Why doesn't composer install drush on $HOME/bin directory?

Question

I'm trying to learn to to use drush.

I installed composer to my $HOME/bin/directory:

$ ls ~/bin
composer  composer.phar  subl  sublime  sublime_config.sh  sublime_text

Then tried to install drush globally:

$ composer global require drush/drush:dev-master
Changed current directory to /home/nnieto/.composer
./composer.json has been updated
Loading composer repositories with package information
Updating dependencies (including require-dev)
  - Installing pear/console_table (1.1.5)
    Downloading: 100%         

  - Installing symfony/yaml (v2.2.1)
    Downloading: 100%         

  - Installing d11wtq/boris (v1.0.8)
    Downloading: 100%         

  - Installing drush/drush (dev-master 31fa220)
    Cloning 31fa220c9ee33a250d135ad0d65b5b6c92c6c188

pear/console_table suggests installing pear/Console_Color (>=0.0.4)
drush/drush suggests installing youngj/httpserver (dev-master#41dd2b7 as 1.0.1)
Writing lock file
Generating autoload files

I expected to find a drush file on ~/bin, but instead I got a nope from Linux:

[nnieto@localhost ~]$ ls ~/bin
composer  composer.phar

What I'm doing wrong?