How Does the Life Settlement Market A¤ect the Primary Life Insurance Market? Hanming Fang Edward Kung Duke University June 19, 2008 Fang and Kung (Duke University) Life Settlements 06/19/2008 1 / 58
Introduction A life settlement is a …nancial transaction in which a life insurance policyholder sells the policy to a third party for more cash than the cash value o¤ered by the original insurer. The third party is then responsible for maintaining premium payments to the insurance company, but is also entitled to the bene…ts at the time of the insured’s death. The life settlements industry is young but growing rapidly: from a few billion dollars in the late 1990s to about $12-15 billion in 2007. Some projections see the industry growing to more than $100 billion in the next decade. Fang and Kung (Duke University) Life Settlements 06/19/2008 2 / 58
The life settlements industry is interesting as it relates to a large IO literature on secondary markets for durable goods, with one key distinction: in life insurance, secondary market transactions directly a¤ect the primary market seller’s payo¤s. The life settlements industry is also interesting in that its emergence has triggered controversies over its e¤ect on consumer welfare: see Doherty and Singer (2002), the Deloitte Report (2005) Despite this, life settlements have received little serious attention from economists, except for a short paper by Daily, Hendel and Lizzeri (2008) on which we base our analysis. Fang and Kung (Duke University) Life Settlements 06/19/2008 3 / 58
We study the e¤ects of the secondary market for life insurance on the structure of primary market life insurance contracts and consumer welfare. Our model builds o¤ of Hendel and Lizzeri (HL, 2003) and Daily, Hendel and Lizzeri (DHL, 2008). HL showed that dynamic life insurance contracts can partially insure consumers against reclassi…cation risk via front-loading . Fang and Kung (Duke University) Life Settlements 06/19/2008 4 / 58
We show that in the presence of a secondary market, the nature and extent of this dynamic insurance is a¤ected in a qualitatively signi…cant (and potentially severe) manner. We also show that within our framework, the presence of a secondary market is welfare reducing. Finally, we analyze how the choice of cash surrender values can evolve to partially mitigate the e¤ect of the secondary market. Fang and Kung (Duke University) Life Settlements 06/19/2008 5 / 58
Economic Intuition Two main features of life insurance contracts underline the opportunity for a life settlements market. Most life insurance contracts have premiums that stay …xed over the course of the 1 contract (front-loading). Life insurance contracts typically have zero (as in the case of Term policies) or low and 2 non-health-contingent cash surrender values (as in the case of Whole Life policies). The gap between the cash surrender value and the actuarial value of the contract provides an opportunity for gains of trade between policyholders with impaired health and the life settlements companies. Fang and Kung (Duke University) Life Settlements 06/19/2008 6 / 58
To understand the mechanism by which the secondary market may a¤ect primary market contracts, consider a policyholder who no longer needs his policy. Absent a secondary market, the only option available to this consumer is to allow his policy to lapse by failing to pay the premium or surrendering the policy for a very low surrender value. To the extent that the lapsed policy is actuarially favorable to the policyholder (due to front-loading), the life insurance company can pocket the value of the lapsed policy as a pro…t. If the primary market is competitive, lapsation pro…ts can be passed on to consumers through lower pricing of premiums. Fang and Kung (Duke University) Life Settlements 06/19/2008 7 / 58
In the presence of a settlement market, policies that otherwise would have lapsed or been surrendered are now sold to life settlements …rms. Life insurance companies continue to receive premium payments but are also liable for paying the death bene…ts. By denying the insurance companies the returns on lapsed or surrendered policies, the secondary market may make it more costly to provide life insurance on the primary market. These costs may have to be passed on to consumers through higher premiums. As a result, the structure of the contracts chosen in equilibrium may change, and consumers may ultimately be made worse o¤. Fang and Kung (Duke University) Life Settlements 06/19/2008 8 / 58
Baseline (HL) Model: Health, Income and Bequests A perfectly competitive primary market for life insurance operates in 2 periods. For now, assume there is no secondary market. In the …rst period, the policyholder has probability of death p 1 . In the second period, the policyholder has a new probability of death p 2 which is a random variable drawn from �( � ) . The realization of p 2 is not known in period 1 but is symmetrically learned (and thus common knowledge) at the beginning of period 2. Fang and Kung (Duke University) Life Settlements 06/19/2008 9 / 58
In period 1 the policyholder earns an income stream y � g and in period 2 he earns an income stream y + g . In each period, the policyholder cares about two sources of utility. His own, given by u ( � ) , and his dependent’s, given by v ( � ) , should he die. Both u and v are strictly increasing and concave in their arguments. In period 2, there is an exogenous probability, given by (1 � q ) , that the policyholder no longer has a bequest motive. In that case, the policyholder only cares about his own utility u ( � ) . y , g , p 1 , and q are all common knowledge. Fang and Kung (Duke University) Life Settlements 06/19/2008 10 / 58
Baseline Model: Timing, Commitment, and Contracts Life insurance contracts are of the form h ( Q 1 ; F 1 ) ; f ( Q 2 ( p ) ; F 2 ( p )) : p 2 [0 ; 1] gi . Assume one-sided commitment : insurance companies can commit to the contract terms in the second period, but the policyholder may renege on the contract by lapsing his premium payment. Fang and Kung (Duke University) Life Settlements 06/19/2008 11 / 58
Period 1 Timing: Consumer earns y � g and chooses a contract h ( Q 1 ; F 1 ) ; f ( Q 2 ( p ) ; F 2 ( p )) : p 2 [0 ; 1] gi . He then pays the …rst period premium Q 1 and consumes the remaining y � g � Q 1 With probability p 1 he dies and his dependents receive F 1 . Period 2 Timing: Consumer and life insurance companies learn p 2 . With probability 1 � q the policyholder loses his bequest motive. Consumer earns y + g . He then decides to either stay with his policy, lapse his policy and repurchase insurance on the spot market, or lapse his policy and remain uninsured. If he stays with his contract or repurchases, he pays the premium Q 2 and consumes the remaining y + g � Q 2 : With probability p 2 he dies and his depends receive the face value F 2 of his standing insurance contract, if any. Fang and Kung (Duke University) Life Settlements 06/19/2008 12 / 58
Baseline Model: Equilibrium Characterization In a competitive equilibrium, the insurance company will o¤er a contract h ( Q 1 ; F 1 ) ; f ( Q 2 ( p ) ; F 2 ( p )) : p 2 [0 ; 1] gi that maximizes consumer welfare u ( y � g � Q 1 ) + p 1 v ( F 1 )+ Z (1) (1 � p 1 ) f q [ u ( y + g � Q 2 ( p )) + pv ( F 2 ( p ))] + (1 � q ) u ( y + g ) g d �( p ) subject to the following constraints: Z Q 1 � p 1 F 1 + (1 � p 1 ) q f Q 2 ( p ) � pF 2 ( p ) g d �( p ) = 0 (2) (3) 8 p : Q 2 ( p ) � pF 2 ( p ) � 0 ; Constraint (2) is a zero pro…t condition re‡ecting perfect competition in the primary market. Constraint (3) is a no-lapsation constraint re‡ecting one-sided commitment. Fang and Kung (Duke University) Life Settlements 06/19/2008 13 / 58
Solving the above problem we obtain the following equations characterizing the equilibrium contract: u 0 ( y � g � Q 1 ) = v 0 ( F 1 ) = � (4) � ( p ) u 0 ( y + g � Q 2 ( p )) = v 0 ( F 2 ( p )) = � + 8 p : (5) (1 � p 1 ) q� ( p ) where � > 0 is the Lagrange multiplier for the zero pro…t constraint (2) and � ( p ) � 0 is the Lagrange multiplier for the no-lapsation constraint (3). Conditions (4) and (5) imply that full event insurance is obtained in period 1, and in every health state of period 2. These equations give a one-to-one correspondence between premia and face values in the equilibrium contract. Fang and Kung (Duke University) Life Settlements 06/19/2008 14 / 58
Consider again the no-lapsation constraint (3). If (3) binds, i.e. Q 2 ( p ) = pF 2 ( p ) , then we say the premium is actuarially fair relative to face value F 2 ( p ) . � � Q F I 2 ( p ) ; F F I Let ( p ) be de…ned by: 2 Q F I 2 ( p ) � pF F I ( p ) = 0 2 u 0 ( y + g � Q F I v 0 ( F F I 2 ( p )) = ( p )) 2 � � Q F I 2 ( p ) ; F F I For convenience, we will simply refer to ( p ) as the actuarially fair 2 premium and face value for health state p . If (3) does not bind, i.e. Q 2 ( p ) < pF 2 ( p ) , then we say that the premium is actuarially favorable (or actuarially unfair from the perspective of the …rm) Fang and Kung (Duke University) Life Settlements 06/19/2008 15 / 58
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