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Distinguish mortality risk from longevity risk and outline ways of hedging each.

FRM® Part I · Financial Markets and Products · Insurance Companies and Pension Plans · FRM1.FM.2.c

The idea

Mortality risk is the risk that people die sooner than the tables assumed, which hurts a life insurer because death benefits are paid earlier or in greater number. Longevity risk is the opposite. People live longer than assumed, which hurts those who pay while the person lives, namely pension plans and annuity writers. A pandemic is the typical mortality scenario, and steady medical improvement is the typical longevity scenario. Because the two move in opposite directions, a firm writing both life cover and annuities has a partial natural hedge. Mortality risk can also be hedged with reinsurance and catastrophe mortality bonds, whose principal is cut if a mortality index spikes. Longevity risk can be hedged with longevity bonds, whose coupons rise with survivor numbers. It can also be hedged with longevity swaps. In a longevity swap the hedger pays fixed amounts and receives amounts linked to actual survival. Index-based hedges leave basis risk.

A practice question

From the question bank, with the reason each wrong option is wrong.

Longevity risk is best described as the risk that:

  1. policyholders overstate their health to obtain lower premiumsWhy not: This is adverse selection or misrepresentation, not a risk from changing life expectancy.
  2. people live longer than expected, raising pension and annuity costs - correct
  3. people die earlier than expected, increasing the cost of death benefitsWhy not: This is mortality risk, the opposite exposure.
  4. pension assets fall in value because equity markets declineWhy not: This is investment risk; longevity risk concerns the number of years benefits are paid.

Longevity risk hurts anyone paying benefits for as long as people live. Mortality risk, the risk of earlier-than-expected deaths, hurts life insurers.

A harder one

A life insurer is concerned that a severe pandemic could produce a spike in death claims. Which instrument is designed to transfer this risk to capital market investors?

  1. A longevity swap in which the insurer receives payments tied to survival of a reference populationWhy not: Payments tied to survival rise when mortality falls, which hedges the opposite scenario.
  2. A longevity bond whose coupons rise with the number of survivors in a reference cohortWhy not: This pays more when people live longer, increasing exposure for an insurer already hurt by early deaths.
  3. An equity put option on the insurer's own share price, struck below the current priceWhy not: The option payoff depends on the share price, not on a mortality index; it does not match the death claim exposure.
  4. A catastrophe mortality bond whose principal is cut if a mortality index passes a threshold - correct

Mortality bonds pay investors a coupon but lose principal if mortality spikes, so the insurer receives funds exactly when claims rise. Longevity instruments hedge the opposite direction.

The hardest tier

An insurer sells both term life policies and immediate annuities. A permanent 10% rise in mortality rates at all ages raises the present value of term life liabilities by USD 36 million and lowers the present value of annuity liabilities by USD 22 million. What is the net effect on the insurer, and what does it show?

  1. A net loss of USD 14 million, because the two books offset only partly - correct
  2. A net loss of USD 58 million: both books lose when mortality changesWhy not: Adds the two amounts as though annuity liabilities rose; higher mortality reduces annuity liabilities.
  3. A net loss of USD 36 million: the annuity book has no effect on the resultWhy not: Ignores the annuity gain; the two lines move in opposite directions and partly hedge each other.
  4. A net gain of USD 22 million: the annuity gain exceeds the term life lossWhy not: Counts only the annuity side and ignores the USD 36 million increase in term life liabilities.

Net = -36 + 22 = -14 million. Mortality and longevity risks move in opposite directions, but the two books differ in size and age profile, so the offset is only partial.

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