Three Quantitative Strategies

ETF Pair Trade

Equity Index Long Only

Currency Long/Short

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ETF Pair Trade

Regions of Stability with QuantileRegression

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Anson and Ho (2003) showed that event driven and merger arbitrage strategies are equivalent to a short put option on the broader market(top right, Merger Arbitrage and S&P 100 returns together with fitted regression)

Short puts are equivalent to covered calls

In 2010 two new strategy based ETFs began trading: CSMA (merger arbitrage) and PBP (covered call)(bottom right, CSMA & PBP prices 4/10/2010-29/7/2011)

The ETFs are essentially equivalent, thus a profitable pair based strategy may be possible

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Quantile regression produces regression lines fitted to different quantiles of independent variable data

Fitted lines indicate stability of the ratio for some values of the independent variable(top right, Quantile regression for CSMA & PBP prices 4/10/2010-29/7/2011)

The changing slope of the quantileregression lines show a stable relationship between PBP and CSMA prices within certain quantiles of CSMA prices

The ratio fluctuates less than 3% within the .35 - .90 quantiles of CSMA prices(bottom right, Slope of the quantile regression lines for CSMA & PBP prices 4/10/2010-29/7/2011)

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The .35 - .90 quantiles of the empirical cumulative distribution function of CSMA prices corresponds to a range of $20.17 – $20.93 (top right, empirical CDF function of CSMA prices 4/10/2010-29/7/2011)

Values within the range yield a model for PBP prices as a function of CSMA prices:

mPBP = (-0.0298CSMA + 1.6311)CSMA

PBP prices show a tendency to revert to model PBP (mPBP) prices (bottom right, PBP & mPBP 4/10/2010 – 29/7/2011)

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Out of Sample Results

PBP prices significantly depart from model PBP (mPBP) prices, but tendency to revert remains (top right, PBP & mPBP 1/8/2011-26/10/2011)

Conclusion

Quantile regression adds value to pair trading strategies by indicating regions of stability between traded assets

Additional pair trading opportunities may exist among other new strategy based ETFs(bottom right, CSMA and model’s upper & lower bounds 1/8/2011-26/10/2011)

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SPX Index Long Only

Predictive Volatility Model

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Poon & Granger (2003) showed that volatility is forecastable using a variety of methods. The KalmanFilter is one method that is effective in predicting future volatility levels of equity indices(top right, Kalman Filter one-step ahead forecast of 30 day Log volatility of the SPX Index 3/1/1980 –30/12/2005)

Historically, volatility and total returns of the SPX Index tend to have an inverse relationship (bottom right, 30 day volatility and total return of SPX Index 3/1/1980 – 30/12/2005)

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Behavior can be explained by an inverse relationship between kurtosis and volatility.

For assets with positive expected returns, the probability of positive returns, all else being equal, increase with higher levels of kurtosis.(top right, change in kurtosis and probability of positive returns)

Probability of positive returns in the SPX Index and 30day volatility exhibit an inverse relationship.

Predictive, conditional volatility strategy may improve risk adjusted returns by limiting exposure to market declines.(bottom right, probability of positive return for different maximum allowable volatilities)

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Out of Sample Results

Cumulative returns using three different maximum allowable, predicted volatilities. An improvement in absolute returns and a decrease in volatility are achieved(top right, cumulative returns 3/1/2006-8/11/2011 for SPX and maximum volatilities of 8%, 10% and 12%)

Conclusion

Sign forecasting is possible when volatility is forecastable.

Other equity indices may behave similarly to SPX (middle & bottom right, Nikkei 225 & Hang SengIndices with 16% conditional volatility strategies 3/1/2006-17/11/2011)

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Currency Long/Short

Adaptive Momentum

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Momentum in currency markets has been noted by numerous researchers and practitioners

Literature provides examples of a variety of different methods and timelines to measure momentum(top right, USD/CHF, 50day, 100day and 200day simple moving averages 17/11/1982 – 30/12/2005)

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Here we use twelve trading systems using simple moving averages (SMAs) on an exponentially increasing scale from 0-1024 days on the USD/CHF currency pair

Each system performs differently during different market regimes (bottom right, twelve SMA systems 14/1/1986-30/12/2005)

In Mlnarik et al. (2009) a market regime is defined as the amount of correlation between trading systems

Here the correlation between each trading system and a hypothetical system with perfect foresight is measured. (top right, Rolling 30 day correlation between perfect system and 64day system 26/2/1986 – 30/12/2005)

Each system’s correlation with the perfect system is considered a fitness score

At every point of time, the system(s) with the highest fitness score is turned on and its trading signals are followed(bottom right, Rolling 30 day correlation, with system with highest correlation(s) highlighted 26/2/1986 –15/4/1986)

0 day 1 day 2 day 4 day 8 day 16 day 32 day 64 day 128 day 256 day 512 day 1024 day

26/2/1986 -0.98095 0.715967 0.367297 0.367297 0.4981 0.975276 0.980358 0.980358 0.980358 0.980358 0.980358 0.980358

27/2/1986 -0.98239 0.721581 0.366562 0.366562 0.532755 0.976884 0.981831 0.981831 0.981831 0.981831 0.981831 0.981831

28/2/1986 -0.98227 0.70771 0.326544 0.326544 0.550904 0.977947 0.981692 0.981692 0.981692 0.981692 0.981692 0.981692

3/3/1986 -0.98244 0.681141 0.250441 0.250441 0.574937 0.979751 0.981868 0.981868 0.981868 0.981868 0.981868 0.981868

4/3/1986 -0.98272 0.662862 0.187788 0.187788 0.596866 0.981614 0.982165 0.982165 0.982165 0.982165 0.982165 0.982165

5/3/1986 -0.96409 0.506641 -0.03592 -0.03592 0.556399 0.962511 0.962515 0.962515 0.962515 0.962515 0.962515 0.962515

6/3/1986 -0.95226 0.288217 -0.25591 -0.25591 0.484392 0.949943 0.949943 0.949943 0.949943 0.949943 0.949943 0.949943

7/3/1986 -0.94224 0.096561 -0.42403 -0.42403 0.410197 0.939262 0.939262 0.939262 0.939262 0.939262 0.939262 0.939262

10/3/1986 -0.89756 -0.12009 -0.5303 -0.4513 0.440956 0.891694 0.891694 0.891694 0.891694 0.891694 0.891694 0.891694

11/3/1986 -0.86594 -0.27183 -0.59817 -0.48336 0.457242 0.828681 0.857806 0.857806 0.857806 0.857806 0.857806 0.857806

12/3/1986 -0.82426 -0.38155 -0.64523 -0.48696 0.495564 0.777232 0.813284 0.813284 0.813284 0.813284 0.813284 0.813284

13/3/1986 -0.78552 -0.44853 -0.67332 -0.47562 0.545832 0.729117 0.77187 0.77187 0.77187 0.77187 0.77187 0.77187

14/3/1986 -0.76427 -0.51377 -0.70125 -0.49433 0.556631 0.639371 0.748769 0.748769 0.748769 0.748769 0.748769 0.748769

17/3/1986 -0.75 -0.57129 -0.73023 -0.49912 0.574588 0.506843 0.732781 0.732781 0.732781 0.732781 0.732781 0.732781

18/3/1986 -0.73236 -0.61695 -0.75312 -0.49751 0.598297 0.370904 0.71315 0.71315 0.71315 0.71315 0.71315 0.71315

19/3/1986 -0.7003 -0.66622 -0.77004 -0.49654 0.592362 0.198109 0.677504 0.677504 0.677504 0.677504 0.677504 0.677504

20/3/1986 -0.66963 -0.72602 -0.79584 -0.52286 0.557328 0.044382 0.643522 0.643522 0.643522 0.643522 0.643522 0.643522

21/3/1986 -0.64591 -0.78003 -0.82527 -0.57228 0.543122 -0.10446 0.616496 0.616496 0.616496 0.616496 0.616496 0.616496

24/3/1986 -0.55354 -0.82812 -0.86654 -0.66659 0.409445 -0.35312 0.510977 0.510977 0.510977 0.510977 0.510977 0.510977

25/3/1986 -0.33225 -0.87361 -0.91471 -0.78154 0.326626 -0.50177 0.270696 0.270696 0.270696 0.270696 0.270696 0.270696

26/3/1986 -0.12743 -0.89622 -0.93897 -0.84067 0.23721 -0.60904 0.033644 0.055263 0.055263 0.055263 0.055263 0.055263

27/3/1986 0.050704 -0.90445 -0.95466 -0.87841 0.118716 -0.69724 -0.18912 -0.12664 -0.12664 -0.12664 -0.12664 -0.12664

28/3/1986 0.192734 -0.90232 -0.95936 -0.88641 0.047077 -0.74167 -0.33065 -0.26492 -0.26492 -0.26492 -0.26492 -0.26492

31/3/1986 0.332549 -0.89893 -0.96313 -0.89152 -0.03174 -0.78294 -0.45323 -0.39722 -0.39722 -0.39722 -0.39722 -0.39722

1/4/1986 0.466141 -0.89705 -0.96737 -0.89749 -0.14395 -0.82747 -0.57088 -0.52128 -0.52128 -0.52128 -0.52128 -0.52128

2/4/1986 0.604849 -0.90379 -0.97156 -0.90423 -0.16946 -0.84404 -0.65152 -0.64563 -0.64563 -0.64563 -0.64563 -0.64563

3/4/1986 0.665428 -0.89092 -0.96786 -0.90041 -0.0422 -0.80646 -0.64851 -0.68765 -0.6979 -0.6979 -0.6979 -0.6979

4/4/1986 0.732543 -0.88146 -0.96516 -0.89794 0.002601 -0.78783 -0.67592 -0.74656 -0.75773 -0.75773 -0.75773 -0.75773

7/4/1986 0.812777 -0.87457 -0.95545 -0.88199 0.05129 -0.75463 -0.69705 -0.8107 -0.82962 -0.82962 -0.82962 -0.82962

8/4/1986 0.834105 -0.87795 -0.95389 -0.89182 0.08348 -0.72933 -0.71059 -0.83924 -0.84907 -0.84907 -0.84907 -0.84907

9/4/1986 0.823206 -0.87311 -0.94389 -0.88293 0.103393 -0.71064 -0.72079 -0.85222 -0.8393 -0.8393 -0.8393 -0.8393

10/4/1986 0.79572 -0.86244 -0.92885 -0.8616 0.172279 -0.69485 -0.72958 -0.85911 -0.81438 -0.81438 -0.81438 -0.81438

11/4/1986 0.731773 -0.83774 -0.89952 -0.80617 0.310176 -0.65074 -0.73946 -0.85197 -0.75609 -0.75609 -0.75609 -0.75609

14/4/1986 0.688733 -0.81852 -0.87532 -0.76283 0.385873 -0.61601 -0.75508 -0.85415 -0.71647 -0.71647 -0.71647 -0.71647

15/4/1986 0.635142 -0.79864 -0.85078 -0.71419 0.493174 -0.56734 -0.76033 -0.84924 -0.66707 -0.66707 -0.66707 -0.66707

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Out of Sample Results

Results of fitness algorithm on the USD/CHF pair exhibit positive returns on a five year time horizon, but with significant periods of underperformance(top right, USDCHF cumulative results 2/1/2006 – 26/9/2011)

Conclusion

Fitness algorithm shows potential but additional refinement is necessary(bottom right, USDCAD cumulative results 2/1/2006 –26/9/2011)

The fitness algorithm may have profitable applications in other asset classes and with systems of strategies other than momentum

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Thank You

Seth Mallamo

11/17/2011

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