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  Proskauer Rose LLP    1001 Pennsylvania Avenue, NW Suite 600 South    Washington,
  DC 20004-2533

July 18, 2023

VIA EDGAR

Alberto H. Zapata

Senior Counsel

Division of Investment Management

U.S. Securities and Exchange Commission

100 F Street, N.E.

Washington, D.C. 20549

    Re:
    IDR Core Property Index Fund
    Ltd

  Proxy Statement (Preliminary) on Schedule 14A

  (File No. 811-23460)

Dear Mr. Zapata:

On behalf of IDR Core Property Index Fund Ltd
(the “Company”), set forth below are the Company’s responses to the oral comments provided by the
staff of the Division of Investment Management (the “Staff”) of the Securities and Exchange Commission
(the “Commission”) to the Company on July 7, 2023, with respect to the Company’s response (the
 “Prior Response Letter”) to the prior comments provided by the Staff with respect to the Company’s Preliminary
Proxy Statement on Schedule 14A (the “Proxy Statement”) (File No. 811-23460), filed with the Commission
on June 2, 2023. The Staff’s comments are set forth below in italics and are followed by the Company’s responses. Capitalized
terms used below but not otherwise defined herein shall have the meanings ascribed to them in the Proxy Statement. Where revisions to
the Proxy Statement are referenced in the below responses, such revisions are indicated by marked pages from the Proxy Statement
attached as an exhibit hereto.

General

 1. Comment: The Staff notes that
                                            the Company filed a Registration Statement on Form N-2 with the Commission on May 12,
                                            2023 (the “Registration Statement”). Please ensure that the description
                                            of the New ELA in the Registration Statement is consistent with the description in the Proxy
                                            Statement.

Response:
The Company acknowledges the Staff’s comment and confirms that it will align the description of the New ELA in the Registration
Statement with the description in the Proxy Statement.

 2. Comment: Please confirm that
                                            no affiliates of the Company will be receiving any compensation as service providers to the
                                            Company, including in connection with the distribution of its shares, other than as disclosed
                                            in the Proxy Statement.

Response:
The Company advises the Staff on a supplemental basis that no affiliates will be receiving any compensation as service providers to the
Company, including in connection with the distribution of its shares, other than as presently disclosed in the Proxy Statement. In particular,
it is expected that Accordant Investments will provide certain administrative services to the Company as described in the Proxy Statement.
Such administrative services will be provided solely on an expense reimbursement basis, with no profit to Accordant Investments. The
Company further confirms that it currently expects to utilize a third-party distributor in connection with the distribution of its shares,
rather than an affiliated broker-dealer.

Beijing | Boca Raton | Boston | Chicago | Hong
Kong | London | Los Angeles | New Orleans | New York | Paris | São Paulo | Washington, DC

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Q&A

 3. Comment: We note your response
                                            to prior comment no. 7 set forth in the Prior Response Letter. Please provide further analysis
                                            on why the spin-out transaction (the “Spin-Out”), which
                                            led to a change of control of IDR, was not a sale requiring compliance with the safe-harbor
                                            provisions set forth under Section 15(f) of the Investment Company Act of 1940,
                                            as amended (the “1940 Act”), or confirm that the Company intends to comply
                                            with the requirements of Section 15(f).

Response:
The Company advises the Staff on a supplemental basis that it intends to comply with the applicable requirements of Section 15(f).
The Company has made corresponding changes reflecting such compliance throughout the Proxy Statement.

Proxy Statement – Proposal #1

 4. Comment: The Staff notes that
                                            the Company has included additional disclosure regarding the structure of Emphasis Capital.
                                            Please also include similar disclosure regarding the ownership of IDR. In particular, please
                                            note whether there are any other control persons of IDR, other than Emphasis Capital.

Response:
The Company has revised the disclosure included in Proposal #1 and throughout the Proxy Statement in response to the Staff’s comment.

 5. Comment: We note your response
                                            to prior comment no. 13 set forth in the Prior Response Letter. Please explain to the Staff
                                            on a supplemental basis why the line item “Other Expenses” has increased significantly
                                            recently.

Response:
The Company advises the Staff on a supplemental basis that the significant increase in “Other Expenses” primarily reflects
the billing, incurrence and payment of certain legal and other fees and expenses relating to the organization and current private placement
offering by the Company. Given that the Company has raised less than $25 million in aggregate proceeds, such legal and other fees and
expenses represent a large percentage of the Company’s net assets.

 6. Comment: We note your response
                                            to prior comment no. 14 set forth in the Prior Response Letter. Please explain to the Staff
                                            on a supplemental basis why the Company is not listing the total estimated amount of expenses
                                            and waived amounts under the New Advisory Agreement and New ELA.

Response:
The Company advises the Staff on a supplemental basis that the structure of the New ELA is intended to provide the Company with a “unified
fee” structure, whereby the maximum amount that the Company may pay in fees and expenses will be subject to a maximum “cap”
for the one year period following adoption and implementation of the New ELA, based upon a percentage of the Company’s net assets.
Such cap would include the aggregate amount of management fees payable to Accordant Investments, along with the Company’s aggregate
operating and administrative expenses. Given that the cap imposed under the New ELA is prospective in nature, and will apply for at least
one year following its adoption, the Company does not believe that it would be required to show estimated gross expenses, waived amounts
and net expenses in the same manner as it has historically been required to do under the Prior Operational ELAs.

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 7. Comment: We note your response
                                            to prior comment no. 15 set forth in the Prior Response Letter. Please revise the disclosure
                                            included in the Proxy Statement to disclose any benefits to be received by Gary A. Zdolshek
                                            as a result of the matters subject to approval at the Meeting.

Response:
The Company has revised the above-referenced disclosure in response to the Staff’s comment. In addition, the Company advises the
Staff on a supplemental basis that the only benefit Mr. Zdolshek will receive as a result of the transactions contemplated in the
Proxy Statement arise from his equity ownership position in IDR.

Proxy Statement – Proposal #3

 8. Comment: We note your response
                                            to prior comment no. 18 set forth in the Prior Response Letter. Please confirm that the New
                                            ELA will not trigger a new 5-year period for reimbursement of any organizational and offering
                                            expenses.

Response:
The Company advises the Staff on a supplemental basis that the New ELA will not trigger a new 5-year period for reimbursement of any
previously incurred organizational and offering expenses.

If
you have any questions or additional comments concerning the foregoing, please contact William MacGregor by phone at 212.969.3555 or
by email at wmacgregor@proskauer.com, or the undersigned by phone at 202.416.6828 or by email at jmahon@proskauer.com.

  Sincerely,

  /s/ John J. Mahon

  John J. Mahon, Esq.

 cc: Asen
Parachkevov, Branch Chief

Gary A. Zdolshek, Chief Executive Officer and
President

Thomas Bartos, Chief Financial Officer

William MacGregor, Esq.

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