how many rows has your table ? And how many rows has your result set ?
If this is only a small part of your table then an index on AS_ON_DATE may be helpfull. This index will avoid additional sorts.
The tablename Vxxx can lead to a view, so you have to check the view-definition.
And finally if column AS_ON_DATE is a date you may convert the '13-Jun-2012' to a date by yourself not via implicit conversion.
Everyone want to have a single hint that could solve all there database related performance issues. But the thing is there is no such hint. Performance optimization is not some random shot you take, it a constructive step by step approach. You Need to have all possible information (Business and Technical) on hand.
Oracle provides various tools to identify the performance bottle neck. When your query takes too long ... thread talks about some of the available tools. You can have a look into it. Also when you are stuck at some point in your performance tuning process and want to get help from public forum, you cant just throw in some SQL statement and say fix it. You need to provide us with details. The details that are necessary is listed in HOW TO: Post a SQL statement tuning request - template posting thread. Please go through it.