The new life market.
Following swiftly on the heels of the Lucida q-forward transaction, J.P. Morgan recorded a second first in July 2008, this time with Canada Life in the United Kingdom (Trading Risk, 2008; Life & Pensions, 2008). But the hedging instrument in this transaction was different. It was a 40-year maturity 500 million [pounds sterling] longevity swap that was linked not to an index, but to the actual mortality experience of the 125,000plus annuitants in the annuity portfolio that was being hedged. It also differed in being a cash flow hedge of longevity risk. But most significantly, this transaction brought capital markets investors into the Life Market for the very first time, as the longevity risk was passed from Canada Life to J.P. Morgan and then directly on to investors. This has become the archetypal longevity swap upon which other transactions are based.
A longevity survivor swap--frequently abbreviated to simply "longevity swap'--can be either a capital markets derivative or an insurance contract. In either case, it is an instrument that involves exchanging actual pension payments for a series of preagreed fixed payments, as indicated in Figure 10 (Dowd et al., 2006; Dawson et al. 2010). Each payment is based on an amount-weighted survival rate.
In any longevity swap, the hedger of longevity risk (e.g., a pension plan) receives from the longevity swap provider the actual payments it must pay to pensioners and, in return, makes a series of fixed payments to the hedge provider. In this way, if pensioners live longer than expected, the higher pension amounts that the pension plan must pay are offset by the higher payments received from the provider of the longevity swap. The swap therefore provides the pension plan with a long-maturity, customized cash flow hedge of its longevity risk.
Although the J.P. Morgan-Canada Life transaction was the first capital markets longevity swap, there was an earlier publicly announced insurance swap that took place in April 2007 between Swiss Re and Friends Provident, a UK life insurer. Like the J.P. Morgan-Canada Life swap, it was a pure longevity risk transfer and was not tied to another financial instrument or transaction. The swap was based on Friends Provident's 1.7 billion [pounds sterling] book of 78,000 pension annuity contracts written between July 2001 and December 2006. Friends Provident retains administration of policies. Swiss Re makes payments and assumes longevity risk in exchange for an undisclosed premium. However, it is important to note that this particular swap was legally constituted as an insurance contract and was not a capital markets instrument per se.
Table 6 lists the publicly announced longevity swaps that have been executed between 2007 and 2012 in the United Kingdom.
Index Hedges Versus Customized Hedges
Lucida and Canada Life implemented two very different kinds of capital markets longevity hedges in 2008. Lucida executed a standardized hedge linked to a mortality index, whereas Canada Life executed a customized hedge linked to the actual mortality experience of a population of annuitants. It is important to understand the differences between these.
Standardized index-based longevity hedges have some advantages over the customized hedges that are currently more familiar to pension funds and annuity providers. In particular, they have the advantages of simplicity, cost and liquidity. But they also have obvious disadvantages, principally the fact that they are not perfect hedges and leave a residual basis risk (see Table 7) that requires the index hedge to be carefully calibrated.
Coughlan, Epstein, Sinha, et al. (2007) argue that a liquid, hedge-effective market could be built around just eight standardized contracts with:
* a specific maturity (e.g., 10 years);
* two genders (male, female);
* four age groups (50-59, 60-69, 70-79, 80-89).
Figure 11 presents the mortality improvement correlations within the male 70-79 age bucket, which is centered on age 75. These figures show that the correlations are very high and that contracts based on 75-year-old males will provide good hedge effectiveness for plans with members in the relevant age buckets. Coughlan (2007) estimates that the hedge effectiveness is around 87 percent (i.e., the standard deviation of the liabilities is reduced by 87 percent, leaving a residual risk of 13 percent) for a large and well-diversified pension plan or annuity portfolio; see Figure 12. (20)
The Longevity Risk Premium
The provider of any longevity hedge requires a premium to assume longevity risk. This means that the forward rate agreed at the start of any q-forward contract will be below the anticipated (expected) mortality rate on the maturity date of the contract. Similarly, the implied forward life expectancy in any longevity swap will be longer than the anticipated (expected) life expectancy. Figure 13 shows the relationship between the expected and forward mortality rate curves and the risk premium for a particular year (in this case 2017) for ages 65-75. (21) Figure 14 shows the relationship between the expected and forward mortality rate curves and the risk premium for a particular age cohort (in this case 65-year-old English & Welsh males) for years 2005-2025.
A key feature of any derivative transaction, especially after the onset of the Global Financial Crisis in 2008-2009 is collateral. The role of collateral is to reduce if not entirely eliminate counterparty credit risk. This is the risk that one of the counterparties to, say, a q-forward contract defaults owing money to the other counterparty. When a swap is first initiated, both counterparties have zero profit or loss. But over time, as a result of realized mortality rates deviating from the rates that were forecast at the time the swap started, one counterparty's position will be showing a profit and the other will be showing an equivalent loss. Collateral in the form of high-quality securities needs to be posted by the loss-making counterparty to cover such losses. However, the collateral needs to be financed and the financing costs will depend on the level of interest rates. Further, the quality of the collateral and the conditions under which a counterparty can substitute one form of collateral for another need to be agreed. This is done in the credit support annex (CSA) to the ISDA Master Agreement that establishes the swap. The CSA also specifies how different types of collateral will be priced.
All these factors are important for determining the value of the swap at different stages in its life. Biffis et al. (2011) use a theoretical model to show that the overall cost of collateralization in mortality or longevity swaps is similar to or lower than those found in the interest-rate swaps market on account of the diversifying effects of interest rate and longevity risks.
The Life and Longevity Markets Association
In February 2010, the Life and Longevity Markets Association (LLMA) (22) was established in London by AXA, Deutsche Bank, J.P. Morgan, Legal & General, Pension Corporation, Prudential (UK), RBS, and Swiss Re. The original members were later joined by Morgan Stanley, UBS, Aviva and Munich Re. The aim is "to support the development of consistent standards, methodologies and benchmarks to help build a liquid trading market needed to support the future demand for longevity protection by insurers and pension funds." In April 2011, the LifeMetrics indices were transferred to LLMA with the aim of establishing a global benchmark for trading longevity and mortality risk.
Barriers to Further Development
Looking back to Sandor's seven stages of market evolution in Table 1, it is arguable that we are now in stage 4 in the evolution of the Life Market. (23) We need to examine the barriers to the further evolution of the market.
One barrier that remains to the further development of stage 4 is the continuing resistance of pension plan trustees and their advisers, as well as insurers and reinsurers, to imperfect hedging solutions of the capital markets. The industry as a whole still prefers the full risk transfer solutions of insurance indemnification contracts.
Another barrier relates to the differing maturity requirements of hedgers and investors. Hedgers prefer instruments that provide a very long-term hedge of longevity risk, since longevity is a risk that manifests itself over a long timescale. By contrast, most investors prefer shorter dated instruments, particularly for novel kinds of risk such as longevity, as evidenced in the relatively short maturities associated with catastrophe bonds. It has been suggested that a 10-year maturity instrument is a suitable compromise and indeed Lucida and Pall Corporation have transacted q-forward hedges with 10-year maturities. However, these hedges leave a residual roll-over risk beyond 10 years, even beyond the basis risk.
If these barriers can be overcome, then the next stages in the evolution of the Life Market are the development of formal spot and derivatives--especially futures--exchanges. Blake, Cairns, and Dowd (2006) examine the reasons why some futures contracts succeed and why others fail.
A successful futures market--defined as having a consistently high volume of trade and open interest--requires a large, active, and liquid spot market in the underlying, with spot prices being sufficiently volatile to create both hedging needs and speculative interest. The underlying must be homogeneous or have a well-defined grading system. The market also requires active participation by both hedgers and speculators and this clearly depends on end users recognizing a hedging need and the futures contract being effective in reducing risk. However, the market in the underlying must not be heavily concentrated on either the buy or sell side, since this can lead to market distortions, such as price manipulation. Finally, trading costs in futures contracts must not be significantly higher than those operating in any existing cross-hedge futures contract.
It is instructive to examine the history of inflation-related financial futures contracts. These were initially unsuccessful but eventually succeeded, and inflation indices have similar characteristics to mortality indices, especially the low frequency of publication. The first inflation-related contracts were consumer price index (CPI) futures contracts listed on the U.S. Coffee, Sugar and Cocoa Exchange in June 1985. They were delisted in April 1987 with only 10,000 contracts traded. The key reasons for the failure of these contracts were: there was no inflation-linked securities market at the time, the underlying was an infrequently published (i.e., monthly) index, and there was no stable pricing relationship with other instruments to attract the attention of arbitrageurs.
A second attempt came in June 1997 when a futures contract on Treasury inflation-protected securities (TIPS) was listed on the Chicago Board of Trade. The contract was delisted before the end of the year with only 22 contracts traded. The contract failed because TIPS had only started trading 5 months before, there was just a single 10-year TIPS trading, the futures contract competed with the underlying for liquidity, and there was uncertainty over the future of the TIPS program.
In February 2004, the Chicago Mercantile Exchange launched a CPI futures contract that is still trading. This time the contract succeeded because inflation-linked securities have gained acceptance among investors, with TIPS having evolved into a recognized asset class. There is a well-understood pricing relationship allowing for arbitrage opportunities between TIPS, fixed-interest Treasury bonds, and CPI futures. The U.S. Treasury is now committed to long-term TIPS issuance. CPI futures do not compete directly with but rather complement TIPS and use the same inflation index. The contract is traded on the Globex electronic trading platform, which provides automated two-sided price quotes from a leading market maker and thereby enhances liquidity.
What are the lessons for the development of a longevity-linked futures market?
A large, active, and liquid spot market in the underlying is regarded as the most important criterion for the success of a futures market. With one exception, no futures contract has ever survived without a spot market satisfying these conditions. The one exception is weather futures, which were introduced by the Chicago Mercantile Exchange in 1999. This contract has a so-called "exotic underlying" rather than a physical underlying, but nevertheless has been a success despite this. This provides hope for longevity-related futures contracts that can also be said to have an exotic underlying. (24)
The mortality index underlying longevity-linked instruments must be a fair estimate of true mortality and have minimal time basis risk. (25) The CPI index suffers from similar potential problems, so the survival of the CPI futures contract on Chicago Mercantile Exchange suggests these problems can be overcome. Although mortality indices are calculated infrequently (typically annually), spot prices of traded longevity bonds would exhibit a high degree of volatility on account of the bonds' high duration.
The underlying longevity-risk hedging instruments must be few in number and well defined. A small number of contracts helps to increase liquidity, but as already mentioned, also leads to contemporaneous basis risk, arising from the different mortality experience of the population cohort covered by the mortality index and the cohort relevant to the hedger.
One potential weakness in the development of the Life Market is insufficient investor interest. However, Figure 15 shows how the market might eventually come into balance, with increasing numbers of longevity sellers attracted by a suitable risk premium to enter the market to meet the potentially huge demands of longevity buyers.
At the same time as these practical developments in the capital markets were taking place, academics were continuing to make theoretical contributions, building on the original idea of using longevity bonds to hedge macro-longevity risk in the capital markets (Blake and Burrows, 2001). These included:
* Design and pricing of longevity bonds and other longevity-linked products (e.g., Blake, Cairns, Dowd, and MacMinn, 2006; Bauer, 2006; Bauer and Rule, 2006; Denuit et al., 2007; Barbarin, 2008; Bauer, Borger, and Russ, 2010; Chen and Cummins, 2010; Kogure and Kurachi, 2010; Dowd, Blake, and Cairns, 2011; Lane, 2011; Li and Ng, 2011; Mayhew and Smith, 2011; Zhou et al., 2011);
* Design and pricing of longevity-linked derivatives, such as survivor swaps (e.g., Dowd et al., 2006), survivor forwards and swaptions (e.g., Dawson et al., 2010), q-forwards (e.g., Deng et al., 2012), and mortality options (e.g., Milevsky and Promislow, 2001);
* Longevity indices (e.g., Denuit, 2009);
* Longevity risk hedging (e.g., Dahl and Moller, 2006; Friedberg and Webb, 2007; Cairns et al., 2008; Cairns et al., Forthcoming; Coughlan et al., 2008; Tsai et al., 2010; Wang et al., 2010; Coughlan et al., 2011; Li and Hardy, 2011; Tzeng et al., 2011; Wang, Hsieh, and Chiu, 2011);
* Improvements in the analysis and design of longevity-linked retail products (e.g., Gong and Webb, 2010; Stevens et al., 2010; Richter and Weber, 2011; Denuit et al., 2011).
THE MICRO-LONGEVITY RISK MARKET
The principal product subject to micro-longevity risk is a life settlement. This is a life insurance policy sold by its owner for more than the surrender value (26) but less than face value. The secondary market in life insurance policies began in 1844, when Foster and Cranfield auctioned an endowment life insurance policy in the United Kingdom. The U.S. secondary market dates back to 1911, when the U.S. Supreme Court confirmed the legality of selling life insurance policies in the case of Grigsby v. Russell, 222 U.S. 149 (1911). This decision established a life insurance policy as transferable property that contains specific legal rights to: name the policy beneficiary, change the beneficiary designation (unless subject to restrictions), assign the policy as collateral for a loan, borrow against the policy, and sell the policy to another party.
The secondary market in the United States really began to take off in the 1990s when viatical settlements were introduced. Viators are owners of life policies who are very close to dying, such as AIDS sufferers who needed to sell their policies to pay for medical treatment. That market ceased suddenly in 1996 when protease inhibitors were introduced. It was replaced by a senior life settlements (SLS) market that deals with the whole life policies (27) of elderly high-net-worth individuals. Two medical doctors or underwriters are used to assess each policyholder's life expectancy. The most important criterion for successful investment in life settlements is a good estimate of life expectancy (LE). The investor purchasing the life settlement has to continue paying the premiums on the underlying policy while the original policyholder is still alive.
Underestimating LE is the key micro-longevity risk faced by investors in life settlements, since this makes the promised returns on life settlements more attractive than the realized returns. The SLS market experienced a significant setback when, in 2008, the shortest of the LE underwriters revised upward their LEs by between 20 and 25 percent, while the second longest revised upwards by between 5 and 10 percent. LE providers were forced to respond by establishing the Life Expectancy Providers Focus Group in October 2010 with the aim of offering a comprehensive and consistent set of best practices and performance standards to all life markets that make use of life expectancy and mortality information. The group also addresses issues such as privacy, fraud, and confidentiality policies. The group's founding members were Advanced Underwriting Solutions, AVS Underwriting, Examination Management Services, Inc., ISC Services, and 21st Services.
A number of solutions have been put forward to hedge micro-longevity risk or "extension risk" as it is more commonly known. One is a hedge offered by certain investment banks based on a synthetic index of life settlements. Another is known as FAIRE and consists of both individual and portfolio extension risk hedges, priced off the LE underwriter Fasano's LEs. FAIRE is provided by Fasano Associates and Augur Capital, a German investment manager of life insurance and life settlement assets.
In 1994, the Life Insurance Settlement Association (LISA) was established in Orlando, Florida as a trade association for viatical and life settlement companies. (28)
In 2005, the Life Exchange was established with an objective "to provide the secondary life insurance market with the most advanced and independent electronic trading platform available by which to conduct life settlement transactions with the highest degree of efficiency, transparency, disclosure, and regulatory compliance." (29) In 2007, the Institutional Life Markets Association (ILMA), started in New York with the mission is "to expand and apply capital market solutions in life insurance, educate consumers that their insurance may be a valuable asset, expand consumer choices about how to manage it, and support the responsible growth and regulation of the industry. We believe that expanded consumer choice and full disclosure of all fees is good for the consumer and for the industry." (30) In 2008, Institutional Life Services (ILS) and Institutional Life Administration (ILA), a life settlements trading platform and clearing house, were launched by Goldman Sachs, Genworth Financial, and National Financial Partners. ILS/ILA was designed to modernize dealing in life settlements and meet the needs of consumers (by ensuring permanent anonymity of the insured) and of the capital markets (by providing a central clearing house for onward distribution of life settlement assets, whether individually or in structured form). In 2010, National Financial Partners became the sole owner of ILS/ILA.
One of the latest developments is the attempt to introduce a synthetic life settlements market. This is to avoid some of the costs, monitoring, and ethical issues associated with the physical life settlements market. (31) The synthetic market will be based on indices and the returns will depend on the performance of the pool of lives in the index. The first attempt to do this was by Goldman Sachs which introduced a QxX Life Settlements Index in 2007. This market failed to take off--the spreads offered were too wide to making trading profits--and the index was discontinued in 2009. In 2008, Credit Suisse initiated a longevity swap with Centurion Fund Managers, whereby Centurion acquired a portfolio of synthetic life policies, based on a longevity index built by Credit Suisse. In 2010, the Fasano Longevity Life Settlements Index was introduced. In April 2011, the International Society of Life Settlement Professionals (ISLSP) (32) formed a life settlement and derivatives committee and announced that it was developing a life settlement index. The purpose of the index is to benchmark net asset values in life settlements trading. Investors need a reliable benchmark to measure performance and the index will help turn U.S. life insurance policies into a tradable asset class according to ISLSP. The calculation agent for the index is AA Partners.
There are a number of other much smaller secondary markets in life insurance policies, including the following:
* Traded endowment policies in the United Kingdom. The maturity date of policies is fixed, but the maturity value of the policy depends on the performance of an investment fund. The policy premiums are invested in a risk-graded with-profits fund established by the life company selling the policy. There is a fixed minimum return in the event of policyholder dying during term.
* Secondary market for life insurance in Germany. German consumers have been able to sell life and pension insurance policies to professional policy buyers since 1999. The trade body for the secondary market in life insurance is the Bundesverband Vermogensanlagen im Zweitmarkt Lebensversicherungen (BVZL). (33) There is also the European Life Insurance Settlement Association (ELSA). (34)
Some academic studies of life settlements have recently emerged, for example, Deng et al. (2011), Mazonas et al. (2011), and Braun et al. (2012).
Securitization involves the sale of a pool of assets (or liabilities or the rights to a set of cash flows) to a special purpose vehicle (SPV) and the subsequent repackaging of those assets (or liabilities or cash flow rights) into securities that are traded in the capital markets. (35) The SPV finances the purchase of the assets by issuing bonds to investors that are, in turn, secured against the assets or promised cash flows. (36) Six types of securitization have taken place involving longevity-related assets or liabilities: blocks of business, regulatory reserving (XXX), life settlements, annuity books, reverse mortgages, and credit default swap notes. The new securities created are known as ILSs (Krutov, 2006). (37)
Block of Business Securitization
The earliest securitizations were "block of business" securitizations (Cowley and Cummins, 2005). These have been used to capitalize expected future profits from a block of life business, recover embedded values (EVs), or exit from a geographical line of business. The last of these motivations is obvious, and the first two arise from the fact that the cost of writing new life policies is usually incurred in the first year of the policy and then amortized over the remainder of its term. This means that writing new business puts pressure on a company's capital. Securitization helps to relieve this pressure by allowing the company immediate access to its expected future profits, and it is an especially attractive option when the company is experiencing rapid growth in a particular line of business. An example of this type of securitization is the set of 13 transactions carried out by American Skandia Life Assurance Company (ASLAC) between 1996 and 2000.
Regulatory Reserving (XXX) Securitization
Another form of life securitization is regulatory reserving securitization, sometimes also known as reserving funding or XXX securitization. These arrangements are designed to give U.S. life assurers relief from excessively conservative regulatory reserving or capital requirements under Regulation XXX, and are used to release capital that can be used to finance new business or reduce the cost of capital. An early example of this type of securitization was a $300 million deal arranged by First Colony Life Insurance Company through an SPV known as River Lake Insurance Company to obtain capital relief under Regulation XXX. This regulation imposes extremely conservative regulatory reserve requirements on some types of life policies with long-term premium guarantees.
Life Settlement Securitization
Senior life settlement (SLS) securitization began in 2004. The first SLS securitization was Tarrytown Second, involving $63 million SLSs backed by $195 million life policies. Legacy Benefits concluded a $70 million securitization in the same year. Very few securitizations have followed these, although America International Group (AIG) securitized 3,400 life policies with a total value of $8.4 billion in 2009.
A number of reasons have been put forward to explain this low number of life settlement securitizations (see, e.g., Rosenfeld, 2009):
* The use of inaccurate mortality tables with unrealistically low LEs.
* The absence of meaningful protection against extension risk.
* Huge intermediary fees from brokers and portfolio aggregators, which can average more than 20 percent gross proceeds. (38)
* Credit (counterparty) risk: covers life insurance company issuing policy and the participants in the acquisition process (e.g., fraud). This risk can be mitigated by diversifying across insurers and undertaking due diligence of the acquisition chain.
* Operational risk: relates to risks in designing a portfolio and in the procuring and managing the assets. This risk can be mitigated by due diligence and a good pricing model.
* Market risk: a fall in the market value of all policies, regardless of credit quality or LE accuracy. This will depend on the balance between the number of policies available for settlement and the availability of funds to purchase life settlements and pay the premiums. This risk can be partly mitigated by portfolio diversification.
* Market impediments. There are a number of issues here: poor price transparency, since purchase prices are private, and each policy has slightly different terms and conditions, so there is no universal standard trading platform or exchange for life-based products. A possible solution is a trading platform that trades "standard" policies as reference points, with an indication of an individual policy's percentage deviation from the closest reference asset.
* Regulatory and taxation risks. This relates to the risks that the regulations covering life settlements or the taxation regime might change adversely. This risk can be mitigated by following a financially sound and transparent acquisition policy.
Annuity Book Securitization
Annuity book securitizations involve the packaging together and selling off of a life assurer's book of annuity business (Lin and Cox, 2005). The resulting securities are attractive to investors because they are highly leveraged investments in equities. For example, if the liability side of the SPV's balance sheet comprises 90 percent annuities and 10 percent shareholder funds, then this implies a leverage factor of 10. Every 1 bp additional return on equities generates 10 bp return to the investor. This is equivalent to a collateralized debt obligation (CDO) with annuitants as senior debt. Investors are effectively borrowing assets from annuitants. There is established investor interest in CDOs with the added benefit that longevity risk provides diversification from market risk. (39)
Reverse Mortgage Securitization
Reverse mortgages--also known as home equity release plans--allow home owners to borrow from the equity in their homes while still living in them. They are particularly attractive to the elderly who might have low pensions, but substantial net housing wealth (Bishop and Shan, 2008; Sun et al., 2008). They started in United States in the 1980s, where they are available from age 62. The most common type is the home equity conversion mortgage, which allows borrowers to take a reverse mortgage in the form of: a lump sum, a lifetime income (the least popular form), or a line of credit (the most popular form). The amount that can be borrowed is negatively related to the interest rate. Interest (Treasuries + 150 bps) is capitalized and repayable on moving or death, so there is no credit risk. However, the total interest payable is capped at the sale price of property and lenders are protected against total interest costs rising above this limit (40) (as a result of the home owner living a very long time) by a mortgage insurance policy that the borrower is required to take out (at a cost of 2 percent of the amount borrowed + 50 bp p.a.). (41) The securitization of reverse mortgages is a fairly recent phenomenon (Zhai, 2000; Standard & Poor, 2006; Wang et al., 2008; Yang, 2011; Huang et al., 2011).
Mortality-Linked Credit Default Swap Notes
In November 2010, Goldman Sachs issued $200 million in mortality-linked credit default swap (CDS) notes to hedge the mortality risk in a block of level, term-life insurance policies. The notes were issued by the SPV Signum Finance Cayman Ltd and were rated A+ by Fitch Ratings. The proceeds from the issue were used to buy collateral in the form of 15-year senior unsecured bonds issued by Goldman Sachs. The SPV will simultaneously enter into a 15-year CDS with Goldman Sachs and will make payments to GS if the actual mortality experience of the insurance policies exceeds set trigger levels, while the fixed payments from GS to the SPV will be paid to the notes' investors.
Longevity is now recognized as an important risk that is faced by insurers, pension plans, corporations, governments, and individuals. By virtue of its size and prevalence, it is the most significant life-related risk exposure in financial terms and could potentially threaten the whole system of retirement income provision.
The emergence of a traded market in longevity-linked capital market instruments should act as a catalyst to facilitate the development of annuities markets in both the developed and the developing world. This market offers the promise of new capacity for bearing longevity risk, increased flexibility in the way it is transferred, and new tools with which the insurance industry can manage capital and risk. A functional annuity market is an important ingredient in the long-term viability of a stable retirement system. Furthermore, with DB pension plans in decline in many countries, annuities offer the only alternative for individuals to secure retirement income free from longevity risk. Price discovery is an equally important benefit of an efficient Life Market whether this relates to longevity bonds or to life securitizations.
Nevertheless, there are still major challenges that remain and we highlight two of them.
First, the long-term investors, such as endowments, sovereign wealth funds, and family offices, which must ultimately be persuaded to hold longevity-linked assets if the Life Market is to be a success, are still not completely comfortable with the asset class. This can partly be overcome with appropriate education, but it is also necessary to get the design of the investment instrument right. The most successful way to date of hedging longevity risk has been via the longevity swap, but swaps and other derivatives are not the type of investment preferred by these long-term investors. Rather, they are more familiar with, and hence prefer, bonds. While short-term mortality bonds have been a success, long-term longevity bonds have not been successful so far. So important work needs to be done in making the design of longevity bonds more attractive to both issuers and holders. However, the Swiss Re strategy of gradual iteration from a successful innovation--as exemplified in the Kortis longevity note that is a modest adaptation of the mortality bond in terms of design and maturity--appears to show a way forward. The three key prizes, if successful, are a much bigger investor base, much greater market liquidity, and more effective price discovery.
Second, it seems likely that the regulatory responses to the Global Financial Crisis will have some effect in slowing down the growth of the Life Market. Regulations restricting the risk-taking activities of investment banks and new bank capital rules known as Basel III are limiting the role that banks can play in the development of this market. It has become much less attractive for banks to warehouse risk while matching longevity hedgers and longevity investors. Furthermore, it has even become much less attractive for them to intermediate, standing in the middle between hedgers and investors, because the long-dated, illiquid credit exposure associated with longevity transactions now carries increased capital charges. (42)
These two challenges will need to be addressed in the next stage of the development of this market. But innovation has been an important feature of the longevity market since 2006 and there is every reason to believe that this will continue as the different players in the industry seek to reduce costs, optimize capital and manage risks. When this happens, we can move beyond stage 4 in the development of the Life Market.
APPENDIX A: MORTALITY FORECASTING MODELS
There are three classes of time-series-based stochastic mortality forecasting model in existence. (43) The oldest is the Lee-Carter model (Lee and Carter, 1992), which makes no assumption about the degree of smoothness in mortality rates across adjacent ages or years. The most recent is the Cairns-Blake-Dowd (CBD) model (Cairns, Blake and Dowd, 2006), which builds in an assumption of smoothness in mortality rates across adjacent ages in the same year (but not between years). (44) Finally, there is the P-splines model (Currie et al., 2004), which assumes smoothness across both years and ages. (45) These models were subjected to a rigorous analysis by Cairns and colleauges (Cairns et al., 2009; Cairns, Blake, Dowd, Coughlan, Epstein, et al., 2011) and Dowd et al. (2010a, 2010b). The models were assessed for their goodness of fit to historical data and for both their ex ante and ex post forecasting properties.
Cairns et al. (2009) used a set of quantitative and qualitative criteria to assess each model's ability to explain historical patterns of mortality: quality of fit, as measured by the Bayes information criterion (BIC); ease of implementation, parsimony, transparency, incorporation of cohort effects, ability to produce a nontrivial correlation structure between ages, and robustness of parameter estimates relative to the period of data employed. The study concluded that a version of the CBD model allowing for a cohort effect (46) was found to have the most robust and stable parameter estimates over time using mortality data from both England & Wales and the United States. (47)
Cairns, Blake, Dowd, Coughlan, Epstein, et al. (2011) focused on the qualitative forecasting properties of the models (48) by evaluating the ex ante plausibility of their probability density forecasts in terms of the following qualitative criteria: biological reasonableness, (49) the plausibility of predicted levels of uncertainty in forecasts at different ages, and the robustness of the forecasts relative to the sample period used to fit the models. The study found that while a good fit to historical data, as measured by the BIC, is a good starting point, it does not guarantee sensible forecasts. For example, one version of the CBD model allowing for a cohort effect produced such implausible forecasts of U.S. male mortality rates that it could be dismissed as a suitable forecasting model. This study also found that the Lee-Carter model produced forecasts at higher ages that were "too precise," in the sense of having too little uncertainty relative to historical volatility. The problems with these particular models were not evident from simply estimating their parameters: they only became apparent when the models were used for forecasting. The other models (including the age-period-cohort [APC] model (50)) performed well, producing robust and biologically plausible forecasts.
It is also important to examine the ex post forecasting performance of the models. This involves conducting both backtesting and goodness-of-fit and analyses. Dowd et al. (2010a) undertook the first of these analyses. Backtesting is based on the idea that forecast distributions should be compared against subsequently realized mortality outcomes and if the realized outcomes are compatible with their forecasted distributions, then this would suggest that the models that generated them are good ones, and vice versa. The study examined four different classes of backtest: those based on the convergence of forecasts through time toward the mortality rate(s) in a given year, those based on the accuracy of forecasts over multiple horizons, those based on the accuracy of forecasts over rolling fixed-length horizons, and those based on formal hypothesis tests that involve comparisons of realized outcomes against forecasts of the relevant densities over specified horizons. The study found that the Lee-Carter model, the APC model, and the CBD model (both with and without a cohort effect) performed well most of the time and there was relatively little to choose between them. However, another version of the Lee-Carter model allowing for a cohort effect repeatedly showed evidence of instability. (51)
Dowd et al. (2010b) set out a framework to evaluate the goodness of fit of stochastic mortality models and applied it to the same models considered by Dowd et al. (2010a). The methodology used exploited the structure of each model to obtain various residual series that are predicted to be independently and identically distributed (iid) standard normal under the null hypothesis of model adequacy. Goodness of fit can then be assessed using conventional tests of the predictions of iid standard normality. For the data set considered (English & Welsh male mortality data over ages 64-89 and years 1961-2007), there are some notable differences among the different models, but none of the models performs well in all tests and no model clearly dominates the others. In particular, all the models failed to capture long-term changes in the trend in mortality rates. Further development work on these models is therefore needed. It might be the case that there is no single best model and that some models work well in some countries, while others work well in other countries.
The CBD model appears to work well in England & Wales for higher ages, and Figures A1 and A2 show two applications of the model using LifeMetrics data for England & Wales.
The first is a longevity fan chart (Figure A1), which shows the increasing funnel of uncertainty concerning the future life expectancies out to 2062 of 65-year-old males from England & Wales. (52) By 2062, the best expectation of life expectancy is around 26 years, shown by the dark central band and an increase of 6 years on the expectation for the year 2012. This band represents a 10 percent confidence interval, so we can only be 10 percent confident about this projection. Surrounding the central band are eight bands of increasingly lighter shading, each representing a 10 percent confidence interval. Adding these together, the whole fan chart shows the 90 percent confidence interval for the forecast range of outcomes. We can be 90 percent confident that by 2062, the life expectancy of a 65-year-old English & Welsh male will lie between 22 and 29. This represents a huge range of uncertainty. Since every additional year of life expectancy at age 65 adds around 3 percent to the present value of pension liabilities, (53) the cost of providing pensions in 2060 could be 9 percent higher than the best expectation for 2060 made in 2010. (54)
The second is a survivor fan chart that shows the 90 percent confidence interval for the survival rates of English & Welsh males who reached 65 in 2012. Figure A2 shows that there is very little survivorship risk before age 75: a fairly reliable estimate is that 20 percent of this group will have died by age 75. (55) The uncertainty increases rapidly after 75 and reaches a maximum at around age 90, when anywhere between 10 and 45 percent of the original population will still be alive. We then have the long "tail" where the remainder of this cohort dies out some time between 2037 and 2062.
An important recent contribution to mortality forecasting deals with the consistent modeling and hence forecasting of the mortality rates of two or more related populations. Two key studies are Dowd, Cairns (2011) and Cairns, Blake, Dowd, Coughlan, and Khalaf-Allah (2011). (56) Suppose the aim is to forecast the mortality of the members of a small pension plan, but both the quantity and quality of the mortality data are poor. Suppose the quantity and quality of the mortality data of the national population in which the pension plan resides are much better. Because the mortality dynamics of the smaller subpopulation will be related to that of the larger national population, the mortality forecasts of the pensioner population will be improved if it is treated as part of a system that involves the larger population.
Dowd, Cairns, et al. (2011) employed a "gravity" model to do this. The larger population is modeled independently, but the smaller population is modeled in terms of spreads (or deviations) relative to the evolution of the larger population. The spreads in the period and cohort effects between the larger and smaller populations depend on gravity or spread reversion parameters for the two effects. The larger the two gravity parameters, the more strongly the smaller population's mortality rates move in line with those of the larger population in the long run. This is important where it is believed that the mortality rates between related populations should not diverge over time on grounds of biological reasonableness, as would be expected in the example here.
Cairns, Blake, Dowd, Coughlan, and Khalaf-Allah (2011) also make use of a mean-reverting stochastic spread that allows for different trends in mortality improvement rates in the short run, but parallel improvements in the long run. However, this study uses a Bayesian framework that allows the estimation of the unobservable state variables that determine mortality and the parameters of the stochastic processes that drive those state variables to be combined into a single procedure. (57) The key benefits of this include a dampening of the impact of Poisson variation in death counts, (58) full allowance for parameter uncertainty, and the flexibility to deal with missing data.
Building off a good mortality forecasting model estimated using data from an objective, transparent, and relevant set of mortality indices, fan charts provide a very useful tool for both quantifying and visually understanding longevity and survivor risks.
APPENDIX B: KEY ORGANIZATIONS THAT HAVE CALLED ON GOVERNMENTS TO SUPPORT THE DEVELOPMENT OF THE LIFE MARKET (59)
UK Pension Commission
The Pensions Commission has suggested that the government should consider the use of longevity bonds to absorb tail risk for those over 90 or 95, provided it exits from other forms of longevity risk preretirement (which it has done by raising the state pension age to 68 by 2046):
"One possible limited role for government may, however, be worth consideration: the absorption of the 'extreme tail' of longevity risk postretirement, that is, uncertainty about the mortality experience of the minority of people who live to very old ages, say, beyond 90 or beyond 95."
Source: A New Pension Settlement for the Twenty-First Century, Pension Commission, Second Report, 2005, page 229.
UK Insurance Industry Working Group
"Against this background, the government could issue longevity bonds to help pension fund and annuity providers hedge the aggregate longevity risks they face, particularly for the long-tail risks associated with people living beyond age 90."
"By kick-starting this market, the Government would help provide a market-determined price for longevity risk, which could be used to help establish the optimal level of capital for the Solvency II regime of prudential regulation."
Source: Vision for the Insurance Industry in 2020-A Report From the Insurance Industry Working Group, July 2009.
UK Confederation of British Industry (CBI)
"Government should press ahead with changes that make it more possible for schemes to adapt to changing circumstances--for instance ... seeding a market for products that help firms manage their liabilities, like longevity bonds."
"Government should drive development of a market in longevity bonds, a similar instrument to annuities, by which the payments on the bonds depend on the proportion of a reference population that is still surviving at the date of payment of each coupon. This should be done through limited seed capital and supporting policy work on the topic. Government could also consider how best to match government bond issues to pension scheme needs, including the provision of more long-dated bonds and whether government should issue mortality bonds itself."
Source: Redressing the Balance-Boosting the Economy and Protecting Pensions, CBI Brief, May 2009.
Organisation for Economic Co-operation and Development
"Governments could improve the market for annuities by issuing longevity indexed bonds and by producing a longevity index."
Source: Antolin, P., and H. Blommestein (2007) "Governments and the Market for Longevity-Indexed Bonds," OECD Working Papers on Insurance and Private Pensions, No. 4, OECD Publishing.
World Economic Forum
"Given the ongoing shift toward defined contribution pension arrangements, there will be a growing need for annuities to enhance the security of retirement income. Longevity-indexed bonds and markets for hedging longevity risk would therefore play a critical role in ensuring an adequate provision of annuities."
Source: World Economic Forum-Financing Demographic Shifts Project, June 2009.
International Monetary Fund
"Although the private sector will further develop market-based transfer mechanisms for longevity risk if it recognizes the benefits of doing so, the government has a potential role in supporting this market. Measures could include provision of better longevity data, better regulation and supervision, and education to promote awareness of longevity risk. Those governments that are able to limit their own longevity risk could consider issuing a limited quantity of longevity bonds to jumpstart the market."
Source: The Financial Impact of Longevity Risk, Chapter 4 of Global Financial Stability Report, April 2012.
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Barbarin, J., 2008, Heath-Jarrow-Morton Modelling of Longevity Bonds and the Risk Minimization of Life Insurance Portfolios, Insurance: Mathematics and Economics, 43: 41-55.
Bauer, D., 2006, An Arbitrage-Free Family of Longevity Bonds, Discussion Paper, University of Ulm.
Bauer, D., F. E. Benth, and R. Kiesel, 2010, Modeling the Forward Surface of Mortality, Discussion Paper, University of Ulm.
Bauer, D., M. Borger, and J., Russ, 2010, On the Pricing of Longevity-Linked Securities, Insurance: Mathematics and Economics, 46: 139-149.
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Bauer, D., and J. Russ, 2006, Pricing Longevity Bonds Using Implied Survival Probabilities, Discussion Paper, University of Ulm.
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Coughlan, G. D., M. Khalaf-Allah, Y. Ye, S. Kumar, A. J. G. Cairns, D. Blake, and K. Dowd, 2011, Longevity Hedging 101: A Framework for Longevity Basis Risk Analysis and Hedge Effectiveness, North American Actuarial Journal, 15: 150-176.
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(1) Although the Life Market can be regarded as the world's first organized longevity-linked capital market, there are a number of historical examples of longevity-linked financial instruments. These include:
* Tontines: invented by the Neapolitan banker Lorenzo de Tonfi in 1653. Each investor paid capital into the tontine and received dividends while alive. When an investor died, his or her share was reallocated to the surviving investors. This process continued until there was only a single survivor. There was no return of principal. The government of King Louis XIV of France became the first government to issue tontine bonds in 1689. The first bond ever issued by the British government in 1693 was a tontine: the proceeds were used to fight the Nine Years War against Louis XIV. Tontines were later banned in the UK and a number of US states because they began to be used to defraud investors. However, they are still legal in other countries. For example, the European Union's First Life Directive allows tontines if they are underwritten by authorized and regulated life offices.
* Sovereign life annuities: sold, for example, by the British government between 1808 and 1929 to members of the public.
* Flower bonds: these are equivalent to a standard bond plus a life insurance policy. They were issued by the U.S. government at a discount to enable their holder to pay federal estate taxes on the holder's death. The bonds were redeemable at par plus accrued interest when the holder died. Flower bonds have not been issued by the U.S. government since 1971.
(2) There are only a few exceptions: a current example is Zimbabwe, where male life expectancy at birth has fallen to 37 for males and to 34 for females.
(3) There is no sign of this trend abating according to a recent study: "Life expectancy in Europe is continuing to increase despite an obesity epidemic, with people in Britain reaching an older age than those living in the United States, according to study of trends over the last 40 years. In a report in International Journal of Epidemiology, population health expert David Leon of the London School of Hygiene and Tropical Medicine said the findings counteract concerns that the rising life expectancy trend in wealthy nations may be coming to an end in the face of health problems caused by widespread levels of obesity. The report comes as news of the US mortality rate fell to an all-time low in 2009, marking the 10th consecutive year of declines as death rates from heart disease and crime dropped. In total, rates declined significantly for 10 of the 15 leading causes of death, including cancer, diabetes and Alzheimer's disease" (Kate Kelland, "European Life Expectancy Rising Despite Obesity Whilst US Mortality Rate Falls to All Time Low," March 18, 2011, inside.thomsonreuters.com/trading/ILS/Pages/Europeanlifeexpectancyrisingdespiteobesity. asp. See also Swiss Re (2010a).
(4) Life annuities are a desirable component of retirement income provision throughout the world: they are the only instrument capable of protecting against individual longevity risk. Without them, pension plans would be unable to perform their fundamental task of protecting retirees from outliving their resources for however long they live.
(5) In the United Kingdom, this would also be known as the FRS 17 (the UK Pension Accounting Standard) basis.
(6) Traditional UK insurers running annuity books interpret UK regulatory capital requirements as restricting them to invest in government and investment-grade corporate bonds and related derivatives.
(7) This volatility is generated by the way in which accounting standards treat DB pension liabilities.
(8) A statutory fund established by the UK Pensions Act 2004 "to provide compensation to members of eligible DB pension schemes, when there is a qualifying insolvency event in relation to the employer, and where there are insufficient assets in the pension scheme to cover the Pension Protection Fund level of compensation."
(9) LCP's Pension Buy-ins, Buy-outs and Longevity Swaps 2012; Hymans Robertson's Managing Pension Scheme Risk Report 2011.
(10) Pensions in the National Accounts: A Fuller Picture of the UK's Funded and Unfunded Pension Obligations, Office for National Statistics, April 27, 2012. World Wide Web: www.ons.gov. uk/ons/rel/pensions/pensions-in-the-national-accounts/uk-national-accounts-supplementary-table-on-pensions-2010- /index.html.
(11) In fact, the lump sum is only being offered to limited cohorts of plan members.
(12) See Blake, Cairns, and Dowd (2006, pp. 155-156) for further details about these five ways of responding to longevity risk.
(13) Basis risk is the risk associated with imperfect hedging where the movements in the underlying exposure are not perfectly correlated with movements in the hedging instrument.
(14) See Katy Burne, "Swiss Re Longevity-Risk Deal Opens Door to More," Wall Street Journal, January 7, 2011.
(15) However, to be effective, arbitrageurs need well-defined pricing relationships between related securities and we are still in the very early days in the development of this market.
(16) This suggestion has been made by Tom Boardman, former director of Prudential PLC and Visiting Professor at the Pensions Institute at Cass Business School.
(17) LifeMetrics is also the name of a toolkit for measuring and managing longevity and mortality risk, designed for pension plans, sponsors, insurers, reinsurers, and investors. LifeMetrics enables these risks to be measured in a standardized manner, aggregated across different risk sources and transferred to other parties. It also provides a means to evaluate the effectiveness of longevity/mortality hedging strategies and the size of basis risk. The components of the toolkit are: (1) Indices: data for evaluating current and historical levels of mortality and longevity, (2) Framework: a set of tools, methods and algorithms for measuring and managing longevity and mortality risk. These are fully documented in the LifeMetrics Technical Document (Coughlan, Epstein, Ong, et al., 2007), (3) Software: software for developing mortality projections (www.lifemetrics.com).
(18) It is important to recognize that the Kortis longevity note was not a true longevity bond in the sense we have described earlier, because it involved transferring the risk associated with the spread (or difference) between the longevity trends for two different population groups rather than the trends themselves.
(20) A subsequent study by Coughlan et al. (2011) confirmed the high degree of effectiveness available with longevity hedges based on national population indices for large pension plans. This study considered a pension fund with a membership whose mortality experience was the same at the UK CMI (Continuous Mortality Investigation) assured lives population; with a hedge based on the England & Wales LifeMetrics Index, hedge effectiveness of 82.4 percent could be achieved. The study also considered a pension fund with a membership whose mortality experience was the same at the population of California; with a hedge based on the U.S. LifeMetrics Index, hedge effectiveness of 86.5 percent could be achieved.
(21) Coughlan, Epstein, Sinha, et al. (2007) show that the forward mortality rate is determined from the expected mortality rate using [q.sup.f] = (1 - T x [lambda] x [sigma])[q.sup.e], where [q.sup.f] is the forward mortality rate, [q.sup.e] is the expected mortality rate, T is the time to maturity, [sigma] is the volatility (annualized standard deviation) of changes in the mortality rate, and [lambda] is the annualized Sharpe ratio required by the counterparty.
(23) This is the same stage that we argued the market was just starting in Blake, Cairns, Dowd, and MacMinn (2008).
(24) At least until a liquid market in longevity bonds develops.
(25) Time basis risk will be low if a hedging instrument with a given maturity date provides a good hedge for an exposure with a different maturity date. This is important because of publication lags. The q-forward example illustrated in Table 4 earlier had a maturity date of 2018, but a reference year for determining the settlement mortality rate of 2017.
(26) This is the value paid by the original life company to cancel the policy.
(27) A whole life policy has two components, a life insurance component and an investment component: periodic premiums (e.g., monthly, quarterly, annual, single) cover the cost of the life insurance, with the surplus going into an investment fund. In the U.S. market, the insurance company typically invests the surplus premium in fixed-income securities to build up a "cash value." The cash value is separate from the "face value" of the policy, which is the guaranteed insurance value.
(31) It is an expensive process to acquire suitable life policies for settlement with a range of intermediaries who need paying. In addition, premiums need to be financed. There is also a laborious process of monitoring policy holders between the purchase and policy maturity dates. In addition, there are ethical issues associated with the sale of policies by elderly individuals: these issues were considered by, among others, Blake and Harrison (2008).
(35) Securitization began in the 1970s when banks in the United States began to sell off pools of mortgage-backed loans.
(36) Most securitizations also involve credit enhancement features to protect one or more participating parties against default risk. These features include overcollateralization (where the value of the assets transferred to the SPV exceeds the value of the securities it issues), subordination (where the SPV issues securities with varying levels of seniority), and external guarantees such as parent company guarantees, letters of credit, credit insurance, and reinsurance. Many SPVs also include an arrangement by which the originating life institution continues to service the original customers. This is especially important in life settlement securitizations where there is a need to ensure that policyholders do not allow their policies to lapse.
(37) See also Cowley and Cummins (2005), Lin and Cox (2005), Dahl (2004), Cairns, Blake, Dowd, Coughlan, Epstein, et al. (2006), Cox and Lin (2007), Biffis and Blake (2010a), Cox et al. (2010), Wills and Sherris (2010), Kim and Choi (2011), Huang et al. (2011), and Yang (2011).
(38) Conning Research has estimated agent, broker, and provider fees to be 9.5 percent of face amount.
(39) Investor interest in CDOs was damaged, at least temporarily, by the Global Financial Crisis.
(40) Known as cross-over risk.
(41) This market has obviously found an effective solution to extension risk.
(42) In April 2012, a number of investment banks--UBS, Credit Suisse and Nomura--pulled out of the Life Market as a result of the additional capital requirements under Basel III. But new insurers and reinsurers entered: Munich Re, Scor, and Prudential (U.S.).
(43) Apart from the extrapolative models considered here, there are two other types of mortality forecasting model: process-based models, which examine the biomedical processes that lead to death, and explanatory or causal models, which use information on factors that are believed to influence mortality rates such as cohort (i.e., year of birth), socioeconomic status, geographical location, housing, education, medical advances, and infectious diseases. These models are not yet widely used, since the relationships between these factors are not sufficiently well understood or because the underlying data needed to build the models are unreliable. Nevertheless, some academic researchers have recently begun experimenting with causal variables (e.g., Hanewald, 2011; Gaille and Sherris, 2011), while practitioners have started to use post code or zip code as a measure of socioeconomic status in their mortality models, especially for pricing annuities. Further, RMS has recently built an infectious diseases model that was briefly described earlier in the "Longevity Notes" section. For more details, see Blake and Pickles (2008).
(44) The CBD model was specifically designed for modeling higher age mortality rates. It has recently been generalized to account for the different structure of mortality rates at lower ages by Plat (2009) and Hunt and Blake (2013).
(45) Other academic studies of mortality models include Booth et al. (2002a, 2002b), Brouhns et al. (2002), Brouhns et al. (2004), Biffs (2005), Czado et al. (2005), Koissi et al. (2005), Renshaw and Haberman (2006), Delwarde et al. (2007), Blake, Cairns, and Dowd (2008), Bauer et al. (2008), Bauer, Benth, and Kiesel (2010), Hari et al. (2008), Hunt and Blake (2013), Biffis, Denuit, and Devolder (2010), Debonneuil (2010), Cox et al. (2010), Yang et al. (2010), D'Amato et al. (2011), Milidonis et al. (2011), Wang, Huang, and Liu (2011), Zhu and Bauer (2011), Aleksic and B6rger (2012), and Hainaut (2012).
(46) A cohort effect recognizes that year of birth (in addition to age) influences life expectancy; see Willets (2004).
(47) The CBD model with a cohort effect is also known as Model M7, a naming convention introduced in Cairns et al. (2009). The original CBD model without a cohort effect is also known as Model M5.
(48) The P-splines model was excluded from the analysis because of its inability to produce fully-stochastic projections of future mortality rates.
(49) A method of reasoning used to establish a causal association (or relationship) between two factors that is consistent with existing medical knowledge.
(50) An extension of the Lee--Carter model to allow for a cohort effect (see Currie, 2006; Osmond, 1985; Jacobsen et al., 2002).
(51) See Renshaw and Haberman (2006).
(52) Note projections run from 2012 based on the CBD model estimated using data for ages 60-80 (higher ages not available) and years 1961-2010.
(53) Pension Protection Fund and the Pensions Regulator (2006, Table 5.6)
(54) Even this might be an underestimate, since companies do not even use up-to-date estimates of current life expectancy; that is, their "best expectation" is too low. A study by Pension Capital Strategies (reported in Pensions Week on November 8, 2007) calculated that the United Kingdom's top 100 companies (i.e., the FTSE100) were underestimating pension liabilities by as much as 40 billion [pounds sterling] (or 3.5 percent of GDP) as a result.
(55) This is one of the reasons why the EIB bond was considered expensive: the first 10 years of cash flows are, in present value terms, the most costly cash flows of a bond, and, in the case of the EIB bond, incorporate a longevity hedge that is not really needed.
(56) See also Li and Lee (2005), Jarner and Kryger (2011), and Li and Hardy (2011).
(57) Dowd, Cairns, et al. (2011), by contrast, used an iterative procedure to do this.
(58) The study used the common assumption that individual deaths follow a Poisson distribution.
David Blake is Professor of Pension Economics and Director of the Pensions Institute, Cass Business School. Andrew Cairns is Professor of Financial Mathematics at the Department of Actuarial Mathematics and Statistics, Heriot-Watt University. Guy Coughlan is a member of the management team at Pacific Global Advisors. Kevin Dowd is Professor of Finance and Economics, Durham Business School. Richard MacMinn is Edmondson-Miller Professor in Insurance and Financial Services at Katie School, Illinois State University. The authors can be contacted via email: A.J.G.Cairns@hw.ac.uk, Guy.Coughlan@PacificGA.com, Kevin.Dowd@hotmail.co.uk, and Richard.Macminn@ilstu.edu
Disclaimer: Information herein is obtained from sources believed to be reliable but Pacific Global Advisors does not warrant its completeness or accuracy. Opinions and estimates constitute the judgment of the authors and are subject to change without notice. Past performance is not indicative of future results. This material is provided for informational purposes only and is not intended as a recommendation or an offer or solicitation for the purchase or sale of any security or financial instrument and should not serve as a primary basis for investment decisions.
TABLE 1 Sanclor's Seven Stages of Market Evolution Number Stage 1 Structural change-leading to a demand for capital 2 Development of uniform commodity/security standards 3 Introduction of legal instruments providing evidence of ownership 4 Development of informal spot and forward markets 5 Emergence of formal exchanges 6 Introduction of organized futures and options markets 7 Proliferation of over-the-counter (OTC) markets, deconstruction Source: Sandor (1994, 2003). TABLE 2 Estimated Loss Probabilities for the Swiss Re Longevity Notes Cumulative (%) Six-Year Annualized (%) Attachment probability 5.31 0.88 Exhaustion probability 1.81 0.30 Expected loss 3.27 0.55 Source: Standard & Poor's. TABLE 3 Estimated Loss Exceedance Probabilities for the Swiss Re Longevity Notes Six-Year Annualized Principal Reduction Factor (%) Exceedance Probability (%) 100 0.30 80 0.38 60 0.47 40 0.58 20 0.72 0 0.88 Source: Standard & Poor's. TABLE 4 An Illustrative Term Sheet for a Single q-Forward to Hedge Longevity Risk Notional amount GBP 50,000,000 Trade date December 31, 2008 Effective date December 31, 2008 Maturity date December 31, 2018 Reference year 2017 Fixed rate 1.2000% Fixed amount payer J.P. Morgan Fixed amount Notional Amount x Fixed Rate x 100 Reference rate LifeMetrics graduated initial mortality rate for 65-year-old males in the reference year for England & Wales national population Bloomberg ticker: LMQMEW65 Index <GO> Floating amount payer ABC Pension Fund Floating amount Notional Amount x Reference Rate x 100 Settlement Net settlement = Fixed amount - Floating amount Source: Coughlan, Epstein, Sinha, et al. (2007, Table 1). TABLE 5 An Illustration of q-Forward Settlement for Various Outcomes of the Realized Reference Rate Reference Rate (Realized Rate) Fixed Rate Notional (GBP) Settlement (GBP) 1.0000% 1.2000% 50,000,000 10,000,000 1.1000% 1.2000% 50,000,000 5,000,000 1.2000% 1.2000% 50,000,000 0 1.3000% 1.2000% 50,000,000 -5,000,000 Note: A positive (negative) settlement means the hedger receives (pays) the net settlement amount. Source: Coughlan, Epstein, Sinha, et al. (2007, Table 1). TABLE 6 Publicly Announced Longevity Swaps in the UK, 2007-2012 Size ([pounds Date Hedger Type sterling]m) Term (years) April 2007 Friends Provident Ins 1,700 Run-off January 2008 Lucida Ins 100 10 July 2008 Canada Life Ins 500 40 February 2009 Abbey Life Ins 1500 Run-off March 2009 Aviva Ins 475 10 May 2009 Babcock PF 500-750 50 July 2009 RSA Ins 1,900 Run-off November 2009 Berkshire Council PF 750 Run-off February 2010 BMW PF 3,000 Run-off July 2010 British Airways PF 1,300 NA January 2011 Pall (UK) PF 70 10 August 2011 ITV PF 1,700 NA November 2011 Rolls Royce PF 3,000 NA December 2011 British Airways PF 1,300 NA January 2012 Pilkington PF 1,000 NA April 2012 Berkshire Council PF 100 Run-off May 2012 Akzo Nobel PF 1,400 NA December 2012 LV= Ins 800 NA Date Format Intermediary April 2007 Reinsurance contract Swiss Re January 2008 Index-based hedge; exposure placed J.P. Morgan with capital market investors July 2008 Exposure placed with capital J.P. Morgan market investors February 2009 Insurance contract Deutsche Bank March 2009 Exposure placed with capital RBS market investors & Partner RE May 2009 Insurance contract Credit Suisse July 2009 Insurance contract; combined with Goldman Sachs/ inflation and interest rate swaps Rothesay Life November 2009 Insurance contract Swiss Re February 2010 Insurance contract Deutsche Bank/ Abbey Life, July 2010 Synthetic buy-in (longevity and Goldman Sachs/ asset swaps) Rothesay January 2011 Index-based hedge; exposure placed J.P. Morgan with capital market investors August 2011 Insurance contract Credit Suisse November 2011 Pensioner bespoke longevity swap Deutsche Bank December 2011 Pensioner bespoke longevity swap Goldman Sachs/ Rothesay January 2012 Pensioner bespoke longevity swap Legal & General April 2012 Insurance contract Swiss Re May 2012 Insurance contract Swiss Re December 2012 Insurance contract Swiss Re Note: Ins--hedger is insurance company; PF--hedger is pension fund. TABLE 7 Standardized Index Hedges Versus Customized Hedges Advantages Disadvantages Standardized * Cheaper than customized * Imperfect hedge: index hedge hedges ** Basis risk * Lower setup/operational ** Roll risk costs ** Base table * Shorter maturity, so estimation risk lower counterparty credit exposure Customized * Exact hedge, so no * More expensive than hedge residual basis risk standardized * Set-and-forget hedge, * High setup and requires minimal operational costs monitoring * Poor liquidity * Longer maturity, so larger counterparty credit exposure * Less attractive to investors Source: Coughlan (2007). FIGURE 11 Annual Mortality Improvement Correlations with England & Wales Males Aged 75 Age 70 88% 71 90% 72 93% 73 96% 74 99% 75 100% 76 99% 77 96% 78 93% 79 90% 80 88% Source: Coughlan, Epstein, Ong, et al. (2007, Figure 9.6). Note: Table made from bar graph.
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|Title Annotation:||p. 527-557|
|Author:||Blake, David; Cairns, Andrew; Coughlan, Guy; Dowd, Kevin; MacMinn, Richard|
|Publication:||Journal of Risk and Insurance|
|Date:||Sep 1, 2013|
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