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Dispersion TradingTrade Dynamics, P&L Drivers And OurOutlook for S&P and SX5E Dispersion
Credit Suisse Equity Derivatives Strategy, May 2015
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Key Points
Investors can go short correlation through building a portfolio of short indexand long stock volatility– a successful carry trade over the last 10 years
Volswap-to-Volswap dispersion has replaced Var-to-Var after the 2008financial crisis as a lower-risk alternative to trading dispersion
Due to particular trade dynamics, you would ask for larger expectedcorrelation P&L before embarking on vol-to-vol dispersion– the recent pushin implied correlations may provide the right incentive
Other factors that impact potential dispersion P&L: neutral to positive marketperformance and extended valuation multiples, and a higher index volatilityskewS&P dispersion ranks high on all factors; SX5E has a more mixed outlook
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A Guide To Dispersion TradingHow To Build A Correlation Exposure
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What’s Implied Correlation? Implied correlation corresponds to the trade-off between an index’s volatility andthat of its single stock constituents. Although there is a more correct (but morecomplex!) formula, for a well diversified index I composed of n stocks with
weights wi and volatilityσi, correlation is usually approximated as:
Implied correlation is derived from implied volatilities or varswap and volswapquotes. Realised correlation corresponds to the actual, average level of pairwisecorrelation realised in the index over the consecutive periodEquity correlation is typically positive, and its distribution more stable (normally
distributed) than volatility, which exhibits large skewness and kurtosis:
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=
S&P CorrelationImplied3M
Implied6M
Implied1Y
Realised3M
Realised6M
Realised1Y
ImpliedVol 6M
RealisedVol 6M
Average Since 1996 42.1% 44.7% 46.2% 32.3% 32.4% 32.5% 20.0% 17.7%Std Dev 11.9% 11.7% 11.7% 12.7% 12.2% 12.1% 6.0% 8.5%Median 42.2% 45.4% 46.8% 30.6% 30.7% 30.5% 19.2% 15.8%Min 8.1% 11.7% 14.5% 8.0% 6.3% 6.1% 10.3% 7.2%Max 81.6% 77.3% 77.5% 75.6% 71.1% 61.9% 55.1% 58.2%Skewness 0.1 -0.1 -0.1 0.9 0.9 0.6 1.3 2.2 Kurtosis -0.2 -0.3 -0.4 0.9 0.7 -0.2 3.1 6.5
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S&P Correlation History
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0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
2005 2007 2009 2011 2013 2015
Implied 6M
Realised 6M
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SX5E Correlation History
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0%
10%
20%
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50%
60%
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80%
90%
100%
2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
Implied 6M
Realised 6M
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Why Go Short Implied Correlation? (1)
Due to supply and demand imbalances, implied correlation tends to bepriced expensively− Index volatility is typically pushed higher by systematic equity hedgers− Single stock volatility is cheapened by systematic stock overwriters− Since 1996, S&P 6M implied correlation has averaged 45% when realised has
averaged only 32% A theoretically great carry trade:− S&P 6M implied vs consecutive realised correlation has been positive 80% of the time
since 2005 with average “P&L” of 11 correl points− Worst loss has been 30 correlation points in 2008
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S&P (1997-2015) SX5E (2009-2015)Correlation P&L 3M 6M 1Y 3M 6M 1Y
Average 9.5% 11.6% 12.2% 5.1% 6.5% 8.4%Median 10.2% 13.2% 13.2% 5.7% 7.7% 8.3%Max Loss -29.9% -29.6% -24.1% -38.9% -20.7% -11.0%5% Percentile -10.4% -10.2% -8.0% -15.2% -14.1% -4.9%% Positive 81% 82% 78% 66% 73% 80%
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Why Go Short Implied Correlation? (2)
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-30%
-20%
-10%
0%
10%
20%
30%
40%
50%60%
1997 1999 2001 2003 2005 2007 2009 2011 2013
SPX
SX5E
6 M
I m p
l i e d M i n u s
C o n s e c u
t i v e
6 M
R e a
l i s e
d C o r r e
l
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Implementing a Correlation Trade
Prior to 2008: short index variance vs long single stock variance, typicallyin a theta-weighted basket; correlation swaps
Post 2008: short index vol swaps vs long single stock vol swaps, after the2008 financials collapse showed the inherent risk for market makers inbeing short single stock variance
Sector correlation trades: index vs sectors with vol or variance swaps;typically when sector rotations drive inter-sector correlations lower, andintra-sector correlations higher
All approaches lead to imperfect exposure to correlation…
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Var-to-Var Dispersion: the world before 2008
In a typical, pre-2008 dispersion trade you were:− Short a variance swap on an equity index with strike K I, realised volσI, and notional NI− Long a portfolio of variance swaps on the index constituents, with strikes Ki (0
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Vol-to-Vol Dispersion: A Less Risky Alternative
After 2008, single stock variance swaps were replaced with volatilityswaps with lower embedded tail risk
Vol-to-Vol dispersion trade P&L can still be decomposed between acorrelation exposure and volatility exposure, but:− Correlation component now depends on the square root of correlation, ie non linear exposure
to correlation− Volatility component depends on single stocks’ realised volatilities, not variance − Overall a less risky P&L than var-to-var (exposure to average vol, not average var, and
concavity of exposure to correlation cushions losses during correlation peaks)
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& − ∗=
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Vol-to-Vol: Profitable, But Imperfect Correlation Trade
Strongly, but not perfectly exposed to correlation:− Equation in slide 3 is only an approximation− Typically investors go long only top 50 names in S&P and most liquid names in SX5E vs
short the index (like we do in backtests below)− Single stock volatility scaling factor
Dispersion P&L: between 1 vega (SX5E) and 1.4 vega (S&P) medianP&L, for circa 70% positive tradesLess favorable P&L to Loss ratio than pure correlation P&L due to crossexposure with volatility, but equivalent to short index variance or volatility
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For 100 VegaCorrelationP&L
DispersionP&L -
Varswap
DispersionP&L -
VolSwapShortIndex Var
ShortIndexVol
CorrelationP&L
DispersionP&L -
VarswapDispersion P&L -
VolSwapShortIndex Var
ShortIndex Vol
Average 11.1% 64 51 231 236 8.0% 217 78 288 206 Median 13.4% 172 143 445 374 8.9% 155 98 457 319Max Loss -29.6% -3478 -1970 -5483 -3486 -27.3% -469 -555 - 4072 -28795% Percentile -15.9% -550 -584 -1532 -1547 -12.8% -158 -271 - 1319 -1291% Positive 80% 79% 73% 82% 78% 78% 86% 70% 79% 71%Median P&L / Loss 0.8 0.3 0.2 0.3 0.2 0.7 1.0 0.4 0.3 0.2
S&P 500 (2005-2015) SX5E (2002-2015)
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Vol-to-Vol Dispersion P&L History
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2002 2004 2006 2008 2010 2012 201
SPX
SX5E
P
& L o
f V o
l - t o - V o
l D i s p e r s
i o n
( 1 0 0 V e g a
)
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Vol-to-Vol vs Var-to-Var
Due to a larger, positive sensitivity to the volatility skew, variance swapsallowed to sell index volatility for slightly more than single stocks, than when using vol swaps Actual, achieved correlation levels were larger with variance swaps(assuming 0.5 vol and 1.5 vol bid ask spreads)
Dispersion P&L using vol swaps are therefore typically lower, but risks arealso 1/3 rd lower (see next slide)This is an academic discussion given that var-to-var does not tradeanymore…
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Av g S&P 6MImplied Correl(1997-2015)
SX5E 6M ImpliedCorrel (2009-2015)
With Vol Swaps 43.4% 58.8%With Var Swaps 46.8% 63.5%
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Vol-to-Vol vs Var-to-Var P&L
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-4000
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-1000
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-3,000 -2,000 -1,000 0 1,000 2,000
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Vol-to-Vol Dispersion P&L (100 vega) V a r -
t o - V a r
D i s p e r s
i o n
P & L ( 1 0 0 v e g a
)
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Theta-Weighted vs Vega-Weighted
An alternative to the theta-weighted scheme consists of using similar vegaon the long and the short (H=1 in the equation on slide 10)
In vol-to-vol dispersion this has the consequence of making the investorlong single stock vol on top of the correlation exposure:
Being long single stock vol helps cushioning losses in the event of asimultaneous correlation and vol shock (typical in an Equity sell-off): maxloss of 13x vega only versus 20 in the theta weighted scheme
This is at the cost of a less interesting carry: median P&L of 0.5x vegaonly versus 1.4 in the theta weighted scheme
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& − ∗=
+(1−=
)∗ ( − ) &=
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Theta-Weighted vs Vega-Weighted (2)
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-1500
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1000
1500
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-3,000 -2,000 -1,000 0 1,000 2,000
SX5E (2005-2015)
SPX (2005-2015)
Vol-to-Vol Theta-Flat Dispersion P&L (100 vega) V o
l - t o - V o
l V e g a - F
l a t D i s p e r s
i o n
P & L
( 1 0 0 v e g a
)
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500
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SX5E (2005-2015)
SPX (2005-2015)
Long Single Stock Vol P&L (100 vega) D i f f B e
t w e e n
V e g a - F
l a t a n
d T h e
t a - F
l a t
V o
l s w a p
D i s p e r s
i o n P
& L ( 1 0 0 v e g a
)
For 100 VegaCorrelationP&L
DispersionP&L - ThetaWeighted
DispersionP&L - VegaWeighted
ShortIndex Var
ShortIndexVol
CorrelationP&L
DispersionP&L - ThetaWeighted
DispersionP&L - VegaWeighted
ShortIndex Var
ShortIndex Vol
Average 11.1% 51 2 231 236 8.0% 78 36 288 206 Median 13.4% 143 46 445 374 8.9% 98 -5 457 319Max Loss -29.6% -1970 -1274 -5483 -3486 -27.3% -555 -659 -4072 - 28795% Percentile -15.9% -584 -366 -1532 -1547 -12.8% -271 -278 -1319 - 1291% Positive 80% 73% 59% 82% 78% 78% 70% 49% 79% 71%Median P&L / Loss 0.8 0.2 0.1 0.3 0.2 0.7 0.4 0.0 0.3 0.2
S&P 500 (2005-2015) SX5E (2002-2015)
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Vol-to-Vol Disp In A Low Vol, High Correl Environment
Because vol-to-vol is exposed to the square root of correlation, a typical 10 pointsdifference between implied and realised correlation translates into lower P&L whencorrelation baseline level is high. This is magnified in a low vol environment
Additionally trading costs take a larger toll when vol is low: at 20% vol and 60% correl,typical trading costs result in an effective correlation of 52%
You would typically ask for larger correlation P&L before embarking on vol-to-voldispersion trades
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t e d P & L F o r 1
0 p
t s C o r r e
l G a
i n
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Effective Correl
Mid Correl
Single Stock Baseline Vol
E f f e c
t i v e
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l ( a s s .
0 . 3
a n
d 1 v o
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p t s c o s t
f o r
i n d e x a n
d s i n g
l e s t o c
k s )
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Enhanced Dispersion TradesImproving the Risk Reward of DispersionExposure
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Enhancement # 1: The Benefits of Diversification
With only 40% correlation between the P&L of S&P and SX5E dispersiontrades since 2005, there is ample diversification benefit to be had byinvesting in a globally diversified dispersion
A portfolio invested in 50/50 S&P and SX5E dispersion allows theinvestor to reach higher average profit than simply S&P– with similar risk
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8090
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170 180 190 200 210 220 230
All
S&P
SX5E
0.5*S&P + 0.5*SX5E
Std Dev of P&L (100 vega)
A v e r a g e
P & L ( 1 0 0 v e g a
)
Weight of S&Pin Basket Mean Median Stdev Min
10%Percentile
100% 118 171 225 -619 -25790% 113 158 216 -559 -25080% 107 146 207 -498 -25170% 101 138 200 -467 -24560% 95 128 194 -439 -23850% 90 121 189 -418 -23040% 84 111 186 -396 -21830% 78 101 184 -375 -20020% 72 93 184 -367 -20210% 67 84 186 -386 -202
0% 61 78 189 -405 -214
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Enhancement #2: Stock Picking
Looming idiosyncratic risks combined with risk aversion, as well as supplyand demand imbalances, may cause some single stock implied volatilitiesto trade at a premiumExcluding stocks with expensive implied volatilities does improve P&L forSX5E dispersion tradesThis comes in exchange of higher replication riskThis is not the case for S&P, where profit improvement is marginalcompared to the larger tracking error
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SX5E Optimised Dispersion
We select stocks based on the difference between implied volatility, andthe average of recent realised and the median realised vol over the last 2yearsSelecting only the 50% best stocks on that metric allows to improve P&L75% of the time, with average outperformance of 0.5 vega, and 85%correlation with full dispersion trade
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% Stocks Excluded From Long Basket 0% 10% 20% 30% 40% 50% 60% 70% 80% Average 68 76 83 91 106 121 143 173 197Median 78 87 93 103 114 124 134 147 150Stdev 188 181 186 187 192 202 228 287 343Max Loss -408 -437 -483 -512 -515 -594 -575 -551 -71210% Percentile -210 -190 -183 -175 -163 -158 -164 -181 -186
% Positive 67% 70% 71% 74% 76% 78% 79% 79% 77% Average 0 8 15 23 38 53 75 105 129Median 0 14 23 29 37 47 59 65 66Stdev 0 45 56 69 91 113 152 224 286Max Loss 0 -297 -291 -264 -305 -409 -404 -426 -59010% Percentile 0 -28 -44 -61 -57 -63 -80 -99 -116% Positive 100% 73% 71% 70% 71% 75% 75% 74% 72%Correlation of Optimised With Full Dispers 100% 97% 96% 94% 89% 84% 76% 64% 56%
O u
t r i g h t
D i s p e r s
i o n
O u
t p e r f o f
O p
t i m
i s e
d B a s k e
t
v s F u l
l D i s p e r s
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S&P Optimised Dispersion
The same selection as implemented for the SX5E shows no significantimprovement in risk rewardS&P is a more balanced index and superior underlying for dispersion withlittle scope for optimisation
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% Stocks Excluded From Long Basket (Top 50) 0% 10% 20% 30% 40% 50% 60% 70% 80% Average 30 20 18 19 23 31 41 54 72Median 132 140 139 140 143 142 142 137 138Stdev 334 357 364 364 368 371 377 390 416Max Loss -1376 -1489 -1543 -1542 -1509 -1574 -1563 -1696 -185110% Percentile -384 -358 -342 -333 -313 -307 -273 -264 -236% Positive 71% 69% 68% 68% 68% 68% 68% 71% 74%
Average 0 -9 -12 -11 -7 2 12 24 42Median 0 4 3 1 0 8 18 24 26
Stdev 0 71 85 95 105 119 134 165 221Max Loss -4 -418 -557 -592 -656 -701 -825 -836 -86710% Percentile 0 -104 -124 -120 -123 -138 -131 -139 -139% Positive 100% 55% 53% 51% 50% 55% 59% 58% 59%Correlation of Optimised With Full Dispers 100% 98% 98% 97% 96% 95% 94% 91% 85%
O u
t r i g h t
D i s p e r s
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B a s k e
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Dispersion P&L DriversHow to Time Your Correlation Exposure
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What Makes Up A Successful Dispersion Trade?
Lower realised correlation:− Fundamental factors: equity performance, valuation, M&A activity
Higher implied correlation:
− Technical factors: systematic prevalence of index hedgers and stockoverwriters, temporary market correction driving vols higher
Higher stock realised volatility
− To turn a correct correlation bet into a significant profit
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Fundamental Drivers Of Realised Correlation
Equity market performance:− Realised correlation is larger during equity market corrections
Equity valuations:− Realised correlation is larger during times of acute crisis when valuation metrics are low− Correlation decreases markedly when equity markets are expensive and investors have
to turn to stock picking in order to generate performance
Little impact of M&A activity: probably because typical dispersion basketsinclude mainly extra large caps, which are not natural M&A targets
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S&P SX5E
FactorCorrelation with 6MRealised Correlation t-Stat
Correlation with 6MRealised Correlation t-Stat
12M Fwd Price-to-Earnings -55.3% -44.9 -5.6% -0.1S&P Coincident Performance -32.7% -23.4 -46.9% -0.5
Agg. $ Consideration of M&A Deals Announced -7.2% -4.9 16.5% 0.2
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Realised Correlation vs Equity Valuations
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0%
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0 5 10 15 20 25 30
SPX (1997-2015)SX5E (2009-2015)
12M Fwd Price-to-Earnings
R e a
l i s e d
C o r r e
l a t i o n
The most efficient predictor of realised correlationPE of 10 = avg 6M realised correl of 60%, PE of 15 = avg correl of40%, PE of 20 = avg correl of 30%
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Realised Correlation vs Equity Market Performance
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0%
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Coincident Index Performance
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Realised Correlation vs Global M&A Activity
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0%
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0 50,000 100,000 150,000 200,000 250,000 300,000 350,000
SPX (1997-2015)
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$ Consideration of Deals Announced
R e a
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d C o r r e
l a t i o n
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What Factors To Watch Before Implementing A Trade?
We look at factors which exhibited good correlation with dispersion P&L inthe past – factors not fully taken into account in implied correlation prices
Selected Factors:− Valuation multiples, coincident market performance− Absolute implied correlation level, index skew− Prior changes in implied correl (in particular for SX5E)
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S&P SX5E
FactorCorrelation to 6M"Correlation P&L" t-Stat
Correlation to 6M"Correlation P&L" t-Stat
Implied Correl Level 53.1% 42.4 60.6% 28.4Coincident Underlying Perf 69.3% 65.1 42.9% 17.7Implied to Realised Correl Spread 39.7% 29.3 13.4% 5.0Index Vol Skew 19.2% 12.9 24.2% 0.3Index Vol Level 6.3% 4.3 35.0% 13.9M&A Activity -8.7% -5.9 -31.5% -12.4Prior Change In Implied Correl (1M) 9.7% 6.6 21.7% 8.212M Forward Price-to-Earnings 3.2% 2.2 -23.9% -9.2Prior Change in Underlying 16.4% 11.2 2.2% 0.8Prior Change in Index Vol -6.2% -4.2 -4.4% -1.6Prior Change in SS Implied Vol (1M ) -4.8% -3.2 -1.5% -0.6SS Implied Vol Level -21.1% -14.6 21.4% 8.2
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Correlation/Dispersion P&L vs Implied Correl Level
Rule of thumb:− Buy 6M dispersion when effective correl level (after transaction costs > 60%)
Implied to realised correlation spread is a less efficient indicator
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Effective Implied Correlation (in %) V o
l - t o - V o
l D i s p e r s i o n
P & L ( 1 0 0 v e g a
)
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Implied Correlation (%)
C o r r e
l P & L ( 1 0 0 v e g a
)
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Correlation/Dispersion P&L vs Equity Performance
Odds improve in times of strong equity performance:− Typically lower volatility and lower correlation in rising markets− 90% probability of achieving >0 P&L if underlying index performance is positive; 70%
probability of >0 P&L for flattish performance (+/- 5%)− SX5E dispersion P&L tends to be less correlated to SX5E performance
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)
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SPX (1997-2015)
Coincident Equity Performance(%)
C o r r e
l P & L ( 1 0 0 v e g a
)
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Correlation/Dispersion P&L vs Valuation Ratios
Dispersion P&L is good when valuations are low: typically after a sell off whenrisk perceptions and implied correlations are highDispersion P&L improves markedly when equity markets are expensive asinvestors have to turn to stock picking in order to generate performancePEs of over 20 were observed only in the late 90s but coincided with profitable
trades (based on correlation P&L)
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FWD Price-to-Earnings Ratio (in %) V o
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i o n
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)
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FWD Price-to-Earnings Ratio
C o r r e
l P & L ( 1 0 0 v e g a
)
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Correlation/Dispersion P&L vs Skew
We find circa 25% correlation between index volatility skew andsubsequent “correlation P&L” − Direct: a higher skew inflates the index vol or variance swap strikes vs ATM volatility
which translates into a higher effective correlation− Indirect: a higher skew could be the sign of stronger demand for equity protection,
lifting the entire index vol surface up versus single stocks
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-40%
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0%
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30%
40%
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0% 2% 4% 6% 8% 10% 12%
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6M 90/110 Volatility Skew
C o r r e l
P & L
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6M 90/110 Volatility Skew V o
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l D i s p e r s
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P & L ( 1 0 0 v e g a
)
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S&P/SX5E Dispersion Performance vs Skew Differential
Since 2012 S&P dispersion has systematically performed better thanSX5E dispersion
Although this can be linked to S&P index outperformance (see slide 27),a likely driver has been the record differential in skewOver the last few years, a booming structured retail market, and general
disaffection for equity and hedging in Europe, has pushed SX5E skew torecord lows, while S&P skew has rebounded to near all-time highs
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2012-2015
2005-2011
S&P/SX5E 6M 90/110 Skew
D i f f B e
t w e e n
S & P a n
d S X 5 E
D i s e r s
i o n
P & L ( 1 0 0 v e g a
)
-2000
-1500
-1000
-500
0
500
1000
-3%
-2%
-1%
0%
1%
2%
3%
4%
2005 2007 2009 2011 2013
Skew Diff
P&L Diff
S & P / S X 5 E 6 M
9 0 / 1 1 0 S k e w
S p r e a
d D i f f B
e t w e en
S & P
a n
d S X
5 E D i s
p er s i on
P & L
( 1 0 0 v e
g a )
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Dispersion Trading In 2015Outlook And Recommendations
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Strong Outlook for S&P Dispersion
S&P dispersion trades have had their best 6-months since 2012 with anestimated profit of circa 4x vega (6M Top 50 dispersion)− Strong correlation P&L (20 correl pts) at lower baseline correl levels than in 2012 (6M
realised correl at 30 to 35pts)− Single stock realised vols still low but at their highest level since 2011 (22%)
PE of 17 and expected flat S&P performance point towards realisedcorrel of 35% for the rest of the year
This compares to implied correl of 58% (top 50 ATM), and effective correlof circa 50%− Below the 60% threshold− But 6M 90/110 skew at 9% is near all-time highs
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S&P Dispersion: History vs Forecasts
38
0%
10%
20%
30%
40%50%
60%
70%
80%
90%
1996 1998 2000 2002 2004 2006 2008 2010 2012 2014
Implied 6M
Realised 6M
Forecast
C o r r e
l a t i o n
L e v e
l
-2000
-1500
-1000
-500
0
500
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
6 M
D i s p e r e s i o n
P & L
( 1 0 0 v e g a
)
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Mixed Outlook For SX5E Dispersion
SX5E dispersion has yielded disappointing results since 2014− Low to outright negative correlation P&L as SX5E has continued to realise over 60%despite the rally
− Low realised volatilities helped mitigate losses in 2014
Mixed outlook for realised correl− SX5E PE ratio (16) at highest on record, which points towards 40% realised correl
according to S&P experience – but will this hold for SX5E?− SX5E expected to rally up to 10% by year end (Credit Suisse Strategy’s target price:
3,900), which in the past has been associated with realised correl of 50% and higher− One should not overestimate the impact of M&A activity
Implied correl of 65% (6M, ATM) but effective correl of 60%− High, but lower than the optimal threshold when SX5E dispersion typically requires a
higher effective correlation than S&P in order to post a profit− 6M 90/110 skew at 5% is low compared to history
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SX5E Dispersion: History vs Forecasts
40
-800
-600
-400
-200
0
200
400
600
800
1000
1200
2002 2004 2006 2008 2010 2012 2014
6 M
D i s p e r e s i o n
P & L ( 1 0 0 v e g a
)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2009 2011 2013
Implied 6M
Realised 6M
Forecast C o r r e
l a t i o n
L e v e
l
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