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

Transcription

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

2 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

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

4 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.

5 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.

6 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.

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

8 Examples of a Mean Reverting Asset Disney this year

9 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

10 Problem Definition What does Mean Reverting Asset Trading encompass?

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

12 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)

13 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.

14 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

15 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.

16 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

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

18 Possible Solution 1 Using the equation: dx t = α β X t dt + σ dw t where X 0 = x α > 0 is the rate of reversion to the mean. β is the equilibrium level / mean value. X t is the stock price s model. σ > 0 is the volatility of the asset. σ dw(t) is the stochastic term causing ups and downs around the mean. Based on a Standard Brownian motion.

19 Possible Solution 1 Analytical Solution Using the equation: dx t = α β X t dt + σ dw t where X 0 = x A solution based on α and β is possible. In practice, these values are not stable and not that easy to find for a given asset.

20 Possible Solution 1 Analytical Solution Buy at x1 and sell at x2

21 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

22 Problems with Solution 1

23 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

24 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

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

26 Mean Reverting Asset Prediction Equation This equation can be used to Predict a stocks price: dx t = α β X t dt + σ dw t Instead of using the analytical solution, you can use simulation with actual values and estimate a solution.

27 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

28 Components 2 Model Recursive Stochastic Approximation Equation θ n+1 = θ n + ε n X n θ n is an exact parameter of the system. X n is a random independent variable of the system and corrupted by noise. ε n is the step size.

29 Mean Reverting Asset Prediction Equation - Estimation Testable Estimator: θ n+1 = θ n + ε n DΦ (θ n, ξ n ) ε n is the step size (seconds, minutes, ) DΦ (θ n, ξ n ) is the Gradient of vectors of correlated and uncorrelated noise θ n is known data values

30 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.

31 Advantages Over Solution 1, continued Multiple 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.

32 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

33 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?

34 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?

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