Indexed Annuity
Product Pricing and Risk Management
Timothy Yi
Enterprise Risk Management
The Hartford
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, 2012
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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 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
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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)
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Source: LIMRA, 4Q 2010 Report
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Recent negative press
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
August 4, 2012
For transcript of Dateline NBC aired on 4/13/2008
http://www.msnbc.msn.com/id/24095230/
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Risk reward profile of fixed vs. variable
Account Value
t
rke
a
M
ull
B
uity
eturn
q
R
E
y
t
nnui
A
d
Fixe
Equ
ity B
ear M
arke
t
Reward:
Gains from
bull market
Risk:
Losses from bear
market
(Some principal
guarantee to protect
downside)
Time
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Risk reward profile of fixed vs. indexed
Account Value
et
k
r
a
ll M
u
ty B
i
u
eturn
R
Eq
y
t
nnui
A
d
e
Fix
Minimum
Equ
ity B
ear M
Reward:
Gains from
bull market
Risk:
Giving up fixed
return
arke
t
Time
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Indexed annuity payout
Account Value
t
rke
a
M
ull
B
uity
q
eturn
R
E
y
t
i
nnu
A
d
e
Fix
Minimum
Equ
ity B
ear M
arke
t
Purchase an equity
call option to
participate in up-side
Purchas a
bond to fund
the minimum
Time
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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 @
104
105
106
107
108
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Actual
4
5
5.67
6
6
Hedged
4
5
6
6
6
Slippage
0
0
+0.33
0
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
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