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I often see trading strategies and portfolio construction that are based on cross-sectional regression. For example, I often see regressing some numbers against some factors.

I was wondering how cross-sectional regression is used in these scenarios? And how does a cross-sectional regression have forecasting power? And how is the goodness-of-fit of the regression related to the forecasting power?

I have been reading some portfolio management books but couldn't find the application of cross-sectional regression and the relation between the regression and the forecasting power.

Could anybody please shed some light for me?

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Hi Luna, your question sounds very vague. I know a bit about cross sectional regression but I can't figure out what your actual question is. Cross-sectional regression is used to fit models all the time. It is impossible to summarize all the ways here. Do you have any specific examples? Also, what do you mean by "forecasting power"? –  Tal Fishman May 31 '12 at 19:42
    
Thank you! Yeah, my question was vague because I don't know how they do it in the quant funds. I know they play with various types of regressions. And I know they not only use regressions and factor models for risk modeling and pnl attributions, but also for alpha generating and forecasting. So I was looking for pointers about how cross-sectional regressions are used and how are they related to forecasting power (strategy performance). Knowing those, we then know which directions to go about improving regression models... –  Luna May 31 '12 at 19:49
    
Mostly I was trying to figure out the relation between goodness-of-fit in cross-section and the forecasting power... thank you! –  Luna May 31 '12 at 22:38
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Luna, if you're going to keep cross-posting to Nuclear Phynance, then don't bother to come here. Seriously. You also keep writing your questions in a way that makes it obvious you haven't read other questions on here. It's embarrassing. And you've never answered a single question across Stack Exchange. I'm not sure what you bring here. It's time you find a different outlet. –  chrisaycock Jun 1 '12 at 11:53
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closed as off topic by Bob Jansen, Dirk Eddelbuettel, chrisaycock Jun 1 '12 at 11:51

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1 Answer

A cross-sectional linear factor model would regress the returns of the securities of interest on attributes that are believed to be priced in. For instance, in period 1, you could regress the return of all the S&P500 stocks against their book-to-market ratios and market capitalizations. It may be appropriate to scale the independent variables to be like Z-scores. The coefficients to these regressions would be like the returns to value (book-to-market) and size (market capitalization) factors. You might also want to look into Fama-Macbeth regressions.

The purpose is not necessarily forecasting as much as it is to understand what drives the returns and risk of the securities. It would still be possible to gather the returns to the factors and perform some sort of time series analysis to determine what their distribution will be in the future.

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Thanks. But I am specifically asking about forecasting, not risk modeling and pnl attribution. Any more thoughts? Thank you! –  Luna May 31 '12 at 19:25
    
You might try picking up a book like QEPM by Chincarini and Kim. –  John May 31 '12 at 20:11
    
Yes, I've read that book but it didn't say why cross-sectional regression has something to do with forecasting power... –  Luna May 31 '12 at 21:19
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