Longevity Bonds: Construction, Valuation and Use
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1 Longevity Bonds: Construction, Valuation and Use D. Blake, A. J. G Cairns, K. Dowd, R. MacMinn Longevity 2 Conference Chicago April 2006
2 Introduction Longevity risk: risk that members of reference population live on average longer than anticipated Longevity risk (LR) is one of the largest sources of risk faced by life companies and pension funds Life expectancy for men aged 60 is 5 years longer in 2005 than anticipated in mortality tables made in 1980s Amounts at risk 2520 bn (about $4424 bn) ) (UK Pensions Commission Report) or 40k ($70k) per person in UK This paper looks at Longevity bonds
3 Main Features of Swiss Re Bond Bond is hedge to issuer; issuer gains if S(t) ) very low Hence, bond is hedge against portfolio dominated by life insurance Bond is short-term term bond to protect issuer against extreme deterioration in mortality S(t) ) is average of 5 national mortality indices Does not involve complicated credit problems Bond is coupon-plus plus-principal principal bond, but only principal is at risk due to LR Spread over LIBOR compensates for principal-at at-risk
4 EIB/BNP Bond Announced in late 2004, to be issued by EIB
5 Main Features of EIB/BNP Bond Hedge to holder; issuer gains if S(t) ) lower than anticipated Bond is hedge against portfolio dominated by annuity issues Bond is long-term bond designed to protect holder against any unanticipated improvement in mortality S(t) ) involves a single national survivor index Bond involves (quite) complex credit issues Bond is annuity-type type bond and all coupon payments at risk
6 Types of Longevity Bond Bond might be issued or held as a hedge
7 Types of Longevity Bond Bond might be issued or held as a hedge Type of portfolio hedged by bond (i.e., life or annuities)
8 Types of Longevity Bond Bond might be issued or held as a hedge Type of portfolio hedged by bond (i.e., life or annuities) Type of bond: coupon-plus plus-principal, principal, annuity bond, etc.
9 Types of Longevity Bond Bond might be issued or held as a hedge Type of portfolio hedged by bond (i.e., life or annuities) Type of bond: coupon-plus plus-principal, principal, annuity bond, etc. Survivor/mortality index used
10 Types of Longevity Bond Bond might be issued or held as a hedge Type of portfolio hedged by bond (i.e., life or annuities) Type of bond: coupon-plus plus-principal, principal, annuity bond, etc. Survivor/mortality index used Credit risks involved
11 Types of Longevity Bond Bond might be issued or held as a hedge Type of portfolio hedged by bond (i.e., life or annuities) Type of bond: coupon-plus plus-principal, principal, annuity bond, etc. Survivor/mortality index used Credit risks involved Nature of payment function and how it is contingent on S(t)
12 Types of Longevity Bond Bond might be issued or held as a hedge Type of portfolio hedged by bond (i.e., life or annuities) Type of bond: coupon-plus plus-principal, principal, annuity bond, etc. Survivor/mortality index used Credit risks involved Nature of payment function and how it is contingent on S(t) LBs can vary across many dimensions
13 Other Types of Longevity Bond Zero LBs: : equivalent to conventional zeros, make single payment contingent on S(t)
14 Other Types of Longevity Bond Zero LBs: : equivalent to conventional zeros, make single payment contingent on S(t) Open-ended ended LBs: : continue to make payments for as long as members of ref pop are alive
15 Other Types of Longevity Bond Zero LBs: : equivalent to conventional zeros, make single payment contingent on S(t) Open-ended ended LBs: : continue to make payments for as long as members of ref pop are alive Principal-at at-risk LBs: : coupon payments conventional
16 Other Types of Longevity Bond Zero LBs: : equivalent to conventional zeros, make single payment contingent on S(t) Open-ended ended LBs: : continue to make payments for as long as members of ref pop are alive Principal-at at-risk LBs: : coupon payments conventional Inverse LBs: : payments are inverse functions of S(t) Comparable to conventional inverse floaters
17 Other Types of Longevity Bond Zero LBs: : equivalent to conventional zeros, make single payment contingent on S(t) Open-ended ended LBs: : continue to make payments for as long as members of ref pop are alive Principal-at at-risk LBs: : coupon payments conventional Inverse LBs: : payments are inverse functions of S(t) Comparable to conventional inverse floaters Collateralized longevity obligations (CLOs( CLOs) ) comparable to CDOs Synthetic equivalents, synthetic CLOs etc.
18 Constructing Longevity Bonds Decomposition method Deconstruct existing govt bonds Use govt. bonds assuming minimal credit risks
19 Constructing Longevity Bonds Decomposition method Deconstruct existing govt bonds Use govt. bonds assuming minimal credit risks Construction using longevity swaps Supplements govt bond with longevity swap
20 Decomposition Method Put conventional govt bond into SPV
21 Decomposition Method Put conventional govt bond into SPV Sell conventional LB as claim on SPV
22 Decomposition Method Put conventional govt bond into SPV Sell conventional LB as claim on SPV Sell residual claims as ILB
23 Decomposition Method Put conventional govt bond into SPV Sell conventional LB as claim on SPV Sell residual claims as ILB In this case, ILB produced as by-product of LB
24 Decomposition Method Put conventional govt bond into SPV Sell conventional LB as claim on SPV Sell residual claims as ILB In this case, ILB produced as by-product of LB Trivial credit risk problems
25 Swap Method Combine conventional govt bond and longevity swap (LS)
26 Swap Method Combine conventional govt bond and longevity swap (LS) LS is a swap involving at least one longevity- dependent payment leg, e.g.,
27 Swap Method Combine conventional govt bond and longevity swap (LS) LS is a swap involving at least one longevity- dependent payment leg, e.g., Floating payment might be S(t)
28 Swap Method Combine conventional govt bond and longevity swap (LS) LS is a swap involving at least one longevity- dependent payment leg, e.g., Floating payment might be S(t) Fixed payment might be (1+π)H(t), ), H(t) ) based on mortality tables, π is the swap premium set to make both legs same value
29 Swap Method Combine conventional govt bond and longevity swap (LS) LS is a swap involving at least one longevity- dependent payment leg, e.g., Floating payment might be S(t) Fixed payment might be (1+π)H(t), ), H(t) ) based on mortality tables, π is the swap premium set to make both legs same value Bank puts bond and LS into SPV, SPV provides LB
30 Constructing Different LBs Conventional bond + pay-fixed LS produces LB with long expsoure to S(t)
31 Constructing Different LBs Conventional bond + pay-fixed LS produces LB with long expsoure to S(t) Conventional bond + pay-floating LS produces inverse LB
32 Constructing Different LBs Conventional bond + pay-fixed LS produces LB with long expsoure to S(t) Conventional bond + pay-floating LS produces inverse LB Conventional bond + one payment pay- fixed LB produces zero LB
33 Constructing Different LBs Conventional bond + pay-fixed LS produces LB with long expsoure to S(t) Conventional bond + pay-floating LS produces inverse LB Conventional bond + one payment pay- fixed LB produces zero LB Annuity bond + zero LB for terminal payment produces principal-at at-risk LB, etc.
34 Complications [1] Availability of govt bonds of sufficiently long maturity Need these to financially engineer LBs
35 Complications [1] Availability of govt bonds of sufficiently long maturity Need these to financially engineer LBs 25 years is too short A lot of risk arises from people living well into 90s
36 Complications [1] Availability of govt bonds of sufficiently long maturity Need these to financially engineer LBs 25 years is too short A lot of risk arises from people living well into 90s French, UK governments starting to issue ultra- long bonds (50 years)
37 Complications [1] Availability of govt bonds of sufficiently long maturity Need these to financially engineer LBs 25 years is too short A lot of risk arises from people living well into 90s French, UK governments starting to issue ultra- long bonds (50 years) If price stability lasts, might expect to see bonds of up to 100 years maturity
38 Complications [2] Credit risk complications
39 Complications [2] Credit risk complications Relatively straightforward if LBs constructed using SPVs
40 Complications [2] Credit risk complications Relatively straightforward if LBs constructed using SPVs Can be more complicated if LBs are constructed using longevity swaps
41 Complications [2] Credit risk complications Relatively straightforward if LBs constructed using SPVs Can be more complicated if LBs are constructed using longevity swaps Swaps can create complex credit exposures
42 Complications [2] Credit risk complications Relatively straightforward if LBs constructed using SPVs Can be more complicated if LBs are constructed using longevity swaps Swaps can create complex credit exposures Example is EIB/BNP bond
43 Complications [2], cont Investors exposed to (AAA) EIB
44 Complications [2], cont Investors exposed to (AAA) EIB Swap means that EIB exposed to (AA) BNP, and BNP exposed to EIB
45 Complications [2], cont Investors exposed to (AAA) EIB Swap means that EIB exposed to (AA) BNP, and BNP exposed to EIB Reinsurance means that BNP also exposed to (AA) Partner Re
46 Complications [2], cont Investors exposed to (AAA) EIB Swap means that EIB exposed to (AA) BNP, and BNP exposed to EIB Reinsurance means that BNP also exposed to (AA) Partner Re Parties involved might also choose further credit enhancement
47 Complications [3] Survivor index problems
48 Complications [3] Survivor index problems Index must reflect payments due if bond is to provide a good hedge
49 Complications [3] Survivor index problems Index must reflect payments due if bond is to provide a good hedge But if there are too many different indices there can be liquidity problems
50 Complications [3] Survivor index problems Index must reflect payments due if bond is to provide a good hedge But if there are too many different indices there can be liquidity problems Need to balance hedging and liquidity
51 Complications [3], cont. Indices constructed from infrequently reported data subject to IBNR problems
52 Complications [3], cont. Indices constructed from infrequently reported data subject to IBNR problems Issues of smoothing methodologies changes in methodology produce uncertainty
53 Complications [3], cont. Indices constructed from infrequently reported data subject to IBNR problems Issues of smoothing methodologies changes in methodology produce uncertainty Reliance on projections and associated model and parameter risk
54 Complications [3], cont. Indices constructed from infrequently reported data subject to IBNR problems Issues of smoothing methodologies changes in methodology produce uncertainty Reliance on projections and associated model and parameter risk Moral hazard and data integrity problems
55 First-Order Sensitivities Interested in first-order sensitivities to shocks in force of mortality µ and r
56 First-Order Sensitivities Interested in first-order sensitivities to shocks in force of mortality µ and r These give approximations to their hedging qualities
57 First-Order Sensitivities Interested in first-order sensitivities to shocks in force of mortality µ and r These give approximations to their hedging qualities Hence, can use them to design hedges against both IR and Longevity Risk
58 First-Order Sensitivities Interested in first-order sensitivities to shocks in force of mortality µ and r These give approximations to their hedging qualities Hence, can use them to design hedges against both IR and Longevity Risk Can measure sensitivities using elasticities
59 Elasticities Mortality elasticity is η(µ,t) ) = ( P/P)/(( )/( µ µ/µ) µ) T
60 Elasticities Mortality elasticity is η(µ,t) ) = ( P/P)/(( )/( µ µ/µ) µ) T IR elasticity is η(r,t) ) = ( P/P)/(( )/( r/r) T
61 Elasticities Mortality elasticity is η(µ,t) ) = ( P/P)/(( )/( µ µ/µ) µ) T IR elasticity is η(r,t) ) = ( P/P)/(( )/( r/r) T Interested in these for illustrative positions for T=1 to 50
62 Illustrative Positions Zero-coupon LBs,, coupons equal to S(t)
63 Illustrative Positions Zero-coupon LBs,, coupons equal to S(t) Classical LBs paying S(t) ) for t=1 to 50
64 Illustrative Positions Zero-coupon LBs,, coupons equal to S(t) Classical LBs paying S(t) ) for t=1 to 50 Principal-at at-risk LBs where principal is S(t) and coupon floats with market r
65 Illustrative Positions Zero-coupon LBs,, coupons equal to S(t) Classical LBs paying S(t) ) for t=1 to 50 Principal-at at-risk LBs where principal is S(t) and coupon floats with market r Principal-at at-risk fixed coupon LBs where principal is S(t)
66 Illustrative Positions Zero-coupon LBs,, coupons equal to S(t) Classical LBs paying S(t) ) for t=1 to 50 Principal-at at-risk LBs where principal is S(t) and coupon floats with market r Principal-at at-risk fixed coupon LBs where principal is S(t) + inverse equivalents
67 Elasticities for Zero LBs Zero LB is long LR and short IR risk Implies zero LB is a good hedge for position that is short LR and long IR risk Note large elasticities esp. for high T E lasticity µ elasticity r elasticity Maturity (Years)
68 Zero LB Example Life company might be short LR and long IR risk
69 Zero LB Example Life company might be short LR and long IR risk If two risk exposures have similar magnitude, might consider hedging both simultaneously using zero LB with 20 year maturity
70 Zero LB Example Life company might be short LR and long IR risk If two risk exposures have similar magnitude, might consider hedging both simultaneously using zero LB with 20 year maturity Or might use an LB to hedge LR and a conventional hedge for remaining IR risk
71 Elasticities for Inverse Zero LBs Inverse zero LB is good hedge for position that is long LR and long IR risk Would want short to medium term maturity E lasticity µ elasticity r elasticity Maturity (Years)
72 Inverse Zero LB Example Annuity provider might be long IR risk and long LR risk
73 Inverse Zero LB Example Annuity provider might be long IR risk and long LR risk If LR exposure a little bigger than IR exposure, might use zero ILB with maturity of 15 years
74 Inverse Zero LB Example Annuity provider might be long IR risk and long LR risk If LR exposure a little bigger than IR exposure, might use zero ILB with maturity of 15 years Or might use an ILB to hedge LR and a conventional hedge for remaining IR risk
75 A General Lesson The type of security we should consider as a hedge depends on nature of LR and (possibly) IR risk exposures
76 A General Lesson The type of security we should consider as a hedge depends on nature of LR and (possibly) IR risk exposures Maturity of hedge instrument depends on the relative sizes of these exposures
77 Elasticities for Classical LBs Similar properties as zeros Elasticities generally not so large Less leverage than zeros Elasticity µ elasticity r elasticity Maturity (Years)
78 Elasticities for Classical ILBs Similar properties as inverse zeros µ elasticity r elasticity 0.5 Elasticity Maturity (Years)
79 Elasticities for Conventional AB Interesting to note that conventional annuity bonds have much greater IR sensitivity Elasticity r elasticity Maturity
80 Floating coupon PAR LBs These are very different from earlier ones Peaks/troughs due to offsetting effects Would hedge a position that is short both risks Elasticity µ elasticity r elasticity Maturity (Years)
81 Floating coupon PAR ILBs No peaks/troughs! Would hedge a position that is long LR and short IR risk Elasticity µ elasticity r elasticity Maturity (Year)
82 Fixed coupon PAR LBs Change of coupon makes no difference to µ curve but makes a big different to r curve Qualitatively similar to zeros Elasticity µ elasticity r elasticity Maturity (Years)
83 Fixed coupon PAR ILBs Again, change of coupon makes no difference to µ curve but makes a big different to r curve Qualitatively similar to inverse zeros Elasticity µ elasticity r elasticity Maturity (Year)
84 Conclusions LBs involve challenging problems, e.g.,
85 Conclusions LBs involve challenging problems, e.g., Valuation problems due to market incompleteness
86 Conclusions LBs involve challenging problems, e.g., Valuation problems due to market incompleteness Hampered by dearth of ultra long bonds
87 Conclusions LBs involve challenging problems, e.g., Valuation problems due to market incompleteness Hampered by dearth of ultra long bonds Credit risk management problems
88 Conclusions LBs involve challenging problems, e.g., Valuation problems due to market incompleteness Hampered by dearth of ultra long bonds Credit risk management problems Index problems
89 Conclusions LBs involve challenging problems, e.g., Valuation problems due to market incompleteness Hampered by dearth of ultra long bonds Credit risk management problems Index problems Contract design problems
90 Conclusions But LBs also very promising, e.g.,
91 Conclusions But LBs also very promising, e.g., Very versatile and flexible
92 Conclusions But LBs also very promising, e.g., Very versatile and flexible Can accommodate different mixes of LR and IR risk exposure
93 Conclusions But LBs also very promising, e.g., Very versatile and flexible Can accommodate different mixes of LR and IR risk exposure Can accommodate desired leverage
94 Conclusions But LBs also very promising, e.g., Very versatile and flexible Can accommodate different mixes of LR and IR risk exposure Can accommodate desired leverage Attractions as low-beta investment opportunities
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