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?