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.

August 4, 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 August 4, 2016 and end on September 1, 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 Daylight Time, on September 1, 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.

At this time, we are pleased to resume the implementation of a regular tender offer process. Our current plan is to offer up to 8% of the Fund’s Net Asset Value (“NAV”) in liquidity via the tender offer process in 2016 (up to 2% quarterly). Starting in 2017, the plan is to offer up to 10% of the Fund’s NAV per year via the tender offer process. While we desire to keep investors informed with our current plans and projections for tender offers, we would like to emphasize that this is an outlook based on projected cash flows and is subject to adjustment with changes to the Fund’s portfolio or broader market environment. Additionally, all tender offers are subject to Board approval, per the Fund’s PPM. For additional important information regarding the tender offer, please refer to the attached Offer to Purchase document. 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.