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?
Best Answer
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:
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.