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Correcting Winner and Loser Counts in Cross-Product Ratio Analysis

Article Quant Q&A · Author: Pierre Bonaparte
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Summary

The document concerns the cross-product ratio (CPR) and its associated Z statistic in hedge fund performance persistence analysis. The questioner struggles to interpret a sigma appearing in different presentations of the equation, especially because the CPR itself is a single calculated value and therefore does not seem to support a standard deviation calculation.

The accepted answer reports that the discrepancy came from using the means of winners and losers instead of the correct total in calculating the CPR and Z statistic. This points to an input-definition error as the source of the mismatch, rather than explaining sigma’s meaning in detail. The note gives no equation, worked example, or independent derivation, so it offers a limited diagnostic rather than a full account of the statistic or its assumptions.

Key ideas

  • The question concerns a sigma term in cross-product ratio analysis of performance persistence.
  • The accepted response traces the calculation mismatch to using winner and loser means instead of the total.
  • The document does not fully derive the statistic or explain its assumptions.

Tags

StatisticsFactor investing
Full text
# Cross Product Ratio Analysis


# Cross Product Ratio Analysis












Can you please advise?

I have been recently trying to sort this out for couple of days but cannot get the same numbers as previous authors:

The equation is shown in Agarwal and Naik Multi-Period Performance Persistence Analysis of Hedge Funds (2001) (link) as:

The question is why is there "sigma" and what does it represent?

I have seen the same equation written in the following way:

And again I can do ln(CPR) and the square root bit but the "sigma" appears again! I cannot do a stdev calculation because the CPR is a single number [that is if sigma represents standard deviation in this case?]

Can you advise what "sigma" may represent in here?

## Answer by Pierre Bonaparte (score 1, accepted)

https://quant.stackexchange.com/a/43726

I have found a solution to the issue. I was using the mean of winners and loser instead of the total [correct] in computation of the CPR and Z-stat.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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