Testing Relative Buy-and-Hold Performance for Correlated Share Classes

Summary

The document asks how to test whether one share class outperforms another over a long holding period following a stock split. The proposed comparison concerns two buy-and-hold price paths, with the difference in their terminal values used to represent accumulated relative performance. The author argues that ordinary t-tests or F-tests on the two series are unsuitable because the share classes are not independent. They also note that comparing raw price differences can produce increasing variance as both prices rise, creating heteroskedasticity.

The author prefers price-path differences to return comparisons because they expect the split-related return differences to be concentrated around the event while compounding may make price differences more visible over longer horizons. No statistical procedure, sample data, or empirical result is provided; the document frames an unresolved inference problem. Any analysis would need to account for dependence between share classes and changing variance, and the split itself may complicate how prices and returns are compared.

Key ideas

• The question concerns long-horizon relative performance of two share classes after a stock split.
• The author identifies dependence between the two share price series as a problem for ordinary independent-sample tests.
• The difference between buy-and-hold price paths may have changing variance as both share prices appreciate.
• The author expects accumulated price differences to reveal effects that are less apparent in long-run return comparisons.
• The document poses a statistical question but provides no tested inference method or empirical evidence.

Tags

# Compare performance buy-and-hold strategies after stock-split


# Compare performance buy-and-hold strategies after stock-split












QUESTION: How should I analyze the statistical significance of the difference between two buy-and-hold strategies (or the relative performance) when the samples are not independent?

Background:

I want to compare the performance of two stock classes from a certain company (e.g. Class A shares and Class B shares) after a stock-split. I want to analyze how this stock-split affects the return of Class B shares relative to Class A shares.

I want to analyze the performance difference over a long time span, hence an event-study is inappropriate. Therefore, I want to use a buy-and-hold strategy. Simple analyzing the statistical differences by conducting a t-test or F-test is not appropriate as both samples are not independent. Hence, I want to analyze the difference in prices between the buy-and-hold strategy holding Class A shares (P1) and the buy-and-hold strategy holding Class B (P2) shares, i.e.:

c = P1 - P2, where c is a constant (e.g. 1)

However, as both shares increase in value over the years the variance increases and I'm left with heteroskedasticity. Thus, analyzing whether the constant is statistically significant also does not make sense. Can someone tell me how I should analyze the statistical significance of the difference between two buy and hold strategies (or the relative performance)? For example, how can I tell whether P2 is higher than P1 and statistically significant?

P.S I do not want to analyze returns as the returns only differ on the days surrounding the stock-split, hence the differences in returns are negligible over longer time periods. On the other hand, differences in prices can vary significantly (my hypothesis) as differences in returns accumulate.

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