M.A.D. Trading SystemA Mathematical HFT Setup
Created and Developed by: Leonardo URBANO
Copyright © 2014 Leonardo Urbano. All rights reserved.
Agenda
Introduction: a bit of theory The idea: how M.A.D. is built and how it works MATLAB Code P&L Sample Transaction Costs Performance Conclusions and Considerations
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
Basics
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
Backgrounds
M.A.D. (Moving Average of Derivatives) was born starting from a Lawrence G. McMillian strategy
It is based on a Volatility Derivative and its underlying M.A.D. comes out from a Multifactorial Model A Long (Short) Underlying Position is opened (closed) daily,
according to algorithm’s signals A Put Option is Sold (Bought) according to trading position
kept on underlying Furthermore, we assume: Monthly Option, ATM, Infinitively
quantity purchasable Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
The VIX (and similars)
VIX is the volatility of a variance swap and not that of a volatility swap (volatility being the square root of variance, or standard deviation). A variance swap can be perfectly statically replicated through vanilla puts and calls whereas a volatility swap requires dynamic hedging. The VIX is the square root of the risk-neutral expectation of the S&P 500 variance over the next 30 calendar days.
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
Multifactorial Model
Daily data 15 years back-testing
horizon Polynomial Functions Buy or sell Signals
M.A.D. Trading System – A Mathematical HFT Setup
Algorithm Performance Analysis
Standard & Poor’s 500 vs. VIXEuroStoxx 50 vs. VSTOXXDax 30 vs. VDAX-NEW
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
An overview of MATLAB Code
• Data Fetching• Making the Fit
• Standardized Data
• Bisquare for Robust Error
• Adjusted R2 as goodness
• Polynomial Function
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
An overview of MATLAB Code - Continued
• Data Destandardization• Calculation of Indicators• Analyzing Calculated
Data
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
GUI Implementation
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
P&L Sample
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
S&P’s 500 Options Transaction Costs
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 20130.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
1.44% 1.48%1.58%
0.38%
0.69%
0.04%
0.79%
1.14%
2.84%
1.68%
2.82%
0.61%
1.45%
0.22%
1.75%
As Percentage of Profit/Loss Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
EuroStoxx 50 Options Transaction Costs
As Percentage of Profit/Loss Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 20130.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
1.22%
0.72%
1.28%
2.56% 2.46%
1.05%
1.74%
2.58%2.23%
1.49%
1.13%1.31%
0.87%1.03%
4.21%
DAX 30 Options Transaction Costs
As Percentage of Profit/Loss Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 20130.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
1.82%
3.93%
1.02%
3.38%
0.76%
2.57%
0.82%
0.45%
2.57%2.91%
0.80% 0.80% 0.71%
1.39%
2.04%
S&P’s 500 Performance
Underlying Performances Derivatives Performance
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
1999
2001
2003
2005
2007
2009
2011
2013
-50%-40%-30%-20%-10%
0%10%20%30%40%
S&P's F'(x) F''(x) MA(5)
1999
2001
2003
2005
2007
2009
2011
2013
-50%-40%-30%-20%-10%
0%10%20%30%40%50%
Stand Alone Cumulative with MA(5)
EuroStoxx 50 Performance
Underlying Performances Derivatives Performance
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
1999
2001
2003
2005
2007
2009
2011
2013
-80%
-60%
-40%
-20%
0%
20%
40%
60%ESXX50 F'(x) F''(x) MA(5)
1999
2001
2003
2005
2007
2009
2011
2013
-30%-20%-10%
0%10%20%30%40%50%60%
Stand Alone Cumulative with MA(5)
Dax 30 Performance
Underlying Performances Derivatives Performance
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
1999
2001
2003
2005
2007
2009
2011
2013
-80%
-60%
-40%
-20%
0%
20%
40%
60%DAX30 F'(x) F''(x) MA(2)
1999
2001
2003
2005
2007
2009
2011
2013
-60.00%
-40.00%
-20.00%
0.00%
20.00%
40.00%
60.00%
80.00%Stand Alone Cumulative with MA(2)
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
S&P's F'(x) F''(x) MA(5) Stand Alone Cumulative with MA(5)TOTAL 69.07% 63.80% -29.78% 26.02% Performance 240.26% 266.29%
-5.27% -98.85% -43.05% Vs. S&P's 500 171.19% 197.22%Volatility 19.11% 14.34% 18.92% 11.60% 18.92% 20.48%
Max 29.60% 22.97% 34.52% 20.39% Vs. S&P's 500 42.48% 39.17%Min -38.47% -23.80% -30.94% -15.10% Vs. S&P's 500 -38.35% -43.20%
DAX30 F'(x) F''(x) MA(2) Stand Alone Cumulative with MA(2)TOTAL 122.86% -36.34% -157.67% -14.70% Performance 275.21% 260.52%
-159.20% -280.53% -137.56% Vs. DAX30 152.35% 137.66%Volatility 26.99% 21.80% 18.88% 15.89% 15.42% 26.48%
Max 38.98% 23.45% 15.66% 19.37% Vs. DAX30 43.65% 63.02%Min -43.94% -44.03% -63.06% -34.71% Vs. DAX30 -3.84% -38.55%
ESXX50 F'(x) F''(x) MA(5) Stand Alone Cumulative with MA(5)TOTAL 37.92% -12.39% -42.75% 72.60% Performance 264.78% 337.39%
-50.31% -80.67% 34.68% Vs. ESXX50 226.86% 299.47%Volatility 24.16% 19.78% 23.96% 13.70% 15.69% 19.20%
Max 46.74% 31.15% 28.21% 27.59% Vs. ESXX50 43.74% 50.28%Min -44.37% -53.14% -61.91% -12.23% Vs. ESXX50 -17.13% -4.73%
Cumulative Returns S&P’s 500
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 20130
200
400
600
800
1000
1200
1400
1600
1800F'(x) F''(x) MA(5) Stand Alone Cumulative with MA(5)
Cumulative Returns EuroStoxx 50
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 20130
200
400
600
800
1000
1200
1400
1600
1800
2000F'(x) F''(x) MA(5) Stand Alone Cumulative with MA(5)
Cumulative Returns DAX 30
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 20130
200
400
600
800
1000
1200F'(x) F''(x) MA(2) Stand Alone Cumulative with MA(5)
A Market distortion
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
-100.00%
-90.00%
-80.00%
-70.00%
-60.00%
-50.00%
-40.00%
-30.00%
-20.00%
-10.00%
0.00%
S&P's 500 vs. VIX Annual Correlation
Corr
elat
ion
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
A Market distortion - Continued
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
-100.00%
-80.00%
-60.00%
-40.00%
-20.00%
0.00%
20.00%
Eurostoxx 50 vs. VSTOXX Annual Correlation
Corr
elat
ion
A Market distortion – Continued
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
-120.00%
-100.00%
-80.00%
-60.00%
-40.00%
-20.00%
0.00%
20.00%
40.00%
60.00%
DAX30 vs. VDAX-NEW Annual Correlation
Corr
elat
ion
Conclusions
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
Does M.A.D. Algorithm works?
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
Yes, it works! Anyway, some considerations must be done:
1. Correlation between VIX and Underlying over a wide time horizon: in years where markets soared the correlation between underlying and its volatility derivative modified (so strongly to become positive in some years!).
2. Volatility: it does not affect directly underlying performances but it affects directly the procedure fitting and, consequently, the goodness of algorithm’s signals.
3. MA: a moving average helps to faster change algorithm’s signal and exploit market swings.
4. Losses: even if strategy outputs are mostly positive, we must pay attention to the high recorded losses in particular years.
5. Goodness of Fit: attention must be paid when fitting process runs. In some years, especially in market crashes or in strong financial/economic crises, it is difficult to have a high R2 that reflects on lower algorithm performance
Thank you for your attention!
Copyright © 2014 Leonardo Urbano. All rights reserved.
M.A.D. Trading System – A Mathematical HFT Setup
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