldcurveandtheaacurve,implyvaluesofusd29,100millionand USD26,600million,respectively. PanelBofTable2showsthecorrespondingresultsfor2008.Weclearlyappreciatetheeffectsofa flighttoquality.aaaandaaspreadswereunusuallyhighatthetime. b. Value,of,other,liabilities, Annuity Insurance companies have liabilities other than annuities. We assume that the market valueofsuchliabilitiesisequaltotheirbookvalue.inaddition,weassumethatovertimetheir marketvaluebehaveslikeashortjtermgovernmentbondindex. c. Value,of, operational,liabilities, WeconsidertheconcernsofJamesandSong(2001),thatmanagingaportfolioofannuitieshas operational costs. To estimate the present value of such costs we consider how much pension fundschargeinchileformanagingprogrammedwithdrawals.atthetimeofthisstudythefeewas 1.25%ofeach payment. If the cost is always a fixedfraction of the flow, then it also is a fixed fractionofthepresentvalueoftheflow.sothepresentvalueofannuityliabilitiesisaugmentedby 1.25%toreflecttheseoperationalliabilities. 8 7 Weuseasreference500CLP/USD. 8 WethankJorgeMatrangeloforthissuggestion. 13

15 d. Market1value,balance,sheets,and,mapping,the,components,to, market,indices, Market1value,balance,sheets, Asexplained,resultsareverysensitivetotheyieldcurvechosentovalueannuityliabilitiesbutnot to the source used for pricing the assets, so we use the Superintendence of Pensions to value themandtheadhocmethodologydescribedpreviouslytovaluemortgagesandleasingcontracts. Table3showsasummaryofthemarketJvaluebalancesheetforeachAIC.Wealsovalueliabilities, as described, using government, AAA and AA yield curves. Total liabilities include other and operational inthiscase.wepresentestimatesfordecember2008and2009.aicsareordered accordingtotheirleverage,usingtheaaacurve. ConsideringtheAAAreferencecurve,weobservethatthesystem saverageleverageis28timesin 2009and71timesin2008.In2009therearetwocompanieswithnegativeequityandnineare abovethemaximumleveragelevelallowedintheregulation. 9 In2008onlytwocompanieswould havecompliedwiththemaximumallowedleverage,ifweusetheaaacurvetodiscountannuity liabilities. Mapping,the,components,to,market,indices, Table4showshowthedifferentcomponentsoftheassetJsideofthebalancesheetsaremapped intomarketindices,forthecaseofoneparticularaic. Themethodologyusedforvaluingannuityliabilitieswasexplainedaboveaswellasthevalueof the operationalliabilities.wemapthe riskfreeannuity toa 9Jyearplus durationbondindex ( LVAZCZ3A ) whosecomponentsareratedaaa. 10 Wecheckedthequalityofanapproximation assuming that this index behaves like a zerojcoupon bond with maturity equal to its average Duration,findingthattheapproximationerrorisminimal,especiallyforthepurposesofestimating variances and covariances. Therefore, in order to consider the differences in Duration between annuityproviders,wetookasreferencetheirroftheindex(lvazcz3a)andconstructedaliability index for each AIC with the same average Duration of their annuities. (We call this index IRVAAAnn, where nn is the number assigned to the AIC). All of these indices returns are perfectly correlated with each other and with the return of the reference index, but may have differentvariancesandcovariancesbecauseofthedifferentdurations. Giventhebehaviorofassetsandliabilitiesandthe2009leverageratio,thebehaviorofequityis residual Whichis20times.As will be explained later, this happens because AICs have neither been required to updatethepresentvalueoftheirliabilitiesusingrecentinterestratelevelsnortousethelatestmortality tablestovalueolderannuities. 10 TheactualindexisconstructedbyLVAIndices.Itrepresentsabuyandholdinvestmentstrategy. 11 NoticethatEquitycanbenegative.Thisdoesn taffecttheoptionvaluecalculationspresentedbelow. 14

16 Other,indicators, We also estimate complementary indicators, by asset class and the Duration of each. Table 5 presents the aggregate summary. Local fixed income has an average Duration of 8.5 years, an Internal Rate of Return of 4.6%. 41.8% of the assets are subject to prepayment risk. However, assuming that other assets have a 1Jyear Duration (with the exception of international fixed income, which is assumed longjterm and currency hedged for these purposes) the average Durationlowersto7.1years. Using the AAA curve, the average liability Duration is 9.6 years, including annuities and other liabilities.giventherelativelyhighaverageleverage(28.5timesusingaaa),theequity sresidual Durationis 63years. Regarding credit risk, 18.5% of the assets have AA or better credit risk rating and 56.7% has a ratingofaorless. 4. Empirical,Results, ThissectionshowsfirstthequasiJmaximumlikelihoodmethodusedtoestimatethefixedincome parametersofthemodelandthecalibrationoftheparametersassociatedtoeachaicportfolio. Then, it presents the liquidity and credit risk adjustment factors for each company. Finally, it showsthevaluesoftheoptionstodefaultandtheireffectonannuities impliedcreditspreads, andtheassetinsufficiencyprobabilitiesofeachaic. a. QML,estimation, To estimate the fixed income parameters of the model we use monthly data consisting on governmentandcorporateaaabondsbetweenjanuary2002andnovember2010.inparticular, weusedataonbondportfoliosprovidedbylvaindicesthatareusedtobuildtheirfixedincome indices.forthegovernmentbondswehave9portfolioswithaveragedurationsrangingfrom0.82 to12.13years,whileforthecorporateaaabondswehavefourportfolioswithaveragedurations from1.53to11.49years. SincethebondportfoliosofLVAIndicesareconstructedwithcouponpayingbondsthatwedon t have in our data set, we build a fictitious bond for each index that matches the descriptors providedbylvaindices(e.g.,irr,duration,convexity,averagematurity).inparticular,wecreatea bondthathasthefollowingfictitiouspaymentstructure, #$,, = 1 (26) ForeachmonthweobtainanoptimalTandgsuchthatalinearfunctionofthesquaredifference oftheduration,convexityandmaturitybetweenthedataandthefictitiousbondisminimized. Oncewehavethefictitiousbondsthatreplicatethedata,weestimatethefixedincomemodel usingthemaximumlikelihoodmethodologyproposedbychenandscott(1993)andpearsonand Sun (1994). In our affine model, the state variables,, have a multivariate Gaussian 15

17 distribution, which implies that the logarithm of the zerojcoupon bonds and their IRR have a Normal distribution. However, in our case the IRR of the fictitious bonds have a different distribution, because these are couponjpaying bonds. Fisher and Gilles (1996) and Duffee and Stanton(2004)suggestthatareasonablewaytoestimatethesemodelsiswithaquasiJmaximum Likelihoodmethodology,wherethedensityoftheobservedIRRsisapproximatedbyaGaussian distribution.let =,, and betheobservedirr.inthemodel,theirrofthebondsare anonlinearfunctionofthestatevariables, = h.weassumethatthreeirrsareobserved without error and back out the state variables = h, numerically. The three errorjfree IRRsare:thegovernmentbondswithaveragedurationsof0.82and7.86years,andtheAAAbond withanaveragedurationof1.53years.fromthefirsttwoirrswebackouttheshortjandlongj terminterestratestatevariables,whiletheliquidityspreadisobtainedfromtheaaabond.the approximateconditionaldistributionoftheirris: 1 # 1 (27) where istheapproximatejacobiantransformationfrom to,i.e., = # h which isalsoobtainednumerically.forthequasijmaximumlikelihoodestimatorwecalculatethefirst two conditional moments from 1 Normal. and assume that the likelihood function is Once we have the state variables for each period,, we obtain the remaining crossjsection IRRs,whichare7governmentportfoliosand3AAAportfolios.Weassumethattheseobservations havemeasurementerrorsthatfollowar(1)processes: = + with = 1 + (28) where the errors are jointly Normally distributed with zero mean and covariance matrix.theconditionallikelihoodfunctionformeasurementerrorsis 1 = (29) Thelikelihoodfunctionforthepaneldataistheproductofboththelikelihoodoftheobserved data without error and the likelihood of the measurement errors. More details about the estimation procedure can be found in the empirical appendices of CollinJDufresne and Solnik (2001)andCasassusandCollinJDufresne(2005). Table6showstheQMLestimatesofthefixedincomemodel.Theestimatesshowthatthethree statevariablesfollowstationaryprocessesalthoughwithdifferentdegreesofmeanreversion.the liquidity shocks are only temporary ( = 3.724), while the shocks to the longjterm rates are highly persistent ( = 0.065). The longjterm (real) interest rate is 5.4% and the longjterm liquidity spread is 20 bp. The shortj and longjterm interest rates are negatively correlated (i.e., < 0)asarealsotheshortJtermrateandtheliquidityspread (i.e., < 0).Finally,the constantriskpremiaforeachriskfactoraresignificantatleastatthe10%level. 16

18 To calibrate the parameters of the dynamics of AIC s assets, we study in detail the investment portfoliosoftheinsurancecompanies.theappendicesprovidetableswiththebreakdownofthe aggregate investments of the AICs. 12 As expected, corporate bonds dominate the portfolios, followedbysubordinatedbonds,treasurybonds,mortgageloans,realestateandstocks. Duetothelargenumberoffinancialinstrumentsincludedintheseportfolios,itiscrucialtogroup assets with similar characteristics (e.g. same asset class, same currency, and similar maturity, quality and liquidity). The objective is to determine the composition of the AIC portfolios at an aggregatelevel,butalsotogatherinformationaboutthedynamicsofeachoftheseassetgroups. For the latter we need to map each asset class on one of the many indexes provided by LVA Indices,asexplainedintheprevioussection(seeTable4).Wechoosetheportfoliocompositionof theaicsasofdecember2009toobtaintherepresentativeweightsoneachassetclass.oncethe portfolios have been mapped we assume that the companies keep the same composition over time.afterobtainingtheweightsandconsideringthetimejseriesofeachoneoftheindexes,itis straightforwardtoobtainaproxyforthetimejseriesoftheassetsofeachaic. Tocalibratethecovariancecoefficientsoftheassetsinequation(18),werunanOLSregressionfor therealizedassetreturnsusingtheriskjfreeinterestrateandtheotherfixedjincomefactorsas explanatory variables. The regression error corresponds to the uncorrelated factor of each company,,. b. Liquidity,and,credit,risk,factors, WearguethatMWRsshouldbeadjustedforliquidityandcreditrisk.Table7showsthesefactors foreachannuityinsurancecompany.theseadjustmentfactorsdependonthebalancesheetand risks of each AIC and are independent of the type of policy, i.e., gender, early retirement, survivors,etc.thisimpliesthattheadjustmentfactorsshouldbeappliedtoalltheannuityholders ofthecompany. Thetableshowsthatthefactorsvaryconsiderablyacrosscompanies.Inparticular,theliquidity factorrangesfrom0.944to0.989andisloweringeneralforcompaniesthataremorelevered. Thecreditriskfactorsdecreasewithregulatoryhorizonbecausetheoptionvalueincreaseswithit. ThecrossJsectionalvariabilityofthesefactorsalsoincreaseswiththehorizonandtherangesare 0.964J1.000, 0.947J0.997 and 0.934J0.992 for 1, 3 and 5 years, respectively. These factors are lower (i.e., credit risk is more important) for the most levered companies. Considering the two adjustmentfactorstogetherbringsdownthemultiplierstorangesof0.917j0.989,0.898j0.986and 0.885J0.981for1,3and5years,respectively. Overall,bothadjustmentsconsideredhereallowustojustifyMWRupto1.1,afigurethatiseven largerthanthemwrsreportedinrocha,moralesandthorburn(2008)(theaveragemwrin2004 was1.064).indeed,ifweadjustthemwrsfromrochaet.al.(2008)wegetawmrsbelowone. 12 TheportfoliodetailsforeachAICareavailableuponrequest. 17

19 Thus,liquidityandcreditriskadjustmentscanpotentiallyexplainthehighMWRofferedinsome particularmarkets. c. Value,of,the,default,option, Oneoftheobjectivesofthisworkistovaluethelifeannuitiesconsideringthatannuityproviders candefault.asexplainedbefore,theannuityisworththediscountedpresentvalueofexpected futurepaymentsminusthevalueoftheoptiontodefaultheldbytheshareholdersoftheannuity insurancecompany. Table8showstheleverageratiosandthevaluesofthedefaultoptionsforeachAIC,asafraction oftheirequityasofdecember2009fordifferentregulatoryhorizons.thesecondcolumnshows the leverage ratio of each AIC considering the market value of the assets and the liabilities discounted with the illiquid AAA yields. The third to fifth columns present the default option values as a fraction of each AIC s equity (for regulatory horizons of 1, 3 and 5 years). The companiesareorderedfromhightolowoption/equityratio,arankingthatalmostcoincideswith theoneusingtheleverageratio.noticethatequityvaluesincludethedefaultoptionvalue. Itisimportanttonotethat,conceptually,someonemustbearthecostoftheoptiontodefault:it couldbethestate,theannuitantsortheshareholdersincasetheydecidetoinvestmoreequity capitalinthecompanytoavoidbankruptcy.theaggregatevalueofthisoptionisusd460million fora1jyearregulatoryhorizon,usd1billionfora3jyearhorizonandusd1.4billionfora5jyear horizon. In absolute terms, the value of the option to default increases with the regulatory horizon.however,asafractionofequity,thepercentagemightdecreasewiththehorizonifthe marketvalueofequitywithouttheoptionisnegative,asisthecaseofthefirsttwoaicsinthe table. Since the regulatory leverage ratio for this industry is relatively high (20), the option value is a significantfractionofthetotalequityvalue,evenforthecompaniesthatarenearthisthreshold. However, the relevant question for the annuitants is how affected their life annuities may be becauseoftheoptiontodefault.inotherwords,howimportantisthedefaultoptionvalueforthe AIC sliabilities.wefindthatintheaggregate,defaultoptionsrepresent1.7%,3.6%and5.1%of the riskless illiquid liability for regulatory horizons of 1, 3 and 5 years. These don t seem to be large numbers; nevertheless, they can imply IRRs for the liabilities significantly above the correspondingilliquiddefaultjfreeyield. Indeed,Table9showstheIRRandthespreadswithrespecttotheAAAcurve.Asareference, considerthatindecember2009theaveragespreadoftheaacurveovertheaaacurvewas34 basispoints(seetable1).table9showsthatforthe1jyearregulatoryhorizon(thirdcolumnfrom right to left) the majority of annuities qualify as having implied spreads similar to a AA bond. However, when the regulatory horizon is increased, most companies increase their risk exponentiallyandfora3jyearhorizononly4outof16companieshaveimpliedspreadslowerthan theaaspread.fora5jyearhorizon,only2companiesmaintainlowimpliedcreditspreads. 18

20 Toillustratethispointfurther,Figure3showstheadjustedannuityIRRconsideringthedifferent regulatoryhorizons.notethatfora5jyearhorizonsomeaicshaveirrsthatarehigherthanfor thecorrespondingbbbbonds. AfinalexerciseistoestimatetheAIC sdefaultprobabilities(seetable10).notethatthereisa closerelationshipwiththepreviousresults,i.e.,companieswhosedefaultoptionvalueislarger, also have a higher default probability. An interesting difference is the effect of the expected return,becausetheprobabilityofdefaultmightdecreaseifitishigh.toreconcilethisresultwith thepreviousones,itisnecessarytoconsiderthat,althoughtheprobabilityfalls,theexpectedleftj tailvalueintheprobabilitydistributionincreases. d. Discussion, We have found that using the AAA yield curve reference, leverage ratios for most annuity insurancecompaniesareabovethemaximumallowedlevelsbythelocalregulation(whichis20 times).wealsofindthatdefaultoptionsrepresentasignificantfractionoftotalequityformost AICs,especiallyconsideringlongerpossibledefaulthorizons,evenforthecompaniesthatwould complywiththemaximumleverageratio.allofthisisrelatedwithasignificantprobabilityofasset insufficiencyatdifferenthorizons.finally,inadditiontotheilliquidityadjustmentfactorthatwe propose for Money s Worth Ratios (which averages 0.95), the credit risk adjustment factor averagesbetween0.98and0.95,dependingonthepossibledefaulthorizon.forsomecompanies these adjustment factors are significantly lower. Together, these factors justify observing measuredmwrsashighas1.1,whichdon tmeanthatannuitantsgetgooddealsinthechilean market. Aninterestingquestioniswhatincentiveshavebroughttheannuityindustrytothispoint.Inwhat followswepresentafewfactsthathelpexplainthesefindings. The SVS has regulated the annuity industry with two main tools: the matching rule (Norma de CalceorNDC,inSpanish)andtheAssetSufficiencyTest(TestdeSuficienciadeActivosorTSA,in Spanish). 13 The NDC adds the future cash flows of all fixed income investments and classifies them in 10 successivematuritytranches.allinflationjindexedfixedincomepaymentsareconsideredforall the tranches except for the last 2 ones (starting in year 21), which exclude prejpayable assets flows.theseaggregatecashflowsarecomparedwiththeaggregateexpectedliabilityflows(e.g. theannuities ).Forthepurposesofcalculatingthereserverequirements,ifthereareenoughasset flows as to cover the liabilities in any tranche, asset flows are discounted back to the present usinggovernmentbondmarketinterestrates;ifnot,thedeficitisdiscountedbacktothepresent using relatively low interest rates (3%, inflationjadjusted), increasing in this way the reserve requirement. 13 Circular1512andNCG209,respectively. 19

21 However,accordingtotheNDCrule,marketinterestratesusedforvaluingannuitiesneednotbe updated.theycorrespondtotheprevailinginterestrateswhentheannuitywassold. 14 Therefore, the registered annuity liabilities do not take into account that interest rates have dropped systematicallyinabout3percentagepointssince2000,suggestingasizeableunderestimationof itsvalue. On the other hand, there are instructions which indicate that the industry must use updated mortality tables only gradually. 15 Given that life expectancy has increased over time, here is anotherreasonthatexplainswhyannuityliabilitiesareunderestimated. Finally,theassetsufficiencytest(TSA)triestodeterminewhetherunderstressthepresentvalue of asset flows is enough to cover liabilities using a 3% (real) discount rate. Again, the TSA regulationconsidersallassetflows(aslongastheyareinflationjindexed)andrequiressubtracting afractionofthepaymentsofeachinstrumentdependingonitsriskrating,toaccountforcredit risk.forexample,for(local)bbbjratedinstruments,thefactoris3%.the3%flowwritejoffina10j yeardurationbondisequivalenttoaspreadof30basispoints.thisisseveralordersofmagnitude smallerthanthemarketspread,whichiscloseto250basispoints(seefigure3).similarly,a(local) BBJratedbondallowsconsidering93%ofitsflows,whichisequivalenttoa70basispointspread withrespecttoriskjfreebondsina10jyeardurationbond.themarketspreadforbbjratedbonds ismuchhigher.mortgagesandleasingcontractflowsareexcludedonlyiftheyarebehindintheir scheduledpayments. Thissuccinctrevisionoftheregulationallowsustoconcludethatitisnotatallsurprisingtofind thatmarketjvalueleverageratiosareabovetheirregulatorylimit.annuityinsurancecompanies are not required to fully account for the effects of lower interest rate levels and of higher life expectancy.ontheotherhand,theexistingregulationsprovideincentivesforsellingsaferassets and buying riskier ones. Selling government or AAA bonds and buying BBJrated ones implies liberating reserves. This gives rise to regulatory arbitrage, 16 making the default option more valuable. Therefore, our results can be explained by a perfect storm : high levels of competition in the annuityindustry;dropsinrealinterestratelevels;increasesinlifeexpectancy;andaregulation, which inadequately measures the leverage ratios and provides incentives for higher riskjtaking. This leads previously reported Money s Worth Ratios to overstate the valuejforjmoney that annuitantsgetinthechileanmarket.thereisnopuzzle. 14 Theonlyexceptionistheweightgiventothe low interestratewhenthelevelofcashflowmismatching changes. 15 Forexample,ruleNCG178of2005establishesthatAICshaveuptoyear2015torecognizetheeffectsof the2004mortalitytableupdate.thelatestupdateis Forexample,seeBlack(1995)orBodie(1995),whoanalyzesstockinvestmentsbydefinedbenefitpension plans. 20

22 5. Conclusions, The Money s Worth Ratio (MWR) of an annuity is a measure of actuarial fairness. MWRs are estimated asthediscountedpresentvalueofexpectedfutureannuitypaymentsdividedbythe money(orpremium)paidinadvancefortheannuity. InthisarticlewearguethatMoney sworthratios(mwr)ofirrevocablelifeannuitiesshouldbe adjusted to consider at least two factors: illiquidity and credit risk. Without these adjustments, measuredmwrsareupwardbiased, in the sense that they do not reflect the valuejforjmoney obtainedbyannuitybuyers. As intuitive as this may be, measuring these adjustment factors is not trivial, since it requires detailedknowledgeofthenatureofannuity(andother)liabilities,oftheassetportfoliosusedto backtheannuitiesandofthestochasticprocessesfollowedbyassetsandliabilities. Hereweproposeaclosedformsolutionformoney sworthratioswhichconsidersboth,illiquidity anddefaultriskinthecontextofamultijfactorcontinuousjtimemodel.wecallittheadjusted Money s Worth Ratio (AMWR). The adjustments are done by taking as reference an illiquid defaultjriskjfreereplicatingportfolioofbondswithpaymentsidenticaltotheexpectedannuities andthenadjustingfordefaultriskusingoptionpricingtheory,inthespiritofmerton(1974). We define a regulatory horizon after which the supervising authority will check whether the marketvalueofassetssufficestocoverliabilities.ifnot,aicequityholdersmustcapitalizethe companyordefault.sothedefaultoptionissimilartoanexchangeoption(margrabe,1978)by means of which equity holders can give the AIC s assets in exchange of the liabilities, with no furtherobligations. Asexpected,riskissummarizedinthevolatilityoftheannuityprovider sequity,whichdependson leverage, maturity mismatching, illiquidity mismatching and other assets volatilities. These parameters themselves depend on the meanjreversion in interest rates and in liquidity premia, amongotherfactors. WeillustrateourresultswithadataJintensiveapplicationtotheChileanpensionannuityindustry, whichisconsideredtobequitecompetitive.theaveragemwrreportedinrochaetal.(2008)is 1.064for2004,withanupwardtrendsince1999.HighMWRsareoftenconsideredapuzzle. We use a quasijmaximum likelihood method to estimate the fixed income parameters of the modelandto calibrate the parameters associatedwith each annuityinsurancecompany s(aic) assetportfolio.thisallowsestimatingtheliquidityandcreditjriskadjustmentfactorsforeachaic, in addition to the default option values, the implied annuity credit spreads, and the asset insufficiency(ordefault)probabilities. TheaggregatevalueoftheoptiontodefaultisUSD460millionfora1Jyearregulatoryhorizon, USD1billionfora3JyearhorizonandUSD1.4billionfora5Jyearhorizon.Sincetheregulatory 21