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Lecture 6:Back-testing statistical-arbitrage
strategies
Marco Avellaneda
G63.2936.001
Spring Semester 2009
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Simulation of trading Profit/Loss
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Examples of Leverage
Long-only:
Long-only, Reg T:(margin acct)
Long-short $-Neutral, Reg T:
:Long-short, Equal target
position in each stock
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Sharpe Ratio
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Expected returnover simulation period
Variance over
simulation period
Sharpe Ratio
The Sharpe ratio measures returns above the risk-free rate.
It is independent of the leverage of the strategy (dimensionless).
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Modeling the Evolution of StockResiduals
Daily sampling frequency
Statistical Estimation Window=3 months (~ 60 business days)
Stock returns a sum of the market returnand a residual process
Residual= drift component (expectedexcess return above mkt.) + incrementof a stationary process
Ornstein-Uhlenbeck
AR-1 process
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Defactoring using ETFs
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If stock I is in sector j
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Regress returns on sectorETF returns
In some cases, we construct ``synthetic ETFs (e.g., if the ETF did not exist
in the past). These are taken to be Capitalization-Weighted
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Trading Signals
Introduce the s-score for each stock:
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