Session#10 Asuransi Kerugian dan Asuransi Jiwa
[email protected] http://boykepurnomo.staff.ugm.ac.id/
` `
` `
` ` `
Insurance itself is not a problem. Suffering a loss without adequate protection is a problem. Insurance is part of the solution. solution But most people are more afraid of the solution than they are of the problem. Insurance is a solution to the problem of less. Insurance is about security. It is about a peace of mind
`
`
`
Historian trace insurance roots to ancient traders among the Phoenicians and h Babylonians, B b l i Ph i i d Chinese Chi 14th Century – Lombardia, the traders paid socalled-Premiums ca ed e u s to protect p otect ttheir e ca cargo go During the Romans Empire – fraternal societies paid death benefits to the survivors of its members ( (early l fform off life lif insurance) i ) and d th the members b burial cost met by the society
Insurance History
Abad ke 14-16 Tahun 1575 Marine cargo Office of Assurance Build
Tahun 1680
Underwriting
Tahun 1720
Marine Cargo become special business.
Bubble Act Abad ke 18
1550
1600
1650
1700
1750
1800
1850
1900
1950
2000
Marine Ordinary Life Fire Personal Accident Industrial Life Engineering Liability Thefts Permanent Health Loss of Profit Motor Contractor All Risk 1550
1600
1650
1700
1750
1800
1850
1900
1950
2000
Indonesia Insurance Historyy The Beginning g g of insurance companies in Indonesia: • Semarang Sea • Java Sea Ardjoena • Veritas V it • Mercurius
1886
• NV Indiche Lloyd • PT Lloyd Indonesia
1912
O.L.Mij.Boemi Poetra
1916
now
` `
`
Perusahaan asuransi menggunakan the law of large numbers sebagai dasar operasinya Semakin banyak eksposur atau risiko yang serupa, semakin kecil penyimpangan kerugian yang terjadi dari kerugian yang diperkirakan. diperkirakan Contoh: untuk individu, risiko atau ketidakpastian yang berkaitan dengan kematian sangat tinggi. Tetapi jika eksposur atau risiko kematian tersebut dikumpulkan oleh perusahaan h asuransi, i risiko i ik k kematian i tersebut b menjadi j di llebih bih mudah dan lebih akurat untuk dihitung. Jika eksposur atau risiko kematian yang dikumpulkan mencapai 500.000, maka kematian yang sesungguhnya akan menyimpang dari yang d k k tidak d k llebih bhd % Æ akurasi k k diperkirakan dari 1% meningkat
`
`
`
p in business Æ “caveat emptor” p Common p principle (let the buyer beware) Insurance contract subject to rule of “uberrima fides” (utmost good faith) fides Consequences: ◦ Duty of disclosure
x What x When (during negotiation, during contract, renewal)
◦ Material fact ◦ Warranty Æ is an undertaking by insured that something shall be done or shall not be done or that a certain state of facts exists or doesn’t exist x Express Æ written in a contract x Implied Æ not written (marine insurance)
` `
`
`
q y contract insurance Basic requirement of any Subject matter of contract Æ financial interest which person has in the subject matter of insurance Subject matter of insurance Æ things (goods or person) Insurable interest Æ legal right to insure, arising out of a financial relationship recognized at law between the insured and the subject matter of insurance
`
` `
p p Purpose Æ exact financial compensation sufficient in the same position before loss occurred Exclusion Æ life and personal accident insurance F t Factors li limiting iti paymentt off iindemnity d it ◦ ◦ ◦ ◦ ◦
Sum insured Limit of indemnity Average, when under insured = (SI/VAR)*Loss Deductible Coinsurance
`
`
The active and efficient cause which sets in motion a train of events which brings about a result, with out intervention of any force starting and working actively from a new and independent source The proximate cause is not necessarily the first cause nor the last cause: it is the dominant cause ◦ Ex#1: Roth vs South Easthope Farmer Mutual Insurance Co. (1918) ◦ Ex#2: Gaskart vs Law Union Insurance Co. (1876)
` `
pp y Applies when a contract is one of indemnity Right of insurer to claim another parties when the insurer have admitted the insured’s claim and paid it. it
`
`
`
y be covered under more than Arise when a loss may one policy The right of an insurer to call upon others similarity but not necessarily equally liable to the similarity, same insured, to share the cost of an indemnity payment How contribution may arise: ◦ Two or more polices of indemnity exist ◦ The policy cover a common interest, common peril or common subject matter
`
`
g disputes, p p y those of technical Referring particularly nature, to arbitration rather than to a court of law Adv: ◦ Comparatively private ◦ Less formal, more quickly ◦ Less expensive
`
Di Dis-adv: d
◦ Insured tends to be suspicious of arbitration ◦ In the public’s mind the decision of a judge is infinitely preferable ◦ Any misconduct of the proceedings will seriously undermine the reputation of arbitration
` ` ` ` ` `
Risiko bisa ditentukan dan diukur Risiko yang memiliki kemiripan dan banyak Terjadi karena ketidaksengajaan atau karena kecelakaan Kerugian tidak diakibatkan oleh bencana Kerugian yang besar Probabilitas terjadinya kerugian tidak terlalu tinggi
Investment Income
Expected Claim Cost
Administrative Cost
Fair Insurance Premium
Fair Profit Loading
` `
Moral Hazard Adverse Selection
`
Problem yang biasa terjadi ◦ moral hazard ◦ adverse selection
`
`
`
Moral hazard Æ perilaku yang tidak berhati-hati (ceroboh). Asuransi cenderung d mendorong d terjadinya d perilaku l k morall hazard
Adverse selection Æ kecenderungannya adalah mereka yang perilakunya ceroboh akan membeli asuransi asuransi, karena dia merasa membutuhkan perlindungan untuk perilakunya yang ceroboh. Orang yang berhati-hati akan lebih berhatihati at pula pu a dalam da a membeli e be asuransi, asu a s , karena a e a kebutuhan ebutu a akan a a perlindungan (asuransi) tidak sebesar kebutuhan dari orang yang tidak berhati-hati. Perusahaan asuransi akan dirugikan oleh kedua perilaku tersebut
Support functions
Sales
Underwriting
Investment
Claim Management
Market M k t Structure St t
1999
2000
2001
2002
2003
178
178
175
173
173
Life Insurers
62
62
61
60
60
General Insurers
107
107
104
104
104
Professional Reinsurers
4
4
4
4
4
Social Insurer & Jamsostek
2
2
2
2
2
Civil Servant & Armed Forces
3
3
3
3
3
Insurance and Reinsurance Brokers
83
78
91
118
141
Loss Adjuster
23
23
23
25
25
Actuarial Consultants
18
18
18
19
20
Number of Registered Insurers :
S b I d i IInsurance 2003 ti d i id Sumber:Indonesian 2003, dik dikutip darii www.aaui.or.id
`
`
Terdapat empat jenis asuransi yaitu asuransi jiwa (life insurance), asuransi kerugian (general insurance), asuransi sosial (social insurance) dan civil servant & army insurance Lembaga pendukung asuransi adalah re-insurer, broker, loss adjuster dan actuarial consultant
Insurance Development Per Capita Expenditure (Rp)***
1999
2000
2001
2002
2003
69.099
81.914
112.246
65.645
67.301
38.160.700
41.611.660
64.825.992
77.589.087
94.094.322
- Life Sum Insured
16,3
19,3
18,90
7,22
9,30
- Life Premium
0,49
0,57
0,01
1,04
0,98
- Non Non-life life and Reinsurance Gross Premium
0 57 0,57
0 56 0,56
0 01 0,01
0 86 0,86
0 69 0,69
- Life Asset
1,50
1,45
0,02
1,63
0,00
- Non-Life and Reinsurance Asset
1,01
0,98
0,01
0,98
0,82
Total Industry Asset (Million) A % off GDP As
Sumber:Indonesian Insurance 2003, dikutip dari www.aaui.or.id *** Total Gross Premium/ Number of Population
`
Pengeluaran per kapita penduduk untuk asuransi masih rendah, dengan penyebaran yang merata baik pada asuransi kerugian maupun asuransi jiwa
Life Insurance Data
1999
2000
2001
2002
2003
3.668.634
6.824.511
6.824.511
7.863.281
11.496.464
50.121.978
89.965.174
89.965.174
116.303.773
194.014.311
2.941.084
3.844.975
4.395.998
5.379.882
6.619.164
22.284.424
24.256.579
25.293.099
24.246.485
30.867.931
182.439.976
249.055.936
281.843.052
237.140.801
467.560.630
5.508.288
9.139.671
9.139.671
11.436.363
13.911.913
10,80
11,90
12,10
15,15
19,69
Premium Reserve (Rp Million)
11.157.458
12.545.986
12.545.986
20.703.044
28.143.440
Total Asset (Rp Million)
16.822.142
22.551.268
22.551.268
26.320.521
32.933
Total New Business except PA and Health Number of Policies (In Unit) Sum Insured (Rp Million) Annual Premium (Rp Million) Total Business In Force : Number of Policies (In Unit) Sum Insured (Rp Million) Annual Premium (Rp Million) Number of Policies as % of Population
Sumber:Indonesian Insurance 2003, dikutip dari www.aaui.or.id
General Insurers
1999
2000
2001
2002
2003
Gross Premium (Rp Million)****
6.421.693 6 421 693
7.287.619 7 287 619
10.354.022 10 354 022
13.857.561 13 857 561
14.482.899 14 482 899
Net Premium (Rp Million) :
2.838.519
3.541.937
4.768.775
4.696.943
5.078.732
44%
49%
46%
34%
35%
48,46
53,60
68,41
48,06
47,30
Earned Premium
2.509.685
2.915.672
3.674.250
4.696.943
5.078.732
Incurred Claim
1.216.188
1.562.783
2.513.658
2.257.214
2.404.495
265.751
394.733
648.552
678.173
974.997
1 293 497 1.293.497
1 352 889 1.352.889
1 160 591 1.160.591
2 439 729 2.439.729
2 674 237 2.674.237
1.115.224
1.307.167
1.536.449
1.685.445
1.970.400
51,54
46,40
31,59
51,94
52,66
854.263
839.806
877.460
466.847
787.400
11.103.768 103 768
11.178.769 178 769
11.309.645 309 645
869 067 869.067
11.204.300 204 300
11.339.303
12.629.721
14.808.599
15.768.204
17.175.400
Retention Ratio (%) : Incurred Loss Ratios (%) ***** : Underwriting Surplus ( Rp Million)
Net Commission Underwriting Profit Management Expense Underwriting Profit as % of Earned Premium Net Investment Income (Rp Million) Net Profit (Rp Million) Total Asset (Rp Million)
Sumber:Indonesian Insurance 2003, dikutip dari www.aaui.or.id **** Direct Premium + reinsurance premium inward from abroad ***** Claims Cl i Incurred/Premiums I d/P i E Earned d
`
Dalam asuransi kerugian terdapat 11 class of business (COB) utama yaitu: ◦ property, motor, cargo, marine hull, Aviation, satellite, engineering, liability, personal accident & health, credit & surety bond dan Others
`
`
45% premi yang terkumpul adalah merupakan motor insurance M i h Marine hull ll merupakan k COB yang paling li ti tinggii lloss rationya (45% - 72%)
Social Insurer & JAMSOSTEK
1999
2000
2001
2002
2003
(in Rp Million) Premium Written Technical Reserve Annual Benefit Total Asset
797.862
929.440
1.296.159
1.796.758
1.877.168
9.896.981
12.174.878
15.703.507
19.934.665
25.832.059
386.330
404.762
551.293
782.986
936.777
11.077.228
13.138.475
17.180.668
22.176.991
27.908.600
Sumber:Indonesian Insurance 2003, dikutip dari www.aaui.or.id
Civil Servant & Army Insurers
1999
2000
2001
2002
2003
(in Rp Million) Premium Written
1.114.482
1.144.497
2.658.259
3.090.552
3.866.494
Technical Reserve
5.870.738
6.245.633
9.226.223
11.596.638
13.977.179
Annual Benefit
2.164.766
1.677.135
3.472.190
3.985.486
4.729.488
Total Asset
7.135.255
7.932.285
10.397.076
13.323.372
16.076.800
Sumber:Indonesian Insurance 2003, dikutip dari www.aaui.or.id
Potensi Pasar Asuransi Indonesia (2004-2008), trilyun Rp
Tahun
Asuransi Jiwa
Asuransi Kerugian
Asuransi Konvesional
Asuransi Syariah
2004
18.19
20.662
38.852
0.78
2005
19.856
25.622
45.478
1.82
2006
21.675
31.771
53.446
3.21
2007
23.66
39.396
63.056
5.04
2008
25.828
48.851
74.679
7.47
Sumber: Majalah PROTEKSI No. 165 tahun XXV
Industri asuransi akan terus berkembang dengan tingkat pertumbuhan rata-rata 19% - 21 % p p per tahun Asuransi syariah memiliki pertumbuhan yang paling pesat dengan rata-rata 45% -57% per tahun
Struktur populasi berdasar kelompok umur Age structure
Indonesia (%) 2000
2003
2010
0 – 14
30 5 30.5
27 7 27.7
26 2 26.2
15 – 64
64.8
68.2
64.5
> 65
4.7
4.1
9.3
Total
100
100
100
Sumber: BPS, 2004, Welfare Statistic 2004
`
` `
K i i penduduk d d kb b k piramida i id d k Komposisi berbentuk dengan perut yang gemuk di tengah +/- 65% penduduk adalah usia produktif yang memiliki penghasilan +/ 65% penduduk tersebut adalah pasar riil industri asuransi +/Indonesia
No
Perusahaan
Jumlah Cabang/ Perwakilan
Tahun Berdiri
1999
2000
2001
2002
2003
2004
Syariah
Konvensional
1
As. Takaful Keluarga
1994
15
20
25
30
32
34
34
0
2
As. Takaful Umum
1996
6
8
10
11
19
23
23
0
3
As. Syariah Mubarokah
1997
40
50
55
60
77
77
77
0
4
As. Great Eastern
2001
1
1
4
4
4
16
5
As. Bumiputera
2002
10
10
10
10
230
6
A Bringin As. B i i Ji Jiwa S Sejahtera j ht
2003
1
1
1
40
7
As. Bringin Sejahtera AM
2003
1
1
1
10
8
As. Tripakarta
2002
6
6
6
6
8
9
MAA General
2000
1
1
1
1
1
1
4
10
MAA Life
2000
4
4
4
4
4
4
8
11
As. Jasindo Takaful
2003
1
1
1
82
12
As. Binagriya
2003
1
1
1
14
13
As. Bumida
2004
1
1
1
30
14
As. Staco Jasa Pratama
2004
4
4
4
5
15
As. Central Asia
2004
1
1
1
36
16
As. Adira Syariah
2004
1
1
20
17
As. Sinar Mas
2004
1
1
30
18
BNI Jiwasraya Syariah
2004
1
1
0
19
Tokio Marine Syariah
2004
1
1
0
20
Reindo Divisi Syariah
2004
1
1
1
174
174
534
JUMLAH Sumber: Majalah PROTEKSI No. 165 tahun XXV
61
83
96
123
163
Economics and Insurance Development Data 1
Population (Million)
2
Employment (in 000)**
1999
2000
2001
2002
2003
200,3
203,5
208,9
211,10
215
Labor Force
94.847
95.651
98.812
100.8
100.3
N mber of Emplo Number Employed ed (Formal Sector)
88 817 88.817
89 838 89.838
90 807 90.807
91 647 91.647
90 785 90.785
101
110
108
110
NA
Number of Employed by Insurance Industry
Sumber:Indonesian Insurance 2003, dikutip dari www.aaui.or.id
` `
Tenaga siap kerja sebesar +/- 47% dari total penduduk, 90% diantaranya bekerja pada sektor formal Industri asuransi mampu menampung 0,11% dari total ttenaga siap i k j kerja
` `
Solvabilitas minimum 120% Investasi ◦ ◦ ◦ ◦ ◦ ◦ ◦
Deposito berjangka Æ max 20% perusahaan Indonesia Æ max 20% Saham p Obligasi perusahaan Indonesia Æ max 20% Reksadana Æ max 20% Penyertaan langsung Æ max 10% Tanah dan bangunan Æ max 20% Pinjaman hipotik Æ max 20%
Property
• Fire and allied • Marine • Crime
Liability or Casualty
Multiple Peril
• General liability
• Commercial peril
• Worker’s compensation & employers’ liability
• Commercial automobile
• Medical malpractice professional liability
• Boiler and machinery
• Others professional liability
• Aircraft
• Environmental liability
Source: Harrington & Niehauss (2004)
Fidelity, Surety & Guaranty
• Surety bonds
• Fidelity bonds • Financial guarantees
Surety Bonds Insurance
• Contracts involve 3 parties: the party that owes performance (the principal), the party to which performance is owed (the obligee), and the surety • The surety is required to respond to the obligee if the principal default • The surety usually has subrogation right or other legal recourse against the principal
•Contract involve 2 parties: insurer and insured (third party liability coverage make payment to injured party that are not party in the contract) •The insurer is required to respond to the policyholder •The insurer generally cannot subrogate against its policyholders
◦ Coverage x x x x
Physical by h l damage d b accident d Third party liability only Third p party, y, fire and theft Comprehensive
`
Single limit
`
Split limits ◦ Example: x 100 100,000 000 per person for bodily injury x 300,000 per accident for bodily injury x 50,000 per accident for property damage
`
Who is insured and when? ◦ Named insured plus
x resident spouse p x other family members x others who use the covered auto with permission
◦ Covered auto is vehicle listed on the policy plus x newly acquired vehicles x temporary substitute vehicles
`
Types of exclusions
Use of the insured car Contractual liability War risk Radioactive contamination and explosive nuclear assembly ◦ Riot and dC Civill commotion ◦ Sonic bangs ◦ Injury to an employee covered under WC ◦ ◦ ◦ ◦
◦ Driver characteristics x x x x x x
Age Gender Marital status Use of the auto Number of autos Other factors
◦ Driving Record ◦ Territory
◦ Examples E l x x x x
Gender G Marital status Use driving experience instead of age (MA) Territory
` ` `
`
`
Perkiraaan kerugian yang harus dibayar perusahaan asuransi akibat kecelakaan adalah Rp1 milyar per tahun Prediksi kontrak asuransi yang dapat diperoleh sepanjang tahun adalah 1.000 kontrak Target g laba dan cadangan g untuk menutup p biaya y adalah Rp200 p ribu per kontrak Premi sebelum target laba = Rp1 milyar/1.000 = Rp1 juta Premi (setelah target laba) = Rp1 juta + Rp200 ribu = Rp1,2 juta
` `
`
`
Dalam beberapa kasus, perusahaan asuransi menargetkan prosentase tertentu t t t t atas t margin i kotornya. k t Dari contoh sebelumnya, jika target margin kotor yang ditetapkan adalah sebesar 30%, maka perhitungan premi adalah: Premi sebelum margin = Rp1 milyar/1.000 = Rp1 juta Premi (setelah target margin) = Rp1 juta + (0,3 X Rp1 juta) = Rp1,3 juta
`
Insurers have discretion to deny coverage in mostt states t t g criteria ==> Underwriting ◦ Typically, lower rates are associated with more stringent g underwriting g criteria x Example: x deny if potential insured drinks alcohol x charge lower rates than competitors who do not use this criteria
◦ Without it, accident costs will not be borne by those who cause accidents x Uninsured do not bear the full cost of their driving g ==> some drive even though benefits of driving < true costs
x Uninsured do not bear the full cost of decisions to drive less safely ==> drive less safely than if forced to purchase insurance with experience rating
◦ Its regressive x I.e., it disproportionately hurts low income people x Forces them to buy insurance to protect other people
◦ Weak enforcement ◦ Better to allow people to opt out by making a t ib ti tto the th state t t (VA contribution (VA, SC)
`
Variety of policies: ◦ ◦ ◦ ◦
Building Æ structure of building Contents Æ content of building only Building and content insurance combined Combined policy
x Not only building and contents, also include caravans, sports equipment, i bi bicycle, l and d private i riding idi h horse
`
Coverage
◦ Fire, Fire lightning, lightning explosion, explosion earthquake ◦ Riot, civil commotion, strike, labor or political disturbances, malicious damage or vandalism ◦ Storm or flood ◦ Falling tress ◦ Escape of water ◦ Escape of oil ◦ Theft or attempted theft ◦ Impact ◦ Breakage g or collapse p of television or radio receiving g aerials ◦ etc
`
`
Household goods and personal effects of every description, belonging to the insured or for which the insured is responsible ◦ ◦ ◦ ◦
Fixture and fittings others than landlord’s fixture and fittings TV, satellites, and radio Telephones Gas and electric cookers and maters
◦ ◦ ◦ ◦ ◦ ◦
Property more specifically insured Cash, bank and currency notes Securities, certificates and document Motor vehicle,, motor and accessories while on or in them Animals Any part of structure of dwelling, ceiling, wallpaper and the like
Exclusion
`
`
Life insurance bukan merupakan kontrak indemnitas i d i Risiko yang bisa diasuransikan ◦ Risiko meninggal gg dini ◦ Risiko sumber dana untuk hidup terlalu lama ◦ Risiko kesehatan buruk
` `
Temporary vs Permanent Term vs Cash Value policies
◦ Term Æ pure life insurance ◦ Cash value policies Æ pure life insurance + savings accumulation
◦ Death benefit = amount beneficiaries receive ◦ Cash value = amount of savings accumulation ◦ Death protection = amount amo nt of p pure re 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)
` ` ` ` `
Di Indonesia biasa disebut asuransi berjangka Uang pertanggungan dibayarkan jika U t dib k hanya h jik kematian terjadi selama masa pertanggungan Premi meningkat jika dilakukan perpanjangan Jenis paling tua dan sederhana Tiga hal kunci: ◦ ◦ ◦ ◦
`
TSI (face amount for protection or death benefit), Premi (cost to the insured), Durasi (term) Kombinasi dapat 3 faktor tersebut p dilakukan pada p
Produk yang dijual annual renewable term,
mortgage insurance
`
Whole life (as. jiwa seumur hidup)
◦ Manfaat meninggall dibayar kapan saja kematian terjadi f db k k d (death protection + cash value) ◦ Kekurangan:
x Pembayaran premi relatif tidak flexibel x Return elemen tabungan kurang kompetitif x Premi biasanya lebih tinggi dibanding term insurance (dalam j jangka k pendek), d k) namun secara akumulatif k l tif hampir h i sama jika jik polis bertahan sd usia harapan hidup
◦ Struktur:
h value l ↑ over time i x cash x death protection ↓ over time
`
Universal life
◦ Mirip dengan whole d h l life l f insurance namun lebih l b h flexibel fl b l dalam pembayaran premi ◦ Return lebih baik dinding whole of life insurance. ◦ Cash value tidak harus sama dengan skedul, tapi dapat berbeda tergantung: x policyholder’s premium payments x insurer’s expense and mortality charges x rate insurer uses to credit interest to cash value x minimum rate usually guaranteed x rate often linked to short term interest rates
Cash value at beginning of period + Premium payments at beginning of period Mortality charge at beginning of period Expense charge at beginning of period + Interest credited at end of period = Cash value at end of period
◦ Mirip dengan whole life insurance ◦ Perbedaaannya: x Cash value does not follow a fixed schedule; it varies with x return earned on portfolio of mutual funds chosen by policyholder
x Death benefit
x minimum is guaranteed, g , x varies with cash value
`
Endowment (as. dwiguna)
◦ Uang pertanggungan dibayarkan kematian terjadi db k kapanpun k k d ◦ Elemen tabungan (Cash value) dibayarkan jika tertanggung bertahan hidup sampai tanggal jatuh tempo polis
`
Personal Accident
◦ Perlindungan atas luka tubuh (bodily injury) atau kematian akibat kecelakaan ◦ Kematian dibayar lump sum, luka tubuh dibayar berjenjang
`
Annuity
◦ Memberikan jaminan pendapatan peserta anuitas selama hidupnya dengan pembayaran tahunan, setengah tahunan, kuartalan atau bulanan setelah periode tertentu (mis: 5 tahun setelah pembelian polis) ◦ Cocok untuk orang yang hidup terlalu lama melebihi sumber keuangannya ◦ Dua periode x Accumulation ccu u at o pe period od (pe (pemegang ega g po polis s baya bayar p premi) e ) x Payout period (perusahaan asuransi memberikan benefit)
`
Unit link
b b ◦ G Gabungan antara k komponen asuransi d dan investasi atau tabungan ◦ Penempatan dana unit link: saham, obligasi, pasar uang, dan campuran ◦ Return paling kompetitif
Characteristic
Variations
Premium payments
(a) Single premium (b) Fixed period, level premium up to an advanced age (c) Flexible premium over time
Annuity benefits begin
(a) Immediately (b) Deferred
Annuity benefits end
(a) Fixed number of years (b) Death of one or more individuals (c) Combination of (a) and (b)
Insurer payments
(a) Fixed (b) Vary with interest rates, with guaranteed minimum (c) Vary with returns on stock and bond funds chosen by policyholder
◦ Ignore expenses and risk load > focus on net premiums ==> ◦ Use mortality table x Probability of dying at age x conditional on living through age x-1 x Example: Probability of male dying at age 40 = 0.00302
◦ Assume
x Premiums paid at beginning of year x Claims paid at end of year
◦ Find fair premium for $100,000 1-year term for 40 year-old year old x Interest rate = 10% x Insurer’s cash flows: Beg. of Year Premium
End of Year -$100,000 with prob 0.00302 $0
with prob. 0.99698
Premium = Present value of expected claim cost = $302 / 1.1 = $275
◦ Find fair premium for $100,000 1-year term for 41 year-old year old x Interest rate = 10% x Insurer’s cash flows: Beg. of Year Premium
End of Year -$100,000 with prob 0.00329 $0
with prob. 0.99671
Premium = Present value of expected claim cost = $329 / 1.1 = $299
E x pe c te d C la im C o sts
◦ Premium increases as probability of dying increases $1,000 $800 $600 $400 $200 $0 35 40 45 50 55 60 65 70 75 80 85 90 95
Age
◦ 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 -$100,000 with prob 0.00302 $0 with prob. 0.99698
End of Year 2 -$100,000 with prob x $0 with prob 1-x
◦ What is x? – it is the probability of a 40 year-old dying in his 42nd year? ◦ Mortality table: Age 40 41
N Number b
Number N b of People of Deaths 937723 2832 934891 3076
Probability of 40 year-old dying in 41st year = 0.00302 2832 937723 Probability of 40 year-old dying in 42nd year = 3076 0.00328 937723
= =
◦ Single premium ◦ Insurer’s expected cash flows Beg. of Year
End of Year 1
End of Year 2
Premium
-$302
-$328
Premium
= PV of expected claim costs = $302 / 1.1
+
= $275 + $271 = $546
$328 / 1.12
◦ Level Premium x same premium paid at beginning of each year (if insured survives)
◦ Insurer’s expected cash flows Beg. of Year Premium
End of Year 1 Premium x 0.99698
End of Year 2
-$302
-$328
Find Premium so that expected d claims l i
PV of expected premiums = PV of
◦ Premium (1 + 0.99698/1.1) = $546 ◦ Premium = $286.41 ◦ Note: x $ $286.41 > 1/2 / of single g p premium ($ ($546)) x Why? x Chance second premium payment will not be made x Second premium is discounted b/c of time value of money
◦ Expected costs of three alternative methods of obtaining coverage: bt i i Beginning
Beginning of 2nd year
off 1 st year
Present value l
Successive one year term policies
$275
$299 x 00.99698 99698 =$298
$546
Level premium two-year term policy
$286
$286 x 0.99698 = $285
$546
Single i l premium i two-year term policy li
$ $546
$ $0
$ $546
◦ Annual premiums for successive term policies reflect the annual cost of insuring x Annual cost = $275
and $298
◦ With 2-year policy,
x premium in year 1 > $275 x premium in year 2 < $298
Essentially, pref di funding costs t
x With this example, size of difference is small x With whole life policies (UL (UL, VL) x difference can be large x gives rise to cash value
◦ Example: Find single premium for a $5,000 life annuity for a 95-year-old x Assume person dies by age 100 x Interest rate = 10%
x Premium = PV of expected payments to annuitant = $4,530
Age 97 $2 797 $2,797 98 $1,322 99 100
Probability Expected of 96-yearPayment old surviving $5,000 x prob 6050/9831 $3077
0
PV of Expected Payment
$3,077 / 1.1 =
3145/9831
$1,600
$1,322 / 1.12 =
1076/9831 0
$547
$547/ 1.13 = $411
0
◦ Apply same principles used with term ◦ Forecast expected to age 100 F d cash h flows fl ◦ Find single g premium = PV of expected cost x Assume x no expenses or profits x 5% interest rate x policy will not lapse
Probability of 40 year old dying in
Expected
Present value of
year at left
claim cost
expected claim cost
40
0.003020
$302.00
$302.00/1.05 =
$288
41
0.003280
$328.00
$328.00/1.052 =
$298
42
0.003538
$353.80
$353.80/1.053 =
$306
43
0.003832
$383.20
$383.20/1.054 =
$315
44
0.004133
$413.30
$413.30/1.055 =
$324
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
96
0.004032
$403.20
$403.20/1.05 57 =
$25
97
0.003098
$309.80
$309.80/1.05 58 =
$18
98
0.002207
$220.70
$220.70/1.05 59 =
$12
99
0.001147
$114.70
$114.7/1.05 60 =
$6
Age
45
Total
22,373
Single Premiu m
◦ Continuous level premium x Same premium is paid until insured dies or reaches 100 x Equivalent E i l to a lif life annuity i
◦ Present value of a life annuity that pays $P starting at age 40 = 16.30 x P payments = PV of costs ◦ Find P so that PV of premium p p y x 16.30 x P = $22,373 ==> P = $1,372.58
◦ Limited payment level premium x Same premium is paid for fixed number of years x Example: 20 years x Equivalent to a 20 year annuity
◦ Present value of a 20 20-year year annuity that pays $P starting at age 40 = $12.58 x P ◦ Find P so that PV of premium payments = PV of costs x 12.58 12 58 x P = $22 $22,373 373 ==> P = $1 $1,778.45 778 45
$100,000 $90,000
C A S h
$80,000 $70 000 $70,000 $60,000
V A L U E S
payments for life 20 Year Payments Single Premium
$50,000 $40,000 $30,000 $20,000 $10,000 $0 40
44
48
52
56
60
64
68
72
Age
76
80
84
88
92
96
◦ Rules of thumb x Death benefit = 8 times income
◦ Forecast beneficiaries sources & uses of funds x Uses:
x Living expenses x Education expenses
x Sources:
x Social security x Earnings
◦ Adjusted cost index x Idea: calculate accumulated future value of all costs x Procedure x x x x
accumulate premiums (P) per $1,000 of coverage less p policyholder y dividends ((D)) for 20 years at a 5% interest rate 20
AC20 = ∑ Pt (1.05) t =1
20− t +1
20
− ∑ D t (1.05)20−t t =1
◦ One approach: use adjusted cost index again x but subtract cash value (CV) at end of 20 years x AC20* = AC20 - CV20 x In p practice adjust j cost indices are scaled to g get interest adjusted cost (IAC): 20
IAC20 = AC 20 / ∑1.05 t t =1
◦ Another ot e app approach: oac ca calculate cu ate implicit p c t rate ate o of return etu
◦ More complex ◦ One approach: x Use interest adjusted cost index subtracting an estimate of cash value x under common assumptions(across policies being compared) about premiums and interest rates
◦ No consensus exists
