Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.
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Transcript of Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.
![Page 1: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/1.jpg)
Return Forecasting by Quantile Regression
QWAFAFEWDecember 20101
Larry Pohlman and Lingjie Ma
![Page 2: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/2.jpg)
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Outline
• The Math• Examples• Multivariate Model• Results
![Page 3: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/3.jpg)
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The Math and Code
• Model
• OLS Estimation
• QR Estimation
• R, S+, Stat, SAS
uXby
2)(minˆ bxy TiibOLS
Tii
Tiixy bxy
Tii
TiibQR bxybxy
))(1()(minˆ
![Page 4: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/4.jpg)
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What does QR do?
T
uT
y
uTT
y
TT
xFxxQ
FxxxF
uδxβxy
))((
)(
)(
1
11
Sample Quantile:
Conditional Quantile:
1,0,:
,yYProb
y
y
FyfQ
F
![Page 5: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/5.jpg)
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Example: Book to Price
![Page 6: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/6.jpg)
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Why QR?
A natural question is under what conditions will QR be “better” than OLS?
1. Full picture view: heterogeneity
If there is heterogeneity, then QR will provide a more complete view of the relationship between variables through the effects of independent variables across quantiles of the response distribution.
2. Robustness: fat-tail distribution
If the conditional return distribution is not Gaussian but fat-tailed, the QR estimates will be more robust and efficient than the conditional mean estimates
![Page 7: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/7.jpg)
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Example Price Momentum
![Page 8: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/8.jpg)
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Example Return on Equity
![Page 9: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/9.jpg)
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Multivariate Model
• Book to Price• Earnings to Price• Cashflow to Enterprise Value• Balance sheet Accruals• Return on Equity• Price Momentum (9 months)• Earnings Momentum (9 months)
![Page 10: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/10.jpg)
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Model Variable Plots
![Page 11: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/11.jpg)
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Results: Equal Weight Quintiles
![Page 12: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/12.jpg)
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Results: Cap Weighted Qunitiles
![Page 13: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/13.jpg)
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Optimized Portfolios TE=3%
![Page 14: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/14.jpg)
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Optimized Portfolios TE=6%
![Page 15: Return Forecasting by Quantile Regression QWAFAFEW December 20101 Larry Pohlman and Lingjie Ma.](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e665503460f94b61d4f/html5/thumbnails/15.jpg)
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Conclusion
■ Conditional mean method is still attractive
■QR provides a full-picture distributional view
■ Link between distribution estimates and point portfolio.