1. The document discusses quantitative trading strategies based on mean reversion using factor models and cointegration analysis. 2. It describes using canonical correlation analysis to decompose markets into stationary and non-stationary factors to identify cointegrated relationships between assets. 3. The strategies aim to maximize expected gains based on these relationships while managing risk through regime-switching models, diversification across different factor types, and continuous portfolio optimization.

1. Don’t Lose Your Shirt
Trading
Mean-Reversion
Quantopian Conference
April 2017

2. A Bit Of History
Edith Mandel | Greenwich Street Advisors, LLC
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3. Guiding Principles
— Bayesian Approach:
— When the market not agreeing with Model,
posterior confidence in Model has to decline
— Et
*[Model_Gains]*pt(Model✓)+λ*pt(Model✗),
— pt: posterior distribution at time=t
— Et
*[Gains|pt]: risk-adjusted forecast
— Target a portfolio Πt with Max{Et
*[Gains|pt]}
— Πt is updated continuously
— Diversified set of trades
— Don’t be fooled by lack of randomness (low
dimensionality)
— Systemic & idiosyncratic risk factors
Edith Mandel | Greenwich Street Advisors, LLC
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4. When A Trend Develops
Et
*[Gains|pt] is Reduced
Existing Trade is Sub-
Optimal Source of Risk
No Longer Part of Optimal
Portfolio
Edith Mandel | Greenwich Street Advisors, LLC
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5. Cointegration via CCA
— Decomposition of the panel, Yt, with covariance
matrix,Σ,into M non-stationary and N-M
stationary (i.e. cointegrated) directions
— M will change throughout economic cycles
— Methodologies to generate cointegrated vectors
— Multivariate MLE, Johansen (1988)
— CCA, Box-Tiao (1977)
— Multivariate level regressions & CCA, Chou & Ng
(1994)
— Regularized CCA
Edith Mandel | Greenwich Street Advisors, LLC
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6. Cointegration via Box-Tiao
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— CCA with {Yt, Yt-1}
— Yt=Yt-1A+εt
— Q=Σ-1AΣAT
— Q is a measure of relative
predictability
— E=Eigenvectors of Q are
the factor loadings of the
Cointegration Model
— Ft=ET Yt are the Factors
(Canonical Variates)

7. Cointegration Challenges
— Larger portfolios are more cointegrated, but
difficult to execute
— D’Aspermont (2008)
— Maximizing mean-reversion under cardinality
constraints
— Changes in cointegrated relationships
— Ft=μt+ktFt-1+εt
— H0: [μt,kt]=[μ0,k0]
— SPC methods (CUSUM-like) applied to εt
— Ploberger, Kramer (1992)
— CUSUM(εt)->Brownian bridge
— Pr(max|CUSUM(εt)|>a) ->Posterior pt
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8. Regimes: Mean-Reversion &
Trend (I)
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9. Regimes: Mean-Reversion &
Trend (II)
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10. Rapid Change
(Permanent Break)
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11. Regime Changes
— ‘Permanent’ breaks are rare
— Regime-Switching Models (RSM) are more
suitable
— Ang, Timmermann (2011)
— 2-State Auto-Regressive Model:
— Ft=μs(t)+ks(t)Ft-1+σs(t) εt
— s(t) is a Markov chain with time-invariant or time-
varying transitions:
— Pr{s(t)=0|s(t-1)=0}=p00,t Pr{s(t)=1|s(t-1)=1}=p11,t
— Assumption of recurrent regimes is supported
by data
Edith Mandel | Greenwich Street Advisors, LLC
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12. Factor-Based Approach
— Factors Ft=ET Yt determine cointegrated vectors
— M non-stationary factors (systemic risk factors), FR
— K strictly stationary factors, FS
— Stable (but small) gains
— Suitable for limit order placement
— N-(M+K) locally stationary factors, FLS
— Recurrent regimes
— 2-State Auto-Regressive RSM
— F=[FR,FS,FLS]
— Factor-replicating portfolios
— Et
*[Gains|pt]=f{Et [Ft (Gains)], ΣF,pt}
Edith Mandel | Greenwich Street Advisors, LLC
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13. Factors of US Trsy Market
Locally Stationary Factor Strictly Stationary Factor
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14. Risk-Management
— Optimal portfolio Πt=Πt-1+wt
— wt: new positions
— σ2(Πt)=EΣFET
— F=[FR,FS,FLS]
— E: factor exposures of Πt-1+wt
Edith Mandel | Greenwich Street Advisors, LLC
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15. ‘Bigger Data’ Approach
— Dynamics of different types of assets
(Stocks, Interest Rates, FX) are different
— Dynamics of cointegrated vectors are
more uniform
— Crossing asset class boundaries
— Far bigger training set to learn from
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