Efficient VA Hedging Instruments for Target Volatility Portfolios Jon Spiegel
For Institutional Investors Only Not for Retail Distribution Efficient VA Hedging Instruments For Target Volatility Portfolios Jon Spiegel, Director 212-250-6054 EBIG Conference - Chicago November 14, 2016-13:30 to 15:00 hours Equity Structuring Global Investment Solutions
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11/12/2016 9:52:13 AM 2010 DB Blue template Efficient VA Hedging Instruments For Target Volatility Portfolios Agenda 1 Target Volatility Risk Properties 2 Target Volatility Puts vs. Vanillas 3 Other Tactical Hedging Instruments 3
11/12/2016 9:52:13 AM 2010 DB Blue template Target Volatility Risk Properties Introduction Over the past five years, the AUM of VA managed volatility funds has grown to over $200bn 1 Target volatility strategies are likely to exhibit long-term volatilities close to their targets, neutralizing the vega exposure of VA guarantees However instantaneous equity risk scenarios still show significant crash-risk. Hedge with vanillas? (1) Source: DB Equity Derivatives Research 4
11/12/2016 9:52:10 AM 2010 DB Blue template Target Volatility Risk Properties Example: S&P 500 Risk Control Indices 300 250 200 150 100 50 0 SPXT10UT SPXT15UT SPXT Source: Bloomberg Finance L.P. and DB Structuring 5
Target Volatility Risk Properties Realized Volatility (1yr) 5 45% 4 35% 3 25% 2 15% 1 5% SPXT10UT SPXT15UT SPXT SPXT10UT-Avg SPXT15UT-Avg SPXT-Avg Source: Bloomberg Finance L.P. and DB Structuring 6
Target Volatility Risk Properties Realized Skew: Realized Volatility vs. Returns (Semi-annual, Dec 99 Jun 16) 6 SPXT10UT 6m Realized Vol 5 4 3 2 1 SPXT15UT SPXT y = -0.51x + 0.19 y = -0.02x + 0.15 y = -0.11x + 0.10-3 -2-1 1 2 3 6m Return Source: Bloomberg Finance L.P. and DB Structuring 7
Target Volatility Risk Properties Historical SPX Implied Volatility vs. Subsequent Realized (12/31/1999 5/10/2016) 7 6 5 4 SPX 6m ATM Implied Vol SPX 6m 9 Implied Vol Subsequent 6m Realized 3 2 1 Source: Bloomberg Finance L.P., DB Structuring and DB Equity Derivatives Research 8
Target Volatility Risk Properties SPX 6m Implied vs. Subsequent Realized Spread (12/31/1999 5/10/2016) 3 ATM Implied - Realized 2 9 Implied - Realized 1-1 -2-3 -4 Strike Avg Since Dec 99 Avg Since Jan 09 9 5.58% 8.07% 10 1.8 3.75% Source: Bloomberg Finance L.P., DB Structuring and DB Equity Derivatives Research 9
11/12/2016 9:52:17 AM 2010 DB Blue template Target Volatility Puts vs. Vanillas Introduction Intuitively it should be more efficient to hedge liabilities linked to target volatility funds using puts on target volatility indices to avoid overpaying for implied volatility and skew We compare the performance of hypothetical target volatility puts with the performance of comparable listed options Caveats: (1) The target vol index is a systematic proxy for portfolios which generally contain discretionary funds with diverse mandates (2) Target volatility puts are not widely traded, so pricing is hypothetical 10
11/12/2016 9:52:17 AM 2010 DB Blue template Target Volatility Puts vs. Vanillas Comparable Instruments Methodology We compare the PL from buying puts on target volatility indices with the PL from buying comparable vanilla puts, for each trade date Comparing target volatility puts with vanilla equity puts requires careful consideration as the vanilla equity put embedded in a TV put has changing notional and strike over the life of the trade We adjust the vanilla strike and notional to have equivalent intrinsic value on trade date for all equity scenarios ( equal crash protection ) Dynamic Adjustment: Compare TV put to scaled vanilla put adjusted using most recent TV Participation Static Adjustment: Compare TV put to scaled vanilla put using fixed long-term average TV Participation 11
11/12/2016 9:52:17 AM 2010 DB Blue template Target Volatility Puts vs. Vanillas Comparable Instruments Adjustment Vanilla Notional TV Notional TV Participat ion % Vanilla Strike 100 % 1 TV Strike TV Participat % ion % Strike (e.g. 95%) Notional Adjustment Equity Allocation Target Volatility Index Strike Adjustment Cash Allocation (not to scale) 12
11/12/2016 9:54:44 AM 2010 DB Blue template Target Volatility Puts vs. Vanillas Back-test methodology for TV 1 6m 95% Put, Dynamically Adjusted Select Listed Expiration For each trading day, locate SPX listed expiration closest to 6 months Select Scaled Vanilla Strike For selected expiration, locate strike closest to participation-adjusted TV equivalent Example: 7 participation 1-.05/.7 = 92.85% Adjust TV Tenor and Strike Adjust TV tenor and strike slightly to correspond with listed option used for scaled vanilla Price TV and Vanilla Puts 1 TV 6m 95% put BS: 12.5 1 vol, fwd = libor flat 1 TV 12m 9 put BS: 12.5 1 vol, fwd = libor flat Scaled Vanilla Listed mid-market (1) Indicative and hypothetical 13
Target Volatility Puts vs. Vanillas SPXT10UT 6m 95%; Dynamic Adjustment Average Price and Payoff by Trade Date Year 6% 4% Target Vol Price Target Vol Payoff 2% 6% 4% 2% Scaled Vanilla Price Scaled Vanilla Payoff Source: Bloomberg Finance L.P., DB Structuring and DB Equity Derivatives Research 14
Target Volatility Puts vs. Vanillas SPXT10UT 6m 95%; Dynamic Adjustment PL by Trade Date (Jan 00 Oct 16 1 ) 15% 1 5% -5% -1-15% Scaled Vanilla PL Target Vol PL TV - Scaled Vanilla Trade Date (1) Assuming that options unexpired as of Nov 11, 2016 expire OTM Source: Bloomberg Finance L.P., DB Structuring and DB Equity Derivatives Research 15
Target Volatility Puts vs. Vanillas SPXT10UT 6m 95%; Dynamic Adjustment PL by Trade Date (Since 2009 1 ) 5% 4% 3% 2% 1% -1% -2% -3% -4% -5% Scaled Vanilla PL Target Vol PL TV - Scaled Vanilla Trade Date (1) Assuming that options unexpired as of Nov 11, 2016 expire OTM Source: Bloomberg Finance L.P., DB Structuring and DB Equity Derivatives Research 16
Target Volatility Puts vs. Vanillas Target Vol Behavior in Different Sell-Offs 10 5 Jun-07 Sep-07 Dec-07 Mar-08 Jun-08 Sep-08 Dec-08 Mar-09 Jun-09 10 5 Participation (RHS) SPXT10UT SPXT Jun-15 Jul-15 Aug-15 Sep-15 Oct-15 Nov-15 Dec-15 Jan-16 Feb-16 Participation (RHS) SPXT10UT SPXT 10 8 6 4 2 10 8 6 4 2 Source: DB Structuring, Bloomberg Source: Bloomberg Finance L.P. and DB Structuring 17
Target Volatility Puts vs. Vanillas SPXT10UT 6m 95%; Dynamic Adjustment Target Vol Put vs. Scaled Vanilla PL, Average by Trade Year 5% -5% 2 15% 1 5% -5% -1-15% -2-0.4% 0.7% -0.8% 0.3% 0.9% 0.7% 0.7% 0.3% TV - Scaled Vanilla PL SPX Return SPXT10UT Return -3.6% 0. 0.6% 1. 0.8% 0.7% 0.9% 0.8% 0.6% Since 2000 Since 2009 0.25% (0.5 p.a.) 0.67% (1.34% p.a.) Source: Bloomberg Finance L.P., DB Structuring and DB Equity Derivatives Research 18
Target Volatility Puts vs. Vanillas SPXT10UT 12m 9; Dynamic Adjustment Target Vol Put vs. Scaled Vanilla PL, Average by Trade Year 5% -5% 2-0.3% 0.5% -0.5% 1.5% 0.5% 1.2% 1.1% -0.8% TV - Scaled Vanilla PL -3.8% 0.1% 1.1% 1. 1.6% 1.5% 1.7% Since 2000 0.47% p.a. Since 2009 1.15% p.a. 1. 15% 1 5% -5% -1 SPX Return -15% SPXT10UT Return -2 Source: Bloomberg Finance L.P., DB Structuring and DB Equity Derivatives Research 19
Target Volatility Puts vs. Vanillas Comparable Instruments Methodology We assume that the liability s equity exposure matches the proxy index. But comparing to the vanilla, does a daily dynamic participation adjustment fairly capture equal crash risk? Hedging with vanillas, as participation increases (decreases) would need to buy (sell) puts to hedge crash risk of target vol liability. IE, buy when vol is falling, sell when vol is rising In another comparison we adjust each vanilla put strike and notional using the same long-term participation of 67% 16 14 12 10 8 6 4 2 SPXT10UT Participation Average = 67% Source: Bloomberg Finance L.P. and DB Structuring 20
Target Volatility Puts vs. Vanillas Back-tested PL Comparison 6m 95% Static (67% Participation) Target Vol Put vs. Scaled Vanilla PL, Average by Trade Year 5. 0. -5. -10. 2 15% -0.7% -0.1% -0.4% 0.8% 0.2% -0.1% -0.1% -0.3% TV - Scaled Vanilla PL -5.3% 2.4% 1.3% 2.1% 0.7% 1.1% 0.4% 0. -0.1% Since 2000 0.14% (0.28% p.a.) Since 2010 1. (2. p.a.) 1 5% -5% -1-15% -2 SPX Return SPXT10UT Return Source: Bloomberg Finance L.P., DB Structuring and DB Equity Derivatives Research 21
Target Volatility Puts vs. Vanillas Dynamic vs. Static Hedging with Vanillas 8% Participation (RHS) Scaled Vanilla PL, Dynamic Scaled Vanilla PL, Static 6% 12 10 4% 2% Dynamic buys less, puts expire ITM Dynamic buys less, puts expire OTM 8 6-2% -4% -6% Dynamic buys more, puts expire OTM 4 2 Source: Bloomberg Finance L.P., DB Structuring and DB Equity Derivatives Research 22
11/12/2016 9:52:18 AM 2010 DB Blue template Other Tactical Hedging Instruments 1x2 Put Spread Finance tail risk protection by selling ATM gamma Conditional Up- Variance Swap Monetize skew to buy cheap vega, plus 1- day gap protection Variance KO Put Monetize vol and skew with limited risk 23
11/12/2016 9:52:20 AM 2010 DB Blue template Delta-Hedged 1x2 Put Spread Using vanilla options, VA hedgers can set up a position that provides: Positive carry Long skew, Long convexity, Deep tail risk protection The strategy entails: Selling an ATM or near-atm put Buying 2 OTM puts Delta hedging In return for the above benefits, seller is exposed to high implied or realized volatility without a significant selloff in spot Applicability: Target vol liabilities may incur less daily delta hedging than traditional VA and would be better positioned to sell local gamma 24
Delta-Hedged 1x2 Put Spread SPX 6m, Delta-based strikes Indicative PL Back-test: Sell $1/6 notional every month 14% 12% 1 8% 6% 50d/5d 4% 50d/10d 2% SPX (RHS) -2% 2,500 2,000 1,500 1,000 500 0 Source: Bloomberg Finance L.P. and DB Structuring 25
Delta-Hedged 1x2 Put Spread SPX 6m, Delta-based strikes Strikes Back-test 2500 2000 1500 SPX 50d Avg Strike 5d Avg Strike 10d Avg Strike 1000 500 0 Source: Bloomberg Finance L.P. and DB Structuring 26
Delta-Hedged 1x2 Put Spread SPX 6m, Delta-based strikes Gamma Back-test 0.6% 0.4% 0.2% 0. -0.2% -0.4% -0.6% -0.8% -1. 50d/5d 50d/10d SPX (RHS) 2,500 2,000 1,500 1,000 500 0 Source: Bloomberg Finance L.P. and DB Structuring 27
Delta-Hedged 1x2 Put Spread SPX 6m, Delta-based strikes Vega Back-test 0.25% 0.2 0.15% 0.1 0.05% 0.0-0.05% -0.1-0.15% -0.2 50d/5d 50d/10d SPX (RHS) 2,500 2,000 1,500 1,000 500 0 Source: Bloomberg Finance L.P. and DB Structuring 28
11/12/2016 9:52:20 AM 2010 DB Blue template Conditional Up-Variance Swap Conditional Up-Variance Swaps only accrue variance if the spot price is above a barrier. Applicability: Use ITM (downside) barrier; Provide 1-day gap protection as barrier is observed t-1; Best for portfolios requiring some long vega exposure Payoff Notional OccurenceR atio (UpVarStri ke - UpVarReali zed) UpVarReali zed 252 t N t 1 P ln P t N t 1 ind t t -1 ( P 2 t 1 ind ) ( P t 1 ) OccurenceR atio t N t 1 ind N ( P t ) 1 ind(p t-1 ) equals 0 if spot at t 1 is above barrier, otherwise equal to 1 N is expected number of trading days from Trade to Expiration 29
Conditional Up-Variance Swap Given steep skew, up-variance strikes are lower than regular variance 7 6 5 4 3 2 1 Average Spread = 3.8 1 Indicative SPX 6m Up-Var Strike Indicative SPX 6m Var Strike Barrier = 25% delta put strike (RHS) 94% 92% 9 88% 86% 84% 82% 8 78% 76% (1) Hypothetical back-test Source: DB Structuring Trade Date 30
Conditional Up-Variance Swap Realized Conditional Variance and Occurrence Ratio 9 8 7 6 5 4 3 2 1 Realized 6m Var Realized 6m Up-Var Occurrence Ratio (RHS) 12 10 8 6 4 2 Source: Bloomberg Finance, LP and DB Structuring Trade Date 31
11/12/2016 10:00:42 AM 2010 DB Blue template Conditional Up-Variance Swap Except for Trades done in 2008, Up-Var generally would have outperformed regular Var 7 6 5 4 3 2 1-1 -2 6m Var PL 6m Up-Var PL (Equal Var Notional) Average Spread =.44 1 vols Since 2009 = 2.95 1 vols (1) Hypothetical back-test Source: Bloomberg Finance, LP and DB Structuring Trade Date 32
Conditional Up-Variance Swap Vega scenarios (6m, 92% barrier) 1.20 1.00 Regular Var Vega Upvar Vega 0.80 0.60 0.40 0.20 0.00 Source: 4 6 8 10 12 14 16 18 Bloomberg Finance, LP and DB Structuring Spot % of Initial 33
11/12/2016 9:52:32 AM 2010 DB Blue template Variance Knock-Out Put A Variance Knock-Out Put pays zero if the realized variance surpasses a budget during the life of the trade. Otherwise it pays the same as a vanilla. Applicability: Typically traded by hedge funds. Structure is short-vega and skew, with limited liability. Target volatility hedgers may be positioned to sell vega and skew opportunistically Example: Underlying: Tenor: SPX 6m Realized Variance t t ln S PX S PX i 1 i 1 i 2 Strike: ATM Spot Variance Budget: (Implied Variance)^2 * 0.5 Implied Variance: 0.19 Indicative Cost: 1.3% (72% discount to Vanilla) Vanilla 6m ATM Put: 4.6% 34
11/12/2016 9:52:32 AM 2010 DB Blue template Variance Knock-Out Put Implied skew and convexity premia cause the VKO to price the survival rate lower than statistically observed Most negative SPX Returns Avg SPX Return Survival Rate Avg VKO Px/ Vanilla Px 1 to 5% -36.27% 0. 28.5% 5% to 1-15.89% 22.9% 28.4% 1 to 15% -7.89% 54.3% 28.4% 15% to 2-4.42% 65.7% 28.8% 2 to 25% -2.35% 46.2% 29.1% 25% to 3-0.19% 81.9% 29.5% 3 to 35% 1.78% 89.5% 35.9% 35% to 4 2.93% 94.3% 33.2% Quantile Analysis: SPX 6m ATM VKO; barrier = 6m SPX implied variance on trade date Trade Dates Jan 08 to Apr 16 (1) Hypothetically back-tested Source: Bloomberg Finance L.P and DB Structuring 35
Variance Knock-Out Put Vega Evolution: SPX 6m ATM VKO (19.4% budget) Back-Tested from 10/30/2015 3.5% 3. 2.5% 2. 1.5% 1. 0.5% 0. Oct-15 Nov-15 Dec-15 Jan-16 Feb-16 Mar-16 Source: VKO Price SPX (Right) 0.2% 0.1% 0. -0.1% -0.2% -0.3% -0.4% -0.5% VKO Vega Vol MTM of Varswap (Right) -0.6% Oct-15 Nov-15 Dec-15 Jan-16 Feb-16 Mar-16 Bloomberg Finance L.P and DB Structuring 2150 2100 2050 2000 1950 1900 1850 1800 1750 1700 1650 23% 21% 19% 17% 15% 36
11/12/2016 9:52:33 AM 2010 DB Blue template Final Thoughts Target volatility strategies exhibit less skew as well as more predictable volatility than pure equity. Hedging strategies should benefit from both of these characteristics. Buying puts on TV Indices may provide crash protection with less risk premium cost. Light Exotics such as Conditional Variance and VKO s can monetize expensive skew. Ongoing work: -- Assessing tracking error of VA Portfolios vs. TV Indices. Designing custom benchmarks where appropriate -- Price discovery for Target Volatility Puts -- Portfolio diversification from trading combinations of these instruments 37