JGH Nuveen Global High Income Fund

1

NAME OF REPORTING PERSON

Saba Capital Management, L.P.

2

CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP

(a) ☐

(b) ☐

3

SEC USE ONLY

4

SOURCE OF FUNDS

OO (see Item 3)

5

CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDING IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)

☐

6

CITIZENSHIP OR PLACE OF ORGANIZATION

Delaware

NUMBER OF
SHARES
BENEFICIALLY
OWNED BY
EACH
REPORTING
PERSON WITH:

7

SOLE VOTING POWER

-0-

8

SHARED VOTING POWER

2,288,325

9

SOLE DISPOSITIVE POWER

-0-

10

SHARED DISPOSITIVE POWER

2,288,325

11

AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH PERSON

2,288,325

12

CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES
 

☐

13

PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

9.9%

14

TYPE OF REPORTING PERSON

PN; IA

1

NAME OF REPORTING PERSON

Boaz R. Weinstein

2

CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP

(a) ☐

(b) ☐

3

SEC USE ONLY

4

SOURCE OF FUNDS

OO (see Item 3)

5

CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDING IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)

☐

6

CITIZENSHIP OR PLACE OF ORGANIZATION

United States

NUMBER OF
SHARES
BENEFICIALLY
OWNED BY
EACH
REPORTING
PERSON WITH:

7

SOLE VOTING POWER

-0-

8

SHARED VOTING POWER

2,288,325

9

SOLE DISPOSITIVE POWER

-0-

10

SHARED DISPOSITIVE POWER

2,288,325

11

AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH PERSON

2,288,325

12

CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES
 

☐

13

PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

9.9%

14

TYPE OF REPORTING PERSON

IN

1

NAME OF REPORTING PERSON

Saba Capital Management GP, LLC

2

CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP

(a) ☐

(b) ☐

3

SEC USE ONLY

4

SOURCE OF FUNDS

OO (see Item 3)

5

CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDING IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)

☐

6

CITIZENSHIP OR PLACE OF ORGANIZATION

Delaware

NUMBER OF
SHARES
BENEFICIALLY
OWNED BY
EACH
REPORTING
PERSON WITH:

7

SOLE VOTING POWER

-0-

8

SHARED VOTING POWER

2,288,325

9

SOLE DISPOSITIVE POWER

-0-

10

SHARED DISPOSITIVE POWER

2,288,325

11

AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH PERSON

2,288,325

12

CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES
 

☐

13

PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

9.9%

14

TYPE OF REPORTING PERSON

OO

Item 1.

SECURITY AND ISSUER

This statement on Schedule 13D (the "Schedule 13D") relates to the common shares (the "Common Shares"), of Nuveen Global High Income Fund (the "Issuer"). The Issuer's principal executive offices are located at 333 West Wacker Drive, Chicago, IL 60606.

The information set forth in response to each separate Item below shall be deemed to be a response to all Items where such information is relevant.

Item 2.

IDENTITY AND BACKGROUND

(a)

This Schedule 13D is being jointly filed by:

(i)

Saba Capital Management, L.P., a Delaware limited partnership ("Saba Capital");

(ii)

Saba Capital Management GP, LLC, a Delaware limited liability company ("Saba GP"); and

(iii)

Mr. Boaz R. Weinstein ("Mr. Weinstein"),

(together, the "Reporting Persons").  Any disclosures herein with respect to persons other than the Reporting Persons are made on information and belief after making inquiry to the appropriate party.

The filing of this statement should not be construed as an admission that any Reporting Person is, for the purposes of Sections 13 of the Securities Exchange Act of 1934, the beneficial owner of the Common Shares reported herein.

(b)

The address of the business office of each of the Reporting Persons is 405 Lexington Avenue, 58^th Floor, New York, New York 10174.

(c)

The principal business of: (i) Saba Capital is to serve as investment manager to private and public investment funds and/or accounts, (ii) Saba GP is to serve as general partner of the Saba Capital and other affiliated entities, and (iii) Mr. Weinstein, an individual, is managing member of the general partner of Saba Capital and other affiliated entities.

(d)

The Reporting Persons have not, during the last five years, been convicted in a criminal proceeding (excluding traffic violations or similar misdemeanors).

(e)

The Reporting Persons have not, during the last five years, been a party to a civil proceeding of a judicial or administrative body of competent jurisdiction and, as a result of such proceeding, was, or is subject to, a judgment, decree or final order enjoining future violations of, or prohibiting or mandating activities subject to, Federal or State securities laws or finding any violation with respect to such laws.

(f)

Saba Capital is organized as a limited partnership under the laws of the State of Delaware. Saba GP is organized as a limited liability company under the laws of the State of Delaware. Mr. Weinstein is a citizen of the United States.

The Reporting Persons have executed a Joint Filing Agreement, dated December 1, 2020 with respect to the joint filing of this Schedule 13D, and any amendment or amendments hereto, a copy of which is attached hereto as Exhibit 1.

Item 3.

SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION

Funds for the purchase of the Common Shares were derived from the subscription proceeds from investors and the capital appreciation thereon and margin account borrowings made in the ordinary course of business.  In such instances, the positions held in the margin accounts are pledged as collateral security for the repayment of debit balances in the account, which may exist from time to time.  Since other securities are held in the margin accounts, it is not possible to determine the amounts, if any, of margin used to purchase the Common Shares reported herein. A total of approximately $31,541,819 was paid to acquire the Common Shares reported herein.

Item 4.

PURPOSE OF TRANSACTION

The Reporting Persons acquired the Common Shares to which this Schedule 13D relates in the ordinary course of business for investment purposes because they believe that the Common Shares are undervalued and represent an attractive investment opportunity.

The Reporting Persons may engage in discussions with management, the Board of Trustees (the "Board"), other shareholders of the Issuer and other relevant parties, including representatives of any of the foregoing, concerning the Reporting Persons' investment in the Common Shares and the Issuer, including, without limitation, matters concerning the Issuer's business, operations, board appointments, governance, performance, management, capitalization, trading of the Common Shares at a discount to the Issuer's net asset value and strategic plans and matters relating to the open or closed end nature of the Issuer and timing of any potential liquidation of the Issuer. The Reporting Persons may exchange information with any persons pursuant to appropriate confidentiality or similar agreements or otherwise, work together with any persons pursuant to joint agreements or otherwise, propose changes in the Issuer's business, operations, board appointments, governance, management, capitalization, strategic plans or matters relating to the open or closed end nature of the Issuer or timing of any potential liquidation of the Issuer, or propose or engage in one or more other actions set forth herein.

The Reporting Persons may also propose or take one or more of the actions described in subsections (a) through (j) of Item 4 of Schedule 13D, including the solicitation of proxies, and may discuss such actions with the Issuer and Issuer's management and the board of directors, other stockholders of the Issuer and other interested parties. The Reporting Persons may make binding or non-binding shareholder proposals, or may nominate one or more individuals as nominees for election to the Board in connection with their investment in the Common Shares of the Issuer.

The Reporting Persons intend to review their investment in the Issuer on a continuing basis. Depending on various factors, including, without limitation, the outcome of any discussions referenced above, the Issuer's financial position and strategic direction, actions taken by management or the Board, price levels of the Common Shares, other investment opportunities available to the Reporting Persons, conditions in the securities market and general economic and industry conditions, the Reporting Persons may in the future take such actions with respect to their investment in the Issuer as they deem appropriate, including, without limitation, purchasing additional Common Shares or selling some or all of their Common Shares, engaging in short selling of or any hedging or similar transactions with respect to the Common Shares and/or otherwise changing their intention with respect to any and all matters referred to in Item 4 of Schedule 13D. The Reporting Persons may, at any time and from time to time, review or reconsider their position and/or change their purpose and/or formulate plans or additional proposals with respect to their investment in the Common Shares.

The Reporting Persons have not entered into any agreement with any third party to act together for the purpose of acquiring, holding, voting or disposing of the Common Shares reported herein.   

Item 5.

INTEREST IN SECURITIES OF THE ISSUER

(a)

See rows (11) and (13) of the cover pages to this Schedule 13D for the aggregate number of Common Shares and percentages of the Common Shares beneficially owned by each of the Reporting Persons.  The percentages used herein are calculated based upon 23,177,393 shares of common stock outstanding as of 6/30/20, as disclosed in the company's N-CSRS filed with the Securities and Exchange Commission on 9/4/20.

(b)

See rows (7) through (10) of the cover pages to this Schedule 13D for the number of Common Shares as to which each Reporting Person has the sole or shared power to vote or direct the vote and sole or shared power to dispose or to direct the disposition.

(c)

The transactions in the Common Shares effected within the past sixty days by the Reporting Persons, which were all in the open market, are set forth in Schedule A, and are incorporated herein by reference.

(d)

The funds and accounts advised by Saba Capital have the right to receive the dividends from and proceeds of sales from the Common Shares.

(e)

Not applicable.

Item 6.

CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT TO SECURITIES OF THE ISSUER

Other than the Joint Filing Agreement attached as Exhibit 1 hereto, there are no contracts, arrangements, understandings or relationships (legal or otherwise) among the persons named in Item 2 hereof and between such persons and any person with respect to any securities of the Issuer, including but not limited to transfer or voting of any other securities, finder's fees, joint ventures, loan or option arrangements, puts or calls, guarantees of profits, divisions of profits or loss, or the giving or withholding of proxies.

Item 7.

MATERIAL TO BE FILED AS EXHIBITS

Exhibit 1:

Joint Filing Agreement as required by Rule 13d-1(k)(1) under the Act.

SABA CAPITAL MANAGEMENT, L.P.

By:  /s/ Michael D'Angelo

Name: Michael D'Angelo

Title: Chief Compliance Officer

SABA CAPITAL MANAGEMENT GP, LLC

By:  /s/ Michael D'Angelo

Name: Michael D'Angelo

Title: Authorized Signatory

BOAZ R. WEINSTEIN

By:  /s/ Michael D'Angelo

Name: Michael D'Angelo

Title: Attorney-in-fact*

* Pursuant to a power of attorney dated as of November 16, 2015, which is incorporated herein by reference to Exhibit 2 to the Schedule 13G filed by the Reporting Persons on December 28, 2015, accession number: 0001062993-15-006823

Date

Buy/Sell

      Shares

      Price

10/26/20

Buy

          6,361

      13.76

10/23/20

Buy

          4,638

      13.90

10/22/20

Buy

        23,048

      13.86

10/19/20

Buy

        26,610

      13.81

10/15/20

Buy

        22,629

      13.82

10/14/20

Buy

        20,256

      13.87

10/13/20

Buy

              366

      13.85

10/12/20

Buy

        18,640

      13.97

10/09/20

Buy

        15,872

      13.94

10/08/20

Buy

          2,165

      13.91

10/07/20

Buy

        12,086

      13.86

10/06/20

Buy

          6,239

      13.79

10/05/20

Buy

        16,923

      13.69

10/02/20

Buy

          5,544

      13.53

SABA CAPITAL MANAGEMENT, L.P.

/s/ Michael D'Angelo

Name: Michael D'Angelo

Title: Chief Compliance Officer

SABA CAPITAL MANAGEMENT GP, LLC

/s/ Michael D'Angelo

Name: Michael D'Angelo

Title: Authorized Signatory

BOAZ R. WEINSTEIN

/s/ Michael D'Angelo

Name: Michael D'Angelo

Title: Attorney-in-fact*

Title: Attorney-in-fact*