Handling Missing Regional Index Values in a Composite Index

Summary

The document considers an equal-weighted composite of regional equity indexes that have different market holidays. It asks how to handle dates when one region has no observation, noting that simply removing the unavailable index and recalculating the weights changes the composition of the portfolio on that date and can distort the series.

Two practical approaches are described. The simplest is to carry the last observed index value forward, treating the region as unchanged while its market is closed. A more involved alternative estimates the missing region’s return using its historical beta relationship with the other indexes and their returns on that date. The responses favor carrying forward the previous close as a common, straightforward choice. The document does not compare these methods empirically or prescribe one for every purpose; the best treatment may depend on whether the composite is being used to assess risk, compare performance, or serve another analytic goal.

Key ideas

• Regional market holidays create missing observations in multi-market index series.
• Dropping a nontrading index and recalculating equal weights changes the composite’s composition.
• Carrying forward the most recent closing value treats the closed market as unchanged.
• A beta-based estimate can use returns from other indexes to impute a missing regional value.
• The appropriate method may depend on whether the analysis concerns risk or performance.

Tags

# Imputed values in a multi-index


# Imputed values in a multi-index












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 by Matt Wolf (score 4)

https://quant.stackexchange.com/a/7239

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.

## Answer by Richi Wa (score 2)

https://quant.stackexchange.com/a/7238

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.

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