Indexed Annuity Product Pricing and Risk Management Timothy Yi Enterprise Risk Management The Hartford

August 4, After this presentation  You will understand Marketing position of indexed annuity Basic pricing of indexed annuity Risk management of indexed annuity including hedging

August 4, 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

August 4, 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

August 4, Types of annuity crediting method Based 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

August 4, 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)

August 4, Clients are recognizing the appeal Index Annuity Sales (in billions) Source: LIMRA, 4Q 2010 Report

August 4,  Inappropriate sales to seniors  Lack of suitability review  Complicated product design  Long surrender charge schedules  Illiquidity for emergencies, including Long Term Care  Two-tier annuities with illusory benefits Recent negative press For transcript of Dateline NBC aired on 4/13/2008

August 4, Risk reward profile of fixed vs. variable

August 4, Risk reward profile of fixed vs. indexed

August 4, Indexed annuity payout

August 4, 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

August 4, 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

August 4, Sample of option types  European  American  Basket  Rainbow  Look-back  Asian  Barrier  Binary (digital)  Cliquet (forward starting)

August 4, Sample of strategies involving options  Spread Bull spread Bear spread  Butterfly  Straddle  Strangle  Collar Risk reversal  Covered call

August 4, 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

August 4, 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 = – 72 – – 190 = 163 bps

August 4, 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

August 4, 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

August 4, 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

August 4, Risk management consideration  Nothing  Hedging Static hedging Dynamic hedging

August 4, 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

August 4, 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

August 4, 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