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I am calculating betas on intraday trade data at 15-minute intervals. For simplicity sake, let's assume I am modeling

\begin{equation} Y = \beta * X + c \end{equation}

where $Y$ is the return of XLF and $X$ is the return of SPY.

If I want to run this on five days of intraday data, should I remove the jump that happens due to opening gaps on the next day?

How do you guys usually handle this jump in returns ?

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up vote 6 down vote accepted

I assume you're using returns to compute beta, not the prices. And yes, remove the "jumps", though this should happen automatically since you're looking only at intraday returns. One final piece of advice: you'll get more meaningful results if you smooth the returns via a moving average.

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Did you mean smooth the price via moving average ? If not, not really sure how taking a moving average of returns would give more meaningful results. Can you explain – silencer Jan 4 '12 at 3:47
Smooth the returns because that will decrease momentary variation. – chrisaycock Jan 4 '12 at 4:12
@chrisaycock What moving average window would you suggest? At 15 minutes per period, there is only 26 periods/day. – Robert Kubrick Jan 4 '12 at 14:14
@RobertKubrick A five-period average should work well. – chrisaycock Jan 4 '12 at 14:30
@silencer Are you calculating beta to fit a model or to hedge a portfolio? In the first cast I would tend to smooth data less. Also, are you holding positions overnight? – Robert Kubrick Jan 4 '12 at 15:55

In addition to the above I can suggest:

  • ignore data point if returns are more than a certain threshold (2 s.d.)
  • calculate at different sampling intervals and choose most stable beta with the best significance (certain longer intervals "smooth out" small to mid size jumps)
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This answer is much better than your previous answers. Keep it up. – Tal Fishman Jan 4 '12 at 13:09

You can run the regression separately for 5 days, and average the betas you get for different days.

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