FMP2 - Insurance Companies and Pension Plans

Question 1

Describe the key features of the various categories of insurance companies and identify risks facing insurance companies

Answer 1

Categorised as life insurance or property and casualty insurance

Question 2

Describe the use of mortality tables and calculate the premium payment for a policy holder

Answer 2

• P(die at time n) = (1 - P(die t = 0)) * P(die t = 1) * ….
• PV of expected pay-out = sum(t = 0 to n-0.5) P(die at t + 0.5) / ((1 + d)^n)
• P(survive to time n) = P(survive t = 0) * (1 - P(die t = 1)) * …
• PV of expected premium = X * (1 + sum(t = 1 to n) (P(survive to n)) / ((1 + d)^n)
• break even annual premium = face value * (PV expected pay-out / PV expected premium)

Question 3

Distinguish between mortality risk and longevity risk and describe how to hedge these risks

Answer 3

• Longevity risk is people survive longer than expected
• Mortality risk is people die sooner than expected
• Can be hedged using longevity derivatives where payoff linked to expected mortality rate and realised rate

Question 4

Describe benefit plans and defined contribution plans and explain the differences between them

Answer 4

• Defined contribution plans are where funds in pension are invested by the employer
• Defined benefit plans are where contributions are pooled and formula used to find pension when retired

Question 5

Compare different types of life insurance policies

Answer 5

• Whole life insurance is where policyholder makes premium payments each month until death, where beneficiary receive lump sum
• Variable life insurance is similar but policyholder decides how to invest premiums, lump sum can be greater if investments do well
• Term life insurance is where pay-out if policyholder dies within a specified time frame
• Endowment life insurance is where payment occurs at death or the end of the policy term

Question 6

Calculate and interpret loss ratio, expense ratio, combined ratio, and operating ratio

Answer 6

• loss ratio = losses / premiums, greater than one means making a loss
• expense ratio = expenses / premiums
• combined ratio = expense ratio + loss ratio, greater than one means making a loss
• operating ratio is combined ratio with how investment of premiums has performed over the year

Question 7

Describe moral hazard and adverse selection risks facing insurance companies, provide examples of each, and describe how to overcome these problems

Answer 7

• Moral hazard is the risk that the behaviour of the policyholder will change as a result of the insurance - overcome with a deductible and limit
• Adverse is the risk that insurance will be bought only by high-risk policy holders, overcome with risk assessments

Question 8

Evaluate the capital requirements for life and non-life insurance companies

Answer 8

Solvency II implemented and specified minimum capital requirement and solvency capital requirement - MCR lower and insurance company stopped from taking new business if falls below