Pensions, Risks and Capital Markets

 Lord Turner, Senior Advisor, Vice Chairman of Merrill Lynch Europe, a director of United Business Media plc and Siemens Holdings plc, Visiting Professor at the London School of Economics and City of University, and cross bench member of the House of Lords.  He was chair of the UK Low Pay Commission and chair of the UK Pensions Commission,

Demographic Issues in Longevity Risk Analysis

Eric Stallard, Center for Demographic Studies, Duke University
eric@cds.duke.edu

Longevity risk can be defined at individual and aggregate levels.  At the individual level, longevity risk refers to the possibility of living longer than assumed in financial planning for the retirement of a single individual.  At the aggregate level, longevity risk refers to the possibility of a higher average number of years of survival than assumed in designing a retirement security system for the aggregate.  If the aggregate is a cohort of individuals who share a common year of birth, then the longevity risk can be hedged with Survivor Bonds having coupons proportional to the number of cohort survivors at each anniversary after the issue date.  

Survivor Bonds represent a potentially important approach to the management of aggregate longevity risks.  However, before such bonds and other similar instruments become practically feasible, a number of issues must be resolved.  

This paper focuses on demographic issues in longevity risk analysis relating to the measurement and modeling of survival and mortality.  Actuarial, economic, and financial issues are addressed in other conference papers.  

Accurate measurements of the initial size and defining characteristics of each cohort, of decrements due to death, emigration, or other censoring events, and of increments due to immigration or other forms of cohort recruitment, all are necessary to ensure that the coupons accurately reflect the requirement that they be proportional to the number of survivors at each future date.  

Accurate measurements of the inputs to the various models used for forecasting future survival and mortality are necessary for ensuring the validity of the outputs of those models.  

Several models based on generalizations of the basic life table are considered for use in forecasting future survival and mortality.  Factors considered include the following:                                            

      The impact of limits in the rate of increase in life expectancy and its absolute value  

      The stochasticity of life table parameters and its representation in forecasts  

      The changing nature of the mortality process as reflected in underlying- and multiple-cause of death data and death rates  

         The impact of individual-level risk covariates and their change over age, calendar time, and cohort  

        The impact of technological innovation  

Stochastic life table models with or without risk covariates can be used to produce forecasts of the distribution of the proportion of survivors at each future date, allowing the capital markets to set appropriate rates of investment returns for Survivor Bonds and similar instruments.  The accuracy of such forecasts depends on the impact of estimation errors in the model's parameters and the risk that the selected model is not representative of future survival and mortality processes.  

Political Economy of Government Issued Survivor Bonds

Jeffrey Brown, University of Illinois
brownjr@uiuc.edu

 Peter Orszag, Brookings Institution    

The Securitization of Life Insurance and Longevity Risks

J. David Cummins, Wharton
cummins@wharton.upenn.edu             

Killing the Law Large Numbers: Is there a Mortality Risk Premium?

Moshe Milevsky, York University
milevsky@yorku.ca

V. R. Young, University of Michigan

S. D. Promislow, York University

The textbook assumption for pricing life insurance is that mortality risk is completely diversifiable and therefore not priced by markets in economic equilibrium. The law of large numbers is invoked to argue that a large enough portfolio effectively eliminates any idiosyncratic mortality risk.  In this paper we challenge this paradigm by arguing that the uncertainty regarding the evolution of the instantaneous force of mortality will induce dependence than can not be diversified away by selling more claims. We then classify the equilibrium compensation for this risk in terms of the instantaneous Sharpe Ratio.  Our paper discusses the theoretical conditions under which this risk premium exists and it provides some empirical estimates regarding its magnitude using a unique database of life annuity quotes. Our results have implications for hedge funds and other institutional investors who are currently in the process of creating a secondary market for life insurance policies. As well, the existence of this mortality risk premium will affect individuals who are examining the optimal age at which to annuitize their pension.

Annuitization Lessons from the UK: Money-Back Annuities and Other Developments

Tom Boardman, Prudential UK

Dave Dowrich, CSFB
dave.dowrich@credit-suisse.com

Pricing Life Securitizations and their place in Optimal ILS portfolios

Morton Lane, Lane Financial LLC
mlane@lanefinancialllc.com

There have been a half dozen securitizations of life insurance risks in the past few years adding to the menu of insurance linked risks that have been securitized. There will be more. While these life securities, typically involving mortality risk, have been similar in form to well known Cat Bonds, they have their own unique characteristics. This paper looks at the pricing of these life bonds compared with conventional Cat Bonds.  Essentially these novel bonds were issued at a discount to regular Cat Bonds and the intriguing question is whether this discount emanates from their unique features or whether the discount is a temporary novelty premium.

At the same time, longevity bond ideas have been circulated which have not found success in the market. The question arises, what price would they have to garner in order to enjoy market success?

Finally, the inclusion of life risks, mortality or longevity, in a portfolio of insurance risk would appear to bring welcome diversification. The paper examines the question of much capital should be allocated to life in such a portfolio. The question is illustrated with a hypothetical portfolio using important advances in the application of optimization techniques. The answer is not always obvious; life risks are often necessarily bundled together with interest rate risks, and prices may or may not always be generous.

Exponential Tilting and Pricing Implications for Longevity Risk

Shaun Wang, Georgia State University
shaunwang@gsu.edu

Samuel Cox, Georgia State University
samcox@gsu.edu

Yijia Lin, Georgia State University
insyllx@langate.gsu.edu

Shaun Wang and Sam Cox will present Exponential Tilting and Pricing Implications for Longevity Risk. This paper applies the exponential tilting economic pricing framework to longevity risk. The implications include 1) the extreme event correlation matters, 2) the natural hedging of life insurance has an offset effect on the risk premium, and 3) large unexpected long-term medical care cost inflation has a positive effect on the risk premium.  This exponential tilting pricing framework can be viewed as an extension of the Wang transform method

Longevity Bonds: Construction, Pricing and Use

David Blake, City University
d.blake@city.ac.uk

Kevin Dowd, University of Nottingham
kevin.dowd@nottingham.ac.uk

Andrew Cairns, Heriot-Watt University
A.Cairns@ma.hw.ac.uk

Richard MacMinn, Illinois State University
richard@journalofriskandinsurance.org

This paper examines various ways in which survivor bonds can be created from conventional instruments. This is an important issue because survivor bonds are promising hedge instruments but governments have remained reluctant to issue them since they are already long mortality risk.         

There are also arguments that natural private-sector issuers of such bonds are also in short supply. To circumvent these problems we propose two alternative means of creating synthetic survivor bonds: survivor bonds can be created by splitting the coupon payments on existing government bonds, or by combining positions in conventional bonds with survivor swaps. We consider the demand for such instruments, and suggest that capital markets institutions might find it profitable to create them.

A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty

Andrew Cairns, Heriot-Watt University
A.Cairns@ma.hw.ac.uk

This paper examines the evolution of the post-60 male mortality curve in the UK and the impact of associated longevity risk. We introduce a two-factor stochastic morality model, and calibrate it against UK male mortality data. The first factor affects mortality-rate dynamics at all ages in the same way, and the second affects mortality-rate dynamics at higher ages much more than at lower ages.

The paper then uses this model to price longevity bonds. It proposes a method to risk-adjust the market price of a longevity bond, and this method also takes account of uncertainty in the parameter values on which the model is calibrated. It also uses pricing data from the EIB/BNP longevity bond of November 2004 to make inferences about the market prices of the risks in the model. Based on these, it then investigates how future issues be priced to ensure absence of arbitrage between longevity bonds with different characteristics.