Corporate Risk Management
Corporate Risk Management FIN 321
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This 44 page Class Notes was uploaded by Raina Bahringer on Sunday October 25, 2015. The Class Notes belongs to FIN 321 at University of Nevada - Las Vegas taught by Thistle in Fall. Since its upload, it has received 44 views. For similar materials see /class/228619/fin-321-university-of-nevada-las-vegas in Finance at University of Nevada - Las Vegas.
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Date Created: 10/25/15
CHAPTER 8 Insurance Pricing Insurance Pricing 2 El 0 biective 1 Find the premium that equals expected costs including a fair return to capital in Fair Premiumquot principle a Premium that would prevail in a competitive market Determinants of Fair Premiums a El 4 Determinants i Expected Claim Costs D Administrative Costs 1 Investment Income in Fair ProfitLoading El Examine each factor separately Expected Claim Costs II El The premium thot iust covers expected cloim costs is collecl the pure premium I Example I Lorge number of homogeneous buyers ie eoch hos the some loss distribution mm mm 0 95 0 05 D Pure Premium 500 Expected Claim Costs 5 El Foir premium must cover expected cloim costs Heterogeneous Buyers 5 II D What if there are two groups of buyers llLow Risk Group Possible Loss Probabilitl 0 10000 um High Risk Group Possible Loss Probabilitx 0 090 10000 010 Heterogeneous Buyers 7 El Low Risk Elass 500 El High Risk Elass 1000 El For sim licitl e lual numbers El Elass 750 El Low risk group subsidizes high risk group a May opt out i If they do ins to must raise price or go broke Implications of Heterogeneous Buyers I ll El New Scenario allow competition in Selective Insurance Company in can distinguish low or high risk Implications of Heterogeneous Buyers a ll El If Selective assumes Equal Treatment will continue to charge 750 haw claes Selective set price to maximize profits 39I Premium to low risks i Premium to high risks i Profit per policyholder Implications of Heterogeneous Buyers In H El What happens to ET 39l Sells to high risks onlx is loss of 250 per policyholder a ET has suffered from adverse selection in ET will have to classify or go broke Implications of Heterogeneous Buyers II n El Key Points 39I Differences in claims costs lead to differences in prem39ums I Insurers maximize expected profit Consumers prefer lower prices I Classification not too costly Implications of Heterogeneous Buyers i2 ii Profit Maximization Competition Classification Risk a Lack of Classification Competition Adverse Selection Adverse Selection is H El High risks hove higher demand for insurance in Willing to pay more for same coverage El Adverse selection occurs in other sit where there ore differences in willingness to pay El Key issue is how to classify Risk In irntinn Practices u u in Class Rate is applies to all consumers in a given Classification I Underwriter deddex whether a pankular onxumer will be offered overage or he laxx rare uscneaule rating modification of the rate by the underwriter based on specific the racteristics of the consumer applies mos1y io commercial insurance Recouping versus Updating is u El Experience roting refers to practice of bosing rates on post experience El Bosing rates on post experience is often controversial in How do you predict future Eoss Recouping versus Updating In H El Are insurers a recouping past losses is updating expected losses on future business El Competition and low switching costs limit the ability of insurers to recoup s Classification Good for Society u u El Four effects of restricting classification 1 Redistributes income from low risk io high rlsk 2 Classification changes prices to certain groups Therefore changes behavior 1 amount of insurance purchased cl loss control aciivmes s Classification Good for Society n u 3 May decrease classification costs in Costly classification is a waste unless changes behavior in Controversial issues gender age location have low classification costs I Insurance scores based on credit his10ry ls Classification Good for Society 19 H 4 Limiting classification may increase regulatory casts D Monitoring of insurers to enforce restrictions i Need to impose other costly restrictions on insurers I marketing activities I underwriting activities Investment Income 2n n El Premiums paid now claims paid later El Insurers can invest premiums in interval El Key point D Fair premium is reduced to reflect investment income on premiums Investment Income 21 a Fair premium is reduced to re ect investment income on premiums El Equivalently El Fair Premium PV of Expected Casts Effect of Investment Income 22 H Cumulative Percentage ofTotal Losses Paid Over Time for Accidents in Yeart Effect of Investment Income 2 El Assume I no adminisiraiive cosis I one year policies premium received ai beginning I cerrain claim cosrs 100 paid according ro rable below Eqeded Claim Payments Interest Rate year 1 year 2 year 3 5 111 0 0 9391 9524 50 50 0 8678 9297 50 25 25 849 9189 Administrative Expenses 2 El Fair Premium must cover administrative costs such as a marketing in underwriting in premium taxes in underwriting income taxes D etc Expense Loadings as 0 Percentage of HPremium underwnitng EXDEMEX Intal Lois Yype at cenmi Undemriling Auiuurnun inmrnnce Continuum unenm Expenm Expense umcot M 5 16 t Yu in in i1 w Permmi auto t tiiily rs ms nu HS i nmmuii nuiu nnymi dumm a MA 22 v v 6 kars39 nuipl animi 53 in 73 139 iiiiuriiiilriiilv m in 2m 27 Summary of Determinants of Fair Premiums D So far a Fair Premium 7 PV of Expected Costs V of Pure Premium PV of Expenses DAnulysis to tnis poim based on expected values Summary of Determinants of Fair Premiums H u Need to consider uncertainty in insurers neid capital to reduce probability or insolvency u Suppliers or capital need to be compensated rer risk 1 an quotfnir rnte or return Summary of Fair Premium Model 2 H El Fair Premium PV of Expected Costs Profit loading in Other terms for profit loading I risk load I a pilal costs El Two Approaches a Actuarial a Financial Determinants of Profit Loadings 2 ll El Actuarial Models El Idea is to limit probability of insolvency i It losses are p ProbPrem RL S p 8 S 7 Premium Eloss risk loading Risk loading depends on N a a Determinants of Profit Loadings an n El Financial Models El Optimal level of capital given its costs and benefits El Ca ital I roviders need fair return on investment 39l Fair returnquot can be determined by financial models eg CAPM AP Conclusion an H El Fair Premium PV of Expected Claim Costs PV of Expected Admin Costs Profii Loading Pricing Example 1 2 Loee Wim prob o 08 i ooooo Wim prob o 02 20000 0 Wim prob o 90 Find Fair Premium if policy provides full coverage claims are paid ai end of year loss aaiusimem expense 5000Iuim Underwriling 0515 20 of pure premium fair profil 5 of pure premium imeresl rule 8 Pricing Example 1 a II u Solulion a pure premium 3600 a underwriiirig osls 020 x 3600 720 a fair rofil 05 x 3600 180 u expecled LAE 010 x 5000 500 a Fair premium 900 4100108 00 3796 4696 Pricing Example 2 u H iO0000 Wim prob 0 02 Loss 20000 Wim prob 0 08 mp prob 0 90 Find Fair Premium if policy has a 20000 deduaibie claims are paid cu end of year loss udiusimem expense 5000luim underwriling osis 20 of pure premium fair proiii 5 of pure premium I imeresi rule 8 Pricing Example 2 as u 80000 Wim prob 0 02 Game 0 Wimprob 008 0 mi prob 0 90 Pricing Example 2 an n u Soluiion in pure premium 0 02 gtlt 80000 ibOO ii underwriimg oer 0 20 gtlt ibOO 5320 u roirprorir 0 05 gtlt ibOO 80 in expeded LAE 0 02 gtlt 5000 i00 a Fair premium 400 i700i 08 400 i57 sum Capital Shocks amp Underwriting Cycles u H El Fair premium model does not explain everything i Premiums amp coveroge appear to follow cycles hard markets prices high coverage resrricied soft markets prices low coverage dvdilci ble Capital Shocks amp Underwriting Cycles 31 in cm nge following co pital shocks I prices increase coverage resiricled i In long run prices determined by expected costs Higgins Tnisrle 2000 cnoiHordigreeTliisrle 2002 Capital Shocks amp Underwriting Cycles 39 p Price Regulation on H ll Types l Restrict level or change in rates prior approval I file and use I corn pelilive D Restrict underwriting criteria Why Regulate Rates 01 ll Public Interest Perspective a Correct problems in market place collusion among insurers I lock of consumer information Why Regulate Rates oz ll Economic Theory of Regulation D Regulation benefits politically influential groups in Possible beneficiaries of price regulation Insurers as a group lnellicienr insurers High risk consurners Rate SuppressionCompression u H El Rate suppression lower rates below costs El Rate compression restrict differences in rates across classifications Rate SuppressionCompression u u El Suppression anolor compression leacl insurers to not voluntarin offer coverage to some groups in leads to market disruption eg FL homeowners oher Andrew INJ auto in lead to creation of residual market mechanisms JUAs eg FL homeowners Chaptker 6 I InsuranceRegulation 3 i i State Regulation of Insurance I rate insurance departmentor ommission i State insurance code c State insurance col missioner elected J i i appointed i 3 l Ji National Associatioi39i 0 Insurance Commissionersth 39 IlVlodel laws i 39 Regulated Activities Licensing of insurers A talk i Insurer so vency 39 39 Ra i s Residual markels in Content of polic f rrns 1 Contact interpretation and enforcemeng Sales practices and i o mation 39 discl sure i i 39 39 Compulsory in suraince coverage a l l i History of State Regulation I State charters fr 1st state insurance VdepEiI l mant mNH 185 Paul V rginia1 s A Insurance l not cdf hmerce It I Development of y l History of State Regulation I Antitrust Acls 18905 Southeastern Underwriters Assoc Case 1942 Subject to antitrust aws McCarranFerguson Act I Regulation and taxation bystatesisjnf39 the public interest N l Exempt from federal antitrust law I provided activities re st statefr law 4 Ido not involve bo coercionj y Jl i intimidation McCarranFerguson Act I Rsponse of many states 7 I Encouraged insurers to use ratin39g bureaus 39 A I Hior approval rate39iigegulation 1 eliminated by Mapy d uring 1950 l l l Challenges to McCarran Ferguson I Some argue it promotes collusion andr incrases prics I Counter arguments Industry has a competitive sh39uctur I Rating bureaus help rhaller insurer ompe Some argue federalsolvency regulation woLIld e better quot l V 39 r50 Arguments in Favor of Federal Regulation I Lack of uniformity across t t insurer39s compliance costs Arguments in Favor of Federal Regulation l Quality would be uniform at quot and Insurers In other tates NAIC now certi es ll l dept 39 I 39 Some states 39ee ride on other sta 39 Arguments in Favor of State Regulation Can be tailored to local needs Facilitates experim 39 Track record of federal regulation of39 I institutions is not good Public Interest View of Regulation l Regulate if incustry onduct and performance deviates from whatwould occur in a ma at io egulation re can39t expect regulators to nav ber 1e info mauon than market parucipan Public Interest View of Regulation I Characteristics ofa competitiye if T 7 market I I large number of sellers I low entry cosls V 1 l about prices and f uali y V l1 l absence of spillovers e39xternalities l Costly and Imperfect Information I Costly for consumers to e 39 l product quality 2 Regulations that deatwllh this problem liming l sum l J mnssuanuss l sales practices Regulation and Political Pressure I Economic theow of regulation s r Legislators and regulators act i39 their own interest e the warm Dlltltal su art I Regulations re e is obje l not public interest ie l l Economic Theory of Regulation I General prediction Small groups organlzauon cosare low with large per cEi ita stakes 4 potenuallylargefbefte s ll 1 Iwill benefit l V a l I at the expense of largelgroups with low l 39ta stakesi 391 VJ per cap Economic Theory of Regulation I Producers might be 39 regulation I aka capture the y producers cap Economic Theory of Regulation I Application to insurance t at expense of cons I Some think this was true of prior abproval rate regulation in 19ssz land 19605 l emphasis on rate qua cy l I Insurers bene Economic Theory of Regulation l Application to insurance 7 f f Not true of rate regulation in ast 25 yrs Or may reflect politic liRressure oniIns Corry Most rate suppressiorw Hquot a39gto home WC l Insurer Ownership Financial and Operational Structure I Insolvency risk is reduced by insurer capital Capital provides a cushion Greater capital reduces the likelihood of insolvency all else equal I Definitions Capital Assets Policyholder Liabilities Economic values not accounting values Assets market value of securities etc Liabilities present value of expected payments on policies already sold Surplus is another name for capital Example Insurer initially has assets 0f1milli0n amp no liabilities Surplus 1 million It sells 10000 0neyear policies at beginning 0fthe year I expected claim cost 1000 per policy claims paid at end ofyear ignore nonclaim costs and the time value of money Liabilities at beginning ofyear 10 million Assume premiums 11 m all paid at beginning 0ftheyear Then assets at beginning 0fyear 12 million Surplus Capital at beginning 0fyear 2 million surplusassets 212 167 surplusliabilities 210 200 I Eclaim cost 10 million actual claim costs are uncertain I What is the probability of insolvency Claim cost 10m 12m Main Points I Capital reduces Probability of Insolvency I Capital acts as a cushion I More capital gtlower probability of insolvency I What ifthe correlation in losses increased I Distribution ofclaim costs would have greater variance I Holding capital constant probability of insolvency would increase with the correlation in losses I Holding probability of insolvency constant amount of capital needed increaseswith the correlation in losses Policyholder owned Mutuals Reciprocals very small Policyholders are residual claimants Policyholders have limited liability I No assessments Cannot issue equity 39i39ivmin Investor Owned Stock Lloyds Investors are residual claimants Investors have limited liability Stock co is std Corporation Can ISSUe equity Agency problems among owners managers policyholders Stock better control of managers ownerpolicyholder conflict Agency problems among owners managers policyholders Mutual weak control of managers 7 less managerial discretion solves ownerpolicyholderconflict Call option gives holder right but not obligation to buy asset at exercise price Call option gives holder right but not obligation to buy asset at exercise price I Increasing the riskiness ofthe underlying asset increases the value ofthe call option downside risk cut off capture upside gain What happens as incr riskiness ofasset V Application to corp fin lfa firm has debt then equity has same payoff structure as a call option exercise price facevalue ofdebt Equity is a call option on the rm s assets Exercise price face value of debt Why Shareholders can choose to default lfassetsworth less than debt then default Let debtholders keep the assets lfassets worth more than debt then paydebt Buy assetsfrom debtholders for D Increasing riskiness ofassets increases value ofoption equity Increase in value is at expense ofdebtholders A L E Shareholders have incentive to extract value What does this have to do with insurance Insurance policies are debtlike Promise to pay in the future Default risk Stock co shareholders policyholders Mutual shareholder policyholders I Access to capital markets Ins cos rarely issue debt Policies are debt Stock co can sell equity mutual cannot Demutualization conversion from mutual to stock insurance co highly regulated time consuming expensive Why unlock shareholdervaluequot access to capital market optionsto mgt Mutual Holding Co Policyholders own mutual insurer Mutual forms MHC stock co MHC owns subsidian stock ins co Why demutuahze Prwmaryreasonsaccesstocapwtm szwanzthan PICconverLerShaveowSurp uSTAranss years before converswon mum unstramed Marketp acewhere msurance business is transacted most busmessiscommercia msurance remsuramce and automob e Insurance Ownersare caHed names I N2 es mnmbute spam to synmates Carper 2 names have hrmtedhabmty Usedtahavemdmdua san ywunhmxtedhahmty Ehmmated faHavnmg sunda I How much capital should an insurer hold Difficult question for insurers Difficult question for regulators Regulatoryfactors in Chapter 6 amp7 I Our objective Identifyfactors that influence insurers capital decisions in an unregulated environment I Perspective ofan owner I Assume the insurer has some level of capital Identifythe benefits of adding additional capital Identifythe costs of adding additional capital I Additional capital lowers the probability of insolvency I Why is this a good thing for owners Improves the terms of contracts especially with commercial policyholders Protects insurer s franchise value What is the cost ofadding capital Opportunity cost cannot invest elsewhere Doubletaxationstoclltcos agency costs Costs of raising capital issuance costs 39underpricing costs PropertyCasualty Assets 1447193 Liabilities 945948 PolicyholderSurplus 531243 Insolvency risk depends on variability ofclaim costs Variability can be reduced by diversifying across geographical areas diversifying across lines of business Reinsurance is insurance forinsurers Primaiy roles of reinsurance Reduce variance in claim costs by diversification reducing exposure tovery bigb claims Reduce amount of capital needed to achieve a given probability of insolvency Types of policies proportionalprorata nonproportionaldeductible excessrofrlossgt perpolicy stoprloss gt pool treaty facultative Buyeris ceding co cedant I Insolvency risk also depends on riskofassets correlation of assets and liabilities INVESTMENTS BY TYPEH Emmi masin wmmm m x Mm m mmquot Cmmuniluck um DPORTFOLID2 EON minmm h a W WWW Sulumlnwtlnundulhusm6 in uwill And Inle 23 3v Speck mm mu STOCK PORTFOLIO in mm H Moi mui iiimmmiiui Fuhll quothim u pm m m m 31139 Induimluml m 5501 13 2004 2008 7mm subsidmn u Augumnmm andamums nndvevenun my zuv Puhll mlliliu 727 lndumlal andJ Inuusmal and mvscelhneuus misceuaneous may saxx Chaynterii legal liability for Injuries Categories of the law r Sources of tall 0 Common law 0 Statutes r Branches of law 0 Criminal 0 Civil 39 Contract 39 Tort locus olChapter i2 Types of Liability Rules tllllCC lOSS OCCUlS someone must bear cost 0 Liability rules determine who bears cost t No liability y liability for Negligence r Strict liability rAbsolute liability Damages r Compensatory Damages 0 Special damages 39 lostwages 39 medical expenses 0 General damages 39 am and sufferin com ensation 39 loss of consortium r Punitive Damages o punishment 0 egregious conduct Joint and Several Liability What does it mean 0 Multiple parties are liable 0 One cannot pay then the others are responsible Negligence Standard r Burden of proof generally on plaintill gt Conditions for negligence 0 Defendant had duty 0 Breach of duty Did the defendant take all costjustified precautions o Breach was proximate cause of accident 0 lnjury Defenses to Negligence v Assumption of risk v Contributory negligence v Comparative negligence Econ hole of the iiort System i Objectives 0 Optimal safety 0 Optimal loss control 0 Optimal compensation to victims 0 O timal insurance coverage 0 Must considertransaction costs Econ Role of the Tort System i Objectives can conflict 0 Optimal salety might imply too much compensation 0 Optimal compensation might imply too high legal costs v Framework ignores certain issues 0 Distribution of wealth o Socialjustice J Optimal Loss Control Example Marginal Expected Marginal Marginal Prob Safety Loss to Bene t Cost to of LossExpenditure Consumers Consumers Consumers 007 0 700 006 45 600 l00 45 005 l30 500 l00 85 004 225 400 l00 95 003 400 300 l00 l75 002 590 200 l00 l90 00l 900 l00 l00 3l0 Optimal Compensation to Victims v Tort liability is analogous to insurance oCmmmm mmmmmme MmMmhmmwmmmwMMdmwmm mMm Optimal Compensation tn Victims v Optimal compensation equals the amount of insurance coverage that people would have purchased prior to being involved in the accident ii ommmmMMMMMMMMHM OMMWMMWMMMMWMMB ammMMMMWmHMMMMWme All costs legal fees moral hazard adverse selection Optimal Compensation in Victims v Riskaverse people 0 Do not purchase full coverage for economic losses premium loadings moral hazard adverse selection 0 Generally do not purchase coverage for non economic losses Optimal Compensation to Victims s In principle courts award full compensation for economic losses and pain amp suffering v This is more than the optimal level of compensation 0 Why more emphasis on safety incentives Judgment Proof Problem v People can escape payment of damages 0 limited wealth 0 limited liability v Problems 0 May not take optimal level of care 0 Victims might not be compensated v Possible solution 0 Mandatory insurance Safety Regs versus Tort liability v Tradeoffs 0 Who has information 39 Government experts Individuals who deal with the situation 0 Economies of scale in gathering information 0 Judgment proof problem Tort Reform v Modify incentives to bring suits 0 Limits on contingency fees 0 Loser pays v Reducing damages 0 Limitingjury discretion Caps on pain and suffering Caps on punitive damages Alter collateral source rule r Limitjointh several liability Why Have a Tort System i When will the private marketplace fail to minimize the cost of risk 0 People are not fully informed 0 Transaction costs prevent private solutions Info n Optimal Loss Control a Recall Nielson lnc example 0 Optimal safety expenditures 225 a How much will Nielson spend if o It maximizes profits and if 0 No liability Inqu it Optimal loss Control 0 With fully informed consumers 0 Completely uninformed consumers 0 Liability for all losses 39 Completely uninformed consumers Transaction Costs d Loss Control 400 p05 Angler s loss W in ya Sir Ham W A 150 250 Transaction Costs 0 loss Control Cost of Treatment i50 250 PanelA Optimal Outcome Panel B Outcome if factory is liable transaction costs 0 Outcome if factory is not liable transaction costs 0 Transaction Costs 0 loss Control Cost of Treatment 150 250 Panel C Outcome if factory is not liable and transaction costs 55 Outcome if factory is liable transaction costs 55 Summary Economic Role ofthe Tort System s Tort liability can be used to promote optimal loss con rol safety when t o i people are uninformed o 2 transaction costs prevent private solutions gt Similar conclusions with regard to optimal compensation
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