EX-99.1

Exhibit 99.1

Cover Letter to Offer to Purchase and Letter of Transmittal

IF YOU DO NOT WANT TO TENDER YOUR LIMITED PARTNERSHIP INTERESTS FOR REPURCHASE AT THIS TIME FOR ANY REASON, PLEASE DISREGARD THIS NOTICE. THIS IS SIMPLY NOTIFICATION OF THE FUND’S TENDER OFFER.

February 2, 2016

Dear Investor of The Endowment Institutional Fund, L.P.:

We are writing to inform you of important dates related to the tender offer by The Endowment Institutional Fund, L. P. (the “Fund”). If you are not interested in selling your limited partnership interests at this time, please disregard this notice and take no action.

Please note that the sale of your limited partnership interests may be subject to a 2% Early Redemption Fee if you decide to sell your interests in this offer.

The tender offer period will begin on February 2, 2016 and end on March 2, 2016. The purpose of the tender offer is to provide liquidity to investors who hold limited partnership interests. Limited partnership interests can be repurchased by means of a tender offer only during one of the Fund’s announced tender offers.

Should you wish to sell any of your limited partnership interests during this tender offer period, please complete the enclosed Letter of Transmittal (the two page Tender Offer Form will suffice) and contact your financial advisor who services your account for specific return instructions. Allow for additional processing time by your financial intermediary if necessary as the form must ultimately be received by the Fund’s Investment Adviser, Endowment Advisers, L.P. either by mail or by fax in good order by midnight, Central Standard Time, on March 2, 2016. If you do not wish to tender limited partnership interests for repurchase for any reason, simply disregard this notice. No Action is Required if You Do Not Wish to Tender Your Interests for Repurchase at This Time.

For additional important information regarding the tender offer, please refer to the attached Offer to Purchase document. We look forward to resuming the implementation of a regular tender offer process in the future and will provide further details on this process as they become available. If you have any questions, please contact your Financial Advisor or call the Support Desk of the Investment Adviser at (800) 725-9456.

Sincerely,

The Endowment Institutional Fund, L.P.

Cover Letter to Offer to Purchase and Letter of Transmittal

Clients of Merrill Lynch Financial Advisors

IF YOU DO NOT WANT TO TENDER YOUR LIMITED PARTNERSHIP INTERESTS FOR REPURCHASE AT THIS TIME FOR ANY REASON, PLEASE DISREGARD THIS NOTICE. THIS IS SIMPLY NOTIFICATION OF THE FUND’S TENDER OFFER.

February 2, 2016

Dear Investor of The Endowment Institutional Fund, L.P.:

We are writing to inform you of important dates related to the tender offer by The Endowment Institutional Fund, L.P. (the “Fund”). If you are not interested in selling your limited partnership interests at this time, please disregard this notice and take no action.

Please note that the sale of your limited partnership interests may be subject to a 2% Early Redemption Fee if you decide to sell your interests in this offer.

The tender offer period will begin on February 2, 2016 and end on March 2, 2016. The purpose of the tender offer is to provide liquidity to investors who hold limited partnership interests. Limited partnership interests can be repurchased by means of a tender offer only during one of the Fund’s announced tender offers.

Should you wish to sell any of your limited partnership interests during this tender offer period, please contact your Financial Advisor who will provide you a customized Tender Offer Form for your account. The Letter of Transmittal contained in this Offer to Purchase includes a sample Tender Offer Form for your reference only. The Tender Offer Form generated for your account will need to be signed and returned to your Financial Advisor. Upon receiving the signed form, your Financial Advisor will then submit the order. Your Financial Advisor must submit the form by midnight, Central Standard Time, on March 2, 2016. If you do not wish to tender limited partnership interests for repurchase for any reason, simply disregard this notice. No Action is Required if You Do Not Wish to Tender Your Interests for Repurchase at This Time.

For additional important information regarding the tender offer, please refer to the attached Offer to Purchase document. We look forward to resuming the implementation of a regular tender offer process in the future and will provide further details on this process as they become available. If you have any questions, please contact your Financial Advisor.

Sincerely,

The Endowment Institutional Fund, L.P.