Yi Indexed Annuity Basic

8/12/2019 Yi Indexed Annuity Basic

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Indexed AnnuityProduct Pricing and Risk Management

Timothy YiEnterprise Risk Management

The Hartford


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After this presentation You will understand

Marketing position of indexed annuityBasic pricing of indexed annuityRisk management of indexed annuity including hedging


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Disclaimer Any opinions in this presentation are mine and do not represent those ofmy employerProducts illustrated in this presentation are from public information andfor the illustration purpose onlyIn order to illustrate the basic key concepts, lots of simplification will bemade


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Annuity overview Two phases of annuity contracts

Accumulation (deferred) phaseDistribution (payout/income) phase

Annuity usually refers to

accumulation

phase of the contractsIn US, very few contracts are annuitized from accumulation phaseSimilar to certified deposit sold by banks, but usually longerduration guarantee


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Types of annuity crediting methodBased on 2011 non-captive data, fixed/index/variable are 20%/20%/60% of sales

Fixed (Company declares crediting rate)Minimum crediting rateBook-value surrender or Market-value adjustment

Indexed (Crediting rate is linked to index level change)

Minimum crediting rateMinimum participation Variable (Crediting rate is based on underlying mutual fund investmentperformance)

No minimum crediting ratePrincipal protection at death, annuitization or withdrawalEnhanced principal projection such as step-up or roll-up


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Index annuities can be attractive solutionsCan be attractive solutions for clients who

Are dissatisfied with low interest rates Are equity averse and want principal protection Would like the opportunity for higher crediting potential Want their growth to be tax-deferredDesire insurance features and benefits, such as a death benefit,annuity income options (including lifetime options), and a premiumenhancement (not available on all contracts)


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Clients are recognizing the appeal

Index Annuity Sales (in billions)

Source: LIMRA, 4Q 2010 Report


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Inappropriate sales to seniorsLack of suitability reviewComplicated product designLong surrender charge schedulesIlliquidity for emergencies, including Long

Term Care Two-tier annuities with illusory benefits

Recent negative press

For transcript of Dateline NBC aired on 4/13/2008http://www.msnbc.msn.com/id/24095230/


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Risk reward profile of fixed vs. variable

A c c o u n t

V a l u e

Time

E q u i t y B e a r M a r k e t

E q u i t y B

u l l M a r k e

tReward:

Gains frombull market

Risk:Losses from bear

market(Some principal

guarantee to protect

downside)

F i x e d A n n u i t y R e t u

r n


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Risk reward profile of fixed vs. indexed

A c c o u n t

V a l u e

Time

M i n i m u m


E q u i t y B u

l l M a r k e

t

F i x e d A n n u i

t y R e t u r n

Reward:Gains frombull market

Risk:Giving up fixed

return


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Indexed annuity payout

A c c o u n t

V a l u e

Time

M i n i m u m


E q u i t y

B u l l M a r

k e tPurchase an equity

call option to participate in up-side

Purchas abond to fundthe minimum

F i x e d A n n u i t y R e t u

r n


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Derivative basicsDerivatives

Derived a payoff from price of other assetsLong position vs. short positionForward/FutureOption is to take one-side gain for up-front premium paymentZero-sum Game

If you have a long option position, there will be also option seller(short position) to make it zero-sum game


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Option basic

The fighting styles of [a bull and a bear] may have a major impact on thenames. When a bull fights it swipes its horns up; when a bear fights itswipes down on its opponents with its paws. When the market is goingup, it is similar to a bull swiping up with its horns. When the market is

going down it is similar to a bear swinging its paws down.

(Wikipedia)Call-option, right to buy an asset at a fixed strike price, to gain when themarket is upPut-option, right to sell an asset at a fixed strike price, to gain when themarket is down

If you are bullish, purchase a call option and if you are bearish,purchase a put option


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Sample of option typesEuropean

AmericanBasketRainbow

Look-back AsianBarrierBinary (digital)Cliquet (forward starting)


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Sample of strategies involving optionsSpread

Bull spreadBear spread

ButterflyStraddleStrangleCollar

Risk reversal

Covered call


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Illustration of profitability of indexed annuityExample based on a 7-year surrender-charge period productRevenue

Risk-free rateCredit spread less expected default

Contingent surrender charge to recover acquisition expensesExpenses

Acquisition costMaintenance costMinimum crediting rateCost of capital charge plus profit marginOption budget


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Illustration of profitability of indexed annuityRevenue

7-year risk-free rate = 3% (300 bps)Credit spread less expected default = 2.5% (250 bps)7-year contingent surrender charge

(7%/6%/5%/4%/3%/2%/1%/0%)Expenses

5% acquisition cost (72 bps / year)0.25% maintenance cost (25 bps / year)Minimum crediting rate (100 bps / year)

Cost of capital charge plus profit margin (190 bps)Option budget (to solve for) = 163 bps= 300 + 250 72 25 - 100 190 = 163 bps


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Basic design: point-to-pointCredited rate = Max (minimum, index return) where index return =Index(T+1)/Index(T)Index returns are usually price returns excluding reinvestment ofdividends

European call option to hedge index return A call option on a price return index will be cheaper than a total returnindexBased on the option budget, determine either participation rate or cap onindex return


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Hedging: point-to-pointPurchase an European call option (or call spread) to hedge

Call spread is combination of long at-the-money call and short out-of-money callIf the minimum crediting rate is 1% and cap on point-to-point return is 6% then buy101% strike call and sell 106% strike call

Can average caps and purchase a single call spread for given cohort1/3 of 105, 1/3 of 106, and 13 of 107 cap purchase 106 cap

Payoff @ Actual Hedged Slippage104 4 4 0105 5 5 0106 5.67 6 +0.33107 6 6 0108 6 6 0


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Basic design: monthly cliquetEach of monthly returns is capped or floored also, the global cap or flooris applied for the annual returnExample: 2% monthly cap, no monthly floor, 1% annual capMonthly return scenario 1:+5/+5/+5/+5/+5/+5/+5/+5/+5/+5/+5/+5/

+2/+2/+2/+2/+2/+2/+2/+2/+2/+2/+2/+2/ = +24%/yearMonthly return scenario 2:+5/+5/+5/+5/+5/+0/+0/+0/+0/+5/+5/+5/

+2/+2/+2/+2/+2/+0/+0/+0/+0/+2/+2/+2/ = +16%/yearMonthly return scenario 3: +5/+5/+5/+5/+0/+0/+0/+0/+0/-5/-5/-5/

+2/+2/+2/+2/+2/+0/+0/+0/+0/ -5/-4/+0/ = +1%/year


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Risk management consideration

NothingHedging

Static hedgingDynamic hedging


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Dynamic hedging: monthly cliquetExample: 2% monthly cap, no monthly floor, 1% annual capMonthly return scenario 3: +5/+5/+5/+5/+0/+0/+0/+0/+0/-5/-5/-5/

+2/+2/+2/+2/+2/+0/+0/+0/+0/ -5/-5/+1/ = +1%/yearBeginning of month (BoM) 1: buy 1 month 100/102 call spreadBoM 2: buy 1 mo 100/102 call spread & sell 1 mo 100/98 put spreadBoM 3: buy 1 mo 100/102 call spread & sell 1 mo 100/96 put spread

BoM 10: buy 1 mo 100/102 call spread & sell 1 mo 100/90 put spreadBoM 11: buy 1 mo 100/102 call spread & sell 1 mo 100/95 put spreadBoM 12: buy 1 mo 101/102 call spread


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ObservationIn an arbitrage-free frame- work, cant earn credit spread in excess ofexpected default costOption pricing is built upon an arbitrage-free concept

These two concepts are not fully comparable, but in practice mixed in thepricing

Need to consider additional option cost for credit protection


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Traditional asset liability challengesMinimum crediting rate guarantee

Need to invest longer duration to minimize reinvestment risk at lowerrate (duration L)

Book value surrenderNeed to invest shorter duration to minimize market value loss whenselling a bond at higher rate (duration S)

Mixed challengesInvest in a duration between L and S

Purchase options to protect Need to revise the profitability to additional interest rate optioncost

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