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

2. Table of Contents Review Revision of Technique New Search Algorithm
Parallelization
Project Results

3. 1. Review
Mean Reverting Asset + Goal

4. Review – Mean Reverting Asset

5. Example Mean Reverting Asset
Example Generated with:
data=RandomFunction[OrnsteinUhlenbeckProcess[0,1,.1],{0,15,.1}]
ListLinePlot[data,Filling->Axis,AxesLabel->{HoldForm[Time],HoldForm[Worth]},PlotLabel->HoldForm[Mean Reverting Stock Price - Centered at 0],LabelStyle->{12,GrayLevel[0],Bold}]
Via Mathematica. Due to OrnsteinUhlenbeckProcess being a random process, your generated graph will look different, but will maintain the properties required.

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 Review Revision of Technique New Search Algorithm
Parallelization
Project Results

11. 2. Revision of Technique
Mean reverting assets are rare

12. Findings from Previous Work
Finding #1 – Mean Reverting Assets are hard to find.
None of the tech / commodity stocks I tested could be classified as a ‘Mean Reverting Asset’.
Finding #2 – Most stocks follow fairly closely with a regression line.
Finding #3 - Deviation from regression line is parallelizable much more easily than the Stochastic Approximation techniques previously discussed.

13. A New Technique – Deviation from Regression Line
Stocks tend to follow a fairly predictable trend.
Regression is history based and is an attempt to find the overall direction and slope of an asset’s price.
Similar to the ‘mean reversion’ process where volatility pushes the price above and below a known / calculable quantity.
Follow the same strategy of - Buy low Sell High.

14. Table of Contents New Search Algorithm Review Revision of Goals
Parallelization
Project Results

15. 3. New Search Algorithm
Subset of regression deviation ranges

16. Regression Line Search Space
Orange is the regression line
Green is the highest possible
selling point
Red is the lowest possible
buying point

17. Regression Line Search Space - Partitions
Each color band is a range
to test – Buy or Sell ranges
Top 3 are sell ranges
105% of regression normal
110% of regression normal
115% of regression normal
Bottom 3 are buy ranges
95% of regression normal
90% of regression normal
85% of regression normal

18. Independent Search Threads
We have 3 buy ranges and 3 sell ranges (on example graph).
Creating all pairs of 1 buying range and 1 selling range, creates 9 sets.
All of these sets can be optimized independently as they do not overlap.
Optimized - most profit, from buying in buy range and selling sell range.

19. Table of Contents Parallelization Review Revision of Goals
New Search Algorithm
Parallelization
Project Results

20. 4. Parallelization

21. Required work Load training data. Create regression model.
Find high and low points for price deviation from regression line.
Partition work space.
Find best price in assigned ranges to buy & sell.
Calculate profit for assigned ranges buy & sell.
Merge best ranges + find most profitable range.
Calculate + return profit on test data.
Steps 5, 6 are done in parallel.

22. Serial Work Load training data. Create regression model.
Find high and low points for price deviation from regression line.
Partition work space.
Find best price in assigned ranges to buy & sell.
Calculate profit for assigned ranges buy & sell.
Merge best ranges + find most profitable range.
Calculate + return profit on test data.
Clean-Up

23. Top Level Parallel Work
Load training data.
Create regression model.
Find high and low points for price deviation from regression line.
Partition work space.
Find best price in assigned ranges to buy & sell.
Calculate profit for assigned ranges buy & sell.
Merge best ranges + find most profitable range.
Calculate + return profit on test data.
Clean-up
Steps 5, 6 are done in parallel.

24. 2nd Level Parallel Work Load training data. Create regression model.
Find high and low points for price deviation from regression line.
Partition work space.
Find best price in assigned ranges to buy & sell.
Calculate profit for assigned ranges buy & sell.
Merge best ranges + find most profitable range.
Calculate + return profit on test data.
Clean-up
Steps 5, 6 are done in parallel.

25. Work Diagram – See Work Diagram PDF
Steps 5, 6 are done in parallel.

26. Table of Contents Project Results Review Revision of Goals
New Search Algorithm
Parallelization
Project Results

27. 5. Project Results
Sample Results

28. Observations
The larger the deviations from the regression model, the larger the search space and time it takes to find the optimum buy / sell deviation prices.
Small deviation search spaces go REAL quick (in less than a second).
Executor services can take a decent amount of time to clean-up after they are completed.

29. Observations
The largest factor in determining the runtime is the STEP_SIZE variable in the FindOptimumInRange class.
1 cent is the maximal logical STEP_SIZE, but it will max the search timeout for any decently size deviation.

30. Some Statistics Symbols: CVX, GOOGL, AAPL, MSFT Time To Completion
STEP_SIZE
THREAD_POOL_SIZE
PARTITIONS_COUNT
SUB_THREAD_POOL_SIZE
42.396s
0.05 1 4 8
12.975s
0.1
2.117s
0.5
1.869s
43.456s 2
12.191s
2.324s
1.875s
43.649s 3
12.258s
2.436s
2.043s
44.373s
12.388s
2.511s
1.710s

31. SUB_THREAD_POOL_SIZE
Some Statistics
Symbol: CVX
Time To Completion
STEP_SIZE
THREAD_POOL_SIZE
PARTITIONS_COUNT
SUB_THREAD_POOL_SIZE
3.511s
0.01 1
0.484s
0.1
0.360s
0.5
0.313s
3.228s 2
0.375s
0.328s
0.343s
2.119s
0.344s
2.174s 4
0.391s

32. SUB_THREAD_POOL_SIZE
Some Statistics
Symbol: GOOGL
Time To Completion
STEP_SIZE
THREAD_POOL_SIZE
PARTITIONS_COUNT
SUB_THREAD_POOL_SIZE s
0.01 1
24.759s
0.1
1.316s
0.5
0.578s s 2
24.716s
1.325s
0.594s s
13.102s
0.844s
0.437s s 4
7.641s
0.672s
6.757s 8
0.641s

33. SUB_THREAD_POOL_SIZE
Some Statistics
Symbol: AAPL
Time To Completion
STEP_SIZE
THREAD_POOL_SIZE
PARTITIONS_COUNT
SUB_THREAD_POOL_SIZE s
0.01 1
16.216s
0.1
0.978s
0.5
0.485s s 2
17.629s
1.176s
0.641s s
9.384s
0.844s
0.657s s 4
5.690s
0.610s
0.406s
4.501s 8
0.546s

34. SUB_THREAD_POOL_SIZE
Some Statistics
Symbol: MSFT
Time To Completion
STEP_SIZE
THREAD_POOL_SIZE
PARTITIONS_COUNT
SUB_THREAD_POOL_SIZE
0.528s
0.01 1
0.453s
0.1
0.422s
0.5
0.547s 2
0.469s
0.438s
0.516s
0.437s
0.515s 4
0.500s
0.485s
0.483s