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Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Cluster-based Strategy
Anran Lu Huanzhong Xu Atharva Parulekar
Stanford University
May 8, 2018
1
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Summary
Review of classic Statistical Arbitrage
Main idea and steps of cluster-based strategy
Current result and future work
2
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Summary
Review of classic Statistical Arbitrage
Main idea and steps of cluster-based strategy
Current result and future work
3
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Summary
Review of classic Statistical Arbitrage
Main idea and steps of cluster-based strategy
Current result and future work
4
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Review of Statistical Arbitrage
5
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Figure: Stock chart of United Airline, Delta Airline and XTN
6
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Main Idea of Pairs Trading
Basic model:
dPt
Pt= αdt + β
dQt
Qt+ dXt
"Pair": two stocks with similar characteristicsα: negligible compared to dXtβ: determined by regressionXt : key part of the portfolio
"Generalized Pair": a stock and an ETF
7
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Main Idea of Pairs Trading
Basic model:
dPt
Pt= αdt + β
dQt
Qt+ dXt
"Pair": two stocks with similar characteristics
α: negligible compared to dXtβ: determined by regressionXt : key part of the portfolio
"Generalized Pair": a stock and an ETF
8
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Main Idea of Pairs Trading
Basic model:
dPt
Pt= αdt + β
dQt
Qt+ dXt
"Pair": two stocks with similar characteristicsα: negligible compared to dXt
β: determined by regressionXt : key part of the portfolio
"Generalized Pair": a stock and an ETF
9
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Main Idea of Pairs Trading
Basic model:
dPt
Pt= αdt + β
dQt
Qt+ dXt
"Pair": two stocks with similar characteristicsα: negligible compared to dXtβ: determined by regression
Xt : key part of the portfolio
"Generalized Pair": a stock and an ETF
10
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Main Idea of Pairs Trading
Basic model:
dPt
Pt= αdt + β
dQt
Qt+ dXt
"Pair": two stocks with similar characteristicsα: negligible compared to dXtβ: determined by regressionXt : key part of the portfolio
"Generalized Pair": a stock and an ETF
11
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Main Idea of Pairs Trading
Basic model:
dPt
Pt= αdt + β
dQt
Qt+ dXt
"Pair": two stocks with similar characteristicsα: negligible compared to dXtβ: determined by regressionXt : key part of the portfolio
"Generalized Pair": a stock and an ETF
12
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Determine Portfolio by Xt
Cointegration: Ornstein — Uhlenbeck modelling of Xt
dXt = κ(µ− Xt)dt + σdWt
some implicit assumptionsκ: mean reversion speedXt ∼ N (µ, σ
2
2κ) at equilibrium
s = Xt−E XtVar Xt
determines long/short position
13
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Determine Portfolio by Xt
Cointegration: Ornstein — Uhlenbeck modelling of Xt
dXt = κ(µ− Xt)dt + σdWt
some implicit assumptions
κ: mean reversion speedXt ∼ N (µ, σ
2
2κ) at equilibrium
s = Xt−E XtVar Xt
determines long/short position
14
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Determine Portfolio by Xt
Cointegration: Ornstein — Uhlenbeck modelling of Xt
dXt = κ(µ− Xt)dt + σdWt
some implicit assumptionsκ: mean reversion speed
Xt ∼ N (µ, σ2
2κ) at equilibrium
s = Xt−E XtVar Xt
determines long/short position
15
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Determine Portfolio by Xt
Cointegration: Ornstein — Uhlenbeck modelling of Xt
dXt = κ(µ− Xt)dt + σdWt
some implicit assumptionsκ: mean reversion speedXt ∼ N (µ, σ
2
2κ) at equilibrium
s = Xt−E XtVar Xt
determines long/short position
16
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Determine Portfolio by Xt
Cointegration: Ornstein — Uhlenbeck modelling of Xt
dXt = κ(µ− Xt)dt + σdWt
some implicit assumptionsκ: mean reversion speedXt ∼ N (µ, σ
2
2κ) at equilibrium
s = Xt−E XtVar Xt
determines long/short position
17
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Figure: Apple-XLK pair opening and closing signals
18
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Figure: Stock chart of United Airline, Delta Airline and XTN
19
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Main idea and steps of cluster-based strategy
20
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Motivation of our work
Pairs with different "qualities"
Dynamically adjusting pairs based on real time factorsNon-stationary time series and cointegration
Cointegration: Here ut is the stationary residual obtainedafter regressing non-stationary xt and yt which also havea unit root. We can use Dicky Fuller of two step EngelGranger to determine cointegration.
yt − βxt − α = ut
21
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Motivation of our work
Pairs with different "qualities"Dynamically adjusting pairs based on real time factors
Non-stationary time series and cointegration
Cointegration: Here ut is the stationary residual obtainedafter regressing non-stationary xt and yt which also havea unit root. We can use Dicky Fuller of two step EngelGranger to determine cointegration.
yt − βxt − α = ut
22
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Motivation of our work
Pairs with different "qualities"Dynamically adjusting pairs based on real time factorsNon-stationary time series and cointegration
Cointegration: Here ut is the stationary residual obtainedafter regressing non-stationary xt and yt which also havea unit root. We can use Dicky Fuller of two step EngelGranger to determine cointegration.
yt − βxt − α = ut
23
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Motivation of our work
Pairs with different "qualities"Dynamically adjusting pairs based on real time factorsNon-stationary time series and cointegration
Cointegration: Here ut is the stationary residual obtainedafter regressing non-stationary xt and yt which also havea unit root. We can use Dicky Fuller of two step EngelGranger to determine cointegration.
yt − βxt − α = ut
24
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Motivation of our work
Pairs with different "qualities"Dynamically adjusting pairs based on real time factorsNon-stationary time series and cointegration
Cointegration: Here ut is the stationary residual obtainedafter regressing non-stationary xt and yt which also havea unit root. We can use Dicky Fuller of two step EngelGranger to determine cointegration.
yt − βxt − α = ut
25
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Steps of our work
Main idea: We run pairs trading on each stock-ETF pairgiving rize to 5 key factors per stock-ETF pair. We calcu-late these factors for a stock with respect to all 6 ETFs.
Key factors for pair:Residual st . (Non decorrelated st = Xt −m)Mean Reversion Time 1/κCointegration factors
Apply K-means clustering based on the key factors for astock with respect to all ETFs (30 dim vector).
26
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Steps of our work
Main idea: We run pairs trading on each stock-ETF pairgiving rize to 5 key factors per stock-ETF pair. We calcu-late these factors for a stock with respect to all 6 ETFs.
Key factors for pair:Residual st . (Non decorrelated st = Xt −m)Mean Reversion Time 1/κCointegration factors
Apply K-means clustering based on the key factors for astock with respect to all ETFs (30 dim vector).
27
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Steps of our work
Main idea: We run pairs trading on each stock-ETF pairgiving rize to 5 key factors per stock-ETF pair. We calcu-late these factors for a stock with respect to all 6 ETFs.
Key factors for pair:Residual st . (Non decorrelated st = Xt −m)Mean Reversion Time 1/κCointegration factors
Apply K-means clustering based on the key factors for astock with respect to all ETFs (30 dim vector).
28
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Current Result and Future Work
29
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Visualization of Current Result
Figure: PCA scores based on K-means clustering (500 stocks)30
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Future work
General performance estimation and efficiencyimprovement
Trade-off between cointegration and residualAlternative Models
Mean-reverting models to better describe XtEM for clustering
Trade-off between trading frequency and transactioncost
31
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Future work
General performance estimation and efficiencyimprovementTrade-off between cointegration and residual
Alternative ModelsMean-reverting models to better describe XtEM for clustering
Trade-off between trading frequency and transactioncost
32
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Future work
General performance estimation and efficiencyimprovementTrade-off between cointegration and residualAlternative Models
Mean-reverting models to better describe XtEM for clustering
Trade-off between trading frequency and transactioncost
33
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Future work
General performance estimation and efficiencyimprovementTrade-off between cointegration and residualAlternative Models
Mean-reverting models to better describe XtEM for clustering
Trade-off between trading frequency and transactioncost
34
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Future work
General performance estimation and efficiencyimprovementTrade-off between cointegration and residualAlternative Models
Mean-reverting models to better describe XtEM for clustering
Trade-off between trading frequency and transactioncost
35
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Selection of positions
36
Statistical Arbitrage Cluster-based Strategy Current Result and Future Work
Thank you!
37
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