Investment Symposium March 2010 F1: What Are We Hedging Anyway? GAAP, Stat, or Economics? Ross Bowen James Lloyd Moderator Jay Musselman
F1 What Are We Hedging Anyway? GAAP, Stat, or Economic? Ross Bowen, Allianz Life March 22, 2010 Hedging VA Risk Most hedging programs started out hedging GAAP risk Implementation of C3P2 and AG43 have created a disconnect with GAAP or pure economics FAS 157 disconnected GAAP and Economic Multiple constraints and objectives create the need for an interdisciplinary team to approach the problem 1
Economic Economic measures look for sensitivities to the value of promises made Define the value Present value of claims less fees Risk neutral framework Key sensitivities Change in market levels Change in rates Change in volatilities Need a robust scenario generator Match observable prices and greeks GAAP Most similar to economic what are the differences? Treatment of fees Some companies set the value of the embedded derivative to zero at issue apply a factor to the fees so PV = 0 Not all VAGLBs are FAS 133 SOP 03-1 applied to GMIB GMAB clearly FAS 133 GMWB may be a hybrid Gain on hedges impacts k factor 2
GAAP FAS 157 FAS 157 Own Credit Risk Objections value of promise declines as probability of paying declines Release reserves when downgraded? How to determine own credit risk spread? CDS market offers view into credit risk Large writers may have active CDS market To hedge or not to hedge? Sell CDS on self? Sell CDS on similar writers? What is the goal of hedging? Statutory Moving from a factor based world to a Principles Based world AG33 Base Contract AG34 - DB AG39 Living Benefits, accumulation of fees There was a need to modernize AG39 C3P2 came first, then AG43 / VACARVM Real world stochastic Model hedges in a stochastic on stochastic framework Standard scenario comparable values between companies 3
AG43 Hedge Modeling - Stochastic Stochastic scenarios CTE70 worst 30% Possibility that hedges will cost rather than benefit Existing hedges may be run off If CDHS in place, may reflect hedging strategy CTE Reported = E * CTE Best Efforts (1-E) * CTE Adjusted E < 70% or < 30% if hedges not directly modeled Basis risk, transaction risk, hedging mismatch tolerance C3P2 Hedge Efficiency Stochastic scenarios CTE90 worst 10% - more likely that hedges will benefit Existing hedges may be run off If CDHS in place, may reflect hedging strategy CTE Reported = TAR Best Efforts E * (TAR adj TAR best efforts) Adjusted E >5% Basis risk, transaction risk, hedging mismatch tolerance 4
Value of Hedges AG43 SS PV of pre-tax cashflows at the one-year CMT rate less statement value Must be held to hedge these contracts in compliance with state laws Assume hedges are liquidated in one year or exercised if mature prior Assume returns underlying SS, Black Scholes pricing, rate of fiveyear CMT, and solved-for implied volatility Evaluation of Hedge Instruments Review the differences between stat, GAAP, and economic Evaluate hedge performance in the various regimes Choices Futures Puts Swaps Swaptions Calls 5
Evaluation of Hedge Instruments Futures Linear in the market Can be written on different indices Very effective on standard scenario 13.5% / 20% of notional Unlimited losses possible in up market Evaluation of Hedge Instruments Futures Futures Performance in AG43 50,000,000 40,000,000 30,000,000 Gain / Loss 20,000,000 10,000,000 - (10,000,000) (20,000,000) (30,000,000) 000 000) (40,000,000) 700 800 900 1000 1100 1200 1300 mkt gain Hedge Credit Capital Impact S&P Level 6
Evaluation of Hedge Instruments Puts Provide delta protection in Statutory world Vega and rho protection in Economic world Can be very expensive Out of the money attractive (crash protection) Sell a deeper OTM to offset cost Can also fund by selling upside OTM call Sell deeper OTM call to limit losses Puts Zero Cost Collar Economic payoff Payoff profile 300 200 100 0 400 500 600 700 800 900 1000 1100 1200 1300 1400-100 -200-300 7
Zero Cost Collar - Impact Change in value of options as time passes and market levels change Hedge Value 600 700 800 900 1000 1100 1200 1300 10.0 9.0 8.0 7.0 6.0 5.0 4.0 30 3.0 2.0 1.0 0.0 $millions Hedge Value S&P Level Zero Cost Collar - Impact Additional value of hedge credit under AG43 standard scenario Hedge Value plus Hedge Credit 14.0 12.0 10.0 8.0 6.0 4.0 $millions Hedge Value Value After Credit 20 2.0 600 700 800 900 1000 1100 1200 1300 0.0 S&P Level 8
Principle 5 The use of risk management strategies (e.g. hedging) that serve solely to reduce the calculated TAR are inconsistent with these principles. The use of assumptions and risk management strategies should be appropriate to the business and not merely constructed to exploit foreknowledge of the components of the required methodology. Summary Economic, stat, GAAP All behavior differently under market shocks Interdisciplinary project Need input from many financial areas 9
What are we Hedging GAAP STAT Economics? Société Générale Global Markets Cross-Asset Solutions James Lloyd FOR QUALIFIED INSTITUTIONAL BUYER ONLY June 2009 sg-structuredproducts.comstructuredproducts com Equity Derivatives House of the Year Important Information This material is confidential and is provided for information purposes only. There is no assurance that a transaction will be entered into on any indicative terms. SG Americas Securities, LLC ( SGAS ) believes the information in this document is reliable but makes no representation or warranty as to whether the information is current, accurate or complete. SGAS is under no obligation to update, modify or amend this communication or to otherwise notify you that any matter contained herein has changed or subsequently become inaccurate. SGAS and its affiliates expressly disclaim all responsibility for any use of or reliance upon this document. This document is provided solely for informational purposes and may not be construed as an offer to buy or sell, or a solicitation of an offer to buy or sell, any financial instrument or to engage in any particular trading strategy or as an official confirmation of terms. Investors must make their own investment decisions using their own independent advisors while considering their own financial situation and investment objectives. SGAS and its affiliates do not act as a financial adviser or as a fiduciary in respect of any transaction unless such entity expressly agrees so in writing. This document may not be relied upon as investment, accounting, legal, regulatory or tax advice or an investment recommendation. You should refer to the offering document relating to the relevant financial instrument which includes important information, including related risk factors. Financial instruments of the type described herein may involve a high degree of risk and their value may be highly volatile. Such risks include, without limitation, risk of adverse or unanticipated market developments, risk of counterparty or issuer default, risk of adverse events involving any underlying reference obligation or entity and risk of illiquidity. In some financial instruments, counterparties may lose their entire investment or incur an unlimited loss. This brief statement does not disclose all the risks and other significant aspects in connection with transactions of the type described in the materials. You are urged to consider carefully whether any products discussed herein are appropriate for you or any of your clients given your or their objectives, experience, financial and operational resources and other relevant circumstances. This document may not be reproduced, distributed or published by any person for any person without the prior written consent of SGAS. [This document is intended d for use only with Qualified Purchasers, assuch term is defined d in the Investment Company Act of 1940, as amended. Use of this document by any other party is prohibited.] 2009 Société Générale ( SG ), SGAS and their affiliates. SG CIB is the Corporate and Investment Banking arm of SG. Certain services described herein are provided by SGAS, a US registered broker-dealer, member of the NYSE, FINRA and SIPC, and a wholly owned subsidiary of SG. Services provided outside the US may be provided by affiliates of SGAS. 2 1
VA Traditional Hedging Methodologies Description Benefits Delta Hedging Short futures or TRS, adjusted periodically No purchase of implied volatility Limitations Limitations Significant risks retained 3- Greek Dynamic Hedging Hedge interest rate exposure with futures, rate swaps and swaptions Purchase 3-15 year put options, Variance Swaps on major indices to hedge vega exposure Advanced Dynamic Hedging Use of additional derivatives instruments such as lookback, options on basket, hybrid options, Dividend Swap Structured/Static Hedge Customized OTC derivative that fully hedges capital markets exposure Possibility to fully incorporate Insurer actuarial assumption More economic in medium/low volatility environment Allows to mirror MtM movements of liabilities Hedge portfolio of vanilla derivatives can be efficiently rebalanced If listed option used, no counterparty risks Cross Greeks Sensitivity, convexity is hedged Better hedge extreme event Tailored to include guarantee specificities and actuarial assumptions Possibility to do very long term hedge Hedge of all the liabilities under 1 transaction. No infrastructure needed Hedge Volatility has large P&L Impact Path Dependent P&L Infrastructure requirements to compute risk, trade and rebalance Requires a very good communication to investor, analyst and ratings community Model Risk Requires advanced modeling techniques Smaller liquidity, transactions costs Model Risk Calibration of initial modeling required Big Counterparty Risk Actuarial mismatch. Liquidity, Transactions costs Might allow for better Accounting, Capital,.. treatment Reinsurance Full traditional reinsurance Fully hedge Cost and availability 3 Delta Hedging Case Study Objective: attempt to replicate a portfolio of Mutual Funds (equity, bonds and balanced) with two replication baskets: A basket comprised by 5 indices (EAFA, SPX, NDX, RTY, LBUSTRRU) A basket comprised by 11 liquid indices (9 equity and 2 bond indices) plus a basket of CDS Academic Research: Semi-Static hedging with options in jumpy markets and stochastic volatility is > 2.5 X more effective than dynamic with underlying (Appendix 1) Graph 1.1. Illustration of tracking error reduction with different replication vehicles 120% 100% 80% 60% 40% 20% Basket of Mutual Funds Basket comprised by 11 indices + Basket of CDS Basket comprised by 5 indices Back-test Methodology Quarterly adjustments Results a) R 2 = 74% Cost = 40 bps p.a. b) R 2 = 87% Cost = 90 bps p.a. *See appendix 0% Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 Apr-09 Source: SG Analytics. See Appendix for details on the basket components. 4 2
2006: Profitable Year for Dynamic Hedging Strategies 2006: Delta hedging strategies benefited from homogenous conditions across worldwide markets (bullish market, benign volatility and stable interest rates) US exposure in 2006 Diversified Exposure 0.35% 0.30% Cumulative P&L generated by a Delta Hedging Strategy of a GMAB 100% S&P 500, Volatility 15%, Interest Rate 3.5% Cumulative P&L Delta Hedge S&P 500 (basis 100% on Jan 2006) 115% 110% 0.05% 0.04% Cumulative P&L generated by a Delta Hedging Strategy of a GMAB 50% MSCI World, 50% JP Morgan Global Aggregate Bond Index, Volatility 8%, Interest Rate 3.5% Cumulative P&L Delta Hedge Underlying Basket (Basis 100 on Jan 2006) 115% 110% 0.25% 0.20% 0.15% 0.10% 0.05% 0.00% Jan-06 Mar-06 May-06 Jul-06 Sep-06 Nov-06 105% 100% 95% 90% 85% 80% 105% 0.03% 100% 0.02% 02% 95% 0.01% 90% 0.00% 85% Jan-06 Mar-06 May-06 Jul-06 Sep-06 Nov-06 Jan-07-0.01% 80% 5 2007: Subprime Crisis Decouple the US from the Rest of the World 2007: early signs of the subprime crisis started affecting the US market, leading to negative profitability of US hedging strategies. Other markets showed resilience, dynamic hedges profitability remained positive US exposure in 2007 Diversified Exposure in 2007 Cumulative P&L generated by a Delta Hedging Strategy of a GMAB 100% S&P 500, Volatility 15%, Interest Rate 3.5% Cumulative P&L generated by a Delta Hedging Strategy of a GMAB 50% MSCI World, 50% JP Morgan Global Aggregate Bond Index, Volatility 8%, Interest Rate 3.5% 0.60% 0.50% 0.40% 0.30% 0.20% 0.10% Cumulative P&L Delta Hedge S&P 500 (basis 100% on Jan 2006) Subprime Decrease of P&L in the US 0.00% Jan-07 Mar-07 May-07 Jul-07 Sep-07 Nov-07 Jan-08 130% 125% 120% 115% 110% 105% 100% 95% 90% 0.08% 130% 0.07% Cumulative P&L Delta Hedge Underlying Basket (Basis 100 on Jan 2006) 125% 0.06% 120% 0.05% 115% 0.04% 110% 0.03% 105% 0.02% 100% 0.01% 95% 0.00% 90% Jan-07 Mar-07 May-07 Jul-07 Sep-07 Nov-07 Jan-08 6 3
2008: September crack 2008: Crisis went global hitting hedging strategies across the world Gamma losses 1.00% US exposure 2008 Cumulative P&L generated by a Delta Hedging Strategy of a GMAB 100% S&P 500, Volatility 15%, Interest Rate 3.5% Cumulative P&L Delta Hedge S&P 500 (Basis 100 on Jan 2006) 0.20% 130% Diversified Exposure 2008 Cumulative P&L generated by a Delta Hedging Strategy of a GMAB 50% MSCI World, 50% JP Morgan Global Aggregate Bond Index, Volatility 8%, Interest Rate 3.5% Cumulative P&L Delta Hedge Underlying Basket (Basis 100 on Jan 2006) 130% 0.00% -1.00% -2.00% 0.00% 120% 110% -0.20% 100% -0.40% 120% 110% 100% -3.00% 90% -0.60% 90% -4.00% 80% -0.80% 80% -5.00% 70% -1.00% 70% -6.00% 60% Jan-08 Mar-08 May-08 Jul-08 Sep-08 Nov-08 Jan-09-1.20% 60% Jan-08 Mar-08 May-08 Jul-08 Sep-08 Nov-08 Jan-09 7 2009 10 Recovery Performance Attribution Delta Hedge on Close through March From <4.8%> at YE 2008 to MIN <35%> Primarily reflected in rates negative basis <.80%> and Equity interday StDev = 0.42 and Equity intraday StDev = 1.67 Different Hedgers experienced different results PERFORMANCE ATTRIBUTION FOR 40% EQUITY DROP AND 50BP CURVE FALL LIABILITIES FUTURES START $ - $ - CH EQ $ (374,494) $ 125,170 CH RATES $ (934,447) $ 333,786 Performance Attribution Delta Hedge from April 2009 March 2010 PERFORMANCE ATTRIBUTION FOR 60% EQUITY RALLY AND 50BP CURVE FALL LIABILITIES FUTURES START $ - $ - CH EQ $ (9,362) $ 14,044 CH RATES $ (23,361) $ 8,345 20.00% 10.00% 0.00% -10.00% -20.00% -30.00% US exposure 2009 Q110 Cumulative P&L generated by a Delta Hedging Strategy of a GMAB 100% S&P 500, Volatility 15%, Interest Rate 3.5% 120.00% Cumulative P & L Delta Hedge S&P 500 Index (100 on Jan 2006) 100.00% 80.00% 60.00% 40.00% 20.00% -40.00% Jan-09 Apr-09 Jul-09 Oct-09 Jan-10 0.00% 8 4
Strategies seen in the Market with & without Rho hedges That Don t Destroy Capital for Inforce Business Variance Swap or option on VS Timer Puts Volatility budget Capital Puts variance based premia Hybrids selling Vega, buying delta, buying floors Where Rates were unhedged for accounting or under-hedged (STAT vs. economic) Hybrids Inverse Floaters non-cdhs RSAT non-cdhs That address the problem of Cross-Greeks effects Leveraged Puts Hybrids That address Tracking Error problems for Inforce Blocks Factor models CDS s included in tracking basket for balanced funds 9 3-Greek Dynamic Hedging Long Term Vega Risk Hedging Instruments Long Term ATM Puts Gamma: At the Strike Behaviors such as withdrawal and reset impact the strikes and create a complex Vega exposure relative to the spot price Still bought by most insurers Vs. Variance Swaps Gamma: Constant along the strikes (Non Fixed Strike) Hedge strip for variance swap weights downside strikes to maintain constant Vega (1/k 2 ) Constant Vega profile offers different risk profile to fixed strike options Offer attractive ti case due to their constant Vega profile relative to spot and in many cases better liquidity. 10 5
Long Term Vega Risk Case Study Policyholders have struck their rider at different time/spot and with different notional Actuarial assumptions tend to accentuate and flatten the distribution of Vega over all strikes Graph 1.2. Illustration of Vega distribution in a Variance Swap vs. Put vs. VA Rider 140% 120% 100% VEGA (% of Vega ATM) 80% 60% 40% 20% 0% 50% 65% 80% 95% 110% 125% 140% 155% 170% 185% 200% 215% 230% Strikes 10-Year Poly. (Put Put on SPX) on SPX Poly. 10-Year (Var Variance SWAP) Swap Poly. VA Rider (VA Rider) on SPX Source: SG Calculations 11 Advanced Dynamic Hedging Equity- Interest Rate Correlation Risk VA guarantee writers are short equity-interest rate correlation (GMWB for life and GMIB). Graph 3.3 Rolling Correlation between SPX Index and 10 Year US Swap Rate 0.8 5 Year 1 Year 0.6 0.4 0.2 0-0.2-0.4-0.6-0.8 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05 Jan-07 Jan-09 Source: SG Calculations as of October 9, 2009 12 6
3-Greek Dynamic Hedging Rho Risk Hedging Instruments OTCs FRA Swaps Swaptions, Caps, Floors Vs. Listed Zero Coupon Bond Futures Graph 2.1. 10 Year Swap Rate vs 10 Year Treasury Rate 12 USSW10 10 Yr Treasury Spread 1.6 10 1.4 1.2 8 1 6 0.8 4 0.6 0.4 2 0.2 0 Sep-90 Sep-93 Sep-96 Sep-99 Sep-02 Sep-05 Sep-08 Source: Bloomberg as of October 9, 2009. 0 13 Correlation Risk Case Study: Correlation Miscalculation Impact Show the impact in the P&L distribution of a miscalculation between the correlation hedged and realized correlation on a put on a basket of two Underlyings. Put on a basket of 2 Underlyings with: 1. Vol at 20 2. Vol at 25 Hedges in Place: Vega, Rho and Delta hedged. Correlation Hedge Miscalculation Correlation Hedged = 70 Realized Correlation = 82 Option price difference (with correlation at 82 and correlation at 70) = 0.59% Graph 3.2. P&L Distribution 3.50% 3.00% 2.50% Distribution 2.00% 1.50% 1.00% 0.50% 0.00% -3-2.8-2.5-2.3-2 -1.8-1.6-1.3-1.1-0.8-0.6-0.4-0.1 0.1 0.3 0.6 0.8 Source: SG Analytics 14 7
Analysis - C3P2 vs. Real World Stochastic scenarios for C3P2 use volatility parameters (about 16% for Large Caps) which are much lower than the implied volatility (about 28.5% SPX), and drift parameters (about 8% Large Caps) which are much higher the 10Y Swap Rate (about 3.95%). Discount rates are correlated to market ( 10Y Treasury rate +0.50%) As a consequences the sensitivity to market level l and Interest t Rate is different the one you find using market parameters. Risk Neutral Interest rate sensitivity - Rho Interest rate sensitivity of the liability is smaller under C3P2 framework than in real world. Consequently, a company willing to hedge its economic risks will suffer from inefficiency For a block 20% ITM: Rho under C3P2-0.31% per 10 bps move of the curve Rho under Real world parameters -0.63% per 10 bps move of the curve A block properly hedge with IR swap, will suffer if IR goes up. The loss on the hedge will be twice the gain on the C3P2 amount. C3P2 Market Delta Rho Delta Rho 120% 9% ( 0.59) 3.37% ( 0.18) 100% -8% ( 0.58) -37.31% ( 0.21) 80% -27% ( 0.63) -57.63% ( 0.31) 60% -35% ( 0.76) -52.02% ( 0.44) 15 Solution Cell Based Hedge Insurance Liabilities are modeled By cells (representing a group of individual with similar characteristics) Assuming statistical behavior based on mortality table and lapse functions, With the Account value of each cell being represented by a proxy index Cell Based Hedges are long term hedges which perfectly match liability model With respect to reserves and capital: The Hedge will be considered das an Approved Hedge: Consequently, the hedge would stabilize the CTE90 value and SSA. This would lock the difference of price of liabilities using the market parameters and the real world parameters and may have an adverse impact when benefits are ITM If classified as approved hedge, then 100% VACARVM effectiveness for reserve computation (less tracking error) If classified as approved hedge, cashflows are incorporated and 100% of the hedge cashflow will be taken into account when computing capital 16 8
New Hybrids Hybrid option appropriate for GMIB hedging PAYOFF 1: MAX (Strike - Leverage * USSW10 spot - SPX Yield, 0.0) where leverage is a fixed value which determines your rate sensitivity PAYOFF 2: Hybrid swaption with a swaption strike which depends on Equity. Both of them have the same background. The put allows the hedger to choose the notional of the cashflows to pay and the rate part, as multiplier, takes part of the rate sensitivity - due to the discount of all the cashflows. The two structures are made for two different purposes with different convexities for each. Hybrid option appropriate for GMWB hedging PAYOFF 3: leverage on rate * put. [Payoff is: MAX( Strike - SPX Yield,0.0) * Leverage] where leverage is for example: 0 if USSW10 is above 5% 1 if USSW10 is below 3%a linear interpolation, Otherwise, formula is: [1 - (USSW10-3%)/2%] This is a medium term product - created to buy correlation. It allows a hedger to buy a significant amount of sensitivity to correlation plus get access to some cross Greeks. However, it does not match maturity of the liabilities. It does not provide a good Equity hedge or Interest rate hedge. It allows the hedger to mainly realize P&L when correlation increases. PAYOFF4: Put * Discount factor. Payoff is: [MAX(Strike - SPX Yield,0.0) * 1/(1+USSW10)^5] This last product should be viewed more from a cash flow perspective. It's intended to hedge the cashflows - not the Greeks sensitivities (IR equity correlation sensitivity is small). Maturity is a good feature because the hedger buys some equity & interest rate volatility and avoids buying correlation, which, today, is may be viewed as expensive. It may represent a significant portion of any hedging strategy. 17 Conclusion Hedge Economic Liabilities Uncertainty and Recovery combine to tilt the tables in favor of 100% hedge With Capital and Letters of Credit at a premium Variance-based fees minimize the increase of reserves customarily caused by vega hedging RBC ratios have dropped from an average of 380 in 2007 to 285 today (even after $1.2TR) Cost of capital in recent equity and debt offers have risen from 8% to as much as 16% today AG43 has pitched some insurers into SSA sensitivity Hedges or reinsurance now has to cover both tails Rates Down : Equity Down Greatest Reserve Hit Rates up (lapse up) : Equity UP Greatest Lapse Hit Over-hedging/Gamma hedging AG43 opens up the opportunity to treat Reinsurance as Approved Hedge To be included in liability simulations To be included in SSA as an asset that is liquidated down 13.5% Dynamic Hedging is punished under AG43 18 9
Appendix 1 Coleman, Kim, Patron, Robustly Hedging Variable Annuities with Guarantees Under Jump and Volatility Risks, 2004 19 10