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研究生：	黃子菱 Tzu-Ling Huang
論文名稱：	Pairs trading based on statistical learning
指導教授：	孫立憲
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 統計研究所 Graduate Institute of Statistics
論文出版年：	2020
畢業學年度：	108
語文別：	英文
論文頁數：	55
中文關鍵詞：	配對交易、統計套利、共整合、機器學習、卡爾曼濾波、風險價值界限、公差極限
外文關鍵詞：	Pairs trading, Statistical arbitrage, Cointegration, Machine learning, Kalman filter, Value at Risk bounds, Tolerance limits
相關次數：	點閱：23 下載：0
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本文的主要目標是建構可提供超額報酬的彈性投資組合。我們基於機器學習技術和卡爾曼濾波演算法進行共整合配對交易策略，並且使用五種不同的門檻來生成交易訊號。根據獲得的實證結果，我們認為以公差極限作為門檻的策略是更保守的投資組合，而使用風險價值界限作為門檻的策略是更積極的投資組合。此外，我們在冠狀病毒COVID-19大流行期間獲得了更高的報酬率。

The main objective of this thesis is to build a resilience portfolio that provides excess returns. Based on machine learning technology and the Kalman filter algorithm, we conduct a cointegration pairs trading strategy that uses five different thresholds to generate trading signals. According to the empirical results obtained, we believe that the strategy using the tolerance limits as the threshold is a more conservative portfolio, while the strategy using the Value at Risk bounds as the threshold is a more aggressive portfolio. In addition, we obtaine a higher rate of return during the coronavirus COVID-19 pandemic.

Abstract i
Introduction 1
1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Motivation and Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
3 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Research Methodology 4
1 Stocks Screener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1 Universe Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Density-Based Spatial Clustering of Applications with Noise . . . . . . 6
1.4 T-Distributed Stochastic Neighbor Embedding . . . . . . . . . . . . . 7
2 Mean Reversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1 Cointegration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Pair Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Dynamic Hedge Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4 Trade Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.1 Bollinger Bands Width . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2 Value at Risk Bounds for Normal Distribution . . . . . . . . . . . . . . 13
4.3 Tolerance Limits for Normal Distribution . . . . . . . . . . . . . . . . 14
Empirical Results 16
1 Stocks Screener . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.1 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2 PCA Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3 DBSCAN Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2 Mean Reversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1 Cointegration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Pair Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 Dynamic Hedge Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Residual Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 Trade Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1 Pair Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Portfolio Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Portfolio Analysis 31
1 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3 Resilience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Conclusion 39
References 40
                                

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