It is well known that certain types of financial instruments (or portfolios of instruments held by a issuer or sponsor) are mortality-based or mortality-sensitive, i.e., their payment or otherwise performance is correlated to the mortality performance of one or more persons in a population. For example, a typical life insurance contract is mortality-based because it pays a fixed amount to a beneficiary upon the death of the holder. A typical insurance annuity contract is mortality-based because it pays a yearly annuity from the payout start date (e.g., age 65) until the death of the holder. A defined-benefit pension plan is mortality-based because it pays a yearly retirement payment (which may be fixed or adjusted for inflation) from retirement until the death of the pension plan participant.
The above instruments, which may be held or issued by a company having a portfolio of many, are exemplary. There are variants of the mortality-based instruments above, e.g., an insurance annuity contract may give the holder the option of receiving the accumulated funds at a guaranteed interest rate instead of the market rate (so-called “guaranteed annuity option’). There may be entirely different types of mortality-based instruments.
Importantly, mortality-based instruments have mortality risk for the sponsor/issuer/company, sometimes referred to as the “mortality exposure” of a portfolio. Instruments like insurance annuities and pension plans have longevity risk, i.e., there is financial risk associated with the portfolio members living longer than expected or projected, thus receiving more payments over more years. Instruments like life insurance contracts have mortality risk, i.e., there is financial risk associated with the members dying earlier/faster than expected, thus resulting in payoffs occurring earlier than expected at a greater cost to the insurance company.
Both longevity risk and mortality risk are correlated to mortality rates. Longevity risk is associated with falling mortality rates, usually mortality rates falling more quickly than projected and, typically, as factored into the price of the instrument. Mortality risk is associated with either rising mortality rates, or at least, mortality rates failing to fall as quickly as projected and factored into price.
The risk to the portfolios of insurance companies, pension plans, and other holders or issuers of mortality-sensitive instruments, can be profound. For example, a defined-benefit pension plan may be fully-funded (assets projected to meet liabilities) in 2007 based on current mortality rate projections. However, if the actual mortality rates deviate from projections a slight amount (e.g., mortality rate decreases to produce a life expectancy 1 year greater than expected), the liabilities of the pension fund can increase significantly (e.g., liabilities could increase 5% or more). In a $5 billion defined benefit pension plan, that may translate to an unanticipated future $250 million shortfall. Thus, this longevity risk can rapidly turn a fully-funded pension plan into a seriously-underfunded pension plan, especially if the pension plan has other provisions (e.g., inflation adjustment) that provide a multiplier effect to the longevity risk.
A famous example of the potentially catastrophic results of failing to properly account for mortality exposure was the Equitable Life Assurance Society disaster in the late 1990's. That firm offered guaranteed annuity contracts based on 1950's mortality tables that did not reflect falling mortality rates. The longevity risk of those annuities contributed to the eventual downfall of Equitable Life, which closed to new business in 2000.
Traditionally, mortality-based instruments have sought to account for mortality risk by pricing using the mortality rate. The mortality rate is usually expressed as the rate of deaths per unit time in a population, typically the number of deaths per thousand individuals per year. The overall mortality rate of a population corresponds to the aggregation of a series of age-based mortality rates. Thus, the mortality rate is a function of age. For example, the mortality rate of 35 year olds tends to be lower than, the mortality rate of 65 year olds. In the past, actuaries used actuarial tables to price various mortality-based instruments using measured mortality rates as a function of age.
At least through the 19th century, the assumption in accounting for mortality risk by actuaries was that mortality rates were fixed over time, e.g., the mortality rate for a 35 year old in 1950 would be the same for a 35 year old in 1900. That, of course, was the mistake in the Equitable Life debacle, where 1950's mortality rates were applied to contracts issued decades later in a population with significantly-reduced mortality rates.
Over the last several decades, experts have recognized that the mortality rate function is not constant over time, rather, it changes over time. The mortality rate function in 1950 is different than that in 1970, which in turn is very different than that in 2000. In industrialized countries (and in most developing countries), the mortality rate at a given age x has dropped over the course of time, e.g., from 1970 to 2000.
As a result, experts have developed mortality rate models that project mortality rates, which can be expressed as the “force of mortality” •(t, x), where t is time in history (e.g., 2010) and x is the age of the person at which the mortality rate is provided. Some mortality rate functions are based on deterministic models, meaning there is an assumption that future mortality rates can be forecast with some accuracy. If mortality rates can be accurately forecasted, then the mortality risk of mortality-based portfolios can be almost fully accounted for (or otherwise internalized) when pricing the instruments or otherwise structuring those instruments. Additionally, this relative certainty allows portfolio holders like pension plans or insurance company annuity issuers to execute a proper Liability Driven Investment (LDI) strategy to invest assets with minimal risk (not more-than-necessary risk) to meet (not greatly exceed) anticipated liabilities.
However, more recent research asserts that mortality rate is not subject to a deterministic function that accurately predicts future rates. Instead, it is asserted that the force of mortality is a stochastic or random variable. Using actual mortality rate data, force of mortality might be modeled to an appropriate probabilistic function, but not a deterministic function. A probabilistic force of mortality function is useful in predicting the trend of mortality rate, even the expected value in the future, and some measure of variance (how tightly actual mortality data can be expected to cluster around the expected value). But it cannot be used to predict future mortality rates with deterministic certainty.
Various stochastic mortality rate models are discussed in the following articles, J. G. Cairns (Heriot-Watt University), David Blake (Cass Business School), and Kevin Dowd (Nottingham University Business School); “Pricing Frameworks for Securitization of Mortality Risk,” (Jun. 22, 2004); Yijia Lin and Samuel H. Cox, “Securitization of Mortality Risks in Life Annuities” (Apr. 6, 2004); and Kevin Dowd, Andrew J. G. Cairns, and David Blake, “Mortality-Dependent Financial Risk Measures” (Discussion Paper PI-0609) (May 2006: π Pensions Institute).
Since the mortality rate apparently cannot be quantified deterministically, there is no ready mechanism to remove or greatly mitigate mortality risk in mortality-sensitive instruments (or portfolios of them) by adjusting the price or other structural aspects of the instruments. As a result, some have proposed various types of customized derivatives or other customized securities to hedge mortality risk. For example, some have proposed customized private longevity bonds that would hedge longevity risk.
An example of this was the unsuccessful European Investment Bank (EIB)/BNP longevity bond (LB). The EIB LB was a £540 million issue with a 25 year maturity structured as an annuity bond with annual floating coupon payments linked to the survivor index based on the mortality rate of English/Welsh males of age 65 in 2002. The coupon payments would be initially set at £50 million and would be reduced over time by the % of cohorts (cohorts are those in a group having the same birth year) age 65 in 2003 who died by the coupon date.
An example of a customized mortality hedge was the 2003 Swiss Re 3 year “life catastrophic bond” (sometimes referred to as the “Vita Capital I” mortality bond) designed to hedge Swiss Re's risk exposure to a catastrophic increase in short term mortality that might arise, for example, from a massive earthquake, plague, or tsunami. This $400 million principal issue would pay a mortality-independent coupon rate payment based on the 3 month U.S. LIBOR rate plus 136 basis points. The unprotected principal would be repaid based on mortality performance. If the mortality rate in 2007 was less than 1.3 times the rate in 2003, the principal would be paid in full. If the mortality rate in 2007 was greater than 1.3× the 2003 rate, the principal would be reduced 5% for each 0.01 increase in mortality rate until the principal would be exhausted at a mortality rate increase of 1.5. Similar products were developed by Swiss Re in 2005 (“Vita Capital II” morality bond) and Scottish Re in 2006 (“Tartan Capital” mortality bond).
Such customized derivatives to hedge for mortality risk suffer a number of significant drawbacks. Because they are customized to the hedging party, they entail expensive negotiation costs to deal with the custom, non-standard terms.
As customized private derivatives, it may be difficult to find buyers to assume the mortality risk the hedger seeks to transfer.
Because they are customized and non-standard, these customized derivatives tend to be very illiquid, i.e., it is difficult to find secondary buyers and thus virtually impossible to establish a secondary market.
Because the payout of these customized derivatives may be based on a measurement population (e.g., all English/Welsh males aged 65) that does not match or correspond to the portfolio population, there may be “basis risk” that the hedge's reference population does not correspond to the portfolio's member population.
More broadly, there is no systematic technique for determining the mortality risk of individual portfolios, creating a comprehensive portfolio-specific hedge using standardized mortality derivative building blocks, and buying and selling those mortality derivative building blocks in both primary and secondary markets in a highly liquid fashion that permits the efficient transfer of mortality risk from hedging parties to investors.
Other problems and drawbacks also exist.
USPTO Backgrounds
USPTO Backgrounds