Measuring the Tracking Accuracy of a Custom Stock Index

Summary

The document asks how to evaluate a Laspeyres index built from five oil and energy stocks, intended for use in mean-reversion allocation across asset classes. The central suggestion is to measure tracking error or tracking efficiency: compare the index’s performance with the underlying stocks or a suitable reference and quantify how closely it follows them.

The response points to ETF tracking-efficiency methodologies as a starting point and cautions that PCA is not an obvious fit because its results may be difficult to interpret for this purpose. The discussion does not specify a particular tracking-error formula, provide empirical comparisons, or establish which methodology is best for a custom index. The proposed evaluation should therefore be treated as a direction for further analysis, with the choice of metric depending on how the index is constructed and what “accuracy” is meant to capture.

Key ideas

• Tracking error and tracking efficiency are natural measures for assessing how closely a constructed index follows its reference assets.
• PCA may be less suitable when the goal is an interpretable measure of index tracking quality.
• The document suggests consulting ETF tracking-efficiency methodologies but does not select or test a specific metric.

Tags

# Testing the accuracy of a created Index


# Testing the accuracy of a created Index












So long story short, I created a Oil/Energy Index from a basket of 5 stocks in the asset class.

I am looking to use mean-reversion, in order to help rebalance the allocation of funds between difference asset classes. As a result, I had to create my own index, as the package I'm using doesn't have enough historical data on ETFs.

I have created the Index, using Laspeyres as shown here . I'm wondering what would be a good statistical method of testing how accurate this etf is against the performance of the stocks.

I was thinking a PCA, but wasn't sure what this community thought.

## Answer by vonjd (score 1)

https://quant.stackexchange.com/a/39206

Basically what you want to assess is the tracking error or tracking efficiency. A good place to start is the following report from Morningstar:

On The Right Track: Measuring Tracking Efficiency in ETFs

In the report are numerous calculation methodologies (and they give their own on top of that).

I wouldn't say that PCA is a natural choice because of its limited interpretability in this context.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.