VIX ETPs, Inter-Relationships between Volatility Markets and Implications for Investors and Traders

Not a Product of Research / Not for Retail Distribution Citi Equities I U.S. Equity Trading Strategy VIX ETPs, Inter-Relationships between Volatility Markets and Implications for Investors and Traders February 26, 213 Spencer Cross Volatility Head Trader

Jan-1 Mar-1 May-1 Jul-1 Sep-1 Nov-1 Jan-11 Mar-11 May-11 Jul-11 Sep-11 Nov-11 Jan-12 Mar-12 VIX Futures: Settlement and Liquidity VIX Futures Settlement The settlement day is 3 days before the SPX options expiration of the following month (usually on a Wednesday). The settlement price is determined from a Special Opening Quotation of VIX on the settlement day (Wednesday) using opening price of S&P 5 options The last trading day of the future is usually on the Tuesday immediately preceding the settlement day. Settlement price can be significantly different from both the last future price and the last VIX spot price To avoid this price volatility in the last days of the VIX cycle, it is preferable to roll position out the week before expiry Liquidity of VIX Futures The majority of open interest and volume traded in VIX futures is in the 1st and 2nd month expiries This is purely an electronic market, while the options are traded in the crowd. VIX Futures Contract Contracts traded / day Front Month 54, Second Month 41, Third/Fourth month 14,5 Fifth thru eighth month 6,8 1, futures are equivalent to $1m S&P 5 vega Differences to the VIX settlement price Volume of first, second and third futures traded daily 5 4 3 VIX Future at the close of the second to last trading day VIX Future at the close of the last trading day VIX at the close of the last trading day 7, 6, Front Second Third 2 5, 1 4, 3, -1-2 2, -3 1, -4 Mar-11 Apr-11 May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11 Dec-11 Jan-12 Feb-12 2 I Citi Equities

VIX Vega VIX Vega Vega Notional of VIX-linked instruments VIX Futures saw a slow start... but with the 8/9 credit crisis, activity grew 8x Millions -4-35 -3-25 -2-15 -1-5 VXX Other Short-term ETNs Reverse Short-Term ETNs Mid Term Reverse ETNs TVIX Mid Term ETNs VIX Futures Jan-9 Jul-9 Jan-1 Jul-1 Jan-11 Jul-11 Jan-12 Jul-12 Millions 4 35 3 25 2 15 1 5 VIX Vega Outstanding Millions 5 45 4 35 3 25 2 15 1 5 VXX TVIX Mid Term ETNs Reverse Short-Term ETNs (RHS) UVXY Other Short-term ETNs VIX Futures Mid Term Reverse ETNs (RHS) Feb-12 Apr-12 Jun-12 Aug-12 Oct-12 Dec-12 Date Millions -3-25 -2-15 -1-5 3 I Citi Equities

Market Share: VIX ETNs vs. VIX Futures and SPX-linked options VIX ETNs impact on the market is strongest at the short-end of the term structure Total Short Term (front two months) VIX ETNs $171mm (7%) VIX ETNs $169mm (18%) VIX Futures $39mm (17%) SPY Options $212mm (9%) SPX Options $1,59mm (67%) VIX Futures $24mm (26%) SPX Options $462mm (49%) SPY Options $66mm (7%) 4 I Citi Equities

Using VIX options / futures to hedge an equity portfolio: How does one size his VIX hedge to an equity portfolio? 16% VIX front month future 1m returns vs. S&P 5 1m returns since 21 y = -3.9824x +.447 12% R 2 =.6389 8% 4% % -4% y = 16.89x 2-3.681x +.84 R 2 =.691-8% -2% -15% -1% -5% % 5% 1% 15% S&P 5 returns Strongly negative correlation between VIX returns and SPX returns is very well-documented and relatively stable over time. 5 I Citi Equities

beta Using VIX options / futures to hedge an equity portfolio: However, magnitude of the relationship is less stable 6m beta typically varies between -.5 and -5 (average ~ -4) Low beta during strong equity rally and High beta during sell-off A $5M notional of VIX 1m call would provide a similar protection as a $2M notional of SPX puts. Hedge ratio is ~25% To hedge $2M notional of SPX with VIX Mar Fut at 17.5, we need only 3k contracts Rolling beta of VIX front month future 1m returns vs. S&P 5 1m returns -1-2 -3 126-day beta 252-day beta Beta is -2, which means.5 million notional of VIX Future is needed to hedge 1 million S&P 5-4 -5-6 Apr-8 Sep-8 Mar-9 Sep-9 Mar-1 Aug-1 Feb-11 Aug-11 Jan-12 Jul-12 Jan-13 Beta is -5, which means.2 million notional of VIX Future is needed to hedge 1 million S&P 5 6 I Citi Equities

Using VIX options / futures to hedge an equity portfolio: What is the equivalent S&P5 vega exposure? 6m beta of VXX vs. S&P 5 at-the-money implied vol varies per maturity For instance, the 6m beta with S&P 5 1-year implied vol varies between 1.1 to 1.75 (average ~1.5) The beta to implied vol tend to be more stable than the beta to S&P 5 returns A $2mm vega exposure on VXX (roughly $notional x delta) would be equivalent to a $3mm vega exposure to S&P 1-year implied vol ($2mm x 1.5). 126D Rolling Beta of daily moves: 1-month (constant maturity) VIX Futures vs S&P 5 atm volatility 2.25 2. 1.75 1.5 1.25 1-month vol 3-months vol 6-months vol 12-months vol Beta is 1.7, which means 1 million notional of 1-month VIX Futures (VXX) is equivalent to a 1.7 million vega exposure to S&P 1Y 5 implied vol 1..75.5.25 Beta is.8, which means that 1 million notional of 1-month VIX Futures (VXX) is equivalent to a.8 million vega exposure to 1-month S&P 5 implied vol. Apr-8 Apr-9 Apr-1 Apr-11 Apr-12 7 I Citi Equities

Vol Spread Analysis: VIX ETN vs VIX Futures vs SPX Options Bid-Ask Spread for VIX ETN, VIX Futures and SPX Options (Jan 1, 213 Feb 26, 213) 2% 18% 16% VXX Bid-Ask Spread (% of mid) Generic 1st Future Bid-Ask Spread (% of mid) SPX Mar Qtr 149 Straddle Bid-Ask Spread (% of mid) 14% 12% 1% 8% 6% 4% 2% Average bid-ask spread.14% for VXX.36% for VIX Futures 11.64% for SPX Options % 2-Jan-13 16-Jan-13 3-Jan-13 13-Feb-13 27-Feb-13 8 I Citi Equities Security Mid Current Spread Avg Spread Std Dev Spread VXX 24.42.1.14%.7% Generic 1st Future 16.23.5.36%.11% SPX Mar 149 Straddle (Screen) 53.7 3.8 11.64% 3.62% SPX Mar 149 Straddle (Floor) 53.75 1.5 - -

Is Playing Roll Down in VIX worse than Shorting SPX Volatility? Var Comment:: The Strategy in red is a short 1m SPX variance swap with constant initial Vega. We adjusted the Vega of the two strategies to have a similar max drawdown. 9 I Citi Equities

VIX Futures: Is all flow one way or are there sellers offsetting? High Borrow Cost on VIX ETNs justifies using calls rather than outright long VIX ETNs have a high borrow cost (~2.5% for VXX and ~8% for UVXY). Outright longs have an opportunity cost equivalent to borrow rate, justifying going long using calls. Implied Rate Mid Ticker Spot EXP = Jan 214 EXP = Jan 215 VXX 22.75-2.25% -2.63% UVXY 1.1-8.69% -6.46% 1 I Citi Equities

Using VIX options instead of VIX futures: Options provide additional convexity 1-month* VIX Futures daily return vs S&P 5 daily return since Sep 211 1-month 2 Call on VIX** daily return vs S&P 5 daily return since Sep 211 5% 4% 3% y = 17.461x2-3.5634x -.4 5% 4% 3% y = 17.461x2-3.5634x -.4 y = 68.84x2-14.23x +.183 2% 2% 1% 1% % % -1% -1% -2% -3% -4% -5% 1-month VIX Futures ( regression) -4% -3% -2% -1% % 1% 2% 3% 4% S&P 5 Daily Return -2% -3% -4% -5% 1-month VIX Futures ( regression) 1-month VIX 2 Call (regression) -4% -3% -2% -1% % 1% 2% 3% 4% S&P 5 Daily Return 1-month* VIX Futures daily return exhibit some degree of convexity vs. S&P 5 daily returns as shown earlier while options on VIX Futures exhibit an even higher degree of convexity. *1-month constant maturity ** 2 Call on the 1-month constant maturity VIX Futures 11 I Citi Equities

Using VIX options instead of VIX futures: Leverage on rich skew through call spreads VIX Mar'13 Implied Vol of Vol 1-month VIX 2 3 Call Spread* daily return vs S&P 5 daily returnsince Sep 211 16 15 14 13 12 11 1 9 8 7 6 15 17.5 2 22.5 25 27.5 3 32.5 Strike 5% y = 17.461x2-3.5634x -.4 4% y = 68.84x2-14.23x +.183 3% y = 27.228x2-11.25x +.169 2% 1% % -1% -2% 1-month VIX Futures ( regression) -3% 1-month VIX 2 Call (regression) -4% 1-month VIX 2-3 Call Spread (regression) -5% -4% -3% -2% -1% % 1% 2% 3% 4% S&P 5 Daily Return VIX skew is upward sloping. Investors can leverage on rich upside skew by buying call spreads instead on calls thus trading out of some convexity while achieving a lower entry cost. * 2 3 Call Spread on the 1-month constant maturity VIX Futures 12 I Citi Equities

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