FE8827 Q UANTITATIVE T RADING S TRATEGIES PROJECT H IGH F REQUENCY T RADING U SING R EGIME S WITCHING S TRATEGY Huynh Gia Huy (G L) Le Hoang Thai (G G)

R EFERENCE “Developing High-Frequency Equities Trading Models”, Leandro Rafael Infantino, Savion Itzhaki, MBA thesis, MIT, June 2010.

C ONTENTS Simply Guide Model Building: motivation, trading ideas, potential problems and implementation. Simulation Results: without/with transaction costs, development from the thesis. Weaknesses of Trading Signals in the Thesis and Proposed Improvement: mean reverting signals and regime switching signals.

S IMPLE G UIDE To display performance statistics, run rsperf.m file: rsperf(index, rf, lossthreshold) Input: index = 1: regime switching with transaction costs. index = 2: regime switching without transaction costs. index = 3: mean reverting with transaction costs. index = 4: mean reverting without transaction costs. rf: risk free rate lossthreshold: omega loss threshold Ouput: Omega ratio, Sharpe ratio, Omega Sharpe ratio, MaxDD (max drawdown) and MaxDDD (max drawdown duration).

S IMPLE G UIDE To start trading strategies, run regswitch.m file. In this file, turn on/off regime switching by setting regimeSwitching variable to 1 to turn on and 0 to turn off. regimeSwitching = 1; % default value Change line 32 in this file to run simulation for a period of time. Default is whole year running from week 1 to week 52. for week=1:52

M ODEL BUILDING - M OTIVATION In high frequency environment, high precision of the stock return prediction is not required. Fundamental Law of Active Management IR: Information Ratio IC: Information Coefficient (our skill) Breadth: “the number of independent forecasts of exceptional return made per year” Breadth very big => IC can be relatively small => prediction can be less precise

M ODEL BUILDING - T RADING IDEAS Use Principle Component Analysis (PCA) as the basis to compute cumulative returns Depending on the current strategy (mean- reversion or momentum), trading signals are generated if observed cumulative returns differ from model cumulative returns. Predicted – observed > threshold => buy (sell) Predicted – observed sell (buy)

D IFFERENCES BETWEEN THIS PROJECT AND THE PAPER Number of stocks used in the simulation: only first 10 stocks (instead of 50) are chosen to represent the stock universe. Data source: the primary data used in this project is obtained from Thomson Reuters Tick History database, and from two major exchanges: NASDAQ and NYSE; whereas prices used in the thesis are from top of the book bid-ask quotes. Model parameters: various model parameters are not specified in the thesis, thus simulation results can be affected by the choice of different parameter values. Transaction costs are included. Signal in the thesis is found insufficient and has been modified to improve stabilty and performance of returns.

M ODEL BUILDING - P OTENTIAL PROBLEMS - DATA VOLUME Huge volume of data: more than 15Gbs of one year tick data to process (and that’s only for 10 stocks). Simulation time can be very long because of this. Code optimization is important!

I MPLEMENTATION Matlab is chosen as it provides many built-in mathematics functions suitable for rapid model development. Pre-process data before running simulation: Only one mid-price per second per stock Need to duplicate values for missing seconds in raw data. Processed data saved in separate.csv files. Run simulation based on processed data. All daily returns are saved in.csv files.

S OME CODE OPTIMIZATION TECHNIQUES Always pre-allocate memory for matrix and avoid changing matrix size constantly. Avoid loop as much as possible and make use of Vectorization (performance increased dramatically!) Use Matlab profiler to identify areas for improvement. Normal for loopVectorization i = 0; for t = 0:.01:10 i = i + 1; y(i) = sin(t); end t = 0:.01:10; y = sin(t);

S IMULATION RESULTS - THESIS Mean-reversion strategy, without transaction cost.

S IMULATION RESULTS – THIS PROJECT Mean-reversion strategy, without transaction cost.

S IMULATION RESULTS – THIS PROJECT Mean-reversion strategy, without transaction cost. Omega: (Loss threshold: 0) Sharpe: Omega Sharpe: Max Drawdown: Max Drawdown duration: 73 days.

S IMULATION RESULTS - THESIS Regime switching strategy, without transaction cost.

S IMULATION RESULTS – THIS PROJECT Regime switching strategy, without transaction cost.

S IMULATION RESULTS – THIS PROJECT Regime switching strategy, without transaction cost. Omega: (Loss threshold: 0) Sharpe: Omega Sharpe: Max Drawdown: Max Drawdown duration: 226 days.

C OMMENTS The different simulation results between this project and thesis can be due to: Different stock universe Different data source (therefore different mid-prices) Parameters used (thresholds). In the thesis, transaction cost is not taken into account and it is a important factor to consider in high frequency trading model. All profits can be erased by transaction cost. Next step for this project: include transaction cost! To be realistic, transaction cost from Interactive Brokers is used; that is, $0.005 / share / trade

T RANSACTION COSTS : M ODIFICATIONS TO EXISTING STRATEGY In an attempt to factor in the transaction cost, the trading model is modified. Two potential places: Mark-up the threshold by the transaction cost, i.e. new threshold = threshold + transaction cost Lower the log returns. Use this new log returns as input for Principal Components Analysis log_return = log[(current_price - cost) / previous_price + cost)] This project uses the second approach.

S IMULATION RESULT – MODIFIED MODEL Mean-reversion strategy, with transaction cost.

S IMULATION RESULTS – THIS PROJECT Mean-reversion strategy, with transaction cost. Omega: (Loss threshold: 0) Sharpe: Omega Sharpe: Max Drawdown: Max Drawdown duration: 68 days.

S IMULATION RESULT – MODIFIED MODEL Modified regime switching strategy, with transaction cost.

S IMULATION RESULTS – THIS PROJECT Mean-reversion strategy, with transaction cost. Omega: (Loss threshold: 0) Sharpe: Omega Sharpe: Max Drawdown: Max Drawdown duration: 248 days.

W EAKNESSES OF THE TRADING SIGNALS IN THE THESIS – P ROPOSED I MPROVEMENTS Mean reverting signal: In the thesis, if mean reverting signal > 0, we buy and sell when signal < 0. It includes noise due to rounding or computational issues. Solution: set a threshold to filter away noise that creates fault trades. This threshold after trial and error has been determined to be (parameter 1)

W EAKNESSES OF THE TRADING SIGNALS IN THE THESIS - P ROPOSED I MPROVEMENTS Regime Switching Signals: The authors use difference in two consecutive Euclidean distance to signal the regime switching: If E H (t) - E H (t-1) > 0: momentum regime If E H (t) - E H (t-1) < = 0: mean reverting regime This signals introduce noise and cause fault signals and consequently fault trades.

W EAKNESSES OF THE TRADING SIGNALS IN THE THESIS - P ROPOSED I MPROVEMENTS Regime Switching Signals – Noise Diagram of Euclidean distance difference (E H (t) - E H (t-1)) is shown above. According to the authors, the strategy keeps changing the regimes as signals swing around 0 from positive to negative.

W EAKNESSES OF THE TRADING SIGNALS IN THE THESIS - P ROPOSED I MPROVEMENTS Regime Switching Signals – Fault Signals Diagram of Euclidean distance difference (E H (t) - E H (t-1)) is shown above and Euclidean distance(E H (t)) below. One strong pulse in E distance creates one regime switching signal but it contains one up pulse and one down pulse in E distance difference. According to the authors, it creates two signals that causes the system to switch back and forth (mean reverting -> momentum -> mean reverting) within <150 seconds.

W EAKNESSES OF THE TRADING SIGNALS IN THE THESIS - P ROPOSED I MPROVEMENTS Regime Switching Signals – Noise – Solution We set a threshold of 2 standard deviation to filter out noise (parameter 2). Magnitude falls between ± 2 std dev is considered insignificant. Instead of using differences of 2 consecutive E distance (E H (t) - E H (t-1)), we use E H (t) – ewma5(E H (t)) where ewma5(E H (t)) is equally weighted moving averages value of previous 5 seconds of E distance (parameter 3). Ignore 2 consecutive regime switching signals fall into a timespan of less than 250 seconds to remove fault signals (parameter 4).

C ONCLUSIONS Simulation returns are very sensitive to parameters used. All 4 parameters can be improved by employing optimization. Due to the time constraint, we leave this part for future development.