Actuarial Notes

Diversification of Longevity and Mortality Risk

By Stuart Silverman and Dan Theodore · Milliman · 2016 · ILA201-801-25

Study guide: Exam ILA-201U

A Milliman white paper (March 2016) that explores, through a case study of a simple combination of life insurance and payout annuity products, how stochastic projections of future mortality rates compare with deterministic projections with margins. It also demonstrates the relative diversification benefit of the annuity product's longevity exposure along with the life insurance product's mortality exposure.

On the syllabus

  • Exam ILA-201U — Outcomes 3a; ILA201-801-25, the whole paper (as the syllabus states it)

Introduction

  • Prudent actuaries examine results with margins applied to their assumptions, but a margin that feels tangible (such as 10%) may actually be arbitrary.
  • The case study applies stochastic projections of future mortality rates to a simple combination of life insurance and payout annuity products, and compares percentile values from them with results from deterministic projections with margins.

Correlation of Mortality Improvement

  • Actuaries generally believe that the risk of adverse mortality experience on life insurance may be offset by the longevity risk associated with annuity benefits.
  • Over 1960 to 2010 in U.S. population mortality experience, the correlation between annual mortality improvement at age 35 and at age 75 is 1.8% for males and 25.4% for females.
  • The paper concludes that any financial risk model should not presume that the presence of annuity benefits is a near perfect offset for adverse deviations on life insurance risks.

Sample Products Used in Modeling

Are Deterministic Margins Appropriate in Context of the Overall Risk Level?

Introducing Volatility to Mortality Assumptions

  • A Trend risk
  • B Basis risk
  • C Long-term underwriting risk
  • D Other sources of volatility not included in this analysis

Cost of Volatility

  • The stochastic simulations produce consistently lower mean and median distributable earnings than the baseline deterministic values.

Stochastic Projections of Mortality and Longevity

  • The paper generates 1,000 random stochastic mortality scenarios reflecting trend risk, basis risk and long-term underwriting risk, and calculates distributable earnings for the term life insurance and payout annuity products in each scenario.

Savings from Diversification

Fixed Margin vs. Stochastic Modeling

Managing Business Mix Reflecting Desired Risk Tolerance

Conclusion

  • There is real value for an insurer in performing stochastic modeling with volatile mortality assumptions when pricing, setting deterministic margins, determining economic capital and determining its optimal mix of business.

Sources