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I want to predict expected returns for assets using a CAPM, to calculate unexpected (unpredictable, idiosyncratic, non-systemic) returns in portfolios.

My CAPM estimated on monthly total gross returns obviously have some outliers. Instead of throwing out the outlier months, I think I need to ignore entire assets with outlier betas. What range of betas would one consider reasonable?

My model is nothing more complicated to use the 1999-2007 monthly returns relative to the MSCI World total gross returns, and predict for the same period.

(Btw, I know my suggestion makes the beta calculation for the entire portfolio invalid, but I think I can take that loss as I cannot price everything in the portfolio, let alone considering hedging against the investor's consumption stream, swings in human capital, earnings potential, pension claims etc. anyway.)

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One option would be to winsorize all the betas above or below some quantiles. Alternately, you could model the beta itself as mean-reverting so that the extreme betas gradually go back to 1. – John Aug 6 '13 at 18:22
@John, thanks, I am not sure I would model time-varying betas at this point. I am happy to winsorize instead (though then I need to recalculate alpha too for these assets), but again, for what values? Betas larger than 2? 5? Smaller than 0.5? 0.2? – László Aug 6 '13 at 19:25
The point I was trying to make is that I might set it up as the 95th (& 5th) or 99th (& 1st) percentile, or something like that, rather than selecting fixed values. Where to cut it off might be different for different periods of time or different markets or different groups of securities. I'd rather look to the data than make any arbitrary assumptions. – John Aug 7 '13 at 13:54
@John, the first percentile of betas is around -0.85 and the 99th around 4. This is with many Swedish assets against a world benchmark but all (total gross) returns in SEK, thus assuming no currency hedging, I presume. Monthly returns, Jan 99 to Dec 07. Winsorize with these values? (I.e. limit beta to this range and recalculate alphas using these?) – László Aug 9 '13 at 15:26
I can't tell you precisely what to do. Play around with some until you find something you're comfortable with. – John Aug 9 '13 at 16:08

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