Multi-factor Statistical Arbitrage Model

Transcription

1 MS&E 448: Group 6 Grant Avalon Irene Jeon Michael Becich Sreyas Misra Vincent Cao Liezl Puzon Multi-factor Statistical Arbitrage Model 1

2 Overview 1. Background 2. Data Inputs 3. Methods 4. Trading Algorithm 5. Results 6. Discussion 2

3 Background: Statistical Arbitrage Stat. Arb. exploits mispricings between mean-reverting pairs or baskets of stocks. Classic stat arb. identifies pairs of stocks based on how their prices stay together. 3

4 Background: Our Idea Can we pair stocks using not just stock prices/returns but also stock fundamentals? Multi-Factor Statistical Arbitrage Typical strategies re-implement Avellaneda et al. paper; our strategy expands upon these ideas Using only price/returns data creates unstable clusters that are exposed to market risks and don t persist well over time. By incorporating other stock time-series data like fundamentals (P/E ratio, revenue growth, etc.), we can create stabler stock clusters. We can use a modified O-U process to model mean-reversion in case pairs cease to be cointegrated 4

5 Background: Model Design PCA is performed twice: once for returns, once for fundamental factors Lower-Dimensionality Reduction Regressed st Highest Variance 1 PC 5

6 Model Inputs: Incorporating Time-Varying Data So far, we studied the S&P 500 stock index with time series data going back 5 years. S&P 500 Stock Log Returns S&P 500 Fundamental Factors Return Time Series (5Y) Factor Time Series (5Y) N*F Stacked Factors (Google Finance) Python scraper (Quantopian) Python scraper 6

7 Model Inputs: Incorporating Time-Varying Data We incorporated fundamental ratios and performed standardization on stacked matrix 1) 2) 3) 4) 5) P/E -- a means of standardizing the value of one dollar of earnings throughout market PEG -- incorporates future growth expectations; allows us to compare relative valuations of different industries that have very different prevailing P/E P/B -- useful for firms with positive book values and negative earnings; easily comparable to market price ROE -- useful for comparing profitability of a company to other firms in the same industry Debt/Equity -- amount of leverage company is using; gives insight into correlations among capital structure Factor Time Series (5Y) N*F Stacked Factors Standardization Process 7

8 GICS Clustering v. PCA and K-Means Clustering Hypothesis Cointegration analysis on just GICS clusters Characteristic Total Returns Benchmark Sharpe Backtest 1 Time Horizon: % 126% 0.1 Backtest 2 Time Horizon: % 27.2% 1.98 Backtest 3 Time Horizon: With Slippage 9.9% 27.2% 1.78 Stock Pairs in Portfolio: ABT/ABC AIG/SCHW CERN/MCK RF/FITB AN/DIS Performing cointegration on GICS clusters yielded poor performance and non-intuitive pairs 8

9 Clustering Results Pairwise PC-analysis revealed cluster separation, but poor correlation to industry sectors K=3 K=11 GICS Sector Correspondence K=20 9

10 Principal Component Analysis (PCA) & K-means Clustering To reduce dimensionality in noisy system and pre-process groups by largest-variance PC s PCA (Accounting for Variance) K-means (Elbow Method for Optimal K) stock returns across 1275 days -Top 100 PC s represent 75% variation, 200 PC s represent 95% -Elbow Method recommends K=3 for lowest error (SSE) drop -Not enough specificity to differentiate sectors of market (K=20 used ) 10

11 A New Clustering Approach 4 different clustering approaches were tested before settling on our final filtering strategy Clustering by GICS Sector (Financial Services, Health Care, and Consumer) a. Only co-integrated pair candidates within each sector are considered Clustering by log-returns alone (midterm) a. Number of clusters/principle components optimized 3. Clustering by 5 merged fundamentals (P/E, PEG, P/B, ROE, D/E) a. Sparse data not indicative of market activity clusters 4. Clustering by log-returns and fundamentals a. K-value for 3 fundamentals (K=5 by Elbow method) b. K-value for log-returns (K=20 by Silhouette scores) c. 10 PC s per instrument represent >50% variance d. Re-clustered across 5 time horizons eliminates overfitting/survivorship bias from incomplete datasets 11

12 Visualization of Fundamental Clusterings Despite dimensionality reduction, weak separation between clusters (5-year horizons) 12

13 A New Clustering Approach 4 different clustering approaches were tested before settling on our final filtering strategy 1. Clustering by GICS Sector (Financial Services, Health Care, and Consumer) a. Only co-integrated pair candidates within each sector are considered 2. Clustering by log-returns alone (midterm) a. Number of clusters/principle components optimized 3. Clustering by 3 merged fundamentals (Long-term debt equity ratio, price-to-book ratio, return on equity...price/earnings to growth ratio only for 2016 onwards) a. Sparse data not indicative of market activity clusters 4. Clustering by log-returns and fundamentals a. K-value for 3 fundamentals (K=5 by Elbow method) b. K-value for log-returns (K=20 by Silhouette scores) c. 10 PC s per instrument represent >50% variance d. Implemented across 5 time horizons eliminates overfitting/survivorship bias from incomplete datasets 13

14 Attempt to Exponentially Weight Returns/Factors Dimensionality Reduction acts against time-series weighting vs. Strategies contradict -- PCA more robust because it is insensitive to recent versus old history, much like how statistical arbitrage is as effective during bear vs. bull markets 14

15 Trading Algorithm: Co-integrated Stock Pairs* We identified pairs of stocks in the same returns and fundamentals cluster For each cluster i where 1 < size i < IF stock 1 and 2 individually pass Augmented Dickey Fuller Test < checks if both stocks are integrated AND IF < checks if the pair is co-integrated THEN pair(1,2) passes Engel-Granger Test bidirectionally** Stock 1 and 2 are pairs with reversion half life ln(2)/b * Done using MATLAB econometrics toolbox **performs test with both stocks as regressor We selected intuitive pairs with small min(e-g p-value) and fast reversion speeds. 15

16 Trading Algorithm: Execution Mean-Reversion was modelled as an O-U process For each cointegrated pair... Calculate parameters of O-U Process through Maximum Likelihood Estimation Using said parameters and current mispricing, find proportion of portfolio of optimal position If mispricing goes beyond certain threshold, begin unwinding position Unwinding partially protects from the risk that our pair ceases to be cointegrated. 16

17 Trading Algorithm: Trade Conditions For each cointegrated pair trade: Trade N minutes before closing each day (N = 30 minutes) Only run the trading logic at once a day at 3:30PM Eastern Time, which 30-minutes before market closes If spread is within a certain range, allocate capital to pairs trade Trade one pair at a time, after looking at the allocated capital 17

18 Portfolio Comparison for 2017 Comparing portfolios of 5 pairs to examine returns GICS Log Returns (PCA/k-means) Fundamentals Pair 1 ABT and ABC (health care) JPM and PBCT (financials) AJG / IR (financials & util) Pair 2 CERN and MCK (health care) BCR and XRAY (health care) DUK / EFX (util & industrials) Pair 3 AIG and SCHW (financials) BBBY and SPLS (consumer disc.) CMI / HOG (ind. & consumer disc.) Pair 4 RF and FITB (financials) SCHW and HBAN (financials) DHR / TSCO (health & consumer disc. ) Pair 5 AN and DIS (consumer disc.) BCR and SYK (health care) PEP / TRV(consumer staples & financials) PCA/K-means portfolio has the best performance & even though our clusters aren t very industry correlated, our pairs are very similar companies 18

19 Performance Results for the Log Returns PCA/K-means Portfolio Performance graph for our Log Returns PCA/K-means portfolio: 105-day window Time Horizon: 2012 to 2017 Notice that the total returns for Log Returns (14.29%) is better than GICS (11.6%) or Fundamentals (which was worse than GICS) 19

20 Portfolio Comparison: Hybrid Portfolio (PCA/K-means and Fundamentals) Comparing portfolios of 5 pairs to examine returns Hybrid Pair 1 BK / MS (financials) HD / COST (consumer disc. & consumer staples) ALXN / ILMN (health care) DUK / EXC (utilities) Pair 2 CMA / SCHW (financials) DVA / HD (health care & consumer disc.) DVA / SHW (health care & materials) DUK / LNT (utilities) Pair 3 -- DVA / RCL (health care & consumer disc.) SWK / WAT (consumer disc. & health care) FITB / RF (financials) Pair 4 -- TSCO / TJX (consumer discretionary) IT / NWL (info tech & consumer disc.) KEY / LNC (financials) Pair 5 -- LNC / HBAN (financials) DVA / TMO (health care) MAS / TDC (industrials & info tech) 20

21 Performance Results for the Hybrid Portfolio Performance graph for our hybrid (PCA/K-means and fundamentals) portfolio: 105-day window

22 Performance Results for the Hybrid Portfolio Performance graph for our hybrid (PCA/K-means and fundamentals) portfolio: 105-day window

23 Effect of Slippage on Performance Key findings Removing slippage in Quantopian improved performance We made use of naive market order strategy, so slippage was significant Results were encouraging enough to look for better trade execution 23

24 Summary of Findings Review and future directions Filtering stocks using PCA+K-means on log returns provided a better portfolio than filtering by GICS industries. Our hybrid portfolio, incorporating log returns and fundamentals, performed the best. Stocks that were present in multiple pairs are potential industry leaders. Although the S&P did really well, our stat-arb algorithm is a contrarian strategy that does not ride the market. On Quantopian performance results, the benchmark had a significant headstart while our algorithm was building the lookback window. 24

25 Future Directions How can we improve this algorithm? Investigate normalizing fundamentals within GICs buckets (but this could potentially lead to clusters that simply match GICs) Empirically test out more fundamentals, and then come up with the best 5. Scraping data was a big limitation to the types of fundamentals we could pick. Check for cointegration specifically in times of economic distress ( ) to check for cointegration robustness Sort out algorithm quirks such as partiality to pair-ordering 25

26 Thank you! Questions? References: