Derek M. Hodge Virgin Islands Improvement Act of 2013 - Amends the Internal Revenue Code to provide for a reduction of taxes on distributions from certain retirement savings plans designated by an individual under the age of 61 as being under investment by the Virgin Islands Investment Program for at least 30 years. Defines "Virgin Islands Investment Program" for purposes of this Act as a fund with managed amounts of $50 billion or less. Imposes a 1.5% annual tax for 10 years, and 1% thereafter, on managed funds to benefit Virgin Island infrastructure development.