Exhibit (a)(5)(iii)

FOR IMMEDIATE RELEASE
ATTENTION: BUSINESS/FINANCIAL EDITORS
MEDIA CONTACT:
KRISTYNA MUNOZ
(312) 917-8343
KRISTYNA.MUNOZ@NUVEEN.COM

Nuveen Global High Income Fund Announces Preliminary Results of Tender Offer

CHICAGO, January 12, 2015 – Nuveen Investments, a leading global provider of investment services to institutions as well as individual investors, today announced the preliminary results of the tender offer conducted by Nuveen Global High Income Fund (NYSE: JGH).

As previously announced, the fund conducted a tender offer for up to 25 percent of its outstanding common shares for cash at a price per share equal to 98 percent of the net asset value per share determined on the expiration date. The fund’s tender offer, which expired at 5:00 p.m. Eastern time on Friday, January 9, 2015, was oversubscribed. Due to the fact that the number of shares tendered exceeded the number of shares the fund offered for purchase, the fund will purchase the maximum percentage of its outstanding common shares on a pro-rata basis in accordance with the number of shares duly tendered by each shareholder and the terms of the offer to purchase.

Based on preliminary information, 18,340,141 shares were tendered, representing approximately 57.1 percent of the fund’s common shares outstanding.

These figures do not include shares tendered through notice of guaranteed delivery. The fund currently expects to announce the final results of the tender offer on Friday, January 16, 2015.

Nuveen Investments provides high-quality investment services designed to help secure the long-term goals of institutional and individual investors as well as the consultants and financial advisors who serve them. Nuveen Investments markets a wide range of specialized investment solutions which provide investors access to capabilities of its high-quality boutique investment affiliates—Nuveen Asset Management, LLC, Symphony Asset Management LLC, NWQ Investment Management Company, LLC, Santa Barbara Asset Management, LLC, Tradewinds Global Investors, LLC, Winslow Capital Management, LLC and Gresham Investment Management LLC, all of which are registered investment advisers and subsidiaries of Nuveen Investments, Inc. Funds are distributed by Nuveen Securities, LLC, a subsidiary of Nuveen Investments, Inc. Nuveen Investments operates as a separate subsidiary within TIAA-CREF, which is a leading provider of retirement and financial services in the academic, research, medical and cultural fields. In total, Nuveen Investments managed $229 billion as of September 30, 2014. For more information, please visit the Nuveen Investments website at www.nuveen.com.