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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.

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    $\begingroup$ Please don't remove posts, regardless of whether you get an answer. $\endgroup$
    – Bob Jansen ♦
    Commented Apr 10, 2018 at 7:30
  • $\begingroup$ A warm welcome to Quant.SE and thank you for that interesting question. Please see my answer below. $\endgroup$
    – vonjd
    Commented Apr 10, 2018 at 7:59
  • $\begingroup$ @BobJansen Will keep that in mind, sorry about that... didn't want to spam the board $\endgroup$
    – bobsaget123
    Commented Apr 10, 2018 at 18:56
  • $\begingroup$ No problem, welcome to Quant.SE! $\endgroup$
    – Bob Jansen ♦
    Commented Apr 10, 2018 at 19:35
  • $\begingroup$ @vonjd So i read the paper you linked, but my question is how would I measure the accuracy of the index, against the basket of stocks I used to create it. The paper linked relates the accuracy of ETFs, relative to the Index. Aside from the fact that a general Index like SPY doesn't have enough data, I don't think it's what I'm looking for $\endgroup$
    – bobsaget123
    Commented Apr 10, 2018 at 23:20

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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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  • $\begingroup$ thank you for the direction, will look into it today. Also, would you recommend something other than Laspeyres for the Index... something geometric-based as discussed here: imf.org/external/pubs/ft/wp/2012/wp12105.pdf $\endgroup$
    – bobsaget123
    Commented Apr 10, 2018 at 18:44

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