September 26, 2009Discussion on “Hedging Longevity Risk by Asset Management” 1 Hua Chen

Discussion on “Hedging Longevity Risk by Asset Management –

an ALM Approach”

Hua Chen

Temple University

September 26, 2009

September 26, 2009Discussion on “Hedging Longevity Risk by Asset Management” 2 Hua Chen

Framework of This Paper

Mortality Risk(CBD model)

Longevity Bond

Optimal Hedging?

(Mean-Variance)

Interest Rate Risk(CIR model)

Risk-free Bond

Coupon BondAnnuity Providers

September 26, 2009Discussion on “Hedging Longevity Risk by Asset Management” 3 Hua Chen

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

September 26, 2009Discussion on “Hedging Longevity Risk by Asset Management” 4 Hua Chen

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

September 26, 2009Discussion on “Hedging Longevity Risk by Asset Management” 5 Hua Chen

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

September 26, 2009Discussion on “Hedging Longevity Risk by Asset Management” 6 Hua Chen

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

September 26, 2009Discussion on “Hedging Longevity Risk by Asset Management” 7 Hua Chen

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.

September 26, 2009Discussion on “Hedging Longevity Risk by Asset Management” 8 Hua Chen

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.

September 26, 2009Discussion on “Hedging Longevity Risk by Asset Management” 9 Hua Chen

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 optimiz

ation algorithms, computational efficiency.

September 26, 2009Discussion on “Hedging Longevity Risk by Asset Management” 10 Hua Chen

Questions?

September 26, 2009Discussion on “Hedging Longevity Risk by Asset Management” 11 Hua Chen

Question?

How to estimate?