Managing Longevity Risk via ALM: Strategies and Models

1. Discussion on“Hedging Longevity Risk by Asset Management – an ALM Approach” Hua Chen Temple University September 26, 2009 Discussion on “Hedging Longevity Risk by Asset Management”

2. Framework of This Paper Risk-free Bond Interest Rate Risk (CIR model) Optimal Hedging? (Mean-Variance) Annuity Providers Coupon Bond Mortality Risk (CBD model) Longevity Bond Discussion on “Hedging Longevity Risk by Asset Management”

3. Main Contributions • Consider mortality risk and interest rate risk simultaneously • Employ Mean-Variance Analysis for asset allocation • The usage of longevity bond can significantly reduce the aggregate risk Discussion on “Hedging Longevity Risk by Asset Management”

4. Structured ALM Models • Static Models • Hedge against small changes from the current state of the world. • A term structure is input to the model which matches assets and liabilities under this structure. • Conditions are then imposed to guarantee that if the term structure deviates somewhat from the assumed value, the assets and liabilities will move in the same direction and by equal amounts. • Portfolio immunization • Does not permit the specification of a stochastic process that describes changes of the economic conditions Discussion on “Hedging Longevity Risk by Asset Management”

5. Structured ALM Models • Single Period, stochastic model • A stochastic ALM model • Describes the distribution of returns of both assets and liabilities • Ensures movements of both sides are highly correlated. • One period - Myopic • It does not account for the necessity to rebalance the portfolio once some surplus is realized. • It does not recognize the fact that different portfolio may be appropriate to capture the correlations Discussion on “Hedging Longevity Risk by Asset Management”

6. Structured ALM Models • Multiperiod, dynamic and stochastic Model • Captures both the stochastic nature of the problem, but also the fact that the portfolio is managed in a dynamic,multiperiod context. • Dynamic Programming Discussion on “Hedging Longevity Risk by Asset Management”

7. Different Risk Measures • Other dispersion measures • e.g., Mean-Absolute Deviation (MAD) • More robust estimator of scale • Behaves better with distributions without a mean or variance, such as the Cauchy distribution. Discussion on “Hedging Longevity Risk by Asset Management”

8. Different Risk Measures • Higher moment • e.g., Mean-Variance-Skewness (MVS) (Boyle and Ding, 2006) • Mitton and Vorkink (2007) Apparent MV inefficiency of underdiversified investors can be largely explained by the fact that investors sacrifice MV efficiency for higher skewness exposure. • Because a higher skewness means greater likelihood of a large return. Discussion on “Hedging Longevity Risk by Asset Management”

9. Different Risk Measures • Tail measures • e.g., VaR • does not consider the magnitude of loss • undesirable properties such as lack of sub-additivity, • e.g., CVaR • Unlike MV and MAD penalizing both the desirable upside and the undesirable downside outcomes • Unlike VaR, CVaR not only consider probability but also size of loss. • More consistent risk measure than VaR since it is sub-additive and convex. • Unlike MVS, it can be optimized using linear programming (LP) and nonsmooth optimization algorithms, computational efficiency. Discussion on “Hedging Longevity Risk by Asset Management”

10. Questions? Discussion on “Hedging Longevity Risk by Asset Management”

11. Question? How to estimate? Discussion on “Hedging Longevity Risk by Asset Management”