Exhibit 99.1

Stratus Properties Inc. Highlights Strong Performance Implementing Five-Year Strategic Plan to Maximize Value For All Stockholders

Management’s Local Market Expertise Critical to Continued Successful Execution of Plan

AUSTIN, TX, April 15, 2016 – Stratus Properties Inc. (NASDAQ: STRS) (the “Company” or “Stratus”) today issued a letter from its Board of Directors (the “Board”) to its stockholders. The letter highlights the Company’s progress on its five-year strategic plan and outlines the many accomplishments of the Company’s experienced and dedicated management team. The letter follows:

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Dear Fellow Stratus Stockholders:

Our five-year plan, unanimously approved by your Board last year, is simple and clear: the Company will strategically complete development of its properties with the goal of selling assets at the right time to maximize value for all stockholders over a five-year period. Upon completion of that plan, the Company will distribute to stockholders the cumulative cash from sales proceeds. That plan already has yielded several accretive transactions that we believe have unlocked significant value for stockholders. That success is reflected in the significant increase in the pre-tax net asset value (“NAV”) of the Company’s assets and the continued outperformance of the Company’s stock compared to peers, with a 48% rise in stock price during 2015.

We are encouraged by this early progress on the plan. We own a diverse and high-quality asset base, rich with cash flow and development opportunities. Following the Company’s recent transaction that resulted in its full ownership and long-term refinancing of the W Austin Hotel and Residences, the continuing success of the Company’s grocery-anchored retail development program, the completion of regional infrastructure for Barton Creek Section N, and the addition of two highly-qualified directors to the Board, your Board made the decision to authorize management to explore a full range of strategic alternatives for Stratus. In connection with this effort, Stratus has engaged Hentschel & Company, an investment banking advisory firm focused on the real estate industry, as financial advisor. We believe this decision is a prudent measure to facilitate the Company’s five-year plan and enhance future stockholder value.

Protect the value of your Stratus investment. Please support your Company’s highly qualified nominees by voting FOR ALL on the enclosed WHITE proxy card today by telephone, over the Internet, or by signing, dating and returning the WHITE proxy card in the postage-paid envelope provided.

COMMITTED TO DELIVERING THE HIGHEST VALUE TO ALL STRATUS STOCKHOLDERS

While the successful execution of the Company’s five-year plan remains underway, the Board is committed to continuing to assess all opportunities to maximize value for all stockholders.

However, an insurgent stockholder, Carl Berg, is seeking to completely derail this momentum and remove the Chairman, President and CEO of Stratus, William H. “Beau” Armstrong III, and another highly qualified and

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proven director, Charles W. Porter, from the Board. Mr. Berg’s “plan” is to replace Mr. Armstrong and Mr. Porter with two, hand-picked nominees – Mr. David M. Dean and Mr. Michael L. Knapp – who, according to Mr. Berg’s disclosures, have little or no experience as directors of public companies or with the development of real estate in Austin.

Mr. Berg wants to do this even though Mr. Armstrong is responsible for leading the day to day operations of the Company and is the very executive whose extensive experience, relationships and regulatory knowledge of the real estate industry in Austin have been vital to the Company’s successes to date. The second director Mr. Berg seeks to replace, Mr. Porter, has made significant contributions to the Company as a director since 2012 and has over thirty years of experience in the real estate and hospitality industries.

Finally, Mr. Berg also advocates a “prompt” sale of all or substantially all of the Company’s assets. We believe that a “fire sale” is not in the best interests of all stockholders. Your Board, however, remains committed to exploring all opportunities through a comprehensive and methodical process. This is exactly why we engaged an investment banking firm to assist us in exploring a full range of strategic alternatives – a process we believe will yield enhanced value to our stockholders.

Since your Board adopted the five-year plan, we completed the sale of the Parkside Village and 5700 Slaughter commercial properties, both located in the Circle C community, for $32.5 million and $12.5 million, respectively, generating gains of $20.7 million. The net cash proceeds from the sales of $14.3 million exceeded these properties’ NAV, as of December 31, 2014, by approximately 33%.

Importantly, recent actions further demonstrate the Company’s ability to add additional value to its properties through planning, development and completion. Last year, the Company completed the entitlement, engineering, and construction of regional road and utility infrastructure for Barton Creek Section N, enabling the construction of The Santal, the initial 236 unit phase of the Company’s 1,860 unit multi-family portfolio, to proceed on schedule, and positioning the remaining multi-family, as well as the 1.5 million feet of office and retail components, for build-out and sale.

Additionally, we have increased cash flow following the acquisition of our former partner’s interest in the W Austin Hotel & Residences property in 2015, which was subsequently refinanced at a lower fixed interest rate with an extended loan maturity. We maintain $8 million in net investment and expect to continue to generate more than $5 million in cash flow annually from this property.

These actions demonstrate the value of management’s development efforts, market expertise and the effectiveness of our five-year plan. While we continue to create value in our other assets, which are supported by strong demand for properties in the Austin area, the Board remains open to all options for value creation. Our recently announced review of strategic alternatives will include the evaluation of additional asset development, stock purchase or asset sale opportunities, taking into consideration the various stages of completion of each property as well as a potential sale of the entire Company, among other opportunities.

THE RIGHT TEAM TO MAXIMIZE VALUE FOR ALL STRATUS STOCKHOLDERS

Stratus management’s experience and strong market knowledge have been key components of the significant value creation to date and are critical to the successful execution of any plan to maximize stockholder value. The current Board and management team, led by Mr. Armstrong, have transformed the Company since Mr. Armstrong was appointed to the Board in 1998. Relying on their local market expertise and established relationships, management resolved the complex and contentious entitlement, regulatory and utility issues that, historically, had burdened Stratus’ assets. Stratus is performing well compared to its peers. Cumulative total stockholder return on our common stock over the five years ending December 31, 2015 of 124% exceeded comparable returns for the S&P 500 Stock Index of 81%, the Dow Jones U.S. Real Estate Index of 67% and a group of real estate related companies including Alexander & Baldwin, Inc., Consolidated-Tomoka Land Co., Forestar Group Inc., The Howard Hughes Corporation, Maui Land & Pineapple Company, Inc., The St. Joe Company and Tejon Ranch Co. of 31%, as set forth in our 2015 annual report.

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The core strength of Stratus lies in management’s long-term understanding of the Austin area and its key relationships with the State of Texas, the City of Austin, regulators, environmental and community stakeholder groups, utility districts, tenants, lenders and construction companies. This knowledge is critical for navigating the Austin area’s complex and extensive city, county and state rules and regulations regarding zoning, permitting, utilities and water quality, as well as related federal rules and regulations. By contrast, Mr. Berg wants to remove Mr. Armstrong from the Board and has proposed director nominees with minimal, if any, experience in the Austin market.

The continued success of Stratus is dependent on Mr. Armstrong’s skills and relationships in order to complete the final stages of orderly development and marketing of our properties. With the support of a leading investment banking advisory firm in the real estate industry, management and the Board are prepared to continue to guide the Company to deliver enhanced value to all of our stockholders.

YOUR VOTE IS A VOTE TO MAXIMIZE THE VALUE OF STRATUS PROPERTIES INC.

The highly qualified Stratus director nominees, Mr. Armstrong and Mr. Porter, are committed to acting in your best interest and have a proven track record. The Board is executing a successful strategy and remains open to evaluating all opportunities for value creation through a comprehensive and methodical process – not a “fire sale” liquidation. The Board needs your support to continue to maximize the value of Stratus for the benefit of all stockholders.

YOUR VOTE IS IMPORTANT NO MATTER HOW MANY SHARES YOU OWN – MAKE YOUR VOICE HEARD

PLEASE VOTE THE WHITE PROXY CARD TODAY

Your vote is critical to ensure that Stratus’ five-year plan and review of strategic alternatives are successfully completed. Whether or not you plan to attend Stratus’ Annual Meeting, you have the opportunity to protect your investment by voting the WHITE proxy card TODAY. The Company urges you to vote today by telephone, over the Internet, or by signing, dating and returning the enclosed WHITE proxy card in the postage-paid envelope provided.

We invite you to join us in pursuing the value we can build in our properties. Thank you for your support.

Sincerely,

The Board of Directors of Stratus Properties Inc.

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Important Additional Information

Stratus Properties Inc., its directors and certain of its executive officers are participants in the solicitation of proxies from Stratus stockholders in connection with the matters to be considered at Stratus’ 2016 Annual Meeting. Stratus has filed its definitive proxy statement and form of WHITE proxy card with the U.S. Securities and Exchange Commission (the “SEC”) on April 15, 2016 in connection with any such solicitation of proxies from Stratus stockholders. STRATUS STOCKHOLDERS ARE STRONGLY ENCOURAGED TO READ SUCH PROXY STATEMENT, ACCOMPANYING WHITE PROXY CARD (INCLUDING ANY AMENDMENTS AND SUPPLEMENTS THERETO) AND ALL OTHER DOCUMENTS FILED WITH THE SEC CAREFULLY AND IN THEIR ENTIRETY 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) in the section “Investor Relations” 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 2016 Annual Meeting 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, is set forth in the definitive proxy statement and other materials to be filed with the SEC in connection with Stratus’ 2016 Annual Meeting. 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.

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.

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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.

This press release also includes measures of estimated pre-tax net asset value (“NAV”), which are not recognized under U.S. generally accepted accounting principles (“GAAP”). We do not believe there is a directly comparable GAAP measure to NAV. We believe this measure can be helpful to investors in evaluating our business because NAV illustrates current embedded value in our real estate, which is carried on our GAAP balance sheet primarily at cost. Our management uses NAV as one of the metrics in evaluating progress on our five-year plan. NAV is not intended to be a performance measure that should be regarded as more meaningful than GAAP measures. Other companies may calculate this measure differently. For a discussion of NAV, including how our NAV is calculated, please see the Investor Presentation dated March 15, 2016, including the “Cautionary Statement,” available on our website at www.stratusproperties.com.

About Stratus Properties Inc.

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.

Contact:

Media: The Abernathy MacGregor Group

Sydney Isaacs, 713-343-0427

Investors: Innisfree

Scott Winter/Larry Miller, 212-750-5833

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