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Quantitative Trading and
Derivatives Strategy
Not So Contrarian AnymorePopular trading wisdom holds that low stock volatilityis a bearishsignal while high vol indicates a rally. This used tobe acontrarian idea: high volatility meant .fear., meaningthe weakhands have already been shaken out, while on lowvol.complacency. markets may falter. These days,however, theVIX indicator is pretty mainstream, as likely to becited on CNBCor by taxi drivers as by contrarian extremists.Of course the mainstream also once thought that thetrend is
your friend in tulip bulbs, and more recent crowds of investorsloved Pets.com at $11. Clearly its best not always tolisten to
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.people,. whether mainstream, contrarian or whatever.Historical data makes a more reliable source, thoughcare mustalways be taken not to torture it into falseconfessions.To find out whether implied volatility might reallyhave thesignalling power its credited with, we tested thecorrelation of the VIX relative level to subsequent moves in theS&P 500..Relative level. here is defined as the ratio of the VIXto its ownN-day moving average, minus one. So, for example,if the VIX
was 15.0, and its N-day moving average was 10.0,its relativelevel would be 15 / 10 - 1 = -50%. The S&P 500return was takenfrom the VIX close to K days out.Surprisingly (at least to cynical efficient marketeerslikeourselves), our results suggest that the VIX hasbeen a strongindicator of direction since its inception in 1993. Andin this case
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one can be unusually confident in the results.notbecausesome particular combination of N and K worked,which mightresult from data-mining.but rather because they all did! Whenit comes to the VIX as a directional indicator, thetulip-bulbersare quite right. But don.t scour eBay for oldPets.com sharecertificates quite yet; some caveats apply.Derivatives StrategyStephen Chadwick(212) 325-0281Can the VIX Signal Market Direction?Summary
.Contrarians. are all in agreement (?) that a lowVIX signals caution while a high VIX heralds rallies.They are right. Backtesting shows the ratio of the VIX to its 186-day MA has about 10% predictive power over theSPX 5-month return. The signal is worse at predicting short-termmoves, while a low reading really means .buy puts.rather than .sell. VIX predictions have worked well over the last 3yrs. Today the VIX is 20% below its MA.exerciseextreme caution!
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Figure 1. The CBOE.s VIX Volatility Index is nearall-time lows, and about 20% below its 186-daymoving average. A sell signal? Not exactly.
051015202530354045502-Jan-92
2-Jan-932-Jan-942-Jan-952-Jan-962-Jan-972-Jan-982-Jan-992-Jan-002-Jan-012-Jan-022-Jan-032-Jan-04
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2-Jan-052-Jan-062-Jan-07VIX Index Level & Moving Average020040060080010001200140016001800S&P 500 Index LevelQuantitative Trading and Derivatives Strategy
2Interpreting the ResultsThe VIX is Best at Predicting Medium-TermMovesThe highest degree of linear predictive power from1990-2006occured using a 186 trading day (9 calendar month)movingaverage for the .new. VIX, predicting 114 tradingdays (5 months)
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out on the S&P 500. However, the results werenearly as strong for any K and N within a month or two of these values(Fig 2 .)Short predictive periods (low values of K) are lesseffective, thoughwhat guidance they do provide is in the samedirection as for longer periods. It should be noted that in technicalanalysis it isoften the re -crossing of the moving average and notthe initialcrossing that is used as a signal, along with other inputs. Since thisstudy looks only at the raw divergence from the MA,it is possible
that there is other information in the signal that our test does notpick up. Also, while the information content in eachshort-swingprediction is lower, this may be compensated by theincreasednumber of trading opportunities.indeed the bestresults we foundin backtested trading strategies used only a 4-dayhorizon.High Relative VIX is the Most Important Signal
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An X-Y scatterplot of signals vs. returns for theoptimal parametersN=186, K=114 provides important insights ( Fig. 3 .) Note that thischart uses the natural log of the divergence toprovide a morelinear signal. On the Y-axis (S&P return) it makeslittle difference.The bottom-right quadrant, which indicates periodsof relativelyhigh VIX, but negative S&P returns, is by far theleast populated.Only 20% of 1622 high VIX signals in the samplewere wrong in their prediction of a market rise. By contrast, out of 2473low VIX
signals, 64% (1590) wrongly called for a decline.This is misleading, though, since the S&P 500 rosefairly steadilyover the last two decades, meaning that many more5-monthperiods experienced rises than falls. Eliminating thismarket drift,low VIX signals achieved a 57% correct battingaverage, whilehigh VIXes called the market correctly 63% of thetime. We
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conclude that the VIX is a better signal of 5-monthrallies than ofselloffs, but that both signals have merit as
timing indicators.Old VIX, New VIX, Whatever. Its all Good.Results for the .new. VIX index, which the CBOEintroduced in late2003 to match variance swap pricing, are onlyslightly better thanfrom the .old. VIX index. This suggests that thepredictive power of the index comes mainly from overall volatilitylevels, rather thanskew (i.e. relative prices of puts vs. calls.)Figure 3. VIX 186-day log-divergence vs.subsequent 114-day S&P 500 return
1990 - Presenty = 0.3073xR2 = 0.0977-40%-30%-20%-10%0%10%20%30%
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40%-40%-30%
-20%-10%0%10%20%30%40%Natural Log of Divergence from 186-Day VIXMoving AverageSubsequent 114-Day SPX ReturnIntuitive "best-fit" line"Best-fit" by linear regression
Area of veryhigh densityFigure 2. Correlation of VIX level relativeto N-day moving average vs. subsequentK-day S&P 500 return
0501001502002500
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35701051401750.000.050.100.150.200.250.300.35CorrelationN: VIX MovingAverage Days
K: Days ofS&P ReturnPredictive peak atN=186 days, K=114daysQuantitative Trading and Derivatives Strategy
3Data Bunching: Small Down Signals Mean .BuyPuts,. not .Sell.
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It seems strange that the best-fit trend line of a linear regression inFigure 3 goes nowhere near the line one wouldintuitively draw byeye. This happens because a large number of points, invisible onthe chart because they overlap, are bunched aroundthe X-axisfor VIX relative levels of 0 to -10%. In other words,when the VIX istrending slightly below its moving average the S&P500 usuallydoes almost nothing, rather than falling asconventional wisdompredicts. However, it is also clear that the biggestdrops in the
index do tend to occur when the VIX is low.One can conclude that a mildly low VIX is not areliable sign of animpeding selloff, but that it might well be anecessary precursor toone.after all, only very few of the S&P 500.s sharpdrops tookplace in a high implied volatility environment (lower rightquadrant.) Since a low VIX is obviously also adirect indicator of
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low option prices, those are opportune times toswitch intoprotective puts and calls : Buy 3-6 month puts withstrike prices of 95% or below, perhaps financing them by selling110 calls to makea protective .collar. position.On average, low VIX readings work as a puredirectional signal,but it makes more sense to use options to takeadvantage of theasymmetric dispersion of returns that occur duringthese periods.But Does it Still Work? Yes.probablyWhether the VIX is still a meaningful indicator is ahard question to
answer, simply because there can never be enoughrecent datato know, especially using the long predictionhorizons that haveworked best. For what it is worth, the indicator hasnever beenmore accurate than over the past 3 years (Figure4), during whichit has provided a spectacular 29% predictive power (=0.54.)Even more remarkably, many of the most accuratepredictions
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were from slightly low readings.perhaps it is best toignore theprevious paragraphs on data bunchingBut, of course, past performance is never aguarantee of futurereturn. This was a period of steady upward trendingon lowvolatility, which may not be representative of thenext few years.
Also, this 3-year period contains only about 6independentsamples (our analyses uses overlapping data), sothe possibilitythat the results are due to luck is higher than thecharts make itappear. That said, we would venture to pronounce
the VIXindicator alive and well.and to note that it is a goodtime to becautious as the VIX is around 20% below its 186-daymovingaverage.Note: The risk from buying protective puts is equal to the premium paid. The risk from selling uncovered calls is unlimited.y = 0.3994x + 0.0013R2 = 0.2922
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-40%-30%-20%
-10%0%10%20%30%40%-40%-30%-20%-10%0%10%20%
30%40%Natural Log of Divergence from 186-Day VIXMoving AverageSubsequent 114-Day SPX ReturnFigure 4. VIX 186-day log-divergence vs.subsequent 114-day S&P 500 returnJan. 1, 2003 - Present
Quantitative Trading and Derivatives Strategy
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4Footnote: Instant Hedge Fund.A VIX TimingStrategy
Optimizing the signal.s time horizons to maximizeSharpe ratioinstead of linear predictive ability, we obtaineddifferentparameters for N and K; The averaging period N isnearlyunchanged at 202, but we found the best risk/returnwith a shortholding period of 4 days.The strategy used in the backtest was simply to puton a long or short position each day in a size inverselyproportional to the log of
the ratio of the VIX to its moving average, then holdit for K days.For our benchmark return we used an outright longS&P position ina size equal to the RMS average of the teststrategy.s long or shortamounts (this is a forward-looking measure, but it isonly for scalingand risk measurement; it does not affect thestrategy.s returns.)This yielded an annualized Sharpe Ratio of 0.38excluding trading
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costs.More importantly, this strategy has very low long-term correlation(=0.10) and virtually zero beta ( =0.02) to the buy-and-holdstrategy.in other words, it provides a nearly purealpha overlay.Performance over the past three years has beenslightly worsethan the long-term results (Sharpe drops to 0.12),but it still beatthe index return through a steady rally, whileproviding significantdiversification benefits. With K set to 2 days, theSharpe Ratio over the past 3 years goes back up to 0.38, suggesting
the best holdingperiod going forward might be somewhere in-between, such asK=3 days.
0.000.050.100.150.200.25Cumulative Return
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VIX Trade (K=4 days)S&P Buy and Hold-0.30-0.20-0.100.000.100.200.300.4002-Jan-9002-Jan-9102-Jan-9202-Jan-9302-Jan-9402-Jan-95
02-Jan-9602-Jan-9702-Jan-9802-Jan-9902-Jan-0002-Jan-0102-Jan-0202-Jan-0302-Jan-0402-Jan-0502-Jan-0602-Jan-07
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Signal Strength(Position Size)SELLBUYFigure 5. Cumulative Return on VIXstrategy vs. S&P 500 total return
Quantitative Trading and Derivatives Strategy
5
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Backtested, hypothetical or simulated performanceresults have inherent limitations. Simulated resultsare achieved by the
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retroactive application of a backtested model itself designed with the benefit of hindsight. Thebacktesting of performance differsfrom the actual account performance because theinvestment strategy may be adjusted at any time, for any reason and cancontinue to be changed until desired or better performance results are achieved. Alternativemodeling techniques or assumptionsmight produce significantly different results andprove to be more appropriate. Past hypotheticalbacktest results are neither anindicator nor a guarantee of future returns. Actualresults will vary from the analysis.
Past performance should not be taken as an
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changes in market factors. This material does notpurport to contain all of the information that aninterested party may desire and, infact, provides only a limited view of a particular market.Stephen Chadwick Peter Yuen StanislasBourgoisTel. +1-212-325-0281 Tel. +852-2101-7468 [email protected]@[email protected] Hocaoglu, PhD Ralph CookeTel. +1-212-325-0722 Tel. +44 20 7888 [email protected]@credit-suisse.com
Victor Lin Colin GoldinTel. +1-212-325-5362 Tel. [email protected] [email protected] Liu Hisaomi Iwata Graham EwenTel. +1-212-538-4775 Tel. +813-4550-7105 [email protected]@[email protected] MackintoshTel. +1-212-325-5263
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[email protected] K. TomTel. [email protected] YorkCredit Suisse Quantitative Trading & DerivativesStrategyHong Kong LondonStephen Chadwick , Global Head, [email protected] Trading and Derivatives Strategy
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