Exhibit (h)(2)(d)

EXPENSE LIMITATION UNDERTAKING

ALLIANCEBERNSTEIN L.P.

66 Hudson Boulevard East

New York, New York 10001

Sanford C. Bernstein Fund, Inc.

66 Hudson Boulevard East,

New York, New York 10001

Dear Sirs:

AllianceBernstein L.P. herewith undertakes that for the Expense Limitation Period, as defined below, we shall cause the aggregate operating expenses of every character incurred by your AB Core Bond Portfolio (the “Portfolio”) (formerly known as Intermediate Duration Portfolio) but not including (i) extraordinary expenses; (ii) interest expense; (iii) the fees and expenses of registered investment companies or series thereof in which the Portfolio invests (“Acquired Funds”) other than investment advisory fees of Acquired Funds for which we serve as investment adviser; (iv) expenses associated with securities sold short; (v) taxes; and (vi) brokerage commission and other transaction costs (the “Limitation”) to be limited to 0.28% in case of Core Bond Class shares and 0.28% in the case of Class Z shares, in each case of the Portfolio’s average daily net assets on an annualized basis.

To determine the amount of your expenses in excess of the Limitation, the amount of allowable fiscal-year-to-date expenses shall be computed daily by prorating the Limitation based on the number of days elapsed within your fiscal year (the “Prorated Limitation”). The Prorated Limitation shall be compared to your expenses recorded through the current day in order to produce the allowable expenses to be recorded and accrued for your current day (the “Allowable Expenses”). If your expenses for the current day exceed the Allowable Expenses, we shall be responsible for such excess and will for the current day (i) reduce our advisory fees and/or (ii) reimburse you accordingly.

For purposes of this Undertaking, the Expense Limitation Period shall mean the period commencing on the date hereof and shall remain in effect until January 31, 2027. The Expense Limitation Period and the Undertaking given hereunder will automatically be extended for additional one-year periods unless we provide you with at least 60 days’ notice prior to the end of any Expense Limitation Period of our determination to modify or to terminate this Undertaking at the end of its then current period.

We understand and intend that you will rely on this Undertaking in preparing and filing your Registration Statement on Form N-1A with the Securities and Exchange Commission, in accruing your expenses for purposes of calculating your net asset value per share and for other purposes and expressly permit you to do so.