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I have two time series of daily returns on two stock indices (S&P 500 and BOVESPA) that I would like to estimate the portfolio value at risk (VaR) for. Since these are indices from two different regions they do not naturally line up smoothly as their business days are unequal due to some country specific holidays.

An example would be on the 4th of July, when the return of the S&P would be 0 and the BOVESPA a positive or negative number. Including this sample in the empirical returns distribution would include a 0 return which never happened.

As I am interested in the portfolio VaR I would prefer returns on days where both markets were open so as to catch the implicit correlations in the returns of the indices. However, this would mean I will remove 250 paired observations (over a 20 year period) where either one of them have a zero value.

Are there any better ways to handle the data?

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  • $\begingroup$ Interesting question, welcome on this site! I edited the title to emphasize some broader underlying statistical issues. I hope I understood the question correctly and the new title is OK. $\endgroup$
    – Gala
    Sep 19 '13 at 12:51
  • $\begingroup$ Do you want to perform historical simulation or covariance estimation? Anyway I suggest moving this to quant.stackexchange.com $\endgroup$
    – Quartz
    May 18 '15 at 17:07
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Dealing with missing values is certainly a topic of interest. In my opinion, working with the data where both markets were open at the same time seems logical to me. Actually, I do not think something critical happened those days.

But if you want to 'fill the gaps' there are some strategies:

  • First of all, hold the last value. In this case, I think this is the most suitable option. When a market is closed, the current value of the market is the value acquired the former day.
  • The other solutions are based on making some prediction on this value. I am not fan of this methods since you are already predicting, you are not working with real data. What I'd do on this case is to see what are the benefits of each solution (filling the gaps vs remaining the gaps empty) and which one obtains better results.

According to this criteria you can choose which substitution method (if any) is the most suitable one. Here you may find a previous post on this topic.

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