
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                  SCHEDULE 13G


                   UNDER THE SECURITIES EXCHANGE ACT OF 1934

                              (AMENDMENT NO. 4  )*


                               Bancroft Fund Ltd
            -------------------------------------------------------
                                (NAME OF ISSUER)

                                  Common Stock
            -------------------------------------------------------
                         (TITLE OF CLASS OF SECURITIES)

                                   59695106
            -------------------------------------------------------
                                 (CUSIP NUMBER)

                              December 31, 2020
            -------------------------------------------------------
            (DATE OF EVENT WHICH REQUIRES FILING OF THIS STATEMENT)

Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

     [X]  Rule 13d-1(b)

     [_]  Rule 13d-1(c)

     [_]  Rule 13d-1(d)

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).

---------------------                                    -----------------------
CUSIP NO. 59695106                   13G                   PAGE 2 OF 5 PAGES
---------------------                                    -----------------------

--------------------------------------------------------------------------------
1    Name of Reporting Persons.
     I.R.S. Identification Nos. of above persons (entities only).

     Advisors Asset Management, Inc.
     20-0532180
--------------------------------------------------------------------------------
2    Check the Appropriate Box if a Member of a Group (See Instructions)
     (a) [_]
     (b) [_]
--------------------------------------------------------------------------------
3    SEC Use Only

--------------------------------------------------------------------------------
4    Citizenship or Place of Organization
     Delaware, U.S.A.
--------------------------------------------------------------------------------
                 5    Sole Voting Power
                      479,912
 NUMBER OF       ---------------------------------------------------------------
   SHARES        6    Shared Voting Power
BENEFICIALLY          0
  OWNED BY       ---------------------------------------------------------------
    EACH         7    Sole Dispositive Power
 REPORTING            483,267
PERSON WITH      ---------------------------------------------------------------
                 8    Shared Dispositive Power
                      0
--------------------------------------------------------------------------------
9    Aggregate Amount Beneficially Owned by Each Reporting Person
     483,267
--------------------------------------------------------------------------------
10   Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See
     instructions)            [_]
--------------------------------------------------------------------------------
11   Percent of Class Represented by Amount in Row 9
     8.758%
--------------------------------------------------------------------------------
12   Type of Reporting Person (See instructions)
     BD
     IA
--------------------------------------------------------------------------------

---------------------                                    -----------------------
CUSIP NO. 59695106                   13G                   PAGE 3 OF 5 PAGES
---------------------                                    -----------------------

--------------------------------------------------------------------------------


ITEM 1.

      (a)  Name of Issuer:

                Bancroft Fund Ltd

      (b)  Address of Issuer's Principal Executive Offices:

                65 Madison Avenue, Suite 550
                Morristown, NJ 07960

ITEM 2.

      (a)  Name of Person Filing:

                Advisors Asset Management, Inc.

      (b)  Address of Principal Business Office:

                18925 Base Camp Road, Monument, Colorado 80132

      (c)  Citizenship:  Delaware, U.S.A.

      (d)  Title of Class of Securities:  Common Stock

      (e)  CUSIP Number:    59695106

ITEM 3.  If this statement is filed pursuant to ss. 240.13d-1(b) or
           240.13d-2(b) or (c), check whether the person filing is a:

      (a) [X] Broker or dealer registered under section 15 of the Act
              (15 U.S.C. 78o).

      (b) [_] Bank as defined in section 3(a)(6) of the Act
              (15 U.S.C. 78c).

      (c) [_] Insurance company as defined in section 3(a)(19) of the Act
              (15 U.S.C. 78c).

      (d) [_] Investment company registered under section 8 of the Investment
              Company Act of 1940 (15 U.S.C. 80a-8).

      (e) [X] An investment adviser in accordance with ss. 240.13d-1(b)(ii)(E).

      (f) [_] An employee benefit plan or endowment fund in accordance with
              ss. 240.13d-1(b)(1)(ii)(F).

      (g) [_] A parent holding company or control person in accordance with
              ss. 240.13d-1(b)(1)(ii)(G).

      (h) [_] A savings association as defined in Section 3(b) of the
              Federal Deposit Insurance Act (12 U.S.C. 1813).

      (i) [_] A church plan that is excluded from the definition of an
              investment company under section 3(c)(14) of the Investment
              Company Act of 1940 (15 U.S.C. 80a-3).

      (j) [_] Group, in accordance with ss. 240.13d-1(b)(1)(ii)(J).



                                       3

---------------------                                    -----------------------
CUSIP NO. 59695106                  13G                   PAGE 4 OF 5 PAGES
---------------------                                    -----------------------

--------------------------------------------------------------------------------


ITEM 4.  Ownership:

      (a)  Amount Beneficially Owned:  483,267

      (b)  Percent of Class: 8.758%

      (c)  Number of Shares as to which such person has:

          (i)  Sole power to vote or to direct the vote:  479,912

         (ii)  Shared power to vote or to direct the vote:  0

        (iii)  Sole power to dispose or to direct the disposition of:  483,267

         (iv)  Shared power to dispose or to direct the disposition of:  0

ITEM 5.  Ownership of Five Percent or Less of a Class:

     If this statement is being filed to report the fact that as of the
     date hereof the reporting person has ceased to be the beneficial owner
     of more than five percent of the class of securities, check the
     following [ ].



ITEM 6.  Ownership of More than Five Percent on Behalf of Another:

     Advisors Asset Management, Inc. is sponsor of several unit investment
     trusts which hold shares of common stock of the issuer.  No unit investment
     trust sponsored by Advisors Asset Management, Inc. holds 5% or more of the
     issuer's common stock.  Advisors Asset Management, Inc. disclaims
     beneficial ownership of such shares of the issuer identified in this
     filing.

ITEM 7.  Identification and Classification of the Subsidiary Which Acquired the
         Security Being Reported on by the Parent Holding Company:

     See Item 6

ITEM 8.  Identification and Classification of Members of the Group:

     N/A

ITEM 9. Notice of Dissolution of Group:

     N/A

ITEM 10. Certification:

By signing below I certify that, to the best of my knowledge and belief, the
securities referred to above were not acquired and are not held for the purpose
of or with the effect of changing or influencing the control of the issuer of
the securities and were not acquired and are not held in connection with or as a
participant in any transaction having that purpose or effect.



                                       4

---------------------                                    -----------------------
CUSIP NO. 59695106                  13G                   PAGE 5 OF 5 PAGES
---------------------                                    -----------------------

--------------------------------------------------------------------------------


                                    SIGNATURE

     After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.


Advisors Asset Management, Inc.


By: /s/ Scott Colyer
-------------------------------                       -----------------------
Scott Colyer
Chief Executive Officer















ATTENTION: INTENTIONAL MISSTATEMENTS OR OMISSIONS OF FACT CONSTITUTE FEDERAL
CRIMINAL VIOLATIONS (SEE 18 U.S.C. 1001)



                                       5

BANCROFT FUND LTD SC 13G/A