Mean Reverting Asset Trading Project Presentation CSCI-5551 Grant Meyers

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

1. Review Mean Reverting Asset + Goal

Review – Mean Reverting Asset 

Example Mean Reverting Asset

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.

Goal – Price Selection  Better:

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

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

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

2. Search Algorithm Recursive Refinement Search

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.

Stochastic Differential Equation 

Stochastic Approximation 







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

3. Parallelization Recursive Refinement Search

Equation Level Parallelism 

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

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.

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.

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

Sample Results

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)  2014 becomes 2015 – ~41% gain

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)  2011 becomes 2012 – ~60% gain

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)  2013 becomes 2015 – ~48% gain

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

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)  2013 becomes 2015 – ~48% gain

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)  2011 becomes 2012 – ~60% gain

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.

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?