Obama wasn't inaugurated on September 29. He was inaugurated TODAY and his reign starts TODAY!
The years of kings are marked from the Rosh Hashannah of the year that the king was installed.
“reign” -?
Technically, we have no king, yet. Even Obama, not yet made Emperor by Congress, or Protector of the City, of whatever, began to serve his term of office.
I understand this may seem a distinction without a difference, at a time like this, but it is legally correct, for the moment.