Indexed AnnuityProduct Pricing and Risk Management

Timothy YiEnterprise Risk ManagementThe Hartford

August 4, 2012 2

After this presentation You will understand

Marketing position of indexed annuity Basic pricing of indexed annuity Risk management of indexed annuity including

hedging

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Disclaimer Any opinions in this presentation are mine and do not

represent those of my employer Products illustrated in this presentation are from public

information and for the illustration purpose only In order to illustrate the basic key concepts, lots of

simplification will be made

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Annuity overview Two phases of annuity contracts

Accumulation (deferred) phase Distribution (payout/income) phase Annuity usually refers to “accumulation” phase of the

contracts In US, very few contracts are annuitized from

accumulation phase Similar to certified deposit sold by banks, but

usually longer duration 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 rate Book-value surrender or Market-value adjustment

Indexed (Crediting rate is linked to index level change) Minimum crediting rate Minimum participation

Variable (Crediting rate is based on underlying mutual fund investment performance) No minimum crediting rate Principal protection at death, annuitization or

withdrawal Enhanced principal projection such as step-up or

roll-up

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Index annuities can be attractive solutions Can 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-deferred Desire insurance features and benefits, such as a

death benefit, annuity income options (including lifetime options), and a premium enhancement (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 CareTwo-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

Acc

ount

Val

ue

Time

Equity Bear Market

Equity B

ull Marke

t

Reward:Gains from bull market

Risk: Losses from bear

market(Some principal

guarantee to protect downside)

Fixed Annuity Return

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Risk reward profile of fixed vs. indexed

Acc

ount

Val

ue

Time

Minimum

Equity Bear Market

Equity B

ull Mark

et

Fixed Annuity Return

Reward:Gains from bull market

Risk: Giving up fixed

return

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Indexed annuity payoutA

ccou

nt V

alue

Time

Minimum

Equity Bear Market

Equity B

ull Mark

etPurchase an equity

call option to participate in up-side

Purchas a bond to fund the minimum

Fixed Annuity Return

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Derivative basics Derivatives

Derived a payoff from price of other assets Long position vs. short position Forward/Future Option is to take one-side gain for up-front premium

payment Zero-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 the names. When a bull fights it swipes its horns up; when a bear fights it swipes down on its opponents with its paws. When the market is going up, 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 the market is up

Put-option, right to sell an asset at a fixed strike price, to gain when the market 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 types European American Basket Rainbow Look-back Asian Barrier Binary (digital) Cliquet (forward starting)

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Sample of strategies involving options Spread

Bull spread Bear spread

Butterfly Straddle Strangle Collar

Risk reversal Covered call

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Illustration of profitability of indexed annuity Example based on a 7-year surrender-charge period

product Revenue

Risk-free rate Credit spread less expected default Contingent surrender charge to recover acquisition

expenses Expenses

Acquisition cost Maintenance cost Minimum crediting rate Cost of capital charge plus profit margin Option budget

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Illustration of profitability of indexed annuity Revenue

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-point Credited rate = Max (minimum, index return) where

index return = Index(T+1)/Index(T) Index returns are usually price returns excluding

reinvestment of dividends European call option to hedge index return A call option on a price return index will be cheaper

than a total return index Based on the option budget, determine either

participation rate or cap on index return

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

Call spread is combination of long at-the-money call and short out-of-money call

If the minimum crediting rate is 1% and cap on point-to-point return is 6% then buy 101% strike call and sell 106% strike call

Can average caps and purchase a single call spread for given cohort

1/3 of 105, 1/3 of 106, and 13 of 107 cap purchase 106 cap Payoff @ Actual Hedged Slippage 104 4 4 0 105 5 5 0 106 5.67 6 +0.33 107 6 6 0 108 6 6 0

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Basic design: monthly cliquet Each of monthly returns is capped or floored also, the

global cap or floor is applied for the annual return Example: 2% monthly cap, no monthly floor, 1% annual

cap Monthly 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%/year Monthly 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%/year Monthly 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

Nothing Hedging

Static hedging Dynamic hedging

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Dynamic hedging: monthly cliquet Example: 2% monthly cap, no monthly floor, 1% annual cap Monthly 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%/year Beginning of month (BoM) 1: buy 1 month 100/102 call spread BoM 2: buy 1 mo 100/102 call spread & sell 1 mo 100/98 put spread BoM 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

spread BoM 11: buy 1 mo 100/102 call spread & sell 1 mo 100/95 put

spread BoM 12: buy 1 mo 101/102 call spread

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Observation In an arbitrage-free frame-work, can’t earn credit

spread in excess of expected default cost Option pricing is built upon an arbitrage-free concept These two concepts are not fully comparable, but in

practice mixed in the pricing Need to consider additional option cost for credit

protection

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Traditional asset liability challenges Minimum crediting rate guarantee

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

Book value surrender Need to invest shorter duration to minimize market

value loss when selling a bond at higher rate (duration S)

Mixed challenges Invest in a duration between L and S Purchase options to protect

Need to revise the profitability to additional interest rate option cost