Probability and Life Insurance Risk - PowerPoint by weq97779

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									Life Insurance and Annuities

 Terminology
 Types of life insurance products
 Tax treatment of life insurance
 Term insurance
 Endowment insurance
 Whole life insurance
 Universal insurance
 Variable insurance


                   Ins301 Chp15 –Part1   1
Terminology
   Death benefit = amount beneficiaries receive
   Cash value = amount of savings accumulation
   Death protection = amount of pure death protection
                     = death benefit - cash value
   Face amount = stated amount of coverage
        = death benefit (for term, whole life, & some universal life)
        = death benefit - cash value (for some universal life)
   Cash surrender value = the amount of money that the
    policyholder can withdraw (=cash value - surrender
    penalty)

                         Ins301 Chp15 –Part1                            2
Life Insurance Products: General
Introduction
       Term insurance
            pure life insurance
       Cash value life insurance
            pure life insurance + Savings accumulation
            whole life
            universal life
            variable life
            Variable universal life




                          Ins301 Chp15 –Part1             3
Tax Treatment of Life Insurance

       Death benefits are not taxed
       Income tax is not paid on increases in cash value while
        the policy is in force
       Upon surrender, income tax is paid on
         Cash surrender value - sum of all premiums
         + sum of all policyholder dividends




                     Ins301 Chp15 –Part1                  4
Implications of Tax Treatment

     Implicit returns on savings accumulation
          Escape taxation if insured dies
          Tax deferred if the policy is surrendered
          Partially taxed if policy is surrendered
             Amount which is taxed is less than implicit return b/c part
              of premiums is cost of death protection




                         Ins301 Chp15 –Part1                         5
Term Insurance

     Typically provides pure death protection over a
      fixed term, usually one year or five years. There is
      no savings feature and therefore no cash surrender
      value.
     Data
          1/4 of policies
          almost half of death protection purchased
     Guaranteed renewable
     Premium increases over time. Why?


                        Ins301 Chp15 –Part1            6
Life Insurance Pricing
   Ignore expenses and risk load
    ==> focus on net premiums
   Use mortality table
        Probability of dying at age x conditional on living through
         age x-1
        Example: Probability of male dying at age 40 = 0.00302
   Assume
        Premiums paid at beginning of year
        Claims paid at end of year



                          Ins301 Chp15 –Part1                  7
Pricing 1-Year Term

     Find fair premium for $100,000 1-year term for 40
      year-old
               Interest rate = 10%
               Insurer’s cash flows:

       Beg. of Year                End of Year
                            $100,000 with prob 0.00302
       Loss
                           $0       with prob. 0.99698
       Expected claim cost = ________
       Premium = Present value of expected claim cost
                = __________

                           Ins301 Chp15 –Part1           8
Pricing 1-Year Term

     Find fair premium for $100,000 1-year term for 41
      year-old
            Interest rate = 10%
            Insurer’s cash flows:

       Beg. of Year              End of Year
                         -$100,000 with prob ____________
       Premium
                           $0       with prob. ____________
       Expected claim cost = ___________
       Premium = Present value of expected claim cost
                 = ____________

                        Ins301 Chp15 –Part1                   9
Pricing 1-Year Term

    Premium increases as probability of dying increases




                     Ins301 Chp15 –Part1             10
Pricing 2-Year Term

    Find fair premium for $100,000 2-year term for 40
     year-old
    Insurer’s claim costs:

      Beg. of Year 1   End of Year 1           End of Year 2
                       -$100,000               -$100,000
                       with prob 0.00302       with prob x

                       $0                      $0
                       with prob. 0.99698      with prob 1-x




                         Ins301 Chp15 –Part1                   11
Pricing 2-Year Term

    What is x? – it is the probability of a 40 year-old
     dying in his 42nd year?
    Mortality table:
                      Number           Number
      Age             of People        of Deaths
      40              937723           2832
      41              934891           3076
             
 Probability of 40 year-old dying in 41st year =_____ = ______

 Probability of 40 year-old dying in 42nd year =_____ = ______

                        Ins301 Chp15 –Part1                      12
Pricing 2-Year Term

   Single   premium




   Level   Premium




                 Ins301 Chp15 –Part1   13
Endowment Insurance

     Pays face amount if the insured dies, or if the
      insured survives the policy period
     It is similar to a saving account
     The US no longer grants tax advantage to
      endowment policies unless they have a very long
      duration, such as whole life insurance.




                    Ins301 Chp15 –Part1             14
Whole Life Insurance

     Policy period ends when insured reaches 100
     Equivalent to endowment policy to 100
     Premiums
          single premium
          limited pay – a level premium paid for a 10-year or
           20-year period
          continuous premium – level premium continue until
           the policyholder dies, surrenders the policy, or reaches
           the age of 100 (whichever comes first)



                        Ins301 Chp15 –Part1                    15
Whole Life Insurance

     Premiums generally do not increase over time
          But probability of dying increases over time
           ==> higher upfront premiums than with term

          Policyholder “prepays” part of the cost of future death
           protection
             entitled to prepayments if policy is surrendered
             this is the cash value (savings accumulation)




                         Ins301 Chp15 –Part1                     16
Whole Life Insurance

     If insured dies,
          beneficiaries receive face amount
           = death protection + cash value


     Structured so
          cash value  over time
          death protection  over time




                         Ins301 Chp15 –Part1   17
Whole Life Insurance




             Ins301 Chp15 –Part1   18
Pricing Single Premium Whole Life

     Apply same principles used with term insurance
     Forecast expected cash flows to age 100
     Find single premium
       = PV of expected cost
        Assume

           no expenses or profits
           5% interest rate
           policy will not lapse




                       Ins301 Chp15 –Part1         19
Pricing Single Premium Whole Life




                                    Single
                                    Premium
             Ins301 Chp15 –Part1       20
Continuous Level Premium Whole Life

   Continuous level premium
        Same premium is paid until insured dies or reaches 100
        Equivalent to a life annuity
   Present value of a life annuity that pays $P starting at age
    40 = 16.30 * P
   Find P so that PV of premium payments = PV of costs
        16.30 * P = $22,373 ==> P = $1,372.58




                          Ins301 Chp15 –Part1                 21
Limited Payment Whole Life

     Limited payment level premium
          Same premium is paid for fixed number of years
          Example: 20 years
          Equivalent to a 20 year annuity
     Present value of a 20-year annuity that pays $P
      starting at age 40 = $12.58 x P
     Find P so that PV of premium payments = PV of
      costs
          12.58 x P = $22,373 ==> P = $1,778.45


                       Ins301 Chp15 –Part1                  22
Comparison of Cash Values in Whole
Life




             Ins301 Chp15 –Part1     23
How Much Life Insurance Should be
Purchased?
   Rules of thumb
        Death benefit = 8 times income
   Forecast beneficiaries sources & uses of funds
        Uses:
           Living expenses
           Education expenses
        Sources:
           Social security
           Earnings




                       Ins301 Chp15 –Part1           24
Participating Policies
   Can (and usually does) pay annual dividends
          always with mutual companies
          often with stock companies


   Why? - premiums based on conservative assumptions
          Key assumptions: interest rate levels and mortality rates
          These variables are correlated across policyholders
          Insurer’s methods of dealing with correlated risk:
               Bear the correlated risk and hold a lot of capital
               Share correlated risk with policyholders

   Illustrated versus actual dividends


                             Ins301 Chp15 –Part1                       25
Other Whole Life Policy Provisions
    Surrender Options
       Take cash value

       Use cash value as a single premium for

           paid up whole life
           term policy
    Policy loans
       borrow against cash value

           interest now varies with market rates
           in 1970s & 80s, fixed rate ==> disintermediation
    Front-end expense charges
      ==>     Cash value grows slowly at first
      ==>     Implicit return on savings accumulation
              initially low

                          Ins301 Chp15 –Part1                  26
Universal Life

    Similar to whole life
    Main differences:
         Greater flexibility in premium payments
         Cash value does not follow a fixed schedule; it varies
          with
            policyholder’s premium payments
            insurer’s expense and mortality charges
            rate insurer uses to credit interest to cash value
                minimum rate usually guaranteed
                rate often linked to short term interest rates


                           Ins301 Chp15 –Part1                    27
Factors Affecting UL Cash Value




             Ins301 Chp15 –Part1   28
Death Benefit Options with Universal
Life
     Level death benefit (as with Whole Life)

     Death benefit varies with cash value


            Death
            benefit                    Death
                                       benefit
                       Cash                      Cash
                       value                     value


                           age                           age


                      Ins301 Chp15 –Part1                  29
Variable Life

     Similar to whole life
     Main differences:
          Cash value does not follow a fixed schedule; it varies
           with
             return earned on portfolio of mutual funds chosen by
              policyholder
          Death benefit
             minimum is guaranteed, but varies with cash value




                           Ins301 Chp15 –Part1                       30
Life Insurance and Annuities (part3)

     What is annuities
     The purpose of annuity
     Classification of annuity
     Overview of annuity contracts




                    Ins301 Chp15 –Part1   31
What is Annuity

     An annuity is simply a series of periodic payments.
      An annuity contract is an insurance policy that
      promises to make a series of payments for a fixed
      period or over someone’s lifetime
     It is typically used as long-term retirement funding
      vehicles.




                     Ins301 Chp15 –Part1              32
Two Periods of Annuity

     Accumulation period
       -- the period when the policyholder pays premiums to
         the insurer
     Payout period
       -- the insurer makes payments to the policyholder




                      Ins301 Chp15 –Part1                  33
Purpose of Annuity

 Risk management purpose
      Reduce the risk that savings are exhausted before
       the annuitant dies
 tax-deferred saving vehicle
      Returns earned from these contracts are not taxed
       until the insurer distribute them




                     Ins301 Chp15 –Part1              34
Classification of Annuity

 Immediate annuity and deferred annuity
      Immediate
      Deferred
           Flexible premium deferred annuities (FPDAs)
           Single premium deferred annuities (SPDAs)
 Fixed annuity and variable annuity
      Fixed annuity
      Variable annuity


                        Ins301 Chp15 –Part1               35
Overview of Annuity Contracts




             Ins301 Chp15 –Part1   36

								
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