Following the commit:
commit b9e5c0a949fa627da55ea53fd71dfa96ad8a2b4b
    guix-package: Create ~/.guix-profile when it doesn't exist.

I finally dropped giving the explicit profile parameter to guix-package. 
This results in the following error when installing a package:

Backtrace:
In ice-9/boot-9.scm:
 149: 12 [catch #t #<catch-closure 12f39c0> ...]
 157: 11 [#<procedure 128f0f0 ()>]
In unknown file:
   ?: 10 [catch-closure]
In ice-9/boot-9.scm:
  63: 9 [call-with-prompt prompt0 ...]
In ice-9/eval.scm:
 407: 8 [eval # #]
In unknown file:
   ?: 7 [call-with-input-string "(apply (module-ref (resolve-interface 
'(guix-package)) 'guix-package) (cdr (command-line)))" ...]
In ice-9/command-line.scm:
 174: 6 [#<procedure 120e2a0 at ice-9/command-line.scm:169:3 (port)> 
#<input: string 10b60d0>]
In unknown file:
   ?: 5 [eval (apply (module-ref # #) (cdr #)) #<directory (guile-user) 
12f5d80>]
In ice-9/boot-9.scm:
 149: 4 [catch srfi-34 #<procedure 1290c40 at guix/ui.scm:71:2 ()> ...]
 157: 3 [#<procedure 1753870 ()>]
In /usr/local/bin/guix-package:
 475: 2 [#<procedure 13b8c60 at /usr/local/bin/guix-package:468:4 ()>]
 409: 1 [process-actions (# #)]
In unknown file:
   ?: 0 [symlink "/nix/store/g4bnzikcjgdcgmcj7by815wb9ykz470l-user-
environment" ...]

In fact, a symbolic link $HOME/.guix-profile is created to the non-existing 
file /usr/local/guix-git/var/nix/profiles/per-user/privat/guix-profile 
(where /usr/local/guix-git/ is my installation prefix).

The user environment /nix/store/g4bnzikcjgdcgmcj7by815wb9ykz470l-user-
environment exists in the nix store.

I think the problem is that only the directory /usr/local/guix-
git/var/nix/profiles exists, but that it is empty; maybe one should first 
create the directory $PREFIX/var/nix/profiles/per-user/$USER if it does not 
exist yet?

Andreas