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UNIVERSITI TEKNOLOG I MARA

FINAL EXAMINATION

COURSE

COURSE CODE

EXAMINATION

TIME

ACTUARIAL PRACTICE

ASC569

JANUARY 2013

3 HOURS

INSTRUCTIONS TO CANDIDATES

1 . This question paper consists of five (5) Ques tions.

Answer ALL questions in the Answer Booklet. Start each answer on a new page.

.

3.

Do not bring any material into the examination room unless permission is given by the

invigilator.

Please check to make sure that this examination pack consists of:

i) the Que stion Paper

ii) a two - page Appendix

iii) an Ans wer Booklet - provided by the Faculty

DO NOT TURNT ISP GEUNTILYOU RE TOLD TO DO SO

This exam ination paper consists of printed pages

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CONFIDENTIAL 2 CS/JAN 2013/ASC569

QUESTION 1

You have been assigned to conduct statutory valuation of liabilities for SAK Life Insurance

Company based on the minimum valuation basis of Bank Negara Malaysia Insurance Act

1996.

a) Wh at is the meaning of minimum valuation basis and state the basis used to determine

i) The mortality rate for ma le insured lives and female insured lives.

ii) The interest rate for annu al premium and single premium life insurance policies.

(5 marks)

b) An inforce policy was issued to a male life aged 25 with its 10

th

policy a nniversary falling

on 1 April 2 01 1 . The policy provides for a lifetime de ath benefit payable at the end of

year of death with sum assured, RM 1 00,000 and level premiums are paid for a limited

period of 20 years only.

i) Calculate the 1 0

th

term inal reserves on the policy using statutory basis.

(8 marks)

ii) The com pany's financial year runs from 1 January 201 1 to 31 December 2 01 1 . Use

a suitable approximation to value the company's liability on the policy as at the

2011 valuation date. You should explain briefly the model used in the

approximation.

(8 marks)

QUESTION 2

You are a member of the product development team of a Life Office and are at the stage of

gathering ideas to design a new product.

a) Based on the feedb ack from your field organiza tion, the following product ideas were

proposed to you. In each case, assess the feasibility of developing a product to cover

the risk below:

i) Insuring the risk of having children to cover the expensive cost of raising achild,

ii) Insuring the loss of depen dents' financial support due to incidence of divorce .

(4 marks)

b) Your product developm ent team has decided to enhance the existing products of the

company instead of introducing a totally new product to cut cost and to remain

competitive. Based on your market research, the following benefits would be

incorporated as riders in the existing basic policies:

i) Long-term care benefit.

(7marks)

ii) Critical Illness benefit.

(6 marks)

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Explain the benefit and premium structure of each of the above riders. In each case,

explain wh ether a waiting period is required or not in the des ign of the product.

QUESTION 3

XYZ Life Insurance Company is developing a special twenty-year endowment policy with the

following benefit structure and expense allocation:

Benefit structure:

Death be nefits:

Full sum assured is payable at the instant of death if death occurs during the

term of the policy.

Survival Be nefits:

Equal percentage of sum assured is payable at the end of every five year period

if the insured survives to the end of each period.

Expense allocation:

Agent's commission:

50% of first year prem ium, 20% of premiums collected thereafter.

Administrative and underwriting expense:

RM50 in the first year and RM20 in each subsequent year.

Cost of claim settlement:

RM1 0 per R M1 .000 sum assured at the time of death benefit payment.

RM5 per RM 1 ,000 sum assured at the time of survival benefit payment.

a) Using equivalence principle, write down the equation for the actuarial present value of

gross premiums per 1000 sum assured and determine the gross premium formula in

terms of commutation functions.

(10 marks)

b) Calculate the gross premium in part(a) above for a policy issued to (30) and mortality

follows the DGI 1996 Table at 4% interest. Assume uniform distribution of deaths over

the year of death.

(7 marks)

c) Explain what mo dification is necessary to the equation in part(a) above if on average,

death payment is made at the end of the third quarter of the year of death? Interpret

your result.

(5 marks)

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QUESTION 4

You are responsible to carry out product pricing for a newly proposed participating life

insurance product where there is minimum guarantee on the returns on investment.

a) The chief actuary has advised you to compute gross premiums based on realistic

assumption instead of conservative assumption.

i) Explain the difference between realistic and conserva tive assum ptions, illustrating

your answer with reference to interest and mortality basis. Indicate the impact each

type of assumption has on price, profitability and marketability of the product.

(7 marks)

ii) Based on your explanation in part (b)(i) above, what wo uld be your recom men dation

to the chief actuary for the final set of pricing basis?

(3 marks)

b) You wish to employ the asset share technique to determ ine the price for the product.

i) Explain the meaning of the term asset share and state the difference between

historical

asset shares and projected asset shares?

(5 marks)

ii) Name FOUR 4) factors that you are likely to take into account as cash outflow in

your asset share calculation.

(4 marks)

QUESTION 5

You are asked to conduct premium rating for a private motor-vehicle damage-only portfolio

of a general insurance comp any.

a) GiveTWO(2) examples of rating factors that are likely to be used with respect to each

of the following:

i) Factors assoc iated with the individual proposer,

ii) Factors related to the risk unit.

To each answer, you should briefly justify why the factor is chosen in the premium

rating.

(4 marks)

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b) The number of policies in force for the portfolio is subdivided by No Claim Discount

(NCD) category. You have collected data on the inforce policies at the beginning of

each quarter during 2 01 1 and at the beginning of the first quarter of 201 2 as follows:

DATE

1 1 2011

1 4 2011

1 7 2011

1 10 2011

1 1 2012

NO OF POLICIES INFORCE

FULL PREMIUM

6245

6278

6381

6423

6459

35%

NCD

5990

6167

6175

6233

6274

55% NCD

7608

8165

8374

8549

8 6 11

The number of claims in respect of incidents during 2 11(including Incurred but not

reported claims) total 2874 of which 957 are from policyholders paying full premiums,

865 from those on a 35% NCD, and the rest from those on a 55% NCD.

i) Estimate the claim frequency rates for the three categories using the census

method. Comment on your result. You should state any assumption used.

(11 marks)

ii) You discovered that for the 35% NCD category, only censuses on 1 January 2011

and 1 October 2011 are reliable. Revise your result for the 35% NCD claim

frequency rate based on the two censuses only. You should state your revised

assumption and comm ent on the accuracy of your result com pared to your answer

in part (b)(i) above.

(6 marks)

END OF QUESTION PAPER

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CONFIDENTIAL APPENDIX 1 CS/JAN 2013/ASC569

Commutat ion funct ion s based on DG11 996 Mortal ity Table at 4% interest per annum

X

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

q

x

0.00157

0.00156

0.00149

0.00145

0.00144

0.00144

0.00148

0.00154

0.00163

0.00176

0.00190

0.00207

0.00219

0.00218

0.00211

0.00204

0.00198

0.00192

0.00187

0.00182

0.00178

0.00177

0.00179

0.00185

0.00193

0.00202

0.00214

0.00226

0.00239

0.00254

0.00272

0.00293

0.00319

0.00349

0.00383

0.00419

0.00460

0.00505

0.00552

0.00603

0.00660

0.00721

0.00790

0.00866

0.00946

D

x

6 755 641.7

6 485 610.9

6 226 435.9

5 978 037.0

5 739 777.8

5 511 069.7

5 291 474.8

5 080 426.3

4 877 502.4

4 682 261.6

4 494 250.8

4 313 184.3

4 138 707.7

3 970 811.5

3 809 764.5

3 655 505.7

3 507 738.9

3 366 147.7

3 230 466.1

3 100 408.7

2 975 736.5

2 856 192.0

2 741 477.5

2 631 317.5

2 525 432.3

2 423 613.7

2 325 690.4

2 231 455.2

2 140 780.8

2 053 523.4

1 969 526.4

1 888 624.4

1 810 664.1

1 735 469.3

1 662 896.7

1 592 815.2

1 525 135.8

1 459 731.0

1 396 499.4

1 335 375.7

1 276 272.4

1 219 085.6

1 163 746.2

1 110 146.7

1 058 204.6

N

x

155 874 750.0

149 119 108.3

142 633 497.4

136 407 061.5

130 429 024.5

124 689 246.7

119 178 177.0

113 886 702.3

108 806 275.9

103 928 773.5

99 246 512.0

94 752 261.2

90 439 076.8

86 300 369.1

82 329 557.6

78 519 793.1

74 864 287.4

71 356 548.4

67 990 400.7

64 759 934.7

61 659 525.9

58 683 789.4

55 827 597.4

53 086 119.9

50 454 802.4

47 929 370.1

45 505 756.4

43 180 066.1

40 948 610.9

38 807 830.1

36 754 306.6

34 784 780.2

32 896 155.8

31 085 491.7

29 350 022.4

27 687 125.7

26 094 310.5

24 569 174.7

23 109 443.7

21 712 944.4

20 377 568.7

19 101 296.3

17 882 210.6

16 718 464.5

15 608 317.8

S

x

3 130 429 877.0

2 974 555 127.0

2 825 436 018.7

2 682 802 521.2

2 546 395 459.7

2 415 966 435.2

2 291 277 188.4

2 172 099 011.4

2 058 212 309.2

1 949 406 033.2

1 845 477 259.7

1 746 230 747.7

1 651 478 486.6

1 561 039 409.7

1 474 739 040.6

1 392 409 483.0

1 313 889 689.9

1 239 025 402.6

1 167 668 854.1

1 099 678 453.4

1 034 918 518.7

973 258 992.8

914 575 203.4

858 747 606.0

805 661 486.1

755 206 683.7

707 277 313.6

661 771 557.2

618 591 491.1

577 642 880.2

538 835 050.1

502 080 743.5

467 295 963.4

434 399 807.5

403 314 315.8

373 964 293.5

346 277 167.8

320 182 857.2

295 613 682.5

272 504 238.8

250 791 294.4

230 413 725.7

211 312 429.5

193 430 218.8

176 711 754.3

C

x

10 198.42

9 728.42

8 920.57

8 334.76

7 947.38

7 630.71

7 530.18

7 522.94

7 644.55

7 923.83

8 210.65

8 584.90

8 715.16

8 323.43

7 729.43

7 170.42

6 678.20

6 214.43

5 808.63

5 425.72

5 093.09

4 861.02

4 718.50

4 680.71

4 686.62

4 707.40

4 785.56

4 849.12

4 919.68

5 015.34

5 151.07

5 320.84

5 553.86

5 823.83

6 123.94

6 417.21

6 745.79

7 088.12

7 412.19

7 742.61

8 099.42

8 451.55

8 839.99

9 244.11

9 625.59

759 934.67

749 736.25

740 007.84

731 087.27

722 752.51

714 805.12

707 174.41

699 644.23

692 121.29

684 476.75

676 552.92

668 342.27

659 757.37

651 042.21

642 718.78

634 989.35

627 818.94

621 140.74

614 926.32

609 117.69

603 691.97

598 598.89

593 737.87

589 019.36

584 338.65

579 652.03

574 944.63

570 159.08

565 309.95

560 390.27

555 374.94

550 223.87

544 903.03

539 349.17

533 525.33

527 401.40

520 984.19

514 238.40

507 150.28

499 738.09

491 995.48

483 896.06

475 444.51

466 604.52

457 360.41

R

x

35 426 411.94

34 666 477.27

33 916 741.02

33 176 733.18

32 445 645.91

31 722 893.41

31 008 088.28

30 300 913.88

29 601 269.64

28 909 148.35

28 224 671.60

27 548 118.68

26 879 776.41

26 220 019.03

25 568 976.82

24 926 258.04

24 291 268.69

23 663 449.75

23 042 309.01

22 427 382.69

21 818 265.00

21 214 573.03

20 615 974.14

20 022 236.27

19 433 216.91

18 848 878.26

18 269 226.22

17 694 281.59

17 124 122.51

16 558 812.56

15 998 422.29

15 443 047.35

14 892 823.48

14 347 920.45

13 808 571.28

13 275 045.95

12 747 644.55

12 226 660.36

11 712 421.97

11 205 271.69

10 705 533.60

10 213 538.12

9 729 642.06

9 254 197.54

8 787 593.03

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CONFIDENTIAL APPENDIX 2 CS/JA N 2013/ASC569

Comm utat ion fun ct ion s based on DG11996 Mortal i ty Table at 4% interes t per annum

55

56

57

58

59

60

61

62

6 3

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

q

x

0.01033

0.01122

0.01210

0.01295

0.01381

0.01479

0.01597

0.01741

0.01903

0.02084

0.02286

0.02506

0.02755

0.03019

0.03303

0.03615

0.03961

0.04345

0.04756

0.05200

0.05684

0.06215

0.06799

0.07425

0.08098

0.08824

0.09609

0.10458

0.11367

0.12338

0.13370

0.14466

0.15630

0.16890

0.18230

0.19655

0.21187

0.22867

0.24732

0.26847

0.29242

0.31947

0.35017

0.38527

0.42513

D

x

1 007 878.9

959 103.4

911 867.5

866 186.5

822 085.9

779 550.9

738 482.0

698 738.9

660 167.2

622 696.3

586 268.6

550 833.2

516 374.3

482 834.8

450 248.1

418 631.2

387 978.5

358 279.5

329 531.0

301 787.0

275 090.5

249 475.3

224 971.6

201 611.3

179 463.1

158 586.8

139 031.8

120 838.7

104 039.8

88 666.9

74 737.7

62 255.0

51 201.2

41 537.0

33 193.6

26 098.5

20 162.3

15 279.4

11 332.1

8 201.4

5 768.8

3 924.9

2 568.3

1 604.8

948.6

N

x

14 550 113.1

13 542 234.2

12 583 130.9

11 671 263.4

10 805 076.9

9 982 991.0

9 203 440.1

8 464 958.1

7 766 219.2

7 106 052.0

6 483 355.7

5 897 087.1

5 346 253.9

4 829 879.5

4 347 044.7

3 896 796.6

3 478 165.4

3 090 186.9

2 731 907.4

2 402 376.4

2 100 589.3

1 825 498.8

1 576 023.5

1 351 051.9

1 149 440.6

969 977.5

811 390.7

672 358.9

551 520.2

447 480.5

358 813.6

284 075.9

221 820.9

170 619.7

129 082.7

95 889.1

69 790.6

49 628.3

34 348.9

23 016.8

14 815.4

9 046.5

5 121.6

2 553.3

948.6

s

x

161 103 436.6

146 553 323.5

133 011 089.2

120 427 958.3

108 756 694.9

97 951 618.0

87 968 627.0

78 765 186.9

70 300 228.8

62 534 009.6

55 427 957.5

48 944 601.9

43 047 514.8

37 701 260.9

32 871 381.4

28 524 336.7

24 627 540.0

21 149 374.6

18 059 187.7

15 327 280.3

12 924 903.9

10 824 314.5

8 998 815.7

7 422 792.2

6 071 740.3

4 922 299.6

3 952 322.2

3 140 931.5

2 468 572.6

1 917 052.3

1 469 571.8

1 110 758.3

826 682.4

604 861.5

434 241.8

305 159.1

209 270.0

139 479.3

89 851.1

55 502.1

32 485.3

17 670.0

8 623.5

3 501.9

948.6

c

x

10 010.95

10 347.25

10 609.23

10 785.69

10 916.35

11 086.11

11 339.96

11 697.16

12 079.79

12 477.88

12 886.64

13 272.96

13 678.95

14 016.14

14 299.71

14 551.46

14 776.76

14 968.50

15 069.71

15 089.35

15 034.75

14 908.55

14 707.52

14 393.88

13 973.97

13 455.48

12 845.73

12 151.26

11 371.35

10 518.96

9 608.10

8 659.44

7 694.95

6 745.76

5 818.46

4 932.36

4 107.49

3 359.55

2 694.87

2 117.15

1 622.04

1 205.67

864.75

594.49

387.75

M

447 734.82

437 723.87

427 376.62

416 767.39

405 981.70

395 065.35

383 979.24

372 639.28

360 942.12

348 862.33

336 384.45

323 497.82

310 224.86

296 545.90

282 529.77

268 230.06

253 678.60

238 901.84

223 933.34

208 863.63

193 774.28

178 739.52

163 830.97

149 123.46

134 729.57

120 755.61

107 300.13

94 454.39

82 303.14

70 931.79

60 412.83

50 804.72

42 145.29

34 450.34

27 704.58

21 886.12

16 953.76

12 846.26

9 486.71

6 791.84

4 674.69

3 052.65

1 846.98

982.24

387.75

R

x

8 330 232.61

7 882 497.79

7 444 773.93

7 017 397.31

6 600 629.91

6 194 648.21

5 799 582.86

5 415 603.62

5 042 964.34

4 682 022.22

4 333 159.89

3 996 775.43

3 673 277.61

3 363 052.75

3 066 506.85

2 783 977.08

2 515 747.02

2 262 068.42

2 023 166.58

1 799 233.24

1 590 369.61

1 396 595.33

1 217 855.81

1 054 024.84

904 901.38

770 171.81

649 416.20

542 116.07

447 661.68

365 358.54

294 426.75

234 013.93

183 209.21

141 063.92

106 613.58

78 909.00

57 022.88

40 069.13

27 222.86

17 736.15

10 944.31

6 269.62

3 216.97

1 369.98

387.75

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