Comparing Mean Stock Returns Before and After a Recession

Summary

The document asks how to test whether average monthly stock returns differ between periods before and after a recession, using observations across companies and time. Its central clarification is that the central limit theorem describes how sampling distributions behave under conditions; it is not itself a procedure for testing a claim. A statistical test, whose justification may rely on that theorem, is needed to assess whether the observed difference in means is significant.

The answers suggest a two-sample t-test for comparing the period means. If the groups may have different variances, one response recommends checking that assumption and considering a nonparametric alternative such as the Mann–Whitney test. The document provides no calculated test statistic, p-value, or conclusion about whether returns actually changed. It also does not discuss potential dependence among monthly observations or across firms, so choosing a test requires attention to whether its assumptions fit the return data and the way the samples were constructed.

Key ideas

• The central limit theorem is a convergence result, not a hypothesis test.
• A two-sample t-test can assess a difference between mean returns across two periods.
• Unequal group variances may call for a different test or a method that accommodates them.
• The document reports no empirical result about whether returns changed around the recession.
• Test assumptions and the structure of the return observations matter when selecting a procedure.

Tags

# Using central limit theorem to test whether population average return is the same, before and after the recession


# Using central limit theorem to test whether population average return is the same, before and after the recession












This is the task I have been asked to do. I've read up on what central limit theorem (clt) is, but I feel like I'm missing something.

The data I have is a matrix of monthly stock returns from 50 different companies from 1/1/2000 to 1/8/2014.

I've established I find the cross sectional average return before the recession (Rb), and the average return after the recession(Ra) and;

(Rb - Ra) is my X-bar in the clt, z-score formula.

I apologise for any inaccuracies, my knowledge is very little and I'm thankful for your patience

## Answer by vonjd (score 6, accepted)

https://quant.stackexchange.com/a/16021

You cannot use the clt to test something, it is a theorem about convergence. You can only use a statistical test to test something which basis is in many cases the clt.

In this case you could e.g. use a so called t-test. In R you would e.g. type:

```
t.test(data.Rb,data.Ra)
```

to test whether the difference in the means is significant.

## Answer by SmallChess (score 0)

https://quant.stackexchange.com/a/16045

As vonjd mentioned, you could do a t-test. However, as stated in your comments if you believe the standard deviation for each group is different (maybe you should do a Levene's test), you shouldn't use a t-test for two means. You should consider a non-parametric test such as Mann-Whitney.

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