Exhibit 99.1

Stratus Properties Inc. Announces Board Review of Strategic Alternatives

Company Retains Hentschel & Company, LLC as Financial Advisor

AUSTIN, TX, April 7, 2016 - Stratus Properties Inc. (NASDAQ: STRS) today announced that its Board of Directors has authorized management to explore a full range of strategic alternatives for Stratus to enhance value for stockholders, including, but not limited to, a sale of Stratus, a sale of certain of Stratus’ core assets, a share repurchase program, and continuing Stratus’ long-term plans to develop the value of its properties. After conducting a thorough process of evaluating several financial advisors, Stratus has engaged Hentschel & Company, a premier boutique investment banking advisory firm focused on the real estate industry, as financial advisor in connection with the review of strategic alternatives. Stratus has also retained Vinson & Elkins LLP and Jones Walker LLP as legal counsel to assist in the process.

William H. Armstrong III, Chairman of the Board, President and Chief Executive Officer of Stratus stated, “We believe that our investment and development programs under our current five-year plan have added significant value to our properties. With our recent acquisition resulting in our full ownership of the W Austin Hotel and Residences, the continuing success of our grocery-anchored retail development program, our continued progress executing our five-year plan, and the additions of Jim Joseph and John Schweitzer to our Board, we believe that now is an appropriate time to evaluate our strategic options to provide further value for our stockholders. Today’s announcement to begin the process of thoroughly evaluating strategic alternatives is part of the Board’s ongoing commitment to maximize value to all Stratus stockholders.”

The Board of Directors has not set a definitive timeline for completion of this review process and has not determined to pursue any particular strategic alternative or enter into any transaction. There can be no assurance that this process will result in any change to the previously announced five-year plan, a sale transaction or any other transaction. Stratus does not intend to comment on or disclose developments regarding the process unless it deems further disclosure is appropriate or required.

1

About Stratus Properties

Stratus is a diversified real estate company engaged primarily in the acquisition, entitlement, development, management, operation and sale of commercial, hotel, entertainment, and multi- and single-family residential real estate properties, primarily located in the Austin, Texas area, but including projects in certain other select markets in Texas.

About Hentschel & Company, LLC

Hentschel & Company, LLC is a boutique investment banking advisory firm focused on the real estate and specialty finance industries. Hentschel & Company advises public and private REITs, non-traded REITs, real estate investment funds and other private owners of real estate and real estate debt in connection with developing and executing strategic transactions.

Important Additional Information

Stratus Properties Inc., its directors and certain of its executive officers may be deemed to be participants in the solicitation of proxies from Stratus stockholders in connection with the matters to be considered at Stratus’ 2016 annual meeting of stockholders. Stratus has filed a preliminary proxy statement with the U.S. Securities and Exchange Commission (the “SEC”), and intends to file a definitive proxy statement and white proxy card with the SEC, in connection with any such solicitation of proxies from Stratus stockholders. STRATUS STOCKHOLDERS ARE STRONGLY ENCOURAGED TO READ ANY SUCH DEFINITIVE PROXY STATEMENT AND ACCOMPANYING WHITE PROXY CARD WHEN THEY BECOME AVAILABLE AS THEY WILL CONTAIN IMPORTANT INFORMATION. Information regarding the ownership of Stratus’ directors and executive officers in Stratus stock, restricted stock units and stock options is included in their SEC filings on Forms 3, 4, and 5, which can be found through Stratus’ website (www.stratusproperties.com) under “Investor Relations—SEC Filings” or through the SEC’s website at www.sec.gov. Information can also be found in Stratus’ other SEC filings, including Stratus’ definitive proxy statement for the 2015 annual meeting of stockholders and its Annual Report on Form 10-K for the year ended December 31, 2015. More detailed and updated information regarding the identity of potential participants, and their direct or indirect interests, by security holdings or otherwise, will be set forth in the definitive proxy statement and other materials to be filed with the SEC in connection with Stratus’ 2016 annual meeting of stockholders. Stockholders will be able to obtain any proxy statement, any amendments or supplements to the proxy statement and other documents filed by Stratus with the SEC for no charge at the SEC’s website at www.sec.gov. Copies will also be available at no charge at Stratus’ website at www.stratusproperties.com, by writing to Stratus Properties Inc. at 212 Lavaca Street, Suite 300, Austin, TX 78701, or by calling Stratus’ proxy solicitor, Innisfree M&A Incorporated, toll-free at 888-750-5834.

2

Cautionary Statement Regarding Forward-Looking Statements

This press release contains forward-looking statements in which Stratus discusses factors it believes may affect its future performance. Forward-looking statements are all statements other than statements of historical facts, such as statements regarding the implementation and potential results of Stratus’ five-year plan, projections or expectations related to operational and financial performance or liquidity, reimbursements for infrastructure costs, financing and regulatory matters, development plans and sales of properties, commercial leasing activities, timeframes for development, construction and completion of Stratus’ projects, capital expenditures, liquidity and capital resources, and other plans and objectives of management for future operations and activities. The words “anticipates,” “may,” “can,” “plans,” “believes,” “potential,” “estimates,” “expects,” “projects,” “intends,” “likely,” “will,” “should,” “to be” and any similar expressions and/or statements that are not historical facts are intended to identify those assertions as forward-looking statements.

Stratus cautions readers that forward-looking statements are not guarantees of future performance, and its actual results may differ materially from those anticipated, projected or assumed in the forward-looking statements. Important factors that can cause Stratus’ actual results to differ materially from those anticipated in the forward-looking statements include, but are not limited to, Stratus’ ability to refinance and service its debt and the availability of financing for development projects and other corporate purposes, Stratus’ ability to sell properties at prices its board considers acceptable, a decrease in the demand for real estate in the Austin, Texas market, changes in economic and business conditions, reductions in discretionary spending by consumers and corporations, competition from other real estate developers, hotel operators and/or entertainment venue operators and promoters, business opportunities that may be presented to and/or pursued by Stratus, the termination of sales contracts or letters of intent due to, among other factors, the failure of one or more closing conditions or market changes, the failure to attract customers for its developments or such customers’ failure to satisfy their purchase commitments, increases in interest rates, declines in the market value of its assets, increases in operating costs, including real estate taxes and the cost of construction materials, changes in external perception of the W Austin Hotel, changes in consumer preferences, changes in laws, regulations or the regulatory environment affecting the development of real estate, opposition from special interest groups with respect to development projects, weather-related risks and other factors described in more detail under the heading “Risk Factors” in Stratus’ Annual Report on Form 10-K for the year ended December 31, 2015, filed with the SEC.

Investors are cautioned that many of the assumptions upon which Stratus’ forward-looking statements are based are likely to change after the forward-looking statements are made. Further, Stratus may make changes to its business plans that could affect its results. Stratus cautions investors that it does not intend to update its forward-looking statements notwithstanding any changes in its assumptions, business plans, actual experience, or other changes, and Stratus undertakes no obligation to update any forward-looking statements.

3