Geometric Mean: Bugs in meanrets Package for Portfolios?

[Attaullah Shah]

I was using the mvport package (SSC) written by Alberto Dorantes. The package has meanrets program for finding geometric mean, however, its results seem to be upward biased, I cross checked it with MS EXCEL and another package gmci (SSC), this is to confirm that the meanrets has bugs, or am I missing something. See the following examples

clear
input float(Price t)
12 1 
10 2 
12 3 
15 4 
13 5 
18 6 
24 7 
18 8 
17 9 
22 10 
end
tsset t
gen ri=p/l.p-1
gen gr=ln(p/l.p)

 . meanrets ri gr
Observations to calculate expected simple returns: 10
Expected simple returns (Geometric means):

      Exp ret
ri  .09984347
gr  .06966811

. gmci ri gr, add(1)
 
  Variable  |    Obs     Geometric Mean           [95% Conf. Interval]
------------+-----------------------------------------------------------
        ri  |      9           1.06967           0.89375       1.28021 *
        gr  |      9           1.04302           0.87249       1.24687 *
 
(*) 1 was added to the variable(s) prior to calculating the results

. sum ri gr

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
          ri |          9    .0951679     .244355       -.25   .3846154
          gr |          9    .0673484    .2337455  -.2876821   .3254224

Note that due to non-positive values, I had add option add(1) to the gmci, which later would be deducted.

[daniel klein]

I did not have a deeper look into either package, but official Stata's ameans will calculate geometric (and other) means, so I think there is little need for user-written software here.

Best
Daniel

[Nick Cox]

Adding 1 and then subtracting it at the end is at best going to give an approximation, as taking the geometric mean is **not** a linear operation. Strictly the geometric mean is either not defined or zero in the presence of zeros.

[Alberto Dorantes]

Dear Attaulla:
My command meanrets has to receive a varlist of "continuously compounded" (cc) returns, not simple returns. In your example, the variable gr is the cc returns for your series. If you type help meanrets, you will see the specification about the cc returns. Unlike ameans and gmci, with meanrets you do not have to add 1 to each return, and you do not have to substract one at the end.
Then, in your example, you have to run meanrets with gr, that is the cc return. If you see, the result of meanrets for this variable is 0.06966811, that is the same you got with the gmci (after you substract 1).
Let me know if I was clear.
Thanks for the comment. I am about to release a new version of the mvport package. I will consider your point. Maybe I can change the meanrets by using simple returns instead of cc returns in the command.
Best regards... Alberto