2008 Equity Based Insurance Guarantees Conference

1. Equity-Based Investment
Guarantee Conference
Managing Variable Annuity
Guaranteed Minimum Death &
Living Benefits
8:30 am – 10:00 am
October 28th, 2008
Boston, MA, USA
Frank Zhang, CFA, FRM, FSA, MSCF, PRM
Director, Equity Derivatives
Tel: 1-212-278-6273
FRANK.ZHANG@SGCIB.COM
1987-2007
Equity Derivatives House of the Year
“Modern Great”
in Equity Derivatives

2. Disclaimer
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contained herein changes or subsequently becomes inaccurate. SGAS and its affiliates expressly disclaim all
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3. Lessons learned From
Current Markets
GMxB Solutions 3

4. Lessons Learned from Recent Market Performance
Volatile Markets
History of 10-year swap rates, S&P 500 index, 10-year implied volatility
30% 1,800
1,600
25%
1,400
20% 1,200
1,000
15%
SP500 10Y Implied Vol
800
10Y USD Swap Rate
SP500
10% 600
400
5%
200
0% 0
12/31/99
12/31/00
12/31/01
12/31/02
12/31/03
12/31/04
12/31/05
12/31/06
12/31/07
3/31/00
6/30/00
9/30/00
3/31/01
6/30/01
9/30/01
3/31/02
6/30/02
9/30/02
3/31/03
6/30/03
9/30/03
3/31/04
6/30/04
9/30/04
3/31/05
6/30/05
9/30/05
3/31/06
6/30/06
9/30/06
3/31/07
6/30/07
9/30/07
3/31/08
6/30/08
9/30/08
Choppy markets, high implied vol, and low interest rates have been challenging for VA hedging programs
GMxB Solutions 4

5. Lessons Learned from Recent Market Performance
Markets in Fear
* Source WSJ.com article “What's Behind the Surge in the VIX” 10/23/08
GMxB Solutions 5

6. Hedging programs P/L:
Dynamic hedging program
Dynamic Hedge Performance With Decrements
10,000,000 160,000
140,000
8,000,000
120,000
6,000,000
100,000
4,000,000
co n a e
A c u t V lu
80,000
2,000,000
60,000
-
40,000
(2,000,000)
20,000
(4,000,000) -
0 100 200 300 400 500
Option Value Cum Futures G/(L) + PV of Option Premium Account Value
Delta/Rho dynamic hedging:
In general bleeds money over time through buy high and sell low
The cost of hedge bleeding is equivalent to the up front option premium
But with less certainty even if the realized vol is the same as the implied vol, due to path dependency.
Even if no up front premium is spent initially
The amount can be implicitly assumed borrowed from the collection of future fees
The amount is borrowed and has to be paid back GMxB Solutions 6

7. Example: Delta Hedging Annual Ratchet GMxB
Delta hedging of an annual ratchet GMxB (i.e. look-back options), especially under
real-world conditions, is more costly and difficult than hedging vanilla puts
P/L Dispersion In Hedging Simulations
35%
30%
25%
frequency
20%
Look-back Put
Vanilla Put
15%
10%
5%
0%
-20% -10% -8% -6% -4% -2% 0% 2% 4% 6% 8% 10% More
P/L (% of Initial Value)
GMxB Solutions 7

8. Delta Hedging: Impact of Recent Market Movements
Delta hedging a 5% Roll-Up Guarantee with daily rebalancing
proved a profitable strategy in 2005 and 2006
PnL 2005
0.30% 108.00%
106.00%
0.20%
104.00%
102.00%
0.10%
-> Delta hedging
100.00%
strategies were
SP500
PnL
0.00% 98.00%
17/01/05
23/05/05
18/07/05
21/11/05
03/01/05
31/01/05
14/02/05
28/02/05
14/03/05
28/03/05
11/04/05
25/04/05
09/05/05
06/06/05
20/06/05
04/07/05
01/08/05
15/08/05
29/08/05
12/09/05
26/09/05
10/10/05
24/10/05
07/11/05
05/12/05
19/12/05
profitable in 2005
96.00%
-0.10%
94.00%
92.00%
-0.20%
Daily PnL
90.00%
Index
Cumulative PnL
-0.30% 88.00%
Date
PnL 2006
0.30% 115.00%
0.25%
110.00%
0.20%
105.00%
0.15%
-> Delta hedging
0.10%
strategies were
100.00%
SP500
PnL
0.05%
profitable in 2006
95.00%
0.00%
17/01/06
31/01/06
14/02/06
28/03/06
11/04/06
25/04/06
23/05/06
06/06/06
20/06/06
01/08/06
15/08/06
29/08/06
26/09/06
10/10/06
24/10/06
05/12/06
19/12/06
03/01/06
28/02/06
14/03/06
09/05/06
04/07/06
18/07/06
12/09/06
07/11/06
21/11/06
-0.05% 90.00%
-0.10%
Daily PnL 85.00%
-0.15% Index
Cumulative PnL
-0.20% 80.00%
GMxB Solutions 8
Date

9. Delta Hedging: Impact of Recent Market Movements
HOWEVER, the impact of recent market movements on a 5Y delta hedge of a 5% Roll-Up
Guarantee with daily rebalancing WAS VERY NEGATIVE – realized volatility proved
higher than anticipated leading to significant losses starting August 2007
PnL 2007
0.60% 115.00%
0.40% 110.00%
0.20%
105.00%
0.00%
-> Delta hedging
17/01/07
31/01/07
11/04/07
25/04/07
04/07/07
18/07/07
26/09/07
03/01/07
14/02/07
28/02/07
14/03/07
28/03/07
09/05/07
23/05/07
06/06/07
20/06/07
01/08/07
15/08/07
29/08/07
12/09/07
10/10/07
24/10/07
07/11/07
21/11/07
05/12/07
19/12/07
100.00%
SP500
PnL
-0.20%
strategies were losing
95.00%
-0.40%
money in H2 2007
90.00%
-0.60%
Daily PnL
85.00%
Index
-0.80%
Cumulative PnL
-1.00% 80.00%
Date
PnL 2008
0.10% 105.00%
0.00%
-> Delta hedging
100.00%
8
8
08
08
08
08
16 08
08
08
08
08
08
08
08
08
08
08
08
08
08
08
08
08
08
08
08
/0
/0
1/
1/
1/
1/
1/
2/
2/
2/
2/
2/
2/
1/
1/
1/
1/
1/
1/
1/
1/
2/
2/
2/
2/
2/
1
1
-0.10%
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
/0
strategies have now
15
02
04
06
08
10
12
14
18
20
22
24
26
28
30
01
03
05
07
09
11
13
17
19
21
95.00%
in Q1 2008 already
-0.20%
SP500
PnL
lost almost as much
-0.30%
90.00%
money as in the entire
-0.40%
2007…
Daily PnL 85.00%
-0.50% Index
Cumulative PnL
-0.60% 80.00%
GMxB Solutions 9
Date

10. We are now in high volatility environment…
High Volatility cycle
Low Volatility cycle
35.00% 1600
SP500 3M volatility
1400
30.00% SP500 12M volatility
SP5000 value 1200
25.00%
1000
20.00%
800
15.00%
600
10.00%
400
5.00% 200
0.00% 0
1/1/1990
4/1/1990
7/1/1990
1/1/1991
4/1/1991
7/1/1991
1/1/1992
4/1/1992
7/1/1992
1/1/1993
4/1/1993
7/1/1993
1/1/1994
4/1/1994
7/1/1994
1/1/1995
4/1/1995
7/1/1995
1/1/1996
4/1/1996
7/1/1996
1/1/1997
4/1/1997
7/1/1997
1/1/1998
4/1/1998
7/1/1998
1/1/1999
4/1/1999
7/1/1999
1/1/2000
10/1/1990
10/1/1991
10/1/1995
10/1/1996
10/1/1997
10/1/1992
10/1/1993
10/1/1994
10/1/1998
10/1/1999
Towards a
higher
Volatility
SP500 3M volatility
35.00% 1800
environment?
SP500 12M volatility
1600
30.00% SP5000 value
1400
25.00%
1200
-> Delta hedging
20.00% 1000
strategies are
800
15.00%
now losing
High Volatility 600
10.00%
money
400
cycle with 5.00%
200
declining 0.00% 0
1/3/2000
5/3/2000
9/3/2000
1/3/2001
5/3/2001
9/3/2002
1/3/2003
5/3/2003
9/3/2003
1/3/2004
9/3/2004
1/3/2005
5/3/2005
9/3/2005
1/3/2007
5/3/2007
9/3/2007
1/3/2008
9/3/2001
1/3/2002
5/3/2002
5/3/2004
1/3/2006
5/3/2006
9/3/2006
markets
(unhedged
insurers lost
money) NB: in 1987, the 3 month volatility reached 70% … Low Volatility cycle
when insurers started
delta hedging
GMxB Solutions 10