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Free Writing Prospectus Filed pursuant to Rule 433 Registration Statement No. 333-184193 Dated: November 6, 2012 ProVol([TM]) A Tactical Strategy for Implied Volatility October 31, 2012 |
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Context -- Systematic volatility strategies can underperform or carry significant risk -- Long volatility positions can be expensive over the long term -- carry costs may offset gains (see performance of SandP Short-Term VIX Futures Index(1) below) -- Short volatility positions can suffer sharp drawdowns, potentially eliminating accumulated gains (see performance of DB ImpAct(2) below) -- Entry and exit points are key, but getting those correct is very difficult [GRAPHIC OMITTED] (1) The SandP Short-Term VIX Futures Index (the underlying index for VXX) aims to maintain a constant 1-month maturity exposure to VIX futures by rolling equal fractional amounts from the front month VIX future to the next month VIX future daily (2) DB ImpAct is a systematic short-volatility strategy that sells rolling one-month notional variance swaps on the monthly option expiry dates Source: Deutsche Bank, Bloomberg Finance, L.P., 2012 2 |
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Volatility Allocation: Challenges -- Volatility allocation involves considerable challenges -- Which indicators of future volatility are meaningful? -- Implied volatility, realized volatility, term structure, skew? -- Many indicators are themselves highly volatile -- For instance, the annualized daily volatility of the VIX Index (1-month implied volatility) is frequently over 100 -- Trading volatility products is costly -- Not all markets are liquid, particularly at longer maturities -- Bid-offer spreads can be large -- Carry costs are frequently high Source: Deutsche Bank, Bloomberg Finance, L.P., 2012 Page 3 |
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Volatility Allocation: Solutions -- Deutsche Bank has done substantial work examining a variety of volatility indicators, products and allocation methods -- Implied versus realized vol -- Shorter versus longer dated vol -- Variance versus VIX-based products -- Daily, weekly or monthly allocation -- Deutsche Bank's ProVol([TM]) integrates solutions to these challenges -- Meaningful indicators are combined to offset or reinforce each other -- Allocation to volatility is calculated daily, but is recursive (the starting point is the prior day's allocation), managing trading cost -- Weak signals result in no allocation, reducing cost and risk Page 4 |
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Building ProVol([TM]) -- ProVol goes long or short implied volatility based on a signal -- Underlying investment is the Deutsche Bank Short-Term VIX Futures Index, which aims to hold a 1-month constant maturity position in VIX futures through a weighted position in first and second month futures -- The ProVol Signal is built upon three fundamental volatility indicators -- Volatility "Regime" -- Deutsche Bank's Volatility Regime Model, which aims to capture momentum in realized volatility, is the principal indicator adopted -- Level of Volatility -- The level of implied volatility complements the Regime indicator by aiming to identify suitable entry and exit points -- Volatility Term Structure -- Volatility term structure steepness, a measure of the cost of carry, isolates the potential cost or benefit of holding a long or short volatility position Page 5 |
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Volatility Regimes: What Are They? -- So what are "volatility regimes"? -- DB analysis shows that the SandP 500 has exhibited periods of realized volatility that occur, and tend to remain, within a certain range -- "regimes" -- Intuitively, we know them when we've seen them[] -- 2004-2007 was a "low-vol" regime, 1998-2002 was a "higher-vol" regime, 2008 was an "extreme-vol" regime -- ...but seeing them coming is not so easy -- Deutsche Bank's Volatility Regime Model analyzes SandP 500 realized volatility to estimate daily probabilities for being in each of three defined volatility regimes: Low, Medium and High [GRAPHIC OMITTED] (See Appendix I for a complete discussion of the Volatility Regime Model) Source: Deutsche Bank, Bloomberg Finance, L.P., 2012 Page 6 |
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Volatility Regimes: What Can They Tell Us? -- Our work with the Volatility Regime Model brought to light a couple counterintuitive points -- You don't necessarily need to capture the first spike in volatility -- Periods of high volatility generally do not occur overnight -- Increases in realized vol have frequently been a leading indicator for implied vol -- Buying vol "cheap" isn't cheap -- Periods of low volatility have been persistent -- The cost of holding a long volatility position, particularly when vol is low and term structure is generally steep, can be very expensive -- This knowledge can help us in building a signal that aims to capture returns from both high and low volatility markets -- We aim to avoid unnecessary long positions, and the cost associated with them, by waiting for volatility to start picking up before going long -- We aim to capture returns from being short volatility in low volatility periods Page 7 |
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Level of Implied Volatility -- Level of Implied Volatility -- The Regime Model has historically shown that buying vol at low levels is not generally a good idea and you can wait for vol to start rising before going long -- However, it doesn't mean you should be long vol at any level even during a high volatility regime -- Extreme levels of vol have historically not persisted for long -- At very high levels there is likely to be more downside than upside and the risk may outweigh the potential benefit -- Why 3-month Implied Vol? -- VIX is a measure of 1-month volatility; the 1-month constant maturity holding of VIX futures, therefore, is a measure of 1-month forward 1-month volatility -- This falls between VIX (1-month) and VXV (3-month) -- 1-month implied vol is very noisy and may not be a good indicator of the market's view of volatility direction or true level -- 3-month vol incorporates the market's view of 1-month and 2-month vol Page 8 |
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Implied Volatility Term Structure -- Implied Volatility Term Structure -- The implied volatility term structure is generally upward sloping (longer dated vols higher than shorter dated vols) [] 3-month vol (VXV) has been higher than 1 month vol (VIX) 80% of the time since 2002 -- Though this is often interpreted as an expectation of higher future volatility, this is not always the case, nor the only reason for it to be upward sloping -- Volatility can only go down to zero, but can go infinitely high -- Volatility sellers' risk is to the upside, so they charge a premium, even to expectations -- In this scenario, if you hold a long volatility position for a month and the absolute level of volatility does not change, your position will lose value -- You would need volatility to increase, sometimes substantially, simply to break even -- Being short vol, if you think the probability of vol increasing is low, would be a better investment [GRAPHIC OMITTED] Source: Deutsche Bank, Bloomberg Finance, L.P., 2012 Page 9 |
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Strategy Construction: The Signal and Allocation -- The ProVol Signal is calculated based on the daily levels of the three indicators -- High Vol Regime Probability -- The Volatility Regime Model probability of being in a high-volatility regime -- Higher probabilities increase the Signal (i.e., move it in a "long" direction) -- Volatility Level -- Level of 3-month implied volatility (VXV Index) -- Higher levels decrease the Signal (i.e., move it in a "short" direction) -- Volatility Term Structure -- Ratio between 3-month and 1-month implied volatilities (VXV Index / VIX Index) -- Higher ratios decrease the Signal (i.e., move it in a "short" direction) Page 10 |
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Strategy Construction: The Signal and Allocation (con't) -- The contribution of each of the three indicators to the Signal is based on a fixed weight (Factor Coefficient) -- The prior day's Allocation is added to stabilize the Signal, make changes more gradual and reduce trading costs -- Those four variables (plus a constant) are combined to create the Signal -- A "step-wise" function converts the signal into a daily Allocation -- Weak Signals (= +/- 0.1) result in zero Allocation -- If not a Weak Signal, amount in excess of +/- 0.1 is multiplied by 1.5 -- The Allocation is capped/floored at +/- 0.3 -- See charts on next two pages for a graphical representation and example of the Signal and Allocation process Page 11 |
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Strategy Construction: The Signal and Allocation [GRAPHIC OMITTED] Page 12 |
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Strategy Construction: An Example [GRAPHIC OMITTED] (1)The Prior Day's Allocation is multiplied by the recursion factor of 0.81 (2)The Volatility Level is normalized by (divided by) 20 Page 13 |
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Strategy Construction: The Indices -- The ProVol Allocation is used to create three separate indices -- The Deutsche Bank ProVol Balanced Index -- Uses a balanced 1.5 x long or short Allocation weighting to create a strategy that aims to balance capturing returns from term-structure carry and volatility spikes -- The Deutsche Bank ProVol Carry Index -- Uses a 2 x short Allocation, 1 x long Allocation weighting to create a strategy that aims to capture enhanced returns from term-structure carry versus volatility spikes -- The Deutsche Bank ProVol Hedge Index -- Uses a 1 x short Allocation, 2 x long Allocation weighting to create a strategy that aims to capture enhanced returns from volatility spikes versus term-structure carry -- Each index uses the same daily factors, Signal and resulting Allocation -- Each index takes a long or short position in the Deutsche Bank Short-Term VIX Futures Index Page 14 |
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ProVol Retrospective Historical Allocations [GRAPHIC OMITTED] Note: The ProVol indices did not exist prior to September 24, 2012. All results prior to that date were retrospectively calculated and do not reflect actual returns. Past performance is not necessarily indicative of how an index will perform in the future. The performance of any investment product based on a ProVol Index would have been lower than the ProVol Index as a result of fees and/or costs. Source: Deutsche Bank, Bloomberg Finance L.P., 2012 Page 15 |
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ProVol([TM]) Balanced Retrospective Performance Index Performance (from December 2005) Annual Returns [GRAPHIC OMITTED] [GRAPHIC OMITTED] Performance Analysis ---------------------------- ----------------- Dec '05 - Oct '12 ---------------------------- ----------------- Annualized Returns 44.9% ---------------------------- ----------------- Volatility 19.9% ---------------------------- ----------------- Sharpe Ratio 2.3 ---------------------------- ----------------- Max. Drawdown -19.1% ---------------------------- ----------------- Start Date May 21, 2010 ---------------------------- ----------------- End Date Sep 13, 2010 ---------------------------- ----------------- Monthly Returns ---------------------------- ----------------- % Positive 58% ---------------------------- ----------------- % Negative 16% Average 3.4% ---------------------------- ----------------- Median 0.9% ---------------------------- ----------------- Rolling 3 Month Max/Min 80.5% / -9.8% ---------------------------- ----------------- Rolling 12 Month Max/Min 102.9% / -2.5% ---------------------------- ----------------- Monthly Returns Analysis ------------------------ ----- ------ ----- ----- 2006 2007 2008 2009 2010 2011 2012 ------ ---- ----- ------ ----- ------ ----- ----- Jan 0.0% 0.0% -4.0% 2.1% 1.5% 7.2% 12.8% Feb 0.0% -2.5% -2.1% 0.6% 7.9% 0.9% 2.0% Mar 0.0% 3.8% -0.4% 2.1% 9.3% 6.7% 16.6% Apr 0.0% 0.0% -1.4% -7.5% 4.5% 9.5% -0.9% May 0.0% 0.0% 0.0% -1.4% 0.3% -0.2% -1.3% Jun 0.0% 0.0% -0.4% 6.0% -14.0% 0.0% 13.0% Jul 0.0% 0.0% 1.6% 3.5% 14.8% 0.0% 4.0% Aug 0.0% 0.7% 2.4% 1.4% 0.4% 14.4% 6.8% Sep 0.0% 9.2% 9.4% 7.1% 9.6% 4.0% 0.0% Oct 0.0% 0.1% 45.0% 0.2% 12.4% -2.2% 0.0% Nov 0.0% 3.5% 13.8% 7.1% 1.0% 8.1% Dec 0.0% 2.5% 2.3% 7.5% 12.1% 3.3% ------ ---- ----- ------ ----- ------ ----- ----- Annual 0.0% 18.3% 76.1% 31.4% 73.6% 63.8% 64.4% ------ ---- ----- ------ ----- ------ ----- ----- Note: The ProVol indices did not exist prior to September 24, 2012. All results prior to that date were retrospectively calculated and do not reflect actual returns. Past performance is not necessarily indicative of how an index will perform in the future. The performance of any investment product based on a ProVol Index would have been lower than the ProVol Index as a result of fees and/or costs. Source: Deutsche Bank, Bloomberg Finance L.P., 2012 Page 16 |
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DBVEHUE ProVol([TM]) Carry Retrospective Performance Index Performance (from December 2005) Annual Returns [GRAPHIC OMITTED] [GRAPHIC OMITTED] Performance Analysis ---------------------------- ----------------- Dec '05 - Oct '12 ---------------------------- ----------------- Annualized Returns 52.7% ---------------------------- ----------------- Volatility 21.4% ---------------------------- ----------------- Sharpe Ratio 2.5 ---------------------------- ----------------- Max. Drawdown -18.1% ---------------------------- ----------------- Start Date May 21, 2010 ---------------------------- ----------------- End Date Aug 2, 2010 ---------------------------- ----------------- Monthly Returns ---------------------------- ----------------- % Positive 58% ---------------------------- ----------------- % Negative 16% Average 3.9% ---------------------------- ----------------- Median 0.9% ---------------------------- ----------------- Rolling 3 Month Max/Min 48.9% / -10.1% ---------------------------- ----------------- Rolling 12 Month Max/Min 154.7% / -1.6% ---------------------------- ----------------- Monthly Returns Analysis ------------------------ ----- ------ ----- ----- 2006 2007 2008 2009 2010 2011 2012 ------ ---- ----- ------ ----- ------ ----- ----- Jan 0.0% 0.0% -5.4% 2.3% 1.9% 9.6% 17.3% Feb 0.0% -1.6% -2.9% 0.4% 10.6% 1.3% 2.4% Mar 0.0% 2.5% -0.5% 1.5% 12.5% 9.0% 22.3% Apr 0.0% 0.0% -0.5% -5.0% 6.0% 12.8% -1.2% May 0.0% 0.0% 0.0% 0.2% -0.6% -0.2% -1.9% Jun 0.0% 0.0% -0.6% 6.9% -14.7% 0.0% 17.2% Jul 0.0% 0.0% 2.0% 4.6% 20.1% 0.0% 5.1% Aug 0.0% 0.9% 3.2% 1.8% 0.5% 9.7% 9.1% Sep 0.0% 12.4% 6.2% 9.5% 13.0% 0.9% 0.0% Oct 0.0% 0.2% 28.4% 0.1% 16.7% -1.3% 0.0% Nov 0.0% 4.7% 9.2% 9.4% 1.2% 6.3% Dec 0.0% 3.3% 3.4% 10.1% 16.3% 4.8% ------ ---- ----- ------ ----- ------ ----- ----- Annual 0.0% 23.9% 46.4% 49.2% 113.2% 65.6% 91.5% ------ ---- ----- ------ ------------ ----- ----- Note: The ProVol indices did not exist prior to September 24, 2012. All results prior to that date were retrospectively calculated and do not reflect actual returns. Past performance is not necessarily indicative of how an index will perform in the future. The performance of any investment product based on a ProVol Index would have been lower than the ProVol Index as a result of fees and/or costs. Source: Deutsche Bank, Bloomberg Finance L.P., 2012 Page 17 |
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DBVEHUE ProVol([TM]) Hedge Retrospective Performance Index Performance (from December 2005) Annual Returns [GRAPHIC OMITTED] [GRAPHIC OMITTED] Performance Analysis ---------------------------- ----------------- Dec '05 - Oct '12 ---------------------------- ----------------- Annualized Returns 36.9% ---------------------------- ----------------- Volatility 20.5% ---------------------------- ----------------- Sharpe Ratio 1.8 ---------------------------- ----------------- Max. Drawdown -20.2% ---------------------------- ----------------- Start Date May 21, 2010 ---------------------------- ----------------- End Date Oct 21, 2010 ---------------------------- ----------------- Monthly Returns ---------------------------- ----------------- % Positive 58% ---------------------------- ----------------- % Negative 16% Average 3.0% ---------------------------- ----------------- Median 0.8% ---------------------------- ----------------- Rolling 3 Month Max/Min 117.8% / -10.3% ---------------------------- ----------------- Rolling 12 Month Max/Min 131.6% / -3.3% ---------------------------- ----------------- Monthly Returns Analysis ------------------------ ----- ------ ----- ----- 2006 2007 2008 2009 2010 2011 2012 ------ ---- ----- ------ ----- ------ ----- ----- Jan 0.0% 0.0% -2.6% 1.9% 1.1% 4.8% 8.4% Feb 0.0% -3.3% -1.4% 0.7% 5.3% 0.6% 1.4% Mar 0.0% 5.1% -0.4% 2.6% 6.1% 4.4% 10.9% Apr 0.0% 0.0% -2.4% -9.9% 3.0% 6.2% -0.6% May 0.0% 0.0% 0.0% -3.0% 1.2% -0.1% -0.8% Jun 0.0% 0.0% -0.3% 4.9% -13.4% 0.0% 8.7% Jul 0.0% 0.0% 1.1% 2.3% 9.7% 0.0% 2.7% Aug 0.0% 0.5% 1.6% 0.9% 0.3% 18.9% 4.5% Sep 0.0% 6.1% 12.5% 4.7% 6.4% 7.0% 0.0% Oct 0.0% 0.1% 63.3% 0.2% 8.1% -3.3% 0.0% Nov 0.0% 2.4% 18.5% 4.7% 0.8% 9.7% Dec 0.0% 1.7% 1.1% 5.0% 8.0% 1.8% ------ ---- ----- ------ ----- ------ ----- ----- Annual 0.0% 12.8% 110.6% 15.0% 40.4% 60.7% 40.3% ------ ---- ------------ ----- ------ ----- ----- Note: The ProVol indices did not exist prior to September 24, 2012. All results prior to that date were retrospectively calculated and do not reflect actual returns. Past performance is not necessarily indicative of how an index will perform in the future. The performance of any investment product based on a ProVol Index would have been lower than the ProVol Index as a result of fees and/or costs. Source: Deutsche Bank, Bloomberg Finance L.P., 2012 Page 18 |
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ProVol([TM]) Comparative Retrospective Performance Index Performance (from Dec. 2005; JPM from Sep. 2006)(1) Annual Returns [GRAPHIC OMITTED] [GRAPHIC OMITTED] Performance Analysis ---------------------------- --------------- ----------------- ----------------- Dec '05 - Oct '12 Sep '06 - Oct '12 --------------------------------- ----------------- ProVol Balanced SandP Dyn VIX (XVZ) JPM Str Vol ---------------------------- --------------- ----------------- ----------------- Annualized Returns 44.9% 19.9% 27.7% ---------------------------- --------------- ----------------- ----------------- Volatility 20.3% 25.0% 32.4% ---------------------------- --------------- ----------------- ----------------- Sharpe Ratio 2.2 0.8 0.9 ---------------------------- --------------- ----------------- ----------------- Max. Drawdown (Monthly Returns) -19.1% -25.8% -26.7% ---------------------------- --------------- ----------------- ----------------- Start Date 5/21/10 10/11/10 10/4/11 ---------------------------- --------------- ----------------- ----------------- End Date 9/13/10 8/18/11 10/31/12 ---------------------------- --------------- ----------------- ----------------- Monthly Returns ---------------------------- --------------- ----------------- ----------------- % Positive 57% 51% 59% ---------------------------- --------------- ----------------- ----------------- % Negative 16% 49% 41% Average 3.4% 2.0% 2.9% ---------------------------- --------------- ----------------- ----------------- Median 0.8% 0.0% 2.5% ---------------------------- --------------- ----------------- ----------------- Rolling 3 Month Max/Min 80.5% / -9.8% 129.3% / -13.9% 119.2% / -20.3% ---------------------------- --------------- ----------------- ----------------- Rolling 12 Month Max/Min 102.9% / -2.5% 145.8% / -16.2% 188.4% / -11.7% ---------------------------- --------------- ----------------- ----------------- "SandP Dyn VIX" is the SandP Dynamic VIX Futures ER Index (BBG: SPDVIXP), which is excess return version of the underlying index for Barclay's XVZ iPath ETN "JPM Str Vol" is the JP Morgan Strategic Volatility Index (BBG: JPUSSTVL) (1)The JPM Str Vol index level has been rebased to the ProVol Balanced index level as of September 19, 2006, the first date on which data is available for JPM Str Vol Index. Note: The ProVol indices did not exist prior to September 24, 2012. All results prior to that date were retrospectively calculated and do not reflect actual returns. Past performance is not necessarily indicative of how an index will perform in the future. The performance of any investment product based on a ProVol Index would have been lower than the ProVol Index as a result of fees and/or costs. Page 19 Source: Deutsche Bank, Bloomberg Finance L.P., 2012 |
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Alternative Products Comparison: Monthly Returns ProVol Balanced Index ------ ---- ------------------------- ----- ----- 2006 2007 2008 2009 2010 2011 2012 ------ ---- ------ ----- ----- ------ ----- ----- Jan 0.0% 0.0% -4.0% 2.1% 1.5% 7.2% 12.8% Feb 0.0% -2.5% -2.1% 0.6% 7.9% 0.9% 2.0% Mar 0.0% 3.8% -0.4% 2.1% 9.3% 6.7% 16.6% Apr 0.0% 0.0% -1.4% -7.5% 4.5% 9.5% -0.9% May 0.0% 0.0% 0.0% -1.4% 0.3% -0.2% -1.3% Jun 0.0% 0.0% -0.4% 6.0% -14.0% 0.0% 13.0% Jul 0.0% 0.0% 1.6% 3.5% 14.8% 0.0% 4.0% Aug 0.0% 0.7% 2.4% 1.4% 0.4% 14.4% 6.8% Sep 0.0% 9.2% 9.4% 7.1% 9.6% 4.0% 0.0% Oct 0.0% 0.1% 45.0% 0.2% 12.4% -2.2% 0.0% Nov 0.0% 3.5% 13.8% 7.1% 1.0% 8.1% Dec 0.0% 2.5% 2.3% 7.5% 12.1% 3.3% ------ ---- ------ ----- ----- ------ ----- ----- Annual 0.0% 18.3% 76.1% 31.4% 73.6% 63.8% 64.4% ------ ---- ------ ----- ----- ------ ----- ----- SandP Short-Term VIX Futures Index (VXX) ------------------------------------------------------ 2006 2007 2008 2009 2010 2011 2012 ------ ------ ------ ------ ------ ----- ------- ----- Jan -11.3% -14.0% 7.2% 6.6% -5.7% -14.3% -24.8% Feb -8.1% 5.4% 3.3% 5.4% -18.1% -6.3% -7.9% Mar -6.1% 6.9% 0.5% 4.3% -19.1% -1.9% -32.6% Apr -3.9% -10.2% -20.3% -17.5% 0.3% -21.5% -1.1% May 27.8% -2.4% -14.3% -18.3% 38.0% -8.3% 28.7% Jun -8.9% 14.0% 14.3% -10.8% 7.9% -0.9% -29.1% Jul 1.3% 24.8% -3.1% -9.0% -28.2% 11.6% -9.2% Aug -14.6% 19.5% -7.1% -4.5% -3.4% 66.2% -15.5% Sep -8.5% -15.7% 36.4% -15.9% -20.2% 38.8% -22.7% Oct -23.4% -2.2% 117.1% -3.1% -24.4% -24.2% 5.5% Nov -6.3% 23.6% 16.7% -16.0% -5.6% 2.0% Dec -3.7% -7.1% -17.6% -16.3% -24.1% -13.9% ------ ------ ------ --------------------------- ----- Annual -53.2% 36.6% 123.1% -65.0% -72.0% -3.8% -75.0% ------ ------ -------------------------- ------------- SandP Dynamic VIX Futures Index (XVZ) -------------------------------------------- ----- 2006 2007 2008 2009 2010 2011 2012 ------ ----- ----- ------ ----- ----- ------ ----- Jan -1.1% -2.9% -0.4% 0.1% -1.7% -5.8% 1.3% Feb -2.0% -5.5% 1.9% 3.2% -1.5% -3.9% 3.0% Mar -5.4% -4.0% -1.7% 1.2% 3.0% -4.9% -2.1% Apr 0.0% 0.6% -4.9% -2.6% 4.4% 2.2% -2.2% May 11.4% 3.0% 4.1% -8.2% 10.8% -2.3% 2.3% Jun -3.1% 3.8% -0.6% -0.3% 2.7% -1.2% -0.6% Jul -2.8% 18.7% -5.1% 3.8% -3.0% -6.0% -2.9% Aug 3.2% 6.0% 2.4% 2.6% 7.4% 38.8% 1.5% Sep 3.3% -7.5% 14.3% -0.4% 1.6% 9.6% -6.0% Oct -3.0% 5.5% 77.5% 0.9% -2.2%-12.0% -5.4% Nov -2.7% 11.3% 13.0% 2.7% 0.0% 3.6% Dec 2.0% 1.3% 4.6% -1.9% -1.8% -1.8% ------ ----- ----- ------ ----- ----- ------ ----- Annual -1.2% 31.1% 128.8% 0.6% 20.5% 8.8% -5.8% ------ ----- ------------ ----- ----- ------ ----- JP Morgan Strategic Volatility Index ------ -------------------------------------- ----- 2006 2007 2008 2009 2010 2011 2012 ------ ------- ----- ----- ----- ------ ----- ----- Jan 2.5% -5.4% -3.5% -0.2% -1.7% 5.4% Feb -7.5% 1.4% 10.2% 4.4% -0.5% 6.3% Mar -8.5% -3.5% 4.3% 6.1% -6.1% 5.5% Apr 3.3% 3.7% -1.0% -0.5% 6.3% -1.2% May 2.7% 10.4% 3.1% 1.0% 1.1% -5.9% Jun -4.1% -8.2% 4.6% -11.5% -4.1% 7.3% Jul 3.8% -9.7% 7.7% 10.2% -10.2% -2.4% Aug 11.9% 5.4% 4.1% 8.0% 34.0% 5.7% Sep -8.0% 4.3% 7.1% 7.5% 23.4% -0.9% Oct -1.2% 5.2% 75.8% -1.5% 6.0% -20.1% -5.6% Nov 0.9% -6.2% 19.6% 9.0% -2.2% 2.7% Dec 2.5% 5.1% -3.6% 6.2% 1.6% -2.8% ------ ------- ----- ----- ----- ------ ----- ----- Annual N/A -2.3% 95.5% 62.4% 32.5% 11.9% 20.7% ------ ------- ----- ----- ----- ------ ----- ----- Note: The ProVol indices did not exist prior to September 24, 2012. All results prior to that date were retrospectively calculated and do not reflect actual returns. Past performance is not necessarily indicative of how an index will perform in the future. The performance of any investment product based on a ProVol Index would have been lower than the ProVol Index as a result of fees and/or costs. Source: Deutsche Bank, Bloomberg Finance L.P., 2012 Page 20 |
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Index Costs The calculation of the ProVol indices incorporates a daily deduction of costs meant to approximate the transaction costs associated with trading, or hedging, the indices' notional position in first and second month VIX futures. The cost calculation takes into account changes in the notional VIX futures position associated with both the daily roll from the first month to the second month VIX future as well as any changes in position in relation to the Allocation. Each portion of the cost is calculated as both a fixed amount of the number of contracts notionally traded by the index as well as a percentage amount of the dollar value of the contracts notionally traded by the index. The greater of the two in each case is taken as the cost, with the fixed amount acting as a minimum. The daily roll portion of the cost is calculated in two ways: 1) 0.1 times the total number of contracts bought and sold in conjunction with rolling from the first month VIX future to the second month VIX future, irrespective of any changes to the Allocation, divided by two; or 2) 0.35% times the total dollar value of the contracts bought and sold in conjunction with rolling from the first month VIX future to the second month VIX future, irrespective of any changes to the Allocation. The greater of the two is taken as the daily roll cost. The allocation portion of the cost is calculated in two ways: 1) 0.1 times the total number of contracts bought and sold in conjunction with increasing or decreasing the index's holding of VIX futures in relation to the Allocation, irrespective of any changes due to the daily roll; or 2) 0.35% times the total dollar value of the contracts bought and sold in conjunction with increasing or decreasing the index's holding of VIX futures in relation to the Allocation, irrespective of any changes due to the daily roll. The greater of the two is taken as the allocation cost. The daily roll cost and the allocation cost are added together to determine the daily total trading cost. Page 21 |
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Risk Factors THE PROVOL INDICES ARE SUBJECT TO STRATEGY RISK -- The strategy of the ProVol Indices is to generate returns from the expected volatility of the SandP 500 Index by dynamically adjusting a long or short position in the VIX Futures Index based on the size and direction of the Signal and the resulting Allocation based on that Signal. The Signal aims to determine the likely short-term direction of implied volatility and the level of carrying costs. However, the Signal may not be predictive of the short-term direction of implied volatility and/or the level of carrying costs. The methodology for determining the Signal is based on limited past data and that may not be predictive of future implied volatility. If the Signal is not successful in determining the likely short-term direction of implied volatility and/or the level of carrying costs, then the resulting Allocation based on that Signal may result in a notional long or short position in the VIX Futures Index that declines in value and causes the levels of the ProVol Indices to decrease. THE PROVOL INDICES CONTAIN EMBEDDED COSTS -- In calculating the level of the ProVol Indices, the Index Sponsor will deduct the Index Fee. The Index Fee takes into account changes in the notional VIX futures contracts position measured by each ProVol Index associated both with the daily rolling from the first month to the second month VIX futures contracts underlying the VIX Futures Index as well as with any changes in the size of the notional position in the VIX Futures Index. Thus, large or more frequent shifts in the Signal or greater or more frequent changes in VIX futures contracts prices will require greater reallocation and will result in higher costs. Additionally, lower VIX futures contracts prices, which require a greater number of contracts to be notionally traded in order to achieve the same value, will also result in higher costs. We expect the Index Fee to average between 1.5bps and 2bps (0.015% and 0.02%) per trading day. However, the actual Index Fee may be substantially higher on days when there is a substantial change in the Allocation or prices of the VIX futures contracts, resulting in a substantial number or value of VIX futures contracts notionally traded. From and including 2006 to and including 2011, the annual Index Fees for the ProVol Indices as retroactively calculated have ranged from 0.00% to 7.12% . THE PROVOL INDICES HAVE VERY LIMITED PERFORMANCE HISTORY -- Calculation of the ProVol Indices began on September 24, 2012. Therefore, the ProVol Indices have very limited performance history and no actual investment which allowed tracking of the performance of the ProVol Indices was possible before that date. The index performance data prior to this date shown in this presentation have been retrospectively calculated using historical data and the same methodology as described above since December 20, 2005. Although the Index Sponsor believes that these retrospective calculations represent accurately and fairly how the Index would have performed before September 24, 2012, the ProVol Indices did not, in fact, exist before September 24, 2012. All prospective investors should be aware that no actual investment that allowed a tracking of the performance of the ProVol Indices was possible at any time prior to September 24, 2012. Furthermore, it is impossible to predict whether the ProVol Indices will rise or fall. The actual performance of the ProVol Indices may bear little relation to the retrospectively calculated performance of the ProVol Indices. Page 22 |
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Risk Factors DEUTSCHE BANK AG, LONDON BRANCH, AS THE SPONSOR OF THE PROVOL INDICES, MAY ADJUST EACH INDEX IN A WAY THAT AFFECTS ITS LEVEL AND MAY HAVE CONFLICTS OF INTEREST -- Deutsche Bank AG, London Branch is the sponsor of the Provol Indices (the "Index Sponsor") and will determine whether there has been a market disruption event with respect to the ProVol Indices. In the event of any such market disruption event, the Index Sponsor may use an alternate method to calculate the closing level of the ProVol Indices. The Index Sponsor carries out calculations necessary to promulgate the ProVol Indices and maintains some discretion as to how such calculations are made. In particular, the Index Sponsor has discretion in selecting among methods of how to calculate the ProVol Indices in the event the regular means of determining the ProVol Indices are unavailable at the time a determination is scheduled to take place. There can be no assurance that any determinations made by the Index Sponsor in these various capacities will not affect the value of the levels of the ProVol Indices. Any of these actions could adversely affect the value of securities or options linked to the ProVol Indices. The Index Sponsor has no obligation to consider the interests of holders of securities linked to the ProVol Indices in calculating or revising the ProVol Indices. Furthermore, Deutsche Bank AG, London Branch or one or more of its affiliates may have published, and may in the future publish, research reports on the ProVol Indices or investment strategies reflected by the ProVol Indices (or any transaction, product or security related to the ProVol Indices or any components thereof). This research is modified from time to time without notice and may express opinions or provide recommendations that are inconsistent with purchasing or holding of transactions, products or securities related to the ProVol Indices. Any of these activities may affect the ProVol Indices or transactions, products or securities related to the ProVol Indices. Investor should make their own independent investigation of the merits of investing in contracts or products related to the ProVol Indices. Page 23 |
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Important Notes The distribution of this document and the availability of some of the products and services referred to herein may be restricted by law in certain jurisdictions. Some products and services referred to herein are not eligible for sale in all countries and in any event may only be sold to qualified investors. Deutsche Bank will not offer or sell any products or services to any persons prohibited by the law in their country of origin or in any other relevant country from engaging in any such transactions. Prospective investors should understand and discuss with their professional tax, legal, accounting and other advisors the effect of entering into or purchasing any transaction, product or security related to the ProVol indices (each, a "Structured Product"). Before entering into any Structured Product you should take steps to ensure that you understand and have assessed with your financial advisor, or made an independent assessment of, the appropriateness of the transaction in the light of your own objectives and circumstances, including the possible risks and benefits of entering into such Structured Product. Structured Products are not suitable for all investors due to illiquidity, optionality, time to redemption, and payoff nature of the strategy. Deutsche Bank or persons associated with Deutsche Bank and their affiliates may: maintain a long or short position in securities referenced herein or in related futures or options; purchase, sell or maintain inventory; engage in any other transaction involving such securities; and earn brokerage or other compensation. Any payout information, scenario analysis, and hypothetical calculations should in no case be construed as an indication of expected payout on an actual investment and/or expected behavior of an actual Structured Product. Calculations of returns on Structured Products may be linked to a referenced index or interest rate. As such, the Structured Products may not be suitable for persons unfamiliar with such index or interest rate, or unwilling or unable to bear the risks associated with the transaction. Structured Product denominated in a currency, other than the investor's home currency, will be subject to changes in exchange rates, which may have an adverse effect on the value, price or income return of the products. These Structured Product may not be readily realizable investments and are not traded on any regulated market. Structured Products involve risk, which may include interest rate, index, currency, credit, political, liquidity, time value, commodity and market risk and are not suitable for all investors. The past performance of an index, securities or other instruments does not guarantee or predict future performance. The distribution of this document and availability of these products and services in certain jurisdictions may be restricted by law. In this document, various performance-related statistics, such as index return and volatility, among others, of the ProVol indices are compared with those of the SandP Dynamic VIX Index, the SandP Short-Term VIX Futures Index and the JP Morgan Strategic Volatility Index. Such comparisons are for information purposes only. No assurance can be given that any ProVol index will outperform the SandP Dynamic VIX Index, the SandP Short-Term VIX Futures Index and the JP Morgan Strategic Volatility Index in the future; nor can assurance be given that ProVol will not significantly underperform the SandP Dynamic VIX Index, the SandP Short-Term VIX Futures Index and the JP Morgan Strategic Volatility Index in the future. Similarly, no assurance can be given that the relative volatility levels of ProVol and the SandP Dynamic VIX Index, the SandP Short-Term VIX Futures Index and the JP Morgan Strategic Volatility Index will remain the same in the future. Deutsche Bank does not provide accounting, tax or legal advice. BEFORE ENTERING INTO ANY TRANSACTION YOU SHOULD TAKE STEPS TO ENSURE THAT YOU UNDERSTAND AND HAVE MADE AN INDEPENDENT ASSESSMENT OF THE APPROPRIATENESS OF THE STRUCTURED PRODUCT IN LIGHT OF YOUR OWN OBJECTIVES AND CIRCUMSTANCES, INCLUDING THE POSSIBLE RISKS AND BENEFITS OF ENTERING INTO SUCH STRUCTURED PRODUCT. YOU SHOULD ALSO CONSIDER MAKING SUCH INDEPENDENT INVESTIGATIONS AS YOU CONSIDER NECESSARY OR APPROPRIATE FOR SUCH PURPOSE. Deutsche Bank" means Deutsche Bank AG and its affiliated companies, as the context requires. Deutsche Bank Private Wealth Management refers to Deutsche Bank's wealth management activities for high-net-worth clients around the world. Deutsche Bank Alex Brown is a division of Deutsche Bank Securities Inc. Page 24 |
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Important Notes Backtested, hypothetical or simulated performance results presented herein have inherent limitations. Unlike an actual performance record based on trading actual client portfolios, simulated results are achieved by means of the retroactive application of a backtested model itself designed with the benefit of hindsight. Taking into account historical events the backtesting of performance also differs from actual account performance because an actual investment strategy may be adjusted any time, for any reason, including a response to material, economic or market factors. The backtested performance includes hypothetical results that do not reflect the reinvestment of dividends and other earnings or the deduction of advisory fees, brokerage or other commissions, and any other expenses that a client would have paid or actually paid. No representation is made that any trading strategy or account will or is likely to achieve profits or losses similar to those shown. Alternative modeling techniques or assumptions might produce significantly different results and prove to be more appropriate. Past hypothetical backtest results are neither an indicator nor guarantee of future returns. Actual results will vary, perhaps materially, from the analysis. Structured Products linked to the ProVol indices discussed herein are not insured by the Federal Deposit Insurance Corporation (FDIC) or any other US governmental agency. These Structured Products are not insured by any statutory scheme or governmental agency of the United Kingdom. These Structured Products typically involve a high degree of risk, are not readily transferable and typically will not be listed or traded on any exchange and are intended for sale only to investors who are capable of understanding and assuming the risks involved. The market value of any Structured Product may be affected by changes in economic, financial and political factors (including, but not limited to, spot and forward interest and exchange rates), time to maturity, market conditions and volatility and the equity prices and credit quality of any issuer or reference issuer. Deutsche Bank AG has filed a registration statement (including a prospectus) with the SEC for the offerings to which this communication relates. Before you invest, you should read the prospectus in that registration statement and other documents the issuer has filed with the SEC for more complete information about the issuer and this offering. You may get these documents for free by visiting EDGAR on the SEC Web site at www.sec.gov. Alternatively, the issuer, any underwriter or any dealer participating in the offering will arrange to send you the prospectus if you request it by calling toll-free 1-800-311-4409. Additional information may be available upon request. Any results shown do not reflect the impact of commission and/or fees, unless stated. License Agreement with SandP Any Structured Products are not sponsored, endorsed, sold or promoted by Standard and Poor's, a division of the McGraw-Hill Companies, Inc., which we refer to as SandP. SandP makes no representation or warranty, express or implied, to the owners of the Structured Products or any member of the public regarding the advisability of investing in securities generally or in the Structured Products particularly, or the ability of the SandP 500 ([R]) to track general stock market performance. SandP's only relationship to Deutsche Bank AG is the licensing of certain trademarks and trade names of SandP without regard to Deutsche Bank AG or the Structured Products. SandP has no obligation to take the needs of Deutsche Bank AG or the holders of the Structured Products into consideration in determining, composing or calculating the SandP 500 ([R]). SandP is not responsible for and has not participated in the determination of the timing, price or quantity of the Structured Products to be issued or in the determination or calculation of the amount due at maturity of the Structured Products. SandP has no obligation or liability in connection with the administration, marketing or trading of the Structured Products. SandP DOES NOT GUARANTEE THE ACCURACY AND/OR THE COMPLETENESS OF THE SandP 500 ([R]) OR ANY DATA INCLUDED THEREIN AND SandP SHALL HAVE NO LIABILITY FOR ANY ERRORS, OMISSIONS OR INTERRUPTIONS THEREIN. SandP MAKES NO WARRANTY, EXPRESS OR IMPLIED, AS TO RESULTS TO BE OBTAINED BY DEUTSCHE BANK AG, HOLDERS OF THE STRUCTURED PRODUCTS OR ANY OTHER PERSON OR ENTITY FROM THE USE OF THE SandP 500 ([R]) INDEX OR ANY DATA INCLUDED THEREIN. SandP MAKES NO EXPRESS OR IMPLIED WARRANTIES, AND EXPRESSLY DISCLAIMS ALL WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE OR USE WITH RESPECT TO THE SandP 500([R]) OR ANY DATA INCLUDED THEREIN. WITHOUT LIMITING ANY OF THE FOREGOING, IN NO EVENT SHALL SandP HAVE ANY LIABILITY FOR ANY SPECIAL, PUNITIVE, INDIRECT OR CONSEQUENTIAL DAMAGES (INCLUDING LOST PROFITS), EVEN IF NOTIFIED OF THE POSSIBILITY OF SUCH DAMAGES. "STANDARD and POOR'S", "SandP", "SandP 500" AND "500" ARE TRADEMARKS OF STANDARD and POOR'S FINANCIAL SERVICES LLC AND HAVE BEEN LICENSED FOR USE BY DEUTSCHE BANK AG. STRUCTURED PRODUCTS ARE NOT SPONSORED, ENDORSED, SOLD OR PROMOTED BY SandP AND SandP MAKES NO REPRESENTATION REGARDING THE ADVISABILITY OF PURCHASING ANY OF THE STRUCTURED PRODUCTS. Page 25 |
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Appendix I Volatility Regimes Passion to Perform |
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Volatility Regimes: How Do We Know? -- Using a single volatility metric would have done a poor job of predicting regime transitions or differentiating between volatility spikes and regime changes -- Example: recent points in time when SandP 500 3-month realized vol was 13% -- May 2005: Have we left the low-vol regime following the GM credit crisis? -- July 2007: Have we left the low-vol regime of the mid-2000s? -- June 2011: Have we switched back to a low-vol regime following the financial crisis? -- Getting any one of these wrong could have had serious consequences -- We need a framework which can suggest answers to the following questions: -- What is the probability of being in a given regime currently? -- What was the probability of being in a given regime at a historical point leading up to or following an event? -- What is the probability that a series of observed returns was produced by a given regime? Page 27 |
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Volatility Regime Model: Assumptions -- Regime Model Assumptions -- Three possible equity return distributions -- Low, medium and high volatility regimes -- We can move from one regime to another with a certain probability - -- Defined by a transition matrix -- Each regime's mean daily return and volatility and overall probability of occurrence, along with the transition matrix, are fixed through time -- We make no assumptions about what any of the values will be -- we let the data tell us -- but we may have certain expectations -- Predominantly low or medium vol with shorter periods of high vol -- Regimes are "sticky" -- likely to be persistent [GRAPHIC OMITTED] Page 28 |
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Volatility Regime Model: Results -- Calibration produces the model that would have generated the historical returns with the highest likelihood (a "maximum likelihood estimation") Regime-specific Long-term Regime Regime Annualized Volatility(1) Probability(1) Low-Volatility: 9.4% 47% Medium-Volatility: 18.1% 46% High-Volatility: 44.4% 7% -- Though we did not specify anything about them ahead of time, the calibration has identified regime-specific volatilities and probabilities that make sense intuitively (1)These numbers have been rounded for ease of presentation Page 29 |
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Volatility Regime Model: Transition Matrix -- The model determines that regimes have been sticky: once you are in a regime, you are much more likely to stay in a regime Daily Likelihood of TO: Transitioning Between Regimes(1) Low-Vol Medium-Vol High-Vol Low-Vol: 98.5% 1.5% ~0.0% FROM: Medium-Vol: 1.5% 97.9% 0.6% High-Vol: 0.0% 3.9% 96.1% -- Again, though we did not specify anything ahead of time, the transition matrix makes sense -- For instance, the probability of jumping directly from the low-vol regime to the high-vol regime over night, or vice versa, is near zero (1)These numbers have been rounded for ease of presentation Page 30 |
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Volatility Regime Model: Test Case Outcomes -- So would the regime model have helped in our examples? -- May 31, 2005: the probability that we are still in the low vol regime was 93% -- Right call given the bull market lasts for 2 more years following the GM credit crisis -- July 31, 2007: the probability that we were still in the low-vol regime was less than 1% -- Right call given the impending credit crunch -- June 30, 2011: the probability that we had moved to the low-vol regime was only 7% -- Right call given what happens in July and August 2011 -- So when might the regime model not be helpful or of informative value? -- Non-financial events like 9/11 -- Market events like the "flash crash" of 2010, widely believed to be caused by computer trading systems, that may not be preceded by an increase in volatility [] In both cases the regime model showed a high probability of being in a medium vol regime prior to the event, but a low probability of being in a high vol regime Page 31 |
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Appendix II Index Description Passion to Perform |
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THE DEUTSCHE BANK PROVOL INDICES The Deutsche Bank ProVol Indices (the "ProVol Indices") reflect the economic performance over time, less costs, of a strategy designed to generate returns from the expected volatility of the SandP 500([R]) Index (the "SandP 500") by taking a daily rebalanced notional long or short position in the Deutsche Bank Short-Term VIX Futures Index (the "VIX Futures Index"). There are three versions of the ProVol Indices, the ProVol Balanced Index, the ProVol Carry Index and the ProVol Hedge Index (each a "ProVol Index"). The VIX Futures Index tracks the market's expectation of short-term volatility (also referred to as implied volatility) by means of a daily-rolling notional long position in first month and second month futures contracts on the CBOE Volatility Index([R]) (the "VIX Index"). The VIX Index is a benchmark index that measures the market's expectation of 30-day volatility implicit in the prices of CBOE-listed SandP 500 options. We refer to the futures contracts on the VIX Index as the "VIX futures contracts." ProVol Index Signal and Allocation [GRAPHIC OMITTED] On each Index Business Day (as defined below), each ProVol Index dynamically adjusts its long or short exposure to the VIX Futures Index based on the size and direction of a signal (the "Signal") calculated on that day using three volatility indicators and a resulting allocation to the VIX Futures Index (the "Allocation") based on the Signal. The Signal and Allocation are designed generally to have long exposure to the VIX Futures Index during periods of high realized volatility, when there is a high probability that implied volatility will increase, and/or the cost of carrying VIX futures contracts is low, and generally to have short exposure during periods of low realized volatility, when implied volatility is likely to decrease, and/or the cost of carrying VIX futures contracts is high. As a result, each ProVol Index is generally expected to hold long positions in the VIX Futures Index to capture positive returns during periods of increasing volatility and, during periods of low volatility, to hold no position or short |
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positions to generate returns from high carrying costs. Only a strong positive or negative Signal will result in each ProVol Index taking a long or short position in the VIX Futures Index. To reduce cost and risk, a weak Signal will result in a zero Allocation. By dynamically allocating its exposure, each ProVol Index seeks to capture returns from both high and low volatility markets and keep costs and risk lower by holding VIX futures contracts only when it is expected to be advantageous to do so. The calculation of each ProVol Index incorporates a daily deduction of costs. Volatility is a statistical measure of how much an asset's return varies from the mean of such returns; the more variable the asset's returns, the higher its volatility, and the higher the perceived risk of such asset (all other things being equal). Volatility is one of the market standards for assessing risk. Volatility is generally calculated based on the natural logarithm return of an asset between each observation. Realized volatility is a calculation of this amount of movement historically from prices or levels of the asset observed periodically in the market over a set period. Realized volatility is characterized by the frequency of the observations of the asset price used in the calculation and the period over which observations are made. For example, six-month daily realized volatility denotes realized volatility calculated from daily closing asset prices over a six-month period. Implied volatility is a market estimate of the volatility an asset will realize over a future period of time. Implied volatility is determined from the market prices of listed options on the asset. For example, one-month implied volatility denotes volatility implicit in the prices of the relevant options with one month to expiration. Each ProVol Index allocates long or short exposure to the VIX Futures Index based on the size and direction of the Signal and Allocation calculated on each Index Business Day using three volatility indicators: (i) the probability of being in a high-volatility environment as measured by Deutsche Bank's proprietary Volatility Regime Model (the "High-Volatility Regime Probability"), (ii) three-month implied volatility as measured by the CBOE SandP 500([R]) 3-Month Volatility Index (the "VXV Index") and (iii) the "steepness" of the implied volatility curve as measured by the ratio of the VXV Index to the VIX Index (the "Volatility Term Structure"). Each volatility indicator contributes to the Signal positively or negatively based on a fixed weight assigned to such volatility indicator. In addition to the three volatility indicators, the Signal also takes into account the prior day's Allocation, which harnesses the value of past information and makes changes in the volatility exposure more gradual. High-Volatility Regime Probability. The Volatility Regime Model is designed to estimate probabilities that the SandP 500 is in a low-, medium- and high-volatility environment. The High-Volatility Regime Probability contributes positively to the Signal, meaning that the Signal will increase if the probability of being in a high-volatility environment increases and decrease if the probability of being in a high-volatility environment decreases. VXV Index. The VXV Index is similar to the VIX Index, except that it measures the market's expectation of the volatility the SandP 500 will realize over the next 93 days. When three-month implied volatility is high, the likelihood of implied volatility going down typically outweighs the likelihood of implied volatility going up. As a result, the VXV Index contributes negatively to the Signal, meaning that the Signal will decrease if the three-month implied volatility increases and increase if the three-month implied volatility decreases. Volatility Term Structure. The Volatility Term Structure measures the "steepness" of the implied volatility curve. When the VXV Index level is higher than the VIX Index, reflecting an upward sloping implied volatility curve, longer-dated futures contracts will generally be priced higher than the nearer contracts and spot prices and the market can be described as in "contango." When the VXV Index is lower than the VIX Index, reflecting a downward sloping implied volatility curve, longer-dated futures contracts will generally be priced lower than the nearer contracts and spot prices and the market can be described as in "backwardation." The cost of carrying VIX futures contracts will be positive when the market is in contango and negative (reflecting a profit) when the market is in backwardation. The implied volatility market tends to be in contango most of the time, making it very expensive to continuously carry VIX futures contracts. As the implied volatility curve becomes steeper, the cost of carrying 2 |
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VIX futures contracts will increase. To reduce the carrying cost, the Volatility Term Structure contributes negatively to the Signal, meaning that the Signal will decrease if the "steepness" of the implied volatility curve increases and increase if the "steepness" of the implied volatility curve decreases. Because the Signal is calculated on each Index Business Day by aggregating the weighted levels of the three volatility indicators, the volatility indicators may offset or reinforce each other. Generally speaking, the Signal is positive when realized volatility is high, there is a high probability that implied volatility will increase, and/or the implied volatility market is in backwardation (to generate returns from negative carrying costs) and is negative when realized volatility is low, there is a high probability that implied volatility will decrease, and/or the implied volatility market is in contango (to generate returns from positive carrying costs). In addition to the three volatility indicators, the Signal also takes into account the prior day's Allocation, which harnesses the value of past information and makes changes in the volatility exposure more gradual. The Allocation on each Index Business Day will be calculated based on the Signal; provided that a weak Signal between 0.1 and --0.1 will not result in any Allocation and the Allocation will not exceed the maximum Allocation of 0.3 or --0.3. The ProVol Index family includes three indices: the ProVol Hedge Index, the ProVol Carry Index and the ProVol Balanced Index. The three indices differ in the leverage factors applied to the Allocation. The ProVol Hedge Index aims to capture more returns from increases in implied volatility than from high carrying costs by applying a leverage factor of 200% (2 times) when the Allocation is positive, generating leveraged long exposure and unleveraged short exposure. On the other hand, the ProVol Carry Index does the opposite and aims to capture more returns from high carrying costs than from increases in implied volatility by applying a leverage factor of 200% (2 times) when the Allocation is negative, generating leveraged short exposure and unleveraged long exposure. The ProVol Balanced Index aims for a balanced approach of capturing returns equally from increases in implied volatility and high carrying costs by applying a leverage factor of 150% (1.5 times) regardless of whether the Allocation is positive or negative. The closing level of each ProVol Index will be calculated by the Index Sponsor on each Index Business Day based on closing levels of the VIX Futures Index and the Allocation and leverage factor assigned to each ProVol Index, less an index fee ("the "Index Fee"). The Index Fee takes into account changes in the notional VIX futures contracts position associated with both the daily rolling from the first month to the second month VIX futures contracts underlying the VIX Futures Index as well as any changes in the size of the notional position in the VIX Futures Index. Each portion of the Index Fee is equal to 0.35% of the dollar value of the VIX futures contracts notionally traded on such Index Business Day, subject to a minimum fee equal to the number of VIX futures contracts notionally traded on such Index Business Day times a fixed multiplier of 0.1. The Index Fee is related to the dollar value or number of contracts notionally traded. Thus, large or more frequent shifts in the Signal or greater or more frequent changes in VIX futures contracts prices will require greater reallocation and will result in higher costs. Additionally, lower VIX futures contracts prices, which require a greater number of contracts to be notionally traded in order to achieve the same value, will also result in higher costs. We expect the Index Fee to average between 1.5bps and 2bps (0.015% and 0.02%) per Index Business Day. However, the actual Index Fee may be substantially higher on days when there is a substantial change in the Allocation or prices of the VIX futures contracts, resulting in a substantial number or value of VIX futures contracts notionally traded. From and including 2006 to and including 2011, the annual Index Fees for the ProVol Indices as retroactively calculated have ranged from 0.00% to 7.12% . The ProVol Indices were created by Deutsche Bank AG (the "Index Sponsor") on September 24, 2012 and are calculated, maintained and published by the Index Sponsor. The closing level of each ProVol Index was set to 100 on December 20, 2005 (the "ProVol Base Date"). An "Index Business Day" means a weekday when the New York Stock Exchange, the NASDAQ Stock Market and the Chicago Board Options Exchange are open. 3 |
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The VIX Index The CBOE Volatility Index([R]), which we refer to as the VIX Index, is a benchmark index that measures the market's expectation of the SandP 500's volatility (also referred to as implied volatility) over the next 30 days, calculated based on the prices of certain put and call options on the SandP 500. The VIX Index is a volatility index comprised of options rather than stocks, with the price of each option reflecting the market's expectation of future volatility. Thus, when the market's expectation of volatility over the next 30 days increases, the level of the VIX Index generally increases as well and, when the market's expectation of volatility over the next 30 days decreases, the level of the VIX Index generally decreases. The VIX Index was developed by the Chicago Board Options Exchange (the "CBOE") and is calculated, maintained and published by the CBOE. The CBOE has no obligation to continue to publish, and may discontinue the publication of, the VIX Index. The VIX Index is reported by Bloomberg L.P. under the ticker symbol "VIX." Although the VIX Index measures the 30-day volatility of the SandP 500 implied by the out-of-the-money put and call options on the level of the SandP 500 ("SPX Options"), 30-day options are only available once a month. To arrive at the VIX Index level, a broad range of out-of-the-money SPX Options expiring on the two closest nearby months ("Near Term Options" and "Next Term Options," respectively), usually in the first and second contract months, are selected in order to derive a measure of 30-day market implied volatility. SPX Options having a maturity of less than eight days are excluded at the outset. When the Near Term Options have eight days or less left to expiration, the VIX Index rolls to the second and third contract months in order to minimize pricing anomalies that occur close to expiration. The VIX Index is calculated independently of any particular option pricing model and in doing so seeks to eliminate any biases which may otherwise be included in using options pricing methodology based on certain assumptions. The model-free implied volatility for each month is calculated using a strike-weighted sum of the prices of the options for that month. The 30-day implied volatility is then interpolated from the implied volatilities of these two near expiries. VIX Futures Contracts VIX futures contracts were first launched for trading by the CBOE in 2004. The VIX Index futures have expirations ranging from the front month consecutively out to the eighth month. VIX futures contracts allow investors the ability to invest in forward implied volatility based on their view of the future direction of the VIX Index. Investors that believe the implied volatility of the SandP 500 will increase may buy VIX futures contracts, expecting that the level of the VIX Index will increase. Conversely, investors that believe that the implied volatility of the SandP 500 will decline may sell VIX futures contracts, expecting that the level of the VIX Index will fall. An exchange-traded futures contract provides for the purchase and sale of a specified type and quantity of an underlying asset or financial instrument at a stated delivery time for a fixed price. Because the VIX Index is not a tangible item that can be purchased and sold directly, a VIX futures contract provides for the payment and receipt of cash based on the level of the VIX Index at settlement or liquidation of the contract. Unlike equity securities, futures contracts, by their terms, have stated expirations and, at a specified point in time prior to expiration, trading in a futures contract for the current delivery month will cease. As a result, a market participant wishing to maintain its exposure to a futures contract on a particular asset or financial instrument with the nearest expiration must close out its position in the expiring contract and establish a new position in the contract for the next delivery month, a process referred to as "rolling." For example, a market participant with a long position in November VIX futures contracts that wishes to maintain a position in the nearest delivery month will, as the November contracts near expiration, 4 |
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sell November VIX futures contracts, which serves to close out the existing long position, and buy December VIX futures contracts. This will "roll" the November position into a December position, and, when the November contract expires, the market participant will still have a long position in the nearest delivery month. Roll yield, which can be either positive or negative, is generated as a result of rolling futures contracts. When longer-dated contracts are priced lower than the nearer contract and spot prices, the market is in "backwardation," and positive roll yield may be generated when higher-priced near-term futures contracts are "sold" to "buy" and hold lower priced longer-dated contracts. When the opposite is true and longer-dated contracts are priced higher than the nearer contracts and spot prices, the market is in "contango," and negative roll yields (or roll costs) may result from the "sale" of lower priced near-term futures contracts to "buy" and hold higher priced longer-dated contracts. The VIX Futures Index The VIX Futures Index is an excess return index that tracks 30-day forward implied volatility of the SandP 500 by means of a daily-rolling notional long position in first month and second month futures contracts on the VIX Index. The VIX Futures Index rolls daily throughout each month from the first month VIX futures contracts into the second month VIX futures contracts. As a daily rolling index, the VIX Futures Index aims to maintain a long exposure to VIX futures contracts with a constant weighted average maturity of 30 days. Thus, when the prices of the relevant VIX futures contracts increase, reflecting the market's increased expectation of volatility over the next 30 days, the level of the VIX Futures Index generally increases as well and, when the prices of the relevant VIX futures contracts decrease, reflecting the market's decreased expectation of volatility over the next 30 days, the level of the VIX Futures Index generally decreases. In addition, the VIX Futures Index will benefit from the positive roll yields generated in "backwardation" markets when the second month VIX futures contracts are priced lower than the first month VIX futures contracts, and will be adversely affected by the negative roll yields generated in "contango" markets when the second month VIX futures contracts are priced higher than the first month VIX futures contracts. Contract Rebalancing The VIX Futures Index has a monthly rolling cycle. Each roll period (the "Monthly Roll Period") starts from (and excluding) a Monthly Roll Date and ends on (and including) the next Monthly Roll Date. The Monthly Roll Date for each month is typically the Tuesday prior to the monthly settlement date of the VIX futures contracts, which is generally 31 calendar days prior to the SPX Option expiration date for the following month. Each Monthly Roll Date will be determined based on the following rules: Step 1: Take the third Friday of the following month (if it is not an Index Business Day, the immediately preceding Index Business Day). This is the SPX Option expiration date for the following month. Step 2: Deduct 30 calendar days from the SPX Option expiration date for the following month determined in Step 1. Step 3: The "Monthly Roll Date" is the one Index Business Day prior to the date determined in Step 2. On the first Index Business Day during the Monthly Roll Period, all of the weight in the VIX Futures Index is allocated to the first month VIX futures contracts. On each subsequent Index Business Day in the Monthly Roll Period, a fraction of the first month VIX futures contracts is sold and an equal notional amount of the second month VIX futures contracts is purchased. The fraction, or quantity, of the notional amount of first and 5 |
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second month VIX futures contracts purchased or sold on an Index Business Day is equal to 1/D, where D is the total number of Index Business Days in the current Monthly Roll Period. For example, if there are 20 Index Business Days in the current Monthly Roll Period, 1/20 in the first month VIX futures contracts will be sold and 1/20 in the second month VIX futures contracts will be purchased on each Index Business Day following the Monthly Roll Date. On the last Index Business Day of the Monthly Roll Period (the Monthly Roll Date), the weight of the VIX Futures Index is only 1/20 in the first month VIX futures contracts. This 1/20 position in the first month VIX futures contracts will then be sold at the close on such Index Business Day. In this way, the initial position in the first month VIX futures contracts is progressively moved to the second month VIX futures contracts over the course of the Monthly Roll Period, until the following Monthly Roll Period starts and the old second month VIX futures contracts become the new first month VIX futures contracts. Calculation of the VIX Futures Index The Index Sponsor will calculate the level of the VIX Futures Index (the "VIX Futures Index Level") on each Index Business Day based on (i) the VIX Futures Index Level on the immediately preceding Index Business Day and (ii) the changes in the market value of the notional positions in the first month and second month VIX futures contracts. The VIX Futures Index Level on each Index Business Day is calculated as follows: ILVF(t) = ILVF(t -- 1) + [H1(t) x (P1(t) -- P1(t -- 1)) + H2(t) x (P2(t) -- P2(t -- 1))] where: ILVF(t) = the VIX Futures Index Level on the relevant Index Business Day ILVF(t -- 1) = the VIX Futures Index Level on the immediately preceding Index Business Day H1(t) = the notional holding of the first month VIX futures contracts on the relevant Index Business Day H2(t) = the notional holding of the second month VIX futures contracts on the relevant Index Business Day P1(t) = the settlement price of the first month VIX futures contracts on the relevant Index Business Day P2(t) = the settlement price of the second month VIX futures contracts on the relevant Index Business Day The notional holding of the first month VIX futures contracts on the relevant Business Day (H1(t)) is equal to (i)(a) the VIX Futures Index Level on the immediately preceding Index Business Day divided by (b) the weighted average settlement price for the immediately preceding Index Business Day (PAVG(t -- 1)) multiplied by (ii) the Roll Weight for the first VIX futures contract on such Index Business Day. Similarly, the notional holding of the second month VIX futures contracts on the relevant Business Day (H2(t)) is equal to (i)(x) the VIX Futures Index Level on the immediately preceding Index Business Day divided by (y) the weighted average settlement price for the immediately preceding Index Business Day (PAVG(t -- 1)) multiplied by (ii) the Roll Weight for the second VIX futures contract on such Index Business Day. 6 |
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The "Roll Weight" is designed to reflect the rolling each day from the first month VIX futures contracts into the second month VIX futures contracts. The Roll Weight for the first month VIX futures contracts on each Business Day (RW1(t)) is equal to (i) one plus the number of Index Business Days from (and excluding) such Index Business Day to (and including) the following Monthly Roll Date divided by (b) "D," the total number of Index Business Days from (but excluding) the previous Monthly Roll Date to (and including) the following Monthly Roll Date. The Roll Weight for the second month VIX futures contracts on the same Index Business Day (RW2(t)) is equal to (i) one minus (ii) the Roll Weight for the first month VIX futures contracts as calculated above. For example, if there are 20 Index Business Days in the current Monthly Roll Period, on the fourth Index Business Day during the Monthly Roll Period, the Roll Weight for the first month VIX futures contracts is 17/20 and the Roll Weight for the second month VIX futures contracts is 3/20. The weighted average settlement price for the immediately preceding Index Business Day is calculated as follows: PAVG(t -- 1) = RW1(t) x P1(t -- 1) + RW2(t) x P2(t -- 1) where: PAVG(t -- 1) = the weighted average settlement price for the immediately preceding Index Business Day RW1(t) = the Roll Weight for the first month VIX futures contracts P1(t -- 1) = the first month VIX futures contracts settlement price on the immediately preceding Index Business Day RW2(t) = the Roll Weight for the second month VIX futures contracts P2(t -- 1) = the second month VIX futures contracts settlement price on the immediately preceding Index Business Day Volatility Indicators The ProVol Index allocates long or short exposure to the VIX Futures Index based on the size and direction of the Signal and resulting Allocation calculated on each Index Business Day using three volatility indicators: (1) the High-Volatility Regime Probability, which is the probability of the SandP 500 being in a high-volatility environment as estimated by Deutsche Bank's proprietary Volatility Regime Model; (2) the VXV Index and (3) the Volatility Term Structure. The High-Volatility Regime Probability contributes positively to the Signal, while the VXV Index and the Volatility Term Structure contribute negatively to the Signal. Volatility Indicator 1 -- Volatility Regime Model The High-Volatility Regime Probability is the probability of the SandP 500 being in a high-volatility environment as estimated by Deutsche Bank's proprietary Volatility Regime Model (the "Model"). The Model is designed to calculate probabilities that the SandP 500 is in a low-volatility environment, a medium-volatility environment or a high-volatility environment on any given day based on a statistical review of the observed daily total returns of the SandP 500 during the period from January 4, 1988 (the "Model Base Date") to the day of estimation. 7 |
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The Model is based on the observation that the distribution of equity returns is different in different volatility environments. For example, low-volatility environments have been more likely to generate smaller, positive returns for the SandP 500 over the historical period, while high-volatility environments have been more likely to generate larger, negative returns over the historical period. The Model assumes the performance of the SandP 500 can be classified into three distinct regimes, the "Low-Volatility Regime," "Medium-Volatility Regime" and "High-Volatility Regime," each characterized by certain statistically derived parameters (the "Regime Parameters"), including the expected volatility of the SandP 500 (on a daily and annualized basis), the expected daily return of the SandP 500 and the expected long-term probability that the SandP 500 will be in a particular regime. The probability of the SandP 500 being in a particular regime on a given day (each, a "Regime Probability") is not directly observable through the volatility levels of the SandP 500 on that particular day. Instead, the Model calculates the probability of the SandP 500 being in each regime based on the daily return of the SandP 500 on that day, taking into account the Regime Probabilities for the previous day, which in turn take account of previous probability calculations based on the daily returns of the SandP 500 from the Base Date. Each new daily return of the SandP 500 is processed through the Model as an additional datum, and based on the input of such additional datum, the Model's calculation of Regime Probabilities is updated. Unlike a realized-volatility metric, which on any given day measures the volatility of an underlying asset over a fixed period of time in the past, the Model is intended to help navigate regime transitions by distinguishing between temporary volatility spikes and what the Model counts as true regime changes. The Model is constructed and maintained by Deutsche Bank AG, London Branch (the "Model Sponsor"). On each Calculation Date (as defined below), the Model Sponsor will calculate the Regime Probabilities for such Calculation Date as described below under "Calculation of Regime Probabilities." Features of the Volatility Regime Model Two principal factors affect the calculation of the Regime Probabilities: (i) the magnitude and direction of the daily total return of the SandP 500 on the relevant Calculation Date and (ii) the Model's calculation of the Regime Probabilities on the immediately preceding Calculation Date. In general, the magnitude and direction of the daily total return of the SandP 500 can be expected to have the following effects on each Calculation Date, all else being equal: a particularly volatile day should favor an increase in the Regime Probability for the High-Volatility Regime at the expense of the other two regimes. Conversely, a particularly quiet day should favor an increase in the Regime Probability for the Low-Volatility Regime at the expense of the other two regimes. In addition, a positive daily move in the level of the SandP 500 should favor an increase in the Regime Probability for the Low-Volatility Regime and a decline in the Regime Probability for the High Volatility Regime. Conversely, a negative daily move in the level of the SandP 500 should favor an increase in the Regime Probability for the High-Volatility Regime and a decline in the Regime Probability for the Low-Volatility Regime. The Regime Probability for the Medium-Volatility Regime should be neutral to the direction of a daily move. However, the magnitude of a daily move has significantly more impact on the Regime Probabilities than the direction of such move. For instance, a return that is both large and positive would generally be expected to lead to an increase in the Regime Probability for the High-Volatility Regime, while a return that is both small and negative would generally be expected to lead to an increase in the Regime Probability for the Low-Volatility Regime. 8 |
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The Model's calculation of the Regime Probabilities for each Calculation Date is directly affected by the Regime Probabilities on the Calculation Date immediately preceding such Calculation Date. In that sense, the Model has "memory." In addition, the regimes are "sticky," meaning that to the extent the Model calculates a high probability of being in a given regime, the Model operates in a way that favors maintaining the probability of being in that regime, thus making shifts between volatility regimes less frequent. Regime Parameters and Transition Matrix As noted above, each regime has a set of Regime Parameters including the expected volatility of the SandP 500 (on a daily and annualized basis), the expected daily return of the SandP 500 and the expected long-term probability that the SandP 500 will be in a particular regime. In addition, the Model includes a transition matrix (the "Transition Matrix") that sets forth the expected probability of the SandP 500 staying in the same regime or of transitioning from one regime to another (each, a "Transition Probability"). The Regime Parameters and the Transition Matrix have been determined by applying a statistical procedure known as "Maximum Likelihood Estimation" ("MLE") to the daily total returns of the SandP 500 from the Model Base Date to June 14, 2011 (the "Model Period"). MLE is a method of estimating the parameters of a statistical model. When applied to an observed data set and a given statistical model, MLE can determine the values of the model's parameters that make the observed data the most probable. The MLE procedure starts off by determining the likelihood of a single day observation given a fixed set of model parameters. The total likelihood of an entire data set is the product of the individual likelihood values for every observation in the data set. MLE then searches the entire parameter space to come up with the set of parameters that produce the maximum total likelihood for the given data set. The Regime Parameters in Table 1 below and the Transition Matrix in Table 2 below are the set of parameters that produce the maximum total likelihood for the daily total returns of the SandP 500 during the Model Period using the MLE procedure. The Model Sponsor will not revise the Regime Parameters and the Transition Matrix based on the daily returns of the SandP 500 outside the Model Period. 9 |
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Table 1: Regime Parameters* Low Volatility Medium Volatility High Volatility Expected Long-Term Probability 47% 46% 7% Expected Daily Return 0.1% 0.01% -0.2% Expected Daily Volatility 0.6% 1.1% 2.8% Annualized Expected Volatility 9.5% 18.1% 44.4% * The numbers appearing in Table 1 have been rounded for ease of presentation. As demonstrated by the "Expected Long-Term Probability" parameters, the Model expects the SandP 500 to be in the Low- and Medium-Volatility Regimes most of the time, and only be in the High-Volatility Regime occasionally. The parameters indicate that the Low-Volatility Regime tends to generate small daily returns (i.e. low volatility moves) with a bias towards positive returns, the Medium-Volatility Regime tends to generate somewhat larger daily returns (i.e. medium volatility moves) with little directional bias and the High-Volatility Regime tends to generate large daily returns (i.e. high volatility moves) with a bias towards negative returns. Table 2: Transition Matrix* From Low Volatility From Medium Volatility From High Volatility To Low Volatility 98.5% 1.5% 0.0% To Medium Volatility 1.4% 97.9% 3.9% To High Volatility 0.05% 0.6% 96.1% * The numbers appearing in Table 2 have been rounded for ease of presentation. As demonstrated by the Transition Matrix, which sets the probability of staying in the Low-, Medium- and High-Volatility Regimes at 98.5%, 97.9% and 96.1%, respectively, the Model expects the regimes to be "sticky," meaning that the SandP 500 should generally stay in the same regime and transitions from one regime to another should be infrequent. To the extent the SandP 500 is calculated to be in the Low-Volatility Regime, the probability of jumping into the High-Volatility Regime overnight is close to 0%. Similarly, to the extent the SandP 500 is calculated to be in the High-Volatility Regime, the probability of jumping into the Low-Volatility Regime overnight is close to 0%. However, an extreme single-day move could lead to a transition from the Low-Volatility Regime to the High-Volatility Regime. 10 |
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Calculation of Regime Probabilities On each Calculation Date, the Model will determine the Regime Probabilities through the following steps using the Regime Parameters shown in Table 1 and the Transition Matrix shown in Table 2. First, the Model will determine the expected likelihood of such day's return coming from each of the volatility regimes (each, an "Expected Probability"). The Expected Probability for each regime (which we also refer to as the "current regime") is calculated by adding the following results: (i) the product of the "old" Regime Probability for the current regime on the immediately preceding Calculation Date and the Transition Probability of staying in the current regime and (ii) for each of the other two regimes, the product of the "old" Regime Probability for that regime and the Transition Probability of transitioning from that regime into the current regime. This step will modify the "old" Regime Probabilities by taking into account the probabilities of the SandP 500 transitioning from one regime to another. Second, the Model will determine the single-day likelihood factors for each regime (each, a "Single-Day Likelihood Factor") by comparing the daily total return of the SandP 500 on such Calculation Date with the Regime Parameters. In general, small daily returns (i.e. low volatility moves) tend to generate Single-Day Likelihood Factors in favor of the Low-Volatility Regime and to a less extent the Medium-Volatility Regime. Conversely, large daily returns (i.e. high volatility moves) tend to generate Single-Day Likelihood Factors in favor of the High-Volatility Regime and to a less extent the Medium-Volatility Regime. Moderate daily returns (i.e. medium volatility moves) tend to generate Single-Day Likelihood Factors in favor of the Medium-Volatility Regime. In addition, positive daily returns tend to generate Single-Day Likelihood Factors in favor of the Low-Volatility Regime and not in favor of the High-Volatility Regime. Conversely, negative daily returns tend to generate Single-Day Likelihood Factors in favor of the High-Volatility Regime and not in favor of the Low-Volatility Regime. The Single-Day Likelihood Factor for the Medium-Volatility Regime is approximately neutral to the direction of daily returns. The size of the daily returns has significantly more impact on the Single-Day Likelihood Factors than the direction. The absolute size of the Single-Day Likelihood Factors is not important; it is their size relative to each other that is important in determining the "new" Regime Probabilities on the Calculation Date. Third, after determining the Single-Day Likelihood Factor for each regime, the Model will determine the "new" Regime Probabilities on the Calculation Date by (i) multiplying the Single-Day Likelihood Factor of each regime by the Expected Probability for such regime and (ii) dividing each of the results by the sum of the results for all three regimes. The "new" Regime Probabilities will indicate the probabilities of the SandP 500 being in the Low-, Medium- and High-Volatility Regimes on such Calculation Date. On the next Calculation Date, the new daily return of the SandP 500 will be processed in a similar manner through the Model as an additional datum, and the Model's calculation of Regime Probabilities will be updated based on the input of such additional datum. On the Model Base Date, the Regime Probability for each of the Low-, Medium- and High-Volatility Regimes was set to be equal to the "Expected Long-Term Probability" parameters of 47%, 46% and 7%, respectively. The following example illustrates the calculation of the Regime Probabilities on a Calculation Date and assumes that (i) the Regime Probabilities for the Low-, Medium- and High-Volatility Regimes on the immediately preceding Calculation Date are 75%, 15% and 10%, respectively and (ii) the daily total return of the SandP 500 on such Calculation Date is 1.0% . 11 |
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Step 1: Calculate the Expected Probabilities The Expected Probabilities for each regime will be calculated using the Transition Matrix in Table 2 and the Regime Probabilities on the immediately preceding Calculation Date. For example, the Expected Probability for the Low-Volatility Regime will be equal to the sum of: (i) the product of the Regime Probability for the Low-Volatility Regime on the immediately preceding Calculation Date (75%) and the probability of staying in the Low-Volatility Regime (98.5%); (ii) the product of the Regime Probability for the Medium-Volatility Regime immediately preceding Calculation Date (15%) and the probability of transitioning from the Medium-Volatility Regime into the Low-Volatility Regime (1.5%); and (iii) the product of the Regime Probability for the High-Volatility Regime immediately preceding Calculation Date (10%) and the probability of transitioning from the High-Volatility Regime into the Low-Volatility Regime (0.0%) . The Expected Probabilities for the Medium- and High-Volatility Regimes will be calculated in a similar manner as shown below: For Low-Volatility Regime: 75% x 98.5% + 15% x 1.5% + 10% x 0.0% = 74.1% For Medium-Volatility Regime: 75% x 1.4% + 15% x 97.9% + 10% x 3.9% = 16.1% For High-Volatility Regime: 75% x 0.05% + 15% x 0.6% + 10% x 96.1% = 9.7% Step 2: Calculate the Single-Day Likelihood Factors The Single-Day Likelihood Factors for each regime will be determined by the Model based on the alignment of the daily total return of the SandP 500 and the various Regime Parameters. For example, if the daily total return of the SandP 500 on a Calculation Date is 1.0%, the Single-Day Likelihood Factors would be 21.586, 24.258 and 12.998 for the Low-, Medium- and High-Volatility Regimes, respectively. Because the daily total return of 1.0% (meaning that the daily volatility of the SandP 500 on the Calculation Date is also 1.0%) is closer to the "Expected Daily Volatility" and "Expected Daily Return" parameters of the Low-Volatility and Medium-Volatility Regimes, the Single-Day Likelihood Factors generated by this return are in favor of such regimes. Because the daily total return of 1.0% is positive and the volatility is relatively small in size (as compared to the Expected Daily Volatility of 2.8% for the High-Volatility Regime), the Single-Day Likelihood Factors are not in favor of the High-Volatility Regime. Step 3: Calculate the Regime Probabilities The Regime Probability for each regime will be equal to the quotient, the numerator of which is the product of (i) the Single-Day Likelihood Factor for such regime and (ii) the Expected Probability for such regime, and the denominator of which is the sum of the products of the Single-Day Likelihood Factor and the Expected Probability for each regime. Because the Single-Day Likelihood Factors in this example are more in favor of the Medium-Volatility Regime, less in favor of the Low-Volatility Regime and least in favor of the High-Volatility Regime, the Regime 12 |
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Probability increases from 15% to 18.5% for the Medium-Volatility Regime, increases slightly from 74.1% to 75.5% for the Low-Volatility Regime and decreases from 10% to 6.0% for the High-Volatility Regime. [GRAPHIC OMITTED] "Calculation Date" means a day, as determined by the Model Sponsor, on which the New York Stock Exchange and the NASDAQ Stock Market are open for trading during their regular trading session, notwithstanding any such relevant exchange closing prior to its scheduled closing time. The High-Volatility Regime Probability will be used as a volatility indicator for purposes of calculating the Signal. Volatility Indicator 2 -- The VXV Index The CBOE SandP 500([R]) 3-Month Volatility Index, which we refer to as the VXV Index, was developed by the CBOE and is calculated, maintained and published by the CBOE. The VXV Index is a benchmark index designed to measure the market's expectation of volatility of the SandP 500 over the next 93 days, and calculated based on the prices of certain put and call options on the SandP 500. During periods of market instability, the prices of options linked to the SandP 500 typically increase (assuming all other relevant factors remain constant or have negligible changes). This, in turn, causes the level of the VXV Index to increase. The VXV Index has historically had negative correlations to the SandP 500. The VXV Index is calculated similarly to the VIX Index except that the VXV Index is designed to measure the market's expectation of volatility the SandP 500 over the next 93 days, rather than the next 30 days. The calculation of the VXV Index involves a formula that uses the prices of a weighted series of out-of-the-money SPX Options to derive a constant 93-day forward measure of market volatility. The VXV Index is calculated independently of any particular option pricing model and in doing so seeks to eliminate any biases which may otherwise be included in using options pricing methodology based on certain assumptions. CBOE lists SPX Option series in three near-term contract months plus at least three additional contracts expiring on the March quarterly cycle; that is, on the third Friday of March, June, September and December. To arrive at the VXV Index level, a broad range of out-of-the-money SPX Options with expiration dates that most closely bracket a 93-day maturity are selected. The results of each of the contract months are then interpolated to arrive at a single value with a constant maturity of 93-days to expiration. For example, when SPX contract months are sequential; 13 |
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that is, expiring one month apart, the "roll" is a smooth transition from one set of options to the next. Yet, when the expiration dates of the SPX Options used to calculated the VXV Index are two to three months apart, there is a "jump" in the option weights by as much as 35% in order to maintain a constant weighted average maturity of 93-days to expiration. There are no futures contracts trading on the VXV Index. The VXV Index was launched by the CBOE on November 12, 2007. Volatility Indicator 3 -- Volatility Term Structure The Volatility Term Structure is the "steepness" of the implied volatility curve as measured by the ratio between the VXV Index and the VIX Index. When the VXV Index level is higher than the VIX Index, reflecting an upward sloping implied volatility curve, longer-dated futures contracts will generally be priced higher than the nearer contracts and spot prices and the market is in contango. When the VXV Index is lower than the VIX Index, reflecting a downward sloping implied volatility curve, longer-dated futures contracts will generally be priced lower than the nearer contracts and spot prices and the market is in backwardation. The cost of carrying VIX futures contracts will be positive (reflecting a loss) in a contango market and negative (reflecting a profit) in a backwardation market. The implied volatility market tends to be in contango most of the time, making it very expensive to continuously carry VIX futures contracts. As the Volatility Term Structure increases, reflecting a steeper implied volatility curve, the cost of carrying VIX futures contracts will increase. Calculation of the Signal The Signal is calculated on each Index Business Day by aggregating the weighted levels of the three volatility indicators. Generally speaking, the Signal is positive when realized volatility is high, there is a high probability that implied volatility will increase, and/or the implied volatility market is in backwardation (to generate returns from negative carrying costs) and is negative when realized volatility is low, there is a high probability that implied volatility will decrease, and/or the implied volatility market is in contango (to generate returns from positive carrying costs). In addition to the three volatility indicators, the Signal also takes into account the prior day's Allocation, which harnesses the value of past information and makes changes in volatility exposure more gradual. The Signal will be calculated on each Index Business Day as follows: X(t) = 0.28 + 0.65 x pH(t -- 1) -- 0.29 x VXV(t -- 1)/20 -- 0.05 x [VXV(t -- 1)/VIX(t -- 1)] + 0.81 x F(t -- 1) where: X(t) = The Signal on the relevant Index Business Day pH(t -- 1) = The High Volatility Regime Probability on the immediately preceding Index Business Day VXV(t -- 1) = The level of the VXV Index on the immediately preceding Index Business Day VIX(t -- 1) = The level of the VIX Index on the immediately preceding Index Business Day F(t -- 1) = The allocation to the VIX Futures Index on the immediately preceding Index Business Day 14 |
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The Allocation on each Index Business Day will be calculated based on the Signal; provided that a weak Signal between 0.1 and --0.1 will result in a zero Allocation and the Allocation will not exceed the maximum Allocation of 0.3 or --0.3. The Allocation on each Index Business Day will be calculated as follows: (i) If the Signal on such Index Business Day is equal to or greater than zero, the Allocation will equal the product of (a) 1.5 and (b) the Signal minus 0.1, subject to the minimum Allocation of zero and the maximum positive Allocation of 0.3. (ii) If the Signal on such Index Business Day is less than zero, the Allocation will equal the product of (a) 1.5 and (b) the Signal plus 0.1, subject to the minimum Allocation of zero and the maximum negative Allocation of --0.3. Calculation of the ProVol Indices Each ProVol Index measures the return of a daily rebalanced notional long or short position in the VIX Futures Index. The level of each ProVol Index (the "ProVol Index Level") on each Index Business Day is calculated based on (i) the relevant ProVol Index Level on the immediately preceding Index Business Day and (ii) the changes in the market value of the notional position in the VIX Future Index minus the Index Fee. Each ProVol Index Level on each Index Business Day is calculated as follows: IL(t) = IL (t -- 1) + HVF(t) x [ILVF(t) -- ILVF(t -- 1)] -- C(t) Where, IL(t) = the ProVol Index Level on the relevant Index Business Day IL(t -- 1) = the ProVol Index Level on the immediately preceding Index Business Day HVF(t) = the notional holding of the VIX Futures Index on the relevant Index Business Day ILVF(t) = the VIX Futures Index Level on the relevant Index Business Day ILVF(t -- 1) = the VIX Futures Index Level on the immediately preceding Index Business Day C(t) = the Index Fee on the relevant Index Business Day HVF(t), which is the notional holding of the VIX Futures Index on each Index Business Day, is equal to (i) the ProVol Index Level on the immediately preceding Index Business Day multiplied by (ii) the Weight of the VIX Futures Index on such Index Business Day divided by (iii) the VIX Futures Index Level on the immediately preceding Index Business Day. 15 |
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The weight of the VIX Futures Index in the ProVol Index (the "Weight") on each Index Business Day will be calculated based on the Allocation on such Index Business Day and the applicable leverage factor as follows: (i) If the Allocation is greater than zero, then the Weight will be equal to the product of the Allocation and the long leverage factor for the specific version of the ProVol Index: ProVol Hedge Index: 2 ProVol Carry Index: 1 ProVol Balanced Index: 1.5 . (ii) If the Allocation is equal to zero, then the Weight will be zero. (iii) If the Allocation is less than zero, then the Weight will be equal to the product of the Allocation and the short leverage factor for the specific version of the ProVol Index: ProVol Hedge Index: 1 ProVol Carry Index: 2 ProVol Balanced Index: 1.5 The Index Fee takes into account changes in the notional VIX futures contracts position associated with both the daily rolling from the first month to the second month VIX futures contracts underlying the VIX Futures Index as well as any changes in the size of the notional position in the VIX Futures Index. Each portion of the Index Fee is equal to 0.35% of the dollar value of the futures contracts notionally traded on such Index Business Day, subject to a minimum fee equal to the number of futures contracts notionally traded on such Index Business Day times a fixed multiplier of 0.1. The Index Fee is related to the dollar value or number of contracts notionally traded. Thus, large or more frequent shifts in the Signal or greater or more frequent changes in VIX futures contracts prices will require greater reallocation and will result in higher costs. Additionally, lower VIX futures contracts prices, which require a greater number of contracts to be notionally traded in order to achieve the same value, will also result in higher costs. We expect the Index Fee to average between 1.5bps and 2bps (0.015% and 0.02%) per Index Business Day. However, the actual Index Fee may be substantially higher on days when there is a substantial change in the Allocation or prices of the VIX futures contracts, resulting in a substantial number or value of VIX futures contracts notionally traded. From and including 2006 to and including 2011, the annual Index Fees for the ProVol Indices as retroactively calculated have ranged from 0.00% to 7.12% . The SandP 500 The SandP 500([R]) Index, which we refer to as the SandP 500, is intended to provide a broad performance benchmark for the U.S. equity markets. The daily calculation of the value of the SandP 500 is based on the relative value of the aggregate market value of the common stocks of 500 companies as of a particular time compared to the aggregate average market value of the common stocks of 500 similar companies during the 16 |
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base period of the years 1941 through 1943. The 500 companies are not the 500 largest companies listed on the New York Stock Exchange and not all 500 companies are listed on such exchange. The index sponsor chooses companies for inclusion in the SandP 500 with the objective of achieving a distribution by broad industry groupings that approximates the distribution of these groupings in the common stock population of the U.S. equity market. The index sponsor may from time to time, in its sole discretion, add companies to, or delete companies from, the SandP 500 to achieve the objectives stated above. Relevant criteria employed by the index sponsor include the viability of the particular company, the extent to which that company represents the industry group to which it is assigned, the extent to which the company's common stock is widely held and the market value and trading activity of the common stock of that company. Deutsche Bank AG has filed a registration statement (including a prospectus) with the SEC for the offerings to which this communication relates. Before you invest, you should read the prospectus in that registration statement and other documents the issuer has filed with the SEC for more complete information about the issuer and this offering. You may get these documents for free by visiting EDGAR on the SEC website at www.sec.gov. Alternatively, the issuer, any underwriter or any dealer participating in the offering will arrange to send you the prospectus if you request it by calling toll-free 1-800-311-4409. 17 |