1. Mean Reverting Asset Trading Project Presentation CSCI-5551 Grant Meyers

2. Table of Contents 1. Review 2. Search Algorithm 3. Parallelization 4. Project Results

3. 1. Review Mean Reverting Asset + Goal

4. Review – Mean Reverting Asset 

5. Example Mean Reverting Asset

6. Goal – Price Selection  We want to select 2 prices.  Price 1 is ‘buy’ price, this is an upper limit of when to start purchasing shares.  Price 2 is ‘sell’ price, this is a lower limit of when to start selling shares.

7. Goal – Price Selection  Better:

8. Goal – Optimal Price Selection  What are the best buy / sell prices for a given stock?  How do we find these prices?

9. Goal – Optimal Price Selection  What are the best buy / sell prices for a given stock?  Specific per stock.  How do we find these prices?  Algorithmic search on historic data

10. Table of Contents 1. Review 2. Search Algorithm 3. Parallelization 4. Project Results

11. 2. Search Algorithm Recursive Refinement Search

12. Mathematical Model for Asset Price  A ‘Mean Reverting Asset’ is very similar to an Ito Process or Ornstein Uhlenbeck Process.  This similarity allows for a mathematical definition / prediction of what the stock price will do.  Search is based on historical data and recursively refined the more iterations the simulation is run.

13. Stochastic Differential Equation 

14. Stochastic Approximation 

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18. Table of Contents 1. Review 2. Search Algorithm 3. Parallelization 4. Project Results

19. 3. Parallelization Recursive Refinement Search

20. Equation Level Parallelism 

21.  Equations are ‘auto’ parallelized with Parallelize command.  Mathematica will split the expression parts into sub programs and distribute.

22. Question Level Parallelism  What is the best stock from a set of stocks S over time period P.  S = set of stock symbols, ie {“MSFT”, “AAPL”, “NFLX”, “CVX”, “AMZN”}  P = set of 2 dates, start and end, ie {“1 Jan 2015”, “13 Nov 2015”}  Allows for running all symbols independently of each other, then ‘combining’ results.  Done via ParallelSubmit on stock symbols.

23. Question Level Parallelism  What is the time period for stock S with in limited time period P.  S = stock symbol, ie {“MSFT”}  P = set of 2 dates, start search and end search, ie {“1 Jan 2015”, “13 Nov 2015”}  Allows for processing a single set of data, with multiple concurrent search threads.  ParallelSubmit with function to generate testing sets.

24. Table of Contents 1. Review 2. Search Algorithm 3. Parallelization 4. Project Results

25. Sample Results

26. Sample Results – Time Period  Best stock period for each: {“MSFT”, “AAPL”, “NFLX”, “CVX”, “AMZN”}  Time Period:Jul 2014 – Oct 2015 – Microsoft (MSFT)  Buy + Sell sets: 3 times of 233 shares.  Buy: $42.86Sell: $48.68Profit Per Share: $17.46 ($5.82)  $10,000 @Jul 2014 becomes $14,068.18 @Oct 2015 – ~41% gain

27. Sample Results – Time Period 2  Best stock period for each: {“MSFT”, “AAPL”, “NFLX”, “CVX”, “AMZN”}  Time Period:Feb 2011 – Jul 2012 – Apple (AAPL)  Buy + Sell sets: 3 times of 132 shares.  Buy: $75.60Sell: $90.53 Profit Per Share: $44.79 ($14.93)  $10,000 @Feb 2011 becomes $15,912.28 @Jul 2012 – ~60% gain

28. Sample Results – Time Period 3  Best stock period for each: {“MSFT”, “AAPL”, “NFLX”, “CVX”, “AMZN”}  Time Period:Sep 2013 – Jan 2015 – Netflix (NFLX)  Buy + Sell sets: 3 times of 33 shares.  Buy: $297.90Sell: $346.20Profit Per Share: $144.9 ($48.3)  $10,000 @Sep 2013 becomes $14,781.7 @Jan 2015 – ~48% gain

29. Sample Results – Time Period 4  Best stock period for each: {“MSFT”, “AAPL”, “NFLX”, “CVX”, “AMZN”}  Time Period:Nov 2011 – Jul 2012 - Chevron (CVX)  Buy + Sell sets: 5 times of 101 shares.  Buy: $98.72 Sell: $108.30 Profit per Share: $47.9 ($9.58)  $10,000 @Nov 2011 becomes $14,837.9 @Jul 2012 – 48% gain

30. Sample Results – Time Period 5  Best stock period for each: {“MSFT”, “AAPL”, “NFLX”, “CVX”, “AMZN”}  Time Period:Sep 2013 – Jan 2015 – Amazon (AMZN)  Buy + Sell sets: 3 times of 33 shares.  Buy: $297.90Sell: $346.20Profit Per Share: $144.9 ($48.3)  $10,000 @Sep 2013 becomes $14,781.7 @Jan 2015 – ~48% gain

31. Sample Results – Best Stock in Period  Best stock of: {“MSFT”, “AAPL”, “NFLX”, “CVX”, “AMZN”}  Time Period:Nov 2010 – Nov 2015 – Apple (AAPL)  Buy + Sell sets: 3 times of 132 shares.  Buy: $75.60Sell: $90.53 Profit Per Share: $44.79 ($14.93)  $10,000 @Feb 2011 becomes $15,912.28 @Jul 2012 – ~60% gain

32. Specific Questions to be Answered 1 Data Sample Related  Does the algorithm work when there is a macroscopic change in the overall market?  No. Some sort of capital preservation or opportunity cost maximum needs to be used.  Does changing the training & applying time windows affect the return? How much? Do longer windows fair better or shorter ones?  A) Yes. B) Depends. C) Inconclusive.  Are there any dependable seasonal fluctuations?  Inconclusive.  Does the asset ‘class’ affect the effectiveness of the algorithm?  Yes, most stocks are NOT mean reverting.

33. Specific Questions to be Answered 2 Performance Related  How fast can the Xeon server crunch the numbers?  How fast can the Hydra server crunch the numbers?  Is there a better way to format the data than the default JSON format?  Given the use of common mathematical operations, could they be switched out to a format that uses matrix multiplication?