Mean Reverting Asset Trading Research Topic Presentation CSCI-5551 Grant Meyers

Table of Contents 1. Introduction + Associated Information 2. Problem Definition 3. Possible Solution 1 4. Problems with Solution 1 5. Possible Solution 2 / Research Topic 6. Specific Questions to be Answered

1. Introduction Asset Definition + Properties of a Mean Reverting Asset

Asset Definition  1. A resource with economic value that an individual, corporation or country owns or controls with the expectation that it will provide future benefit.  2. A balance sheet item representing what a firm owns.  This presentation will cover only – stocks which represent an ownership interest in a business.

Properties of a Mean Reverting Asset  Needs some level of volatility in price.  Needs to vacillate around a center value; rising / falling around a dependable ‘Mean’ value.

Properties of a Mean Reverting Asset  Required for a good Mean Reverting Asset:  Preferably a seasonal or otherwise dependable cycle up and down.  High liquidity, being able to buy and sell at optimum prices.  Minimal chance of ‘insider trading’ or other ‘exceptional’ events.

Examples of a Mean Reverting Asset  Chevron over last 5 years

Examples of a Mean Reverting Asset  Disney this year

Table of Contents 1. Introduction + Associated Information 2. Problem Definition 3. Possible Solution 1 4. Problems with Solution 1 5. Possible Solution 2 / Research Topic 6. Specific Questions to be Answered

Problem Definition What does ‘Mean Reverting Asset Trading’ encompass?

Core Questions  Can you make money from the ‘Stock Market’ by trading?  Which companies do you choose?  What are the costs?

Problem Components 1 - Timing  Can you make money from the ‘Stock Market’ by trading?  Maximize profit from buying low + selling high.  When do you buy?  (A) $10,000 of Netflix (NFLX) bought on 16 Dec $45.21 / share = 221 shares  (B) $10,000 of Netflix (NFLX) bought on 6 Aug $ / share = 79 shares  When do you sell?  (A) 221 shares sold on 6 Aug $ / share = $27, (+$17,945.45)  (B) 79 shares sold on 22 Oct $97.32 / share = $7, (-$2,311.72)

Problem Components 2 – Options  Which companies do you choose?  There are 1,868 stocks listed on New York Stock Exchange.  There are 3,300 stocks listed on the Nasdaq.  There are 1,299 stocks listed on Euronext.

Problem Components 3 - Costs  Transaction Cost  Online Self Directed Trade - $8.90  Broker Assisted Trade - $30.99  Opportunity Cost  $10,000 of Amazon (AMZN) bought on 24 Oct 2014 sold today is worth $20,  $10,000 of Apollo Education Group (APOL) on 22 Dec 2014 sold today is worth $2,151.8  Emotional  Loss Aversion - Humans fear loss much more than possible winnings

Variables + Unknowns  Maximize Gain, Minimize Loss  Timing the Buy  Timing the Sell  Minimizing costs  There is no obvious solution, no method always works.  Hindsight may be perfect, but predicting the future with precision is literally impossible.

Table of Contents 1. Introduction + Associated Information 2. Problem Definition 3. Possible Solution 1 4. Problems with Solution 1 5. Possible Solution 2 / Research Topic 6. Specific Questions to be Answered

Possible Solution 1 Based on analytic solution to asset price prediction algorithm.

Possible Solution 1 

Possible Solution 1 – Analytical Solution 

 Buy at x1 and sell at x2

Table of Contents 1. Introduction + Associated Information 2. Problem Definition 3. Possible Solution 1 4. Problems with Solution 1 5. Possible Solution 2 / Research Topic 6. Specific Questions to be Answered

Problems with Solution 1

 Requires model for underlying asset to set calculation constants and determine the rate of reversion to the mean, and the equilibrium level / mean value.  Allows adjustments via main 2 parameters only.  Nearly impenetrable math…

Table of Contents 1. Introduction + Associated Information 2. Problem Definition 3. Possible Solution 1 4. Problems with Solution 1 5. Possible Solution 2 / Research Topic 6. Specific Questions to be Answered

Possible Solution 2 / Research Topic Stochastic Approximation Methods and Applications in Financial Optimization Problems - Chapter 2: Mean-Reverting Asset Trading

Mean Reverting Asset Prediction Equation 

Components 1  Stochastic Approximation  Used to recursively estimate some quantities based on noise corrupted observations.  Originally introduced in 1950s.  Noise Sources  Imperfect sampling period.  Multiple trades executing ‘simultaneously’.  Sampling technique. Midpoint between bid / sell, or last trade price

Components 2 

Mean Reverting Asset Prediction Equation - Estimation 

Advantages Over Solution 1  No model for the underlying asset.  Less rigid, less dependent on human ‘intuition’.  Easily updated for new data & ‘paradigm’ shifts in whole sectors.  Data for stocks is easily available & in an easily processed format.

Advantages Over Solution 1, continued  M ultiple asset data time-resolutions allow for variable scaled action speeds.  If broker takes, on average, 10 seconds to execute a trade, having a regression based on faster time would not necessarily work well.  Using 24 hour scale data, may allow for a more macroscopic view of the asset’s movement.

Table of Contents 1. Introduction + Associated Information 2. Problem Definition 3. Possible Solution 1 4. Problems with Solution 1 5. Possible Solution 2 / Research Topic 6. Specific Questions to be Answered

Specific Questions to be Answered 1 Data Sample Related  Does the algorithm work when there is a macroscopic change in the overall market?  Does changing the training & applying time windows affect the return? How much? Do longer windows fair better or shorter ones?  Are there any dependable seasonal fluctuations?  Does the asset ‘class’ affect the effectiveness of the algorithm?

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?

References  Human Loss Aversion -  Asset Definition -  NYSE Listing Size:  NASDAQ Listing Size:  EuroNext Listing Size:  Average Online Trading Cost: online-brokerage-tradinghttp:// online-brokerage-trading  Zhang and Zhang Reference: Hanqin Zhang, Qing Zhang, Trading a mean- reverting asset: Buy low and sell high, Automatica, Volume 44, Issue 6, June 2008, Pages , ISSN , dx.doi.org.skyline.ucdenver.edu/ /j.automatica dx.doi.org.skyline.ucdenver.edu/ /j.automatica