# Thread: Parametric t-tests for individual / portfolio stock returns

1. ## Parametric t-tests for individual / portfolio stock returns

Hello everyone,

I am relatively rookie with statistical tests and I am trying to perform a parametric t-test for stock returns as follows. I have collected a sample of (high book-to-market) stocks with different binary scores for fundamental strength known as FS_SCORE and I have calculated the 12-month discrete raw and market-adjusted buy-and-hold returns for each stock. I form portfolios at the beginning of July in each sample year t and hold these for portfolios for 12-months.

Thus, I would like to do a t-test to compare the returns of:

1) High FS_SCORE firms against Low FS_SCORE firms

2) High FS_SCORE firms against all (value) stocks

Those who are familiar with finance literature may recognize that I am trying to replicate a study by Piotroski (2000) using a similar binary scoring system for stocks. However, I am confused how to use the t-test as there seems to various ways to do it based on previous financial research. Piotroski (2000) uses two-sample signed rank wilcoxon test, but many studies used the independent or one-sample t-tests. I guess I would prefer the basic parametric tests.

Thus, my core questions are:

1) Should I test the differences between the mean returns by simply computing a two-sample t-test (assuming unequal variances) for individual stock buy-hold-returns? For example, I would choose all high FS_SCORE stocks 12-month buy-and-hold returns as the first variable and all low FS_SCORE stocks 12-month buy-and-hold returns as the second variable (and set H0: Mean High FS_SCORE High = Low)

2) Some kind of one-sample t-test?

3) Or should I compute the monthly returns for all portfolios across the sample years and do a paired t-test as all stocks are from the same index?

Thanks a lot in advance. If someone wants I can also send an example excel file with calculations.

2. ## Re: Parametric t-tests for individual / portfolio stock returns

Hi,
just a rough answer: you would use a paired t-test if you could meaningfully pair each data point from Set A with a data point from Set B and you wanted to eliminate varaiability related to the pairs. A one sample t-test would mean that you compare your sample mean against a known fixed number. In your case if you have some kind of monthly seasonal effect it would make sense to do monthly averages and do a paired test on them.

Regards

3. ## Re: Parametric t-tests for individual / portfolio stock returns

Hi Rogojel,

thank you for your answer. It makes sense as the investment strategies that I am studying also depend on similar factors such as market risk. Thus, like you said, I guess the best way to test whether the mean returns for these strategies are different is to do a paired t-test using monthly portfolio returns. I guess I will have to:

1) Build annual portfolios for all investment strategies (High/Low/All) with monthly returns.

2) Combine these returns into a time-series and then calculate t-statistics across the whole sample period (?).

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