Longevity Bonds: Construction, Valuation and Use

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Longevity Bonds:

Construction, Valuation and

Use

D. Blake, A. J. G Cairns, K. Dowd, R. MacMinn D. Blake, A. J. G Cairns, K. Dowd, R. MacMinn

Longevity 2 Conference Longevity 2 Conference Chicago Chicago April 2006 April 2006

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Introduction

¾

¾ Longevity risk: risk that members of reference _{Longevity risk: risk that members of reference} population live on average longer than

population live on average longer than anticipated

anticipated

¾

¾ Longevity risk (LR) is one of the largest sources _{Longevity risk (LR) is one of the largest sources} of risk faced by life companies and pension

of risk faced by life companies and pension funds

funds

z

z Life expectancy for men aged 60 is 5 years longer in Life expectancy for men aged 60 is 5 years longer in 2005 than anticipated in mortality tables made in

2005 than anticipated in mortality tables made in 1980s

1980s

z

z Amounts at risk £2520 Amounts at risk £2520 bnbn (about $4424 (about $4424 bnbn) (UK ) (UK Pensions Commission Report) or £40k ($70k) per Pensions Commission Report) or £40k ($70k) per

person in UK person in UK ¾

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Main Features of Swiss Re Bond

¾

¾ Bond is hedge to issuer; issuer gains if _{Bond is hedge to issuer; issuer gains if}SS((tt) very low) very low

z

z Hence, bond is hedge against portfolio dominated by Hence, bond is hedge against portfolio dominated by life insurance

life insurance

¾

¾ Bond is Bond is shortshort--termterm bond to protect issuer against bond to protect issuer against

extreme

extreme deterioration in mortalitydeterioration in mortality

¾

¾ SS((tt) is average of 5 national mortality indices) is average of 5 national mortality indices

¾

¾ Does not involve complicated credit problemsDoes not involve complicated credit problems

¾

¾ Bond is couponBond is coupon--plusplus--principal bond, but only principal is principal bond, but only principal is at risk due to LR

at risk due to LR

¾

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EIB/BNP Bond

¾

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Main Features of EIB/BNP Bond

¾

¾ Hedge to holder; issuer gains if _{Hedge to holder; issuer gains if}SS((tt) lower than ) lower than anticipated

anticipated

¾

¾ Bond is hedge against portfolio dominated by _{Bond is hedge against portfolio dominated by} annuity issues

annuity issues

¾

¾ Bond is _{Bond is}longlong--termterm bond designed to protect bond designed to protect holder against

holder against any any unanticipated improvement in unanticipated improvement in mortality

mortality

¾

¾ S_S((tt) involves a single national survivor index) involves a single national survivor index

¾

¾ Bond involves (quite) complex credit issues_{Bond involves (quite) complex credit issues}

¾

¾ Bond is annuity_{Bond is annuity}-type bond and all coupon -type bond and all coupon payments at risk

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Types of Longevity Bond

¾

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Types of Longevity Bond

¾

¾ Bond might be issued or held as a hedge_{Bond might be issued or held as a hedge}

¾

¾ Type of portfolio hedged by bond (i.e., life or _{Type of portfolio hedged by bond (i.e., life or} annuities)

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Types of Longevity Bond

¾

annuities)

¾

¾ Type of bond: coupon_{Type of bond: coupon}--plusplus--principal, annuity principal, annuity bond, etc.

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Types of Longevity Bond

¾

annuities)

¾

bond, etc.

¾

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Types of Longevity Bond

¾

annuities)

¾

bond, etc.

¾

¾ Survivor/mortality index used_{Survivor/mortality index used}

¾

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Types of Longevity Bond

¾

annuities)

¾

bond, etc.

¾

¾ Credit risks involved_{Credit risks involved}

¾

¾ Nature of payment function and how it is _{Nature of payment function and how it is} contingent on

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Types of Longevity Bond

¾

annuities)

¾

bond, etc.

¾

¾ Credit risks involved_{Credit risks involved}

¾

¾ Nature of payment function and how it is _{Nature of payment function and how it is} contingent on

contingent on SS((tt))

¾

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Other Types of Longevity

Bond

¾

¾ Zero LBsZero LBs: equivalent to conventional zeros, make single : equivalent to conventional zeros, make single payment contingent on

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Other Types of Longevity

Bond

¾

payment contingent on SS((tt))

¾

¾ Open-Open-ended ended LBsLBs: continue to make payments for as : continue to make payments for as long as members of ref pop are alive

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Other Types of Longevity

Bond

¾

long as members of ref pop are alive

¾

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Other Types of Longevity

Bond

¾

¾ PrincipalPrincipal--atat--risk risk LBsLBs: coupon payments conventional: coupon payments conventional

¾

¾ Inverse _InverseLBsLBs: payments are inverse functions of : payments are inverse functions of SS((tt))

z

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Other Types of Longevity

Bond

¾

¾ PrincipalPrincipal--atat--risk risk LBsLBs: coupon payments conventional: coupon payments conventional

¾

¾ Inverse _InverseLBsLBs: payments are inverse functions of : payments are inverse functions of SS((tt))

z

z Comparable to conventional inverse floatersComparable to conventional inverse floaters

¾

¾ Collateralized longevity obligations (Collateralized longevity obligations (CLOsCLOs) comparable ) comparable to

to CDOsCDOs

z

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Constructing Longevity

Bonds

¾

Decomposition method

_{Decomposition method}

z

z Deconstruct existing govt bondsDeconstruct existing govt bonds

z

z Use govt. bonds assuming minimal Use govt. bonds assuming minimal credit risks

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Constructing Longevity

Bonds

¾

Decomposition method

_{Decomposition method}

z

z Deconstruct existing govt bondsDeconstruct existing govt bonds

z

z Use govt. bonds assuming minimal Use govt. bonds assuming minimal credit risks

credit risks

¾

_{Construction using longevity swaps}

z

z Supplements govt bond with longevity Supplements govt bond with longevity swap

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Decomposition Method

¾

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Decomposition Method

¾

¾ Put conventional govt bond into SPV_{Put conventional govt bond into SPV}

¾

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Decomposition Method

¾

¾ Sell conventional LB as claim on SPV_{Sell conventional LB as claim on SPV}

¾

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Decomposition Method

¾

¾ Sell residual claims as ILB_{Sell residual claims as ILB}

¾

¾ In this case, ILB produced as by_{In this case, ILB produced as by}--product product of LB

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Decomposition Method

¾

¾ Sell residual claims as ILB_{Sell residual claims as ILB}

¾

¾ In this case, ILB produced as by_{In this case, ILB produced as by}--product product of LB

of LB

¾

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Swap Method

¾

¾ Combine conventional govt bond and longevity _{Combine conventional govt bond and longevity} swap (LS)

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Swap Method

¾

swap (LS)

¾

¾ LS is a swap involving at least one longevity_{LS is a swap involving at least one longevity}- -dependent payment leg, e.g.,

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Swap Method

¾

swap (LS)

¾

dependent payment leg, e.g.,

¾

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Swap Method

¾

swap (LS)

¾

¾ Floating payment might be _{Floating payment might be}SS((tt))

¾

¾ Fixed payment might be (1+_{Fixed payment might be (1+}ππ))HH((tt), ), HH((tt) based on ) based on mortality tables,

mortality tables, ππ is the swap premium set to is the swap premium set to make both legs same value

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Swap Method

¾

swap (LS)

¾

¾ Floating payment might be _{Floating payment might be}SS((tt))

¾

¾ Fixed payment might be (1+_{Fixed payment might be (1+}ππ))HH((tt), ), HH((tt) based on ) based on mortality tables,

mortality tables, ππ is the swap premium set to is the swap premium set to make both legs same value

make both legs same value

¾

¾ Bank puts bond and LS into SPV, SPV provides _{Bank puts bond and LS into SPV, SPV provides} LB

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Constructing Different

LBs

¾

¾ Conventional bond + pay_{Conventional bond + pay}--fixed LS fixed LS produces LB with long

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Constructing Different

LBs

¾

produces LB with long expsoureexpsoure to to SS((tt))

¾

¾ Conventional bond + pay_{Conventional bond + pay}--floating LS floating LS produces inverse LB

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Constructing Different

LBs

¾

produces inverse LB

¾

¾ Conventional bond + one payment pay_{Conventional bond + one payment pay}- -fixed LB produces zero LB

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Constructing Different

LBs

¾

produces inverse LB

¾

¾ Conventional bond + one payment pay_{Conventional bond + one payment pay}- -fixed LB produces zero LB

fixed LB produces zero LB

¾

¾ Annuity bond + zero LB for terminal _{Annuity bond + zero LB for terminal}

payment produces principal

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Complications [1]

¾

¾ Availability of govt bonds of sufficiently long _{Availability of govt bonds of sufficiently long} maturity

maturity

z

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Complications [1]

¾

maturity

z

z Need these to financially engineer Need these to financially engineer LBsLBs ¾

¾ 25 years is too short_{25 years is too short}

z

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Complications [1]

¾

maturity

z

z A lot of risk arises from people living well into 90sA lot of risk arises from people living well into 90s ¾

¾ French, UK governments starting to issue ultra_{French, UK governments starting to issue ultra}- -long bonds (50 years)

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Complications [1]

¾

maturity

z

z A lot of risk arises from people living well into 90sA lot of risk arises from people living well into 90s ¾

¾ French, UK governments starting to issue ultra_{French, UK governments starting to issue ultra}- -long bonds (50 years)

long bonds (50 years)

¾

¾ If price stability lasts, might expect to see bonds _{If price stability lasts, might expect to see bonds} of up to 100 years’ maturity

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Complications [2]

¾

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Complications [2]

¾

¾ Credit risk complications_{Credit risk complications}

¾

¾ Relatively straightforward if _{Relatively straightforward if}LBsLBs constructed using

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Complications [2]

¾

constructed using SPVsSPVs

¾

¾ Can be more complicated if _{Can be more complicated if}LBsLBs are are constructed using longevity swaps

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Complications [2]

¾

constructed using longevity swaps

¾

¾ Swaps can create complex credit _{Swaps can create complex credit}

exposures

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Complications [2]

¾

constructed using longevity swaps

¾

¾ Swaps can create complex credit _{Swaps can create complex credit}

exposures

¾

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Complications [2], cont

¾

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Complications [2], cont

¾

¾ Investors exposed to (AAA) EIB _{Investors exposed to (AAA) EIB}

¾

¾ Swap means that EIB exposed to (AA) _{Swap means that EIB exposed to (AA)}

BNP, and BNP exposed to EIB

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Complications [2], cont

¾

¾ Reinsurance means that BNP also _{Reinsurance means that BNP also}

exposed to (AA) Partner Re

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Complications [2], cont

¾

¾ Reinsurance means that BNP also _{Reinsurance means that BNP also}

exposed to (AA) Partner Re

¾

¾ Parties involved might also choose further _{Parties involved might also choose further}

credit enhancement

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Complications [3]

¾

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Complications [3]

¾

¾ Survivor index problems_{Survivor index problems}

¾

¾ Index must reflect payments due if bond is _{Index must reflect payments due if bond is}

to provide a good hedge

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Complications [3]

¾

¾ But if there are too many different indices _{But if there are too many different indices}

there can be liquidity problems

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Complications [3]

¾

¾ But if there are too many different indices _{But if there are too many different indices}

there can be liquidity problems

¾

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Complications [3], cont.

¾

¾ Indices constructed from infrequently _{Indices constructed from infrequently}

reported data subject to IBNR problems

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Complications [3], cont.

¾

¾ Issues of smoothing methodologies _{Issues of smoothing methodologies}–– changes in methodology produce

changes in methodology produce

uncertainty

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Complications [3], cont.

¾

uncertainty

¾

¾ Reliance on projections and associated _{Reliance on projections and associated}

model and parameter risk

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Complications [3], cont.

¾

uncertainty

¾

¾ Reliance on projections and associated _{Reliance on projections and associated}

model and parameter risk

¾

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First

-

Order Sensitivities

¾

¾ Interested in first_{Interested in first}--order sensitivities to order sensitivities to shocks in force of mortality

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First

-

Order Sensitivities

¾

shocks in force of mortality µµ and and rr

¾

¾ These give approximations to their _{These give approximations to their}

hedging qualities

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First

-

Order Sensitivities

¾

hedging qualities

¾

¾ Hence, can use them to design hedges _{Hence, can use them to design hedges}

against both IR and Longevity Risk

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First

-

Order Sensitivities

¾

hedging qualities

¾

¾ Hence, can use them to design hedges _{Hence, can use them to design hedges}

against both IR and Longevity Risk

¾

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Elasticities

¾

¾ Mortality elasticity is _{Mortality elasticity is}

η

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Elasticities

¾

η η((µµ,,TT) = () = (∆∆PP//PP)/()/(∆µ∆µ//µ)µ)||TT ¾ ¾ IR elasticity is_{IR elasticity is} η η((rr,,TT) = () = (∆∆PP//PP)/()/(∆∆rr//rr))||TT

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Elasticities

¾

η η((µµ,,TT) = () = (∆∆PP//PP)/()/(∆µ∆µ//µ)µ)||TT ¾ ¾ IR elasticity is_{IR elasticity is} η η((rr,,TT) = () = (∆∆PP//PP)/()/(∆∆rr//rr))||TT ¾

¾ Interested in these for illustrative positions _{Interested in these for illustrative positions}

for

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Illustrative Positions

¾

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Illustrative Positions

¾

¾ Zero_Zero--coupon coupon LBsLBs, coupons equal to , coupons equal to SS((tt))

¾

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Illustrative Positions

¾

¾ Classical _ClassicalLBsLBs paying paying SS((tt) for ) for tt=1 to 50=1 to 50

¾

¾ Principal_Principal--atat--risk risk LBsLBs where principal is where principal is SS((tt) ) and coupon floats with market

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Illustrative Positions

¾

and coupon floats with market rr

¾

¾ Principal_Principal--atat--risk fixed coupon risk fixed coupon LBsLBs where where principal is

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Illustrative Positions

¾

and coupon floats with market rr

¾

¾ Principal_Principal--atat--risk fixed coupon risk fixed coupon LBsLBs where where principal is

principal is SS((tt))

¾

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Elasticities

for Zero

LBs

¾

¾ Zero LB is long LR _{Zero LB is long LR} and short IR risk

and short IR risk

¾

¾ Implies zero LB is a _{Implies zero LB is a} good hedge for

good hedge for

position that is short position that is short

LR and long IR risk LR and long IR risk

¾

¾ Note large _{Note large}elasticitieselasticities esp. for high

esp. for high TT

0 5 10 15 20 25 30 35 40 45 50 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 E la s tic it y Maturity (Years) µ elasticity r elasticity

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Zero LB Example

¾

¾ Life company might be short LR and long _{Life company might be short LR and long}

IR risk

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Zero LB Example

¾

IR risk

¾

¾ If two risk exposures have similar _{If two risk exposures have similar}

magnitude, might consider hedging both

simultaneously using zero LB with 20 year

maturity

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Zero LB Example

¾

IR risk

¾

¾ If two risk exposures have similar _{If two risk exposures have similar}

magnitude, might consider hedging both

simultaneously using zero LB with 20 year

maturity

¾

¾ Or might use an LB to hedge LR and a _{Or might use an LB to hedge LR and a}

conventional hedge for remaining IR risk

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Elasticities

for Inverse Zero

LBs

¾

¾ Inverse zero LB is _{Inverse zero LB is} good hedge for

good hedge for

position that is long position that is long

LR and long IR risk LR and long IR risk

¾

¾ Would want short to _{Would want short to} medium term maturity medium term maturity

0 5 10 15 20 25 30 35 40 45 50 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 E la s tic it y Maturity (Years) µ elasticity r elasticity

(72)

Inverse Zero LB Example

¾

¾ Annuity provider might be long IR risk and _{Annuity provider might be long IR risk and}

long LR risk

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Inverse Zero LB Example

¾

long LR risk

¾

¾ If LR exposure a little bigger than IR _{If LR exposure a little bigger than IR}

exposure, might use zero ILB with maturity

of 15 years

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Inverse Zero LB Example

¾

long LR risk

¾

¾ If LR exposure a little bigger than IR _{If LR exposure a little bigger than IR}

exposure, might use zero ILB with maturity

of 15 years

¾

¾ Or might use an ILB to hedge LR and a _{Or might use an ILB to hedge LR and a}

conventional hedge for remaining IR risk

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A General Lesson

¾

¾ The _Thetypetype of security we should consider as of security we should consider as a hedge depends on nature of LR and

a hedge depends on nature of LR and

(possibly) IR risk exposures

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A General Lesson

¾

¾ The _Thetypetype of security we should consider as of security we should consider as a hedge depends on nature of LR and

a hedge depends on nature of LR and

(possibly) IR risk exposures

¾

¾ Maturity_Maturity of hedge instrument depends on of hedge instrument depends on the relative sizes of these exposures

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Elasticities

for Classical

LBs

¾

¾ Similar properties as _{Similar properties as} zeros

zeros

¾

¾ Elasticities_Elasticities generally generally not so large

not so large

¾

¾ Less leverage than _{Less leverage than} zeros zeros 0 5 10 15 20 25 30 35 40 45 50 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 E la s tic it y Maturity (Years) µ elasticity r elasticity

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Elasticities

for Classical

ILBs

¾

¾ Similar properties as _{Similar properties as} inverse zeros inverse zeros 0 5 10 15 20 25 30 35 40 45 50 -1.5 -1 -0.5 0 0.5 1 1.5 E last ic it y Maturity (Years) µ elasticity r elasticity

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Elasticities

for Conventional AB

¾

¾ Interesting to note _{Interesting to note} that conventional that conventional

annuity bonds have annuity bonds have

much greater IR much greater IR sensitivity sensitivity 0 5 10 15 20 25 30 35 40 45 50 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 E las ti ci ty Maturity r elasticity

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Floating coupon PAR

LBs

¾

¾ These are very _{These are very}

different from earlier different from earlier

ones ones

¾

¾ Peaks/troughs due to _{Peaks/troughs due to} offsetting effects

offsetting effects

¾

¾ Would hedge a _{Would hedge a}

position that is short position that is short

both risks both risks 0 5 10 15 20 25 30 35 40 45 50 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 E la s tic it y Maturity (Years) µ elasticity r elasticity

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Floating coupon PAR

ILBs

¾

¾ No peaks/troughs!_{No peaks/troughs!}

¾

¾ Would hedge a _{Would hedge a}

position that is long position that is long LR and short IR risk LR and short IR risk

0 5 10 15 20 25 30 35 40 45 50 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 E las ti ci ty Maturity (Year) µ elasticity r elasticity

(82)

Fixed coupon PAR

LBs

¾

¾ Change of coupon _{Change of coupon} makes no difference makes no difference

to

to µµ curve but curve but makes a big makes a big

different to

different to rr curvecurve

¾

¾ Qualitatively similar _{Qualitatively similar} to zeros to zeros 0 5 10 15 20 25 30 35 40 45 50 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 E las ti ci ty Maturity (Years) µ elasticity r elasticity

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Fixed coupon PAR

ILBs

¾

¾ Again, change of _{Again, change of} coupon makes no coupon makes no

difference to

difference to µµ curve curve but makes a big

but makes a big different to

different to rr curvecurve

¾

¾ Qualitatively similar _{Qualitatively similar} to inverse zeros to inverse zeros 0 5 10 15 20 25 30 35 40 45 50 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 E last ic it y Maturity (Year) µ elasticity r elasticity

(84)

Conclusions

¾

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Conclusions

¾

¾ LBs_LBs involve challenging problems, e.g.,involve challenging problems, e.g.,

¾

¾ Valuation problems due to market _{Valuation problems due to market}

incompleteness

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Conclusions

¾

incompleteness

¾

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Conclusions

¾

incompleteness

¾

¾ Hampered by dearth of ultra long bonds_{Hampered by dearth of ultra long bonds}

¾

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Conclusions

¾

incompleteness

¾

¾ Credit risk management problems_{Credit risk management problems}

¾

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Conclusions

¾

incompleteness

¾

¾ Credit risk management problems_{Credit risk management problems}

¾

¾ Index problems_{Index problems}

¾

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Conclusions

¾

(91)

Conclusions

¾

¾ But _ButLBsLBs also very promising, e.g., also very promising, e.g.,

¾

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Conclusions

¾

¾ Very versatile and flexible_{Very versatile and flexible}

¾

¾ Can accommodate different mixes of LR _{Can accommodate different mixes of LR}

and IR risk exposure

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Conclusions

¾

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Conclusions

¾

¾ Can accommodate desired leverage_{Can accommodate desired leverage}

¾

¾ Attractions as low_{Attractions as low}--beta investment beta investment opportunities