Mean Reverting Asset Trading

Project Presentation

CSCI-5551

Grant Meyers

Table of Contents

1. Review

2. Search Algorithm

3. Parallelization

4. Project Results

1. ReviewMean 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 AlgorithmRecursive 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

Stochastic Approximation

Stochastic Approximation

Stochastic Approximation

Table of Contents

1. Review

2. Search Algorithm

3. Parallelization

4. Project Results

3. ParallelizationRecursive Refinement Search

Equation Level Parallelism

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

4. Project ResultsSample 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: $42.86 Sell: $48.68 Profit Per Share: $17.46 ($5.82)

$10,000 @Jul 2014 becomes $14,068.18 @Oct 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: $75.60 Sell: $90.53 Profit Per Share: $44.79 ($14.93)

$10,000 @Feb 2011 becomes $15,912.28 @Jul 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: $297.90 Sell: $346.20 Profit Per Share: $144.9 ($48.3)

$10,000 @Sep 2013 becomes $14,781.7 @Jan 2015 – ~48% gain

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

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: $297.90 Sell: $346.20 Profit Per Share: $144.9 ($48.3)

$10,000 @Sep 2013 becomes $14,781.7 @Jan 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: $75.60 Sell: $90.53 Profit Per Share: $44.79 ($14.93)

$10,000 @Feb 2011 becomes $15,912.28 @Jul 2012 – ~60% gain

Specific Questions to be Answered 1Data 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 2Performance 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?