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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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  • $\begingroup$ This approach doesn't make much sense to me. If instead of looking at the difference in prices, you look at the difference in log prices, then it won't continue to get larger over time. The fact that it grows larger over time is an artifact of compounding. $\endgroup$
    – John
    May 26, 2015 at 14:44
  • $\begingroup$ Yes I agree it is odd but I don't know how to cope with the large overlap in returns. For example, due to the large correlation (say 0.9 or higher) a 2.5% difference in return after the stock-split will most likely become insignificant. Even though it is a large return difference. $\endgroup$
    – user15050
    May 26, 2015 at 16:01
  • $\begingroup$ I'm not sure I understand what you're talking about here, but the fact that two share classes don't have a statistically significant difference in returns is not surprising. $\endgroup$
    – John
    May 26, 2015 at 16:59
  • $\begingroup$ You're right. You would expect that both shares Classes pose the same returns. However, when there is a stock-split for a certain Class of shares their might be a difference between the classes. However, this only happens for a short window and this effect is only a couple percentage points. If a stock-split where to occur several years in a row this would accumulate (/compound) to large differences in the price of the two share Classes. Since I'm interested in the long term effect I was wondering how I should analyze the statistical significance of this difference. $\endgroup$
    – user15050
    May 27, 2015 at 8:14
  • $\begingroup$ My recommendation would be to focus on the cumulative difference in returns around the splits and to ignore the longer-term. $\endgroup$
    – John
    May 27, 2015 at 15:18

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