BULL MARKET IN FEARGRANT’S FALL CONFERENCE / NEW YORK CITY - OCTOBER 23, 2012                                             ...
We live in uncertain times… a bull market in fear                                                                         ...
What is Volatility?                                                                                               BULL MAR...
Volatility in World’s End Deflation                                                                                       ...
Volatility in Hellfire of Inflation                                                                                       ...
Everything you need to know about trading volatility                                                                      ...
Everything you need to know about trading volatility                                                                      ...
Bull Market in Fear                                                                                  BULL MARKET IN FEAR  ...
Bull Market in Fear                                                                                        BULL MARKET IN ...
Abnormally Steep Volatility Term Structure                                                                                ...
Abnormally Steep Volatility Term Structure                                                                                ...
Volatility is cheap and expensive at the same time                                                                        ...
Volatility Regimes Defined by Central Banking                                                                             ...
Post-Traumatic-Deflation-Disorder (PTDD)                                                                                  ...
High Cost of Tail Risk Insurance                                                                                          ...
Extreme Volatility-of-Volatility and Hyper-Correlations                                                                   ...
Extreme Volatility-of-Volatility and Hyper-Correlations                                                                   ...
Volatility of an Impossible Object                                                                                        ...
Bet on unknown unknowns… don’t hedge known unknowns                                                                       ...
Bet on unknown unknowns… don’t hedge known unknowns                                                                       ...
The more people fear the LEFT TAIL the more you should buy the RIGHT… and vice versa                                      ...
The more people fear the LEFT TAIL the more you should buy the RIGHT…                                                     ...
Fear over Fundamentals                                                                                                    ...
Risk Free Assets are Risky                                                                                                ...
Risk Free Assets are Risky                                                                                                ...
Volatility of an Impossible Object                                                                                        ...
Volatility of an Impossible Object                                                                                 BULL MA...
Post-Modern Economy                                                                                                     BU...
Volatility can be more than just FEAR                                                                        BULL MARKET I...
Artemis volatility presentation 102312
Artemis volatility presentation 102312
Artemis volatility presentation 102312
Artemis volatility presentation 102312
Artemis volatility presentation 102312
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Artemis volatility presentation 102312

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Fascinating presentation that I found on the web discussing volatility and risk.



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Artemis volatility presentation 102312

  1. 1. BULL MARKET IN FEARGRANT’S FALL CONFERENCE / NEW YORK CITY - OCTOBER 23, 2012 For Investment Professional Use. Not for DistributionChristopher Cole, CFAArtemis Capital Management LLCArtemis Vega Fund LP520 Broadway, Suite 350Santa Monica, CA 90401(310) 496-4526 phone(310) 496-4527 faxinfo@artemiscm.com
  2. 2. We live in uncertain times… a bull market in fear BULL MARKET IN FEAR Volatility is the market price of uncertainty “You cannot stop the waves, but you can learn to surf” Jon Kabat-Zinn 1Definition of fear from Merriam-Webster
  3. 3. What is Volatility? BULL MARKET IN FEAR Volatility at World’s End Deflation Imagine the world economy as an armada of ships passing through a narrow and dangerous strait between the waterfall of deflation and hellfire of inflation Our resolution to avoid one fate may damn us to the other 2Illustration by Brendan Wuiff based on concept by Christopher Cole
  4. 4. Volatility in World’s End Deflation BULL MARKET IN FEAR Volatility shocks are rightfully associated with deflationary crashes Volatility at Worlds End Deflation 120 Dow Jones Industrial Index (RHS) vs. 1-month Realized Volatility of DJIA (LHS) 50,000 100 80 DJIA (logarithmic scale)Realized Volatility (%) 5,000 60 40 500 20 0 50 1928 1930 1932 1934 1936 1938 1940 1942 1944 1946 1948 1950 1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 3
  5. 5. Volatility in Hellfire of Inflation BULL MARKET IN FEAR Extreme volatility can also occur in hyperinflation 120 100,000,000 Performance of German Stock Market Performance adj. for fixed exchange 10,000,000 Performance in paper marks (mil) 100 during Weimar Republic Hyperinflaton 1,000,000 100,000 10,000 80 1,000 Adj. according to USD exchange rate 100 60 Adj. according to wholesale index numbers 10 1 40 In paper marks, Weimar 0 0 0 20 0 0 0 0 Feb-18 Feb-19 Feb-20 Feb-21 Feb-22 Feb-23 Nov-18 Nov-19 Nov-20 Nov-21 Nov-22 Nov-23 May-18 May-19 May-20 May-21 May-22 May-23 Aug-18 Aug-19 Aug-20 Aug-21 Aug-22 Aug-23 2,000 Weimar VIX?(1) Realized Volatility of German Stock Market during Weimar Republic Hyperinflation 1,500Volatility (%) (monthly volatility data annualized) 1,000 500 0 Feb-18 Feb-19 Feb-20 Feb-21 Feb-22 Feb-23 Nov-18 Nov-19 Nov-20 Nov-21 Nov-22 Nov-23 May-18 May-19 May-20 May-21 May-22 May-23 Aug-18 Aug-19 Aug-20 Aug-21 Aug-22 Aug-23Source: “Economics of Inflation; A Study of Currency Depreciation in Post-War Germany" by Constantino Bresciani-Turroni Out of Print / 1968 4(1) Based upon monthly realized variance from available stock price data.
  6. 6. Everything you need to know about trading volatility BULL MARKET IN FEAR“There are known knowns; there are things we know that we know. There are known unknowns;that is to say there are things that, we now know we dont know. But there are also unknownunknowns – there are things we do not know, we dont know.” Donald Rumsfeld, United States Secretary of Defense Known Unknowns Unknown Unknowns US Fiscal Cliff  European Crisis China hard landing War with Iran  Global Recession  Fiscal Austerity ? Volatility Volatility of Volatility  Vanilla Options  Realized Volatility  Forward Volatility  Tail Risk Hedging  VIX Index  Variance Swap  Convexity  Vol Curve Trades Risks that you Risks that you Risks that you Risks that you know and can know but can’t don’t know but don’t know and quantity quantify could quantify can’t quantify 5
  7. 7. Everything you need to know about trading volatility BULL MARKET IN FEAR Two very different styles of crash depending… Known Unknowns Unknown Unknowns Debt-Cycle Crash Existential Flash Crash (2008 Crash, Great Depression) Crash occurs over time (months)  ? (Black Monday 1987, 2010 Crash) Hyper-speed crash (days, seconds) Slow recovery  Fast recovery Natural end of leveraging cycle  Market fragmentation High volatility for long period  Extreme volatility for shorter period Elevated volatility-of-volatility  Extreme volatility-of-volatility Start of a recession or depression  Omen of future recession (often) Predictable Unpredictable (in retrospect) (even In retrospect) 6
  8. 8. Bull Market in Fear BULL MARKET IN FEAR What is the “Bull Market in Fear”? New paradigm for pricing risk that emerged after the 2008 financial crisis as related to our collective fear of the next deflationary crashBull Market in Fear is Defined by1. Abnormally Steep Volatility Term-Structure2. Distortions in Volatility from Monetary Policy3. Expensive Portfolio Insurance4. Violent Volatility Spikes and Hyper-Correlation 7
  9. 9. Bull Market in Fear BULL MARKET IN FEAR Structural imbalances in supply-demand dynamics of volatility marketsI. Emotional  Post-traumatic Deflation Disorder  Desire for safety and security at any costII. Monetary Greater  Forced participation in risk assets drives desire for hedging Demand for  Unspoken feeling that gains in financial assets are “artificial” VolatilityIII. Macro-Risks  Debtor-developed economies face structural headwinds  Unrest in Middle EastIV. Regulatory  Government regulation (Dodd-Frank, Volcker rule) has Less Supply constrained risk appetite for banks to supply volatility of Volatility  Lower demand for structured products by investors 8
  10. 10. Abnormally Steep Volatility Term Structure BULL MARKET IN FEAR "There is no terror in the bang, only in the anticipation of it." Alfred Hitchcock Volatility term-structure measures the anticipation of future volatility Bull Market in Fear / VIX Futures Curve (normalized by spot VIX) 1.90x 2004 to Present 1.70xVix Futures/Spot Vix 1.50x 1.30x 1.10x 0.90x 0.70x 0.50x Mar-04 Jun-04 Sep-04 Nov-04 Feb-05 May-05 Aug-05 Oct-05 Jan-06 Apr-06 Jun-06 Sep-06 Dec-06 Mar-07 May-07 Aug-07 Nov-07 Feb-08 Apr-08 Jul-08 Oct-08 Dec-08 Mar-09 Jun-09 Sep-09 Nov-09 Feb-10 May-10 Jul-10 Oct-10 Jan-11 Apr-11 Jun-11 Sep-11 Dec-11 M6 Feb-12 M3 Jul-12 VIX Expiry 9
  11. 11. Abnormally Steep Volatility Term Structure BULL MARKET IN FEAR The most extreme term-structure for S&P 500 index volatility in two decades reflects continued anticipation of a deflationary collapse Ratio of Expected Future Volatility as Ratio to Spot Volatility 2.4x S&P 500 optionsExpected Volatility as a Ratio to Spot Volatility 2.2x 2.0x VIX Index 1.8x 1.6x 1.4x 1.2x 0.08 0.17 0.25 0.33 0.42 0.50 0.58 0.67 0.75 0.83 0.92 1.00 1.08 1.17 1.25 1.33 1.42 1.50 Expiry (1=year) Cumulative Average (1990-Mar 2012) 2012 YTD (avg.) Bull Market of 1990s (avg.) 2000 to Feb 2009 (avg.) 2009 to 2012 Bull Market in Fear 10
  12. 12. Volatility is cheap and expensive at the same time BULL MARKET IN FEAR Low VIX index does not mean cheap volatility 35 Low Volatility? Really? VIX Futures Curve Comparison August 2012 vs. September 2008 30 !Forward VIX index (%) 25 20 August 17, 2012 / Lowest VIX in 5 years 15 September 15, 2008 / Day after Lehman Bros. Bankruptcy 10 Spot Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 11
  13. 13. Volatility Regimes Defined by Central Banking BULL MARKET IN FEAR Volatility spikes consistently occur after the end of central bank balance sheet expansion 130% Fed Balance Sheet Expansion and VIX index 50 No Fed Action LTRO (ECB), 120% QEI Aug 2011 Crash Op Twist (Fed) & QEIII (Fed) 45Fed BS % Change since September 2008 QEII Op. Twist+LTRO(ECB) QEIII 110% VIX QEII 40 Flash Crash VIX Index (%) 100% 35 90% 30 80% 25 70% 20 60% 15 May-09 May-10 May-11 May-12 Mar-09 Mar-10 Mar-11 Mar-12 Sep-09 Sep-10 Sep-11 Sep-12 Nov-09 Nov-10 Nov-11 Jul-09 Jul-10 Jul-11 Jul-12 Jan-10 Jan-11 Jan-12 Since 2008 global central banks have expanded their balance sheets by $9 trillion - enough fiat money to buy every person on earth a 55 wide-screen 3D television 12
  14. 14. Post-Traumatic-Deflation-Disorder (PTDD) BULL MARKET IN FEAR Tail Events are now priced as if they are standard risks Highly unlikely events are either ignored or vastly over weighted based on our collective experiences Lifetime odds of Dying 25% Implied Odds of % Returns for S&P 500 index from these causes is 1 in 4.7(1) SPX Options (1year) Black Swan? 20% Heart Disease Actual from Sep 2008 to Sep 2012 1 in 6 Implied from Jan 1990 to Sep 2008 Implied from Sep 2008 to Sep 2012 Cumulative Probability 15% September 2012 (average) Stroke 1 in 28 10% Car Crash 1 in 88 5% 0% -45% -40% -30% -25% -15% -10% -50% -35% -20% 10% 15% 20% 25% 30% 35% 40% -5% 0% 5% Implied 12m %G/L in S&P 500 Index A “black swan” is not dying because your parachute didn’t open while skydiving…. it is dying because the guy whose parachute didn’t open landed on you while you were golfingNote: Artemis calculates the implied probability distribution using interpolated weights from variance swap pricing. This methodology may occasionally give higher weightings to tails in down markets than other methods like taking the second derivative of call prices, fitting mixture of normal PDFs to recover prices, or fitting vol models (SVI,SABR). 13(1) "Lifetime Odds of Death for Selected Causes, United States, 2007" / National Safety Council 2011 Edition
  15. 15. High Cost of Tail Risk Insurance BULL MARKET IN FEAR Fear of deflation is not MISPLACED but it is MISPRICED You are not smart for hedging what everyone else already knows! S&P 500 Index 12-month % Contribution to Model-Free Variance by Expected Returns (19951995 to 2012 to March 2012) 50% 40% Cumulative Probability 30% 40%-50% 20% 30%-40% 10% 20%-30% 0% 10%-20% 1995 0%-10% 1995 1996 1996 1997 1998 1998 1999 2000 2000 2001 2002 2002 2003 2004 2004 2005 2006 2006 2007 2008 25.0% 2008 10.0% 2009 -5.0% -20.0% 2010 -35.0% -50.0% Implied 12m %G/L in S&P 500 indexNote: Artemis calculates the implied probability distribution using interpolated weights from variance swap pricing. This methodology may occasionally give higher weightings to tails in down markets than other 14 methods like taking the second derivative of call prices, fitting mixture of normal PDFs to recover prices, or fitting vol models (SVI,SABR).
  16. 16. Extreme Volatility-of-Volatility and Hyper-Correlations BULL MARKET IN FEAR Fire Risk is High Today in the Forest Higher correlations are kindling for violent volatility fires (spike) HIGHER CORRELATIONS lead to... 1 S&P 500 Sector Correlation (60 day) 2000 to 2012 0.8 Correlation (0-1) 0.6 0.4 0.2 0 2000 2001 2002 2003 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 205 More VIOLENT VOLATILITY SPIKES 185 Volatility of VIX index (60 day) 165 2000 to 2012Volatility (%) 145 125 105 85 65 45 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 15
  17. 17. Extreme Volatility-of-Volatility and Hyper-Correlations BULL MARKET IN FEAR Volatility is a Shadow Currency in the Bull Market for Fear $USD currency index strength = Higher Volatility Correlation of $USD Index to VIX Index0.6 (1986 to 2012)0.40.2 0-0.2-0.4 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012Note: Prior to 1990 there was not VIX index. We have substituted the CBOE VXO index, the precursor to the VIX, which was available starting in 1986. 16
  18. 18. Volatility of an Impossible Object BULL MARKET IN FEAR How to beat a “Bull Market in Fear” Hedge unknown unknowns and sell known unknowns When the market identifies a risk it is usually overpriced in volatility marketsThe more we fear the left tail the more you should buy the right Tail risk pricing (both left and right) has been consistently late to the game Fear is a better reason to buy than fundamentals Volatility (fear) is an effective leading indicator to inform asset allocation When Risk-Free is Risky… buy Volatility on Safety Itself! when a “bull market in fear” meets a “bubble in safety” bet on interest rate volatility 17
  19. 19. Bet on unknown unknowns… don’t hedge known unknowns BULL MARKET IN FEAR Volatility markets are surprisingly bad at predicting future risk When markets identify a ‘known unknown’ that risk traditionally is overblown or at the very minimum over-hedged Fiscal Cliff or Volatility of Volatility Cliff? 240 Predicted Volatility of VIX vs. Realized Vol of VIX October 2012 220 Volatility of VIX was 200% on Oct 13, 2008 Maximum was 265% on Aug 29, 2011 200 180Volatility of VIX (%) 160 Very 140 Cheap Expensive Fear Fear 120 100 Market Expected Volatility of VIX (local) US Fiscal Cliff 5yr Average Realized Vol-of-VIX 80 1yr Average Realized Vol-of-VIX 60 6mo Average Realized Vol-of-VIX 40 11-Oct-12 6-Nov-12 3-Dec-12 28-Dec-12 25-Jan-13 21-Feb-13 19-Mar-13 15-Apr-13 9-May-13 Forward Period 18
  20. 20. Bet on unknown unknowns… don’t hedge known unknowns BULL MARKET IN FEAR Sell “known unknowns” and Buy “unknown unknowns”… …monetize the bull market in fear by playing the term structure 1.6x Fear Arbitrage (Volatility futures & Options, SPX Vol Term Structure)Forward Volatility Term Structure 1.5x 1.4x 1.3x 1.2x 1.1x Unknown Known-Unknown Crash Unknown Crash 1.0x Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Forward Volatility (October 2012) Historical Average Forward Volatility (since 2004) 19
  21. 21. The more people fear the LEFT TAIL the more you should buy the RIGHT… and vice versa BULL MARKET IN FEAR Role of the trader is not so much to predict the future but to identify mispriced risk The options market is consistently late to the game in pricing both the right and left tails Cross Asset Implied Probability Distribution Comparison (2008 pre-crisis to 2012) Variance Swap Weighting { SPY, EFA, EEM, TLT, IEF, HYG, USO, GLD } Pre-Crisis 2008 2012 60% 60% 60% Right Left 50% 50% Tail 50% tail Bias bias Probability OfOf Return 40% Probability Of Return Probability Return 40% 40% 30% 30% 30% 20% 20% 20% Gold Gold Oil Oil Gold HY Bonds 10% Oil Bonds HY 10% UST 10yr 10% UST 10yr HY Bonds UST 30yr UST 30yr UST 10yr Intl. Equity (Emerg) UST 30yr (Emerg) Intl. Equity Intl. Equity (Dev) Intl. Equity (Dev) Intl. Equity (Emerg) US Equity 0% Intl.Equity (Dev) US Equity 0% 0% US Equity -3.0σ -2.5σ -2.0σ -1.5σ -1.0σ -0.5σ +0.0σ +0.5σ +1.0σ +1.5σ +2.0σ +2.5σ -3.0σ -2.5σ -2.0σ -1.5σ -1.0σ -0.5σ +0.0σ +0.5σ +1.0σ +1.5σ +2.0σ +2.5σ -3.0σ -2.5σ -2.0σ -1.5σ -1.0σ -0.5σ +0.0σ +0.5σ +1.0σ +1.5σ +2.0σ +2.5σ Expected 1yr Asset Return Distribution Expected 1yr Asset Class Return Distribution Expected 1yr Asset Return Distribution by Standard Deviation (Historical) by Standard Deviation (Historical) by Standard Deviation (Historical)Note: Artemis calculates the implied probability distribution using interpolated weights from variance swap pricing. This methodology may give higher weightings to tails in down markets than more traditional methodslike taking the second derivative of call prices, fitting mixture of normal PDFs to recover prices, or fitting vol models (SVI,SABR). 20
  22. 22. The more people fear the LEFT TAIL the more you should buy the RIGHT… BULL MARKET IN FEAR Maybe it is correct to buy tail risk insurance ... but is everyone just hedging the wrong tail? Mirror Reflection: Deflation vs. Hyperinflation 20% S&P 500 Probability Distributions in different Regimes of Risk 1-year Gain-Loss%Cumulative Probability Weighting 15% Implied from March 2012 SPX options Simulated from in 2013-2022 Hyperinflationary Model (1 scenario of 10k) 10% Future? 5% 0% -50% -43% -35% -28% -20% -13% -5% +3% +10% +18% +25% +33% +40% +48% One Year Gain/Loss % in S&P 500 index Note: Artemis created a model to simulate the behavior of the S&P 500 index and volatility during an inflationary shock. The model is not intended to be a prediction of the future but is merely a rudimentary stochastic- based method to understand what modern markets may look like in rampant inflation. The simulation runs 10,000 price scenarios for the S&P 500 index over 10 years modeling daily stock price behavior using a generalized Wiener process (Wiener.. not Weimar) and a drift rate that assumes linkages between annual CPI and equity performance. We assume inflation rises sharply from current levels of 2.87% in 2012 to 26% by 2015 and stays elevated at that level until 2017 (20% a year overall). The average volatility shifts are based upon assumptions regarding equity return to variance parameters observed in prior inflationary episodes 21 (1970s US & 1920s Germany). The simulation shows annualized SPX returns for the decade at +9.94% but adjusted for inflation this drops to -9.8%.
  23. 23. Fear over Fundamentals BULL MARKET IN FEAR It is hard to have a bear market in a bull-market for fear Volatility term-structure is an effective indicator to inform equity exposure It pays to have exposure to stocks when markets are hedged! S&P 500 index portfolio exposure based on Vol Slope 600 1996 to 2012 550 Period of Steep Vol Slope (1yr VarK / VIX > 1.10) 500 S&P 500 Index Tactical Allocation to S&P 500 during periods with Steep Vol Slope 450 400Growth of $100 350 300 250 200 150 100 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 22
  24. 24. Risk Free Assets are Risky BULL MARKET IN FEAR When the “Bull Market in Fear” meets a “Bubble in Safety” a short equity option position and “risk-free’ UST bond have similar risk-to-reward payoffs! Efficient Frontier / Risk to Reward Comparison Long Dated UST Bond vs. 1yr OTM Short Puts (collateralized) 30yr UST Bond Return / Yield SPX Short Put (Strike @-25% OTM) 10yr UST Bond Risk / Unrealized Loss inin Stress Test Scenario Risk / Unrealized Loss Stress Test Scenario SPX Put SPX ↓ -9% to -14% SPX ↓ -25% SPX ↓ -50% Stress Test 68% to 33% probability 13% chance 2% probability UST Bond Rates ↑ 100bps to 200bps Rates ↑ 320bps to 600bps Stress Test 68% to 33% probability 13% to 2% probabilityNote: All data as of September 14, 2012. Estimated unrealized loss on position given stress test scenario. Historic probability data based on period of 1960 - 2012 for the UST bonds and 1950 to 2012 for the S&P 500index. Option pricing based on estimated local volatility shifts, however actual shifts may differ from estimates during a real crash depending. All stress tests are assumed to occur close to the purchase period of the 23instrument. Unrealized losses may differ closer to maturity.
  25. 25. Risk Free Assets are Risky BULL MARKET IN FEAR When risk-free is risky … it is time to buy volatility on safety itself Higher interest rate volatility can be realized in deflation and inflation250 Interest Rate Volatility is Low ... and a better bargain on a forward basis than equity vol Merrill Lynch MOVE Index = VIX for UST Bonds Weighted Volatility of 2yr,5yr,10yr & 20yr UST200150100 50 Oct-08 Oct-09 Oct-10 Oct-11 Oct-12 Dec-08 Dec-09 Dec-10 Dec-11 Apr-09 Apr-10 Apr-11 Apr-12 Feb-09 Aug-09 Feb-10 Aug-10 Feb-11 Aug-11 Feb-12 Aug-12 Jun-09 Jun-10 Jun-11 Jun-12Source: Bloomberg 24
  26. 26. Volatility of an Impossible Object BULL MARKET IN FEAR Modern financial markets are an impossible object Volatility of an impossible object is our changing perception of risk 25Illustration by Brendan Wiuff based on concept by Christopher Cole
  27. 27. Volatility of an Impossible Object BULL MARKET IN FEAR the next “Unknown Unknown” Crash…What is not priced into markets that will seem as obvious in 10 years as it is laughable today? Bull Market in Fear is prepared for yesterday’s crash… you want to be hedged for what happens tomorrow Fracture between the fundamental and the abstract is a source of great risk Today everyone is afraid of the next 2008 I am afraid of the next 1987…. possibly for stocks… but more likely bonds 26
  28. 28. Post-Modern Economy BULL MARKET IN FEAR Post-Modern Economy & “Simulacra and Simulation”Baudrillard recalls Borges fable about cartographers of a great empire who drew a detailed map When the empire collapses the map is accepted as truth and the empire forgotten In the postmodern economy market expectations are more important to fundamental growth than the reality of supply and demand the market was designed to mimicWhat Baudrillard calls “the desert of the real” is what Bernanke identifies as the “wealth effect” The real economy is not slave to the shadow banking system… our economy IS the shadow banking system… the empire is gone and we live in the abstraction 27
  29. 29. Volatility can be more than just FEAR BULL MARKET IN FEARVolatility is the perfect post-modern asset class for our existential economic future… Volatility Markets Volatility Fiat Currency 28

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