Imputed values in a multi-index

Question

I have an equal-weighted index on a number of different Indices (from US, Europe and Asian markets). This compound index is constructed from a time series that has missing values (for example, those regions have different banking holidays). This problem will affect about 10 days out of 250 per year of data. What strategy should I choose to handle those imputed values?

Answer 1

What is the aim of your calculation - rather risk analyis or performance comparison? In either case an easy and valid approach would be to replace missing values with the most recent nonmissing. In R na.locf from the package zoo does this.

Answer 2

I think the simple advice here is to keep the indexes unchanged from the previous closing day (you basically assume unchanged prices).

• A bad idea is to compute essentially a "new" index in that you drop out the index which does not trade and recalculate the denominator. It will greatly skew the results, bad thing to do.

• A better idea would be not only keep the missing index unchanged but to calculate a beta at any given time in the past between the index in question and the other indexes and to then estimate a value for the non-trading index based on the beta and that day's return of the other indexes.

But again, I bet most would simply use the previous day's closing value.