Actuarial Notes

SOA Exam ALTAM Fall 2023, Question 3

Study guide: Exam ALTAM

An insurer sells a 3-year single premium Variable Annuity contract, with the following provisions:

(i) The policyholder deposits the 10,000 premium at the start of the contract.

(ii) The insurer deducts a 2% front-end charge from the premium before allocating the remainder to the policyholder fund.

(iii) At the start of each year after the first, the insurer deducts a management charge of 1% of the fund value.

(iv) The death benefit under the contract is 110% of the fund value at the end of the year of death, payable at that time.

(v) If the policyholder surrenders during the first year, they receive 85% of their fund value at the end of the year. In subsequent years, the policyholder receives the full fund value at the end of the year of surrender.

(vi) The contract has a Guaranteed Minimum Maturity Benefit (GMMB) rider, which is 100% of the premium.

An actuary conducts a stress test of this contract using the following assumptions:

  • Initial expenses are 200 at contract inception.
  • Renewal expenses are 0.6% of the policyholder's fund value (before management charge deductions) incurred at the start of the second and third policy years.
  • Mortality rates are 0.05 each year.
  • At the end of the first and second years, 10% of the surviving policyholders surrender their policies.
  • The policyholder's fund earns 0% in the first year, 0% in the second year, and 5% in the third year.
  • The insurer's funds earn 3% in each year.
  • The insurer holds a reserve of 300, 200, and 100 at the start of years 1, 2, and 3 respectively, for each contract in force at the start of the year.

Part a (1 point)

Show that the policyholder fund value at the end of year 3, assuming the policy remains in force, is 10,100 to the nearest 100. You should calculate the value to the nearest 1.

Part b (5 points)

(i) (3.5 points) Determine the profit vector of the contract using the stress test assumptions.

(ii) (1.5 points) Calculate the net present value of the profit per policy issued, using a hurdle rate of 10% per year.

Part c (3 points)

The actuary is concerned about the GMMB risk.

(i) One colleague suggests selling more policies to mitigate the risk. Explain why this strategy would be ineffective.

(ii) Another colleague suggests a hedging strategy for the GMMB. The price at issue of the required put option is 900.

Describe one advantage and one disadvantage of hedging the guarantee, compared with holding reserves.

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Concepts tested

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