Very high t-statistic from t-test

[Juan Gonzalex]

Hi,

I have divided my data into 5 portfolios according to the change in leverage. I performed regressions for all 5 portfolios with dependent variable the excess return of each portfolio and independent variable the market excess return. I want to test for significance for the differences in alpha of portfolio 1 and 5. I therefore performed a t-test, but I get a very high t-statistic.

What can be the cause of this?

Thanks

[Nick Cox]

We can't see anything about _b_cons but a test comparing two constants can't tell you anything -- if that is what you are doing.

[Juan Gonzalex]

Hi Nick,
I'm replicating a paper in which it says:

What I'm trying to do is get the t-statistic of the penultimate column (1-10) , so the difference between the alpha of portfolio 1 and portfolio 10. In my case I have 5 portfolios (change5) instead of 10, so it would be the difference in alpha between portfolio 1 and 5. But I get a t-statistic of 1.5e+18, which is very very high.

[Nick Cox]

Indeed; you're telling us what you want to do, but nothing about the variable _b_cons and how you calculated it in Stata.

I may fade away from this thread, because I don't work in this territory. I'm just trying to help you pose an answerable question..

[Carlo Lazzaro]

Juan:
I just echo Nick's comment here: at at ist face-value, you're comparing constant vs. constant (no variation=no std.dev=no std. err and so on).
That said, of I remember your second to last query, you asked for a way to have the same value of return for month and/or portfolio. Couldn't it be the reason why you're getting bewildering results when you compare the different portfolios head-to-head?

[Juan Gonzalex]

Hi Nick and Carlo,

To get the alphas, I have used the following code:

bys change5: asreg excess_ri_port mktrf

And my data is as following:

* Example generated by -dataex-. For more info, type help dataex
clear
input long gvkey int year byte month float(change5 excess_ri_port) double _b_cons
100095 2018 8 2  -.2046448 -.19860766514252795
211509 2018 8 1   .7597022  .34486178831877073
216599 2018 8 5  2.1212707   -.852844341150632
102276 2018 8 5  2.1212707   -.852844341150632
322576 2018 8 5  2.1212707   -.852844341150632
102576 2018 8 2  -.2046448 -.19860766514252795
 17828 2018 8 4  -.7894798  -.6877423818268033
208821 2018 8 2  -.2046448 -.19860766514252795
100045 2018 8 2  -.2046448 -.19860766514252795
295113 2018 8 1   .7597022  .34486178831877073
319659 2018 8 5  2.1212707   -.852844341150632
101971 2018 8 3   .2860511  -.4415175238588071
102252 2018 8 4  -.7894798  -.6877423818268033
241456 2018 8 5  2.1212707   -.852844341150632
212782 2018 8 1   .7597022  .34486178831877073
221020 2018 9 5  .07914802   -.852844341150632
224159 2018 9 4   -.123912  -.6877423818268033
 13556 2018 9 4   -.123912  -.6877423818268033
239620 2018 9 1 -1.0541992  .34486178831877073
277043 2018 9 2 -.02776563 -.19860766514252795
244417 2018 9 3 -.35473305  -.4415175238588071
end
format %ty year

For example, all stocks in portfolio 5 (change5) for 08/2018 have the same mean and alpha because they consist of the same stocks. Should I convert the data to only have 5 observations per month (the 5 portfolios) with their respective mean and alpha?

[Carlo Lazzaro]

Juan:
as expected, _b_cons does not change within portfolios:

. tab _b_cons if inlist( change5, 1,5 )

    _b_cons |      Freq.     Percent        Cum.
------------+-----------------------------------
  -.8528443 |          6       60.00       60.00
   .3448618 |          4       40.00      100.00
------------+-----------------------------------
      Total |         10      100.00

.

This makes the -ttest- clearly unfeasible.
What's the fix? I do not know, as I'm not familiar with this kind of stuff.
As a general advice, I would recommend you to skim through the literature in your research field and see what others did (perhaps in the article you refer to) in the past to tackle this issue.