Description of Capital Stock

Exhibit 4.1

DESCRIPTION OF CAPITAL STOCK

Authorized Capital Stock

Under the Company’s certificate of formation, the total number of shares of all classes of stock that it has authority to issue is 127,000,000, of which 125,000,000 are shares of common stock, par value $.01 per share, and 2,000,000 are shares of preferred stock, par value $.01 per share.

The following summary describes certain provisions of the Company’s certificate of formation and bylaws relating to its capital stock. This summary is intended as an overview only and is qualified in its entirety by reference to the Company’s certificate of formation and bylaws, the forms of which are included as exhibits to the Current Report on Form 8-K dated April 23, 2018, as well as the applicable provisions of the Texas Business Organizations Code (“TBOC”).

Common Stock

The Company’s certificate of formation authorizes three series of common stock, Series A common stock, Series B common stock, and Series C common stock. The Company’s certificate of formation authorizes the issuance of 125,000,000 shares of common stock, of which 90,000,000 shares are designated as Series A common stock, 30,000,000 shares are designated as Series B common stock, and 5,000,000 shares are undesignated. No shares of Series C common stock have been designated and issued. Under the Company’s certificate of formation, all outstanding shares of Series B common stock will automatically convert into shares of Series A common stock and the Company may not issue any additional shares of Series B common stock if, as a result of the existence or issuance of such stock, the Company’s Series A common stock would be excluded from trading on the NYSE or any other national stock exchange or quotation system. Except for these limitations, our board has the authority to designate the shares of Series C common stock and to increase or decrease the number of shares of such series prior to or after the issuance of shares of that series, but not below the number of shares of such series then outstanding.

Voting Rights

Generally, the issued and outstanding shares of the Company’s Series A common stock and Series B common stock vote together as a single class on matters submitted to a vote of shareholders. Each issued and outstanding share of Series A common stock is entitled to one vote and each issued and outstanding share of Series B common stock is entitled to 10 votes. Class votes by series, however, are required with respect to (1) any amendment to the Company’s certificate of formation that alters or changes the powers, preferences, or special rights of a series of Company common stock that affects the respective series adversely and (2) any other matters that require class votes under the TBOC. Cumulative voting is not permitted in the election of directors or otherwise.

Transfer Restrictions

Series A common stock is freely transferable. Transferability of the shares of Series B common stock, as such, is limited to certain family members of the holder of the Series B common stock, trusts established for the benefit of the holder and his or her family members, certain affiliated entities of the holder, and certain other permitted transferees. If a holder of Series B common stock transfers such stock to a non-permitted transferee, it will automatically convert into Series A common stock.

Shares of Series B common stock may be pledged as collateral security for indebtedness, provided the shares will not be transferred to or registered in the name of the pledgee and remain subject to the transfer restrictions contained in our certificate of formation. In the event of foreclosure or other similar action by a pledgee, the pledged shares of Series B common stock may only be transferred to a permitted transferee under our certificate of formation or such shares will automatically convert into shares of Series A common stock, as the pledgee may elect.

Conversion of Series B Common Stock at the Election of a Holder

Shares of Series B common stock are convertible on a one-for-one basis into Series A common stock at any time, at the holder’s option. If the Company enters into any consolidation or merger in which the holders of Series A common stock are entitled to receive cash, stock, or any other property with respect to or in exchange for Series A common stock (or in the event of a sale of all or substantially all of the Company’s property or business), a holder of Series B common stock will have the right to convert such shares into the kind and amount of cash, stock, or respective properties that a holder of Series A common stock is entitled to receive and will have no other conversion rights regarding such shares.

Automatic Conversion of Series B Common Stock

All outstanding shares of Series B common stock will automatically, without any further act of any person or the Company, convert into shares of Series A common stock on a share-for-share basis if, as a result of the existence of the Series B common stock, the Series A common stock is excluded from trading on the NYSE or any other national exchange or quotation system. All outstanding shares of Series B common stock will also be converted into shares of Series A common stock at the Company’s option (1) if the Company’s board and the holders of a majority of the outstanding shares of Series B common stock approve the conversion of all of the Series B common stock into Series A common stock or (2) if the Company’s board elects to convert the Series B common stock (a) in order to avoid the exclusion of Series A common stock from trading on the NYSE or any other national exchange or quotation system or (b) due to the requirements of federal or state law, in any such case, as a result of the existence of the Series B common stock. Further, if you transfer your shares of Series B common stock to a non-permitted transferee, such shares will automatically convert into shares of Series A common stock.

Dividends

Holders of a series of common stock are entitled to share equally, on a per share basis, in dividends, if any, that may be declared by the Company’s board. The Company’s shareholders are also entitled to share ratably in the net assets available for distribution to them upon liquidation, dissolution, and winding-up.

Dividends must be paid on both the Series A common stock and Series B common stock, at any time that dividends are paid on either. Stock dividends must be paid at the same rate for each series, with dividends payable in shares of Series A common stock payable only to holders of Series A common stock and dividends payable in shares of Series B common stock payable only to holders of Series B common stock.

Preferred Stock

None of the 2,000,000 shares of authorized preferred stock are outstanding. The Company’s certificate of formation authorizes the Company’s board to issue preferred stock in one or more series, to set from time to time the number of shares to be included in each series, and to determine the designations, powers, preferences, and rights of the shares of each series and the qualifications, limitations, or restrictions thereof. Although the ability of the Company’s board to designate and issue shares of preferred stock provides the Company with flexibility regarding the ability to engage in future public offerings to raise additional capital, the issuance of shares of preferred stock may have adverse effects on the holders of Company common stock. The Company would, for example, be restricted in its ability to declare dividends on its common stock if dividends on shares of its preferred stock have not been paid; the voting power of Company common stock would be diluted to the extent the shares of Company preferred stock have voting rights; or, the participation of the holders of Company common stock in the Company’s assets in a liquidation of the Company would be deferred until the satisfaction of any liquidation preference granted to holders of preferred stock. In addition, the issuance of preferred stock could make it more difficult for a third party to acquire a majority of the Company’s outstanding voting stock and, accordingly, may be used as an “anti-takeover” device. The Company’s board, however, currently does not contemplate the issuance of any shares of preferred stock.

No Preemptive Rights

No holder of any Company stock of any class authorized has any preemptive right to subscribe to any Company securities of any kind or class.

Listing

The shares of Company Series A common stock have been authorized for listing on the NYSE under the trading symbol “AHC.”

Transfer Agent

The transfer agent and registrar for Company common stock is Computershare. The contact information for the transfer agent and registrar is:

Computershare

P. O. Box 505000

Louisville, KY 40233

www-uscomputershare.com/investor

Other Provisions of the TBOC, Certificate of Formation and Bylaws that may Affect the Rights of Shareholders

Business Combinations

Certain provisions of the certificate of formation and the bylaws, descriptions of which are summarized herein, may have the effect, either alone or in combination with each other, of discouraging or making more difficult a tender offer or takeover attempt that is opposed by the board but that a shareholder might consider to be in its best interest or otherwise effect the rights of our shareholders more generally. Such provisions may also adversely affect prevailing market prices for our capital stock. We believe that such provisions are necessary to enable us to develop our business in a manner that will foster our long-term growth without disruption caused by the threat of a takeover not deemed by the board to be in our best interests and those of our shareholders.

The TBOC prohibits certain transactions between a Texas corporation and an “affiliated shareholder,” which is broadly defined as a person that is directly or indirectly a beneficial owner of 20% or more of the outstanding voting shares of a Texas corporation or that owned such shares within the prior three years. This provision, which also applies to affiliates and associates of the affiliated shareholder, prohibits certain business combinations with affiliated shareholders for a period of three years following the shareholder’s acquisition of 20% or more of the corporation’s voting shares unless certain exemptions apply. Prohibited business combinations include (i) mergers, share exchanges and conversions of a company or a majority-owned subsidiary, (ii) sales or other dispositions of assets by a company or a majority-owned or controlled subsidiary having an aggregate market value of 10% or more of (a) the aggregate market value of the consolidated assets of a company, (b) the aggregate market value of the outstanding stock of a company or (c) the earning power or net income of a company on a consolidated basis, (iii) certain transactions that would result in the issuance or transfer of shares of a company to an affiliated shareholder, increase the affiliated shareholder’s proportionate share of ownership in a company or grant the affiliated shareholder disproportionate financial benefits, and (iv) liquidation proposals under an agreement or understanding with, or proposed by, an affiliated shareholder.

Exemptions apply if (i) the transaction is approved by a majority of the board of directors and the affirmative vote by holders of two-thirds of the unaffiliated shares at a meeting held no earlier than six months after the affiliated shareholder acquires ownership of 20% or more of the voting shares, (ii) the board of directors approves the transaction or the purchase of shares by the affiliated shareholder before the affiliated shareholder acquires beneficial ownership of 20% or more of the voting shares, or (iii) two-thirds of the unaffiliated shareholders approve an amendment to the certificate of formation or bylaws that elects that the corporation not be covered by the TBOC business combination provisions (such amendment to take effect 18 months thereafter and not to have retroactive effect).

The certificate of formation includes additional restrictions on business combinations that in many ways are more stringent than the business combination provisions in the TBOC. The certificate of formation provisions must be satisfied, in addition to compliance with the statutory provisions of the TBOC, for a business combination with an affiliated shareholder to be permitted.

The certificate of formation prohibits certain transactions between the Company and an affiliated shareholder, which is broadly defined as a person (including certain affiliates and transferees of such person) that is directly or indirectly a beneficial owner of 10% or more of the outstanding voting power of the Company. This provision prohibits certain business combinations between an affiliated shareholder and the Company indefinitely,

unless certain exemptions apply. Prohibited business combinations include (i) mergers or combinations, (ii) sales or other dispositions of assets of the Company or any subsidiary having an aggregate fair market value of $25 million or more, (iii) issuances or transfers of securities of the Company or a subsidiary to the affiliated shareholder for consideration having a fair market value of $25 million or more, (iv) reclassifications, recapitalizations, mergers or consolidations of the Company into any subsidiary, or any other transactions that, in each case, have the effect of increasing the affiliated shareholder’s proportionate share of ownership of any class of equity or convertible securities of the Company, and (v) plans or proposals for liquidation by or on behalf of the affiliated shareholder.

Exemptions include (i) approval of the business combination by at least 80% of the voting power of all the then outstanding shares of stock voting together, each share having the number of votes granted by the certificate of formation, as well as any class vote required by law or the certificate of formation, (ii) approval of the transaction by a majority of the “continuing directors” (directors who are not affiliated with the affiliated shareholder and who were directors prior to the time the affiliated shareholder became such, and successors of continuing directors who are not affiliated with the affiliated shareholder and are recommended by a majority of the continuing directors), and (iii) compliance with certain fair price and fair terms requirements.

The fair price and terms exemption generally requires that (i) the consideration to be received by shareholders be cash or the same form of consideration used by the affiliated shareholder in acquiring shares during the prior two years, (ii) the value of the consideration to be received by shareholders in the business combination be equal to or greater than the highest of several fair price tests, (iii) unless approved by a majority of the continuing directors, there has been no failure to pay preferred stock dividends and no reduction in the annual dividend rate on common stock, and (iv) the affiliated shareholder has not received the benefit (except proportionately as a shareholder) of any loans, guarantees, pledges, or other financial assistance or tax advantages.

Under this provision, a fair price is generally the highest of (i) the highest price paid by the affiliated shareholder for shares of common stock during the preceding two years or in the transaction in which the affiliated shareholder became such, plus the excess of interest thereon, compounded annually at the prime rate, over the amount of dividends paid thereon, (ii) the higher of the fair market value per share of the common stock on the date of public announcement of the business combination or the date the affiliated shareholder became such, (iii) the price in (ii) multiplied by the ratio of the highest price paid by the affiliated shareholder for shares during the two-year period preceding the announcement of the business combination to the fair market value of the stock on the first day in such two-year period on which the affiliated shareholder acquired stock, and (iv) an amount per share equal to the earnings per share of Company common stock for the four full consecutive fiscal quarters preceding the consummation of the business combination multiplied by the then reported price/earnings multiple (if any) of the affiliated shareholder.

Other Mergers, Consolidations, Conversions, Share Exchanges and Sales, Leases, Exchanges or Other Dispositions

Under the TBOC, except for transactions subject to the business combination provisions of the TBOC and other than certain mergers with subsidiaries, generally a merger, including a merger with more than one surviving corporation, an exchange of ownership interests with another entity, a conversion into another form of entity or a sale, lease, exchange or other disposition of all, or substantially all, of the property and assets of a Texas corporation, if not made in the usual and regular course of its business, requires the approval of the holders of at least two-thirds of all the outstanding shares of the corporation entitled to vote thereon, and the approval of the holders of two-thirds of the outstanding shares of each class or series of shares entitled to vote as a class or series thereon. A parent corporation may merge with a 90% or more-owned subsidiary, and no vote of the shareholders of the parent corporation is generally required if the parent corporation is the survivor in the merger. A conversion may not convert a share of a corporation into an interest in another entity that does not provide limited liability to its interest owners without the shareholder’s consent. Under the TBOC, the transfer of substantially all of a corporation’s assets in such a manner that the corporation continues to engage, directly or indirectly, in one or more businesses after the sale, or applies a portion of the proceeds of sale to the conduct of such business or businesses, is not a sale of all or substantially all of the assets of such corporation. The certificate of formation requires the approval of such transactions by the holders of shares that possess at least two-thirds of the voting power of all the outstanding voting shares of the corporation entitled to vote thereon.

Certificate of Formation Amendments

Under the TBOC, an amendment to the certificate of formation requires the approval of the holders of at least two-thirds of the outstanding shares of the corporation entitled to vote thereon, and the approval of the holders of two-thirds of the outstanding shares of each class or series of shares entitled to vote as a class or series thereon, unless a different amount, not less than a majority, is specified in the certificate of formation.

Under the certificate of formation, amendments to Article Nine (regarding authority of the board to amend the bylaws) and Article Ten (regarding certain extraordinary transactions) require approval of the holders of at least two-thirds of the voting power of the outstanding shares of the Company then entitled to vote thereon, voting as a single class. Amendments to Article Eleven (regarding Business Combinations) require approval of the holders of at least 80% of the voting power of the outstanding shares of the Company then entitled to vote thereon, voting as a single class. All other amendments to the certificate of formation require approval of the holders of at least a majority of the voting power of the Company’s outstanding stock entitled to vote thereon.

Bylaw Amendments

Under the TBOC, the board of directors may amend, repeal or adopt a corporation’s bylaws unless the certificate of formation or the TBOC wholly or partly reserves this power exclusively to the shareholders, or the shareholders in amending, repealing or adopting a particular bylaw expressly provide that the board of directors may not amend, repeal or readopt that bylaw.

The certificate of formation and bylaws provide that the bylaws may be amended, repealed, altered or adopted by the shareholders by the affirmative vote of the holders of at least two-thirds of the voting power of the outstanding shares of the Company then entitled to vote on such matter, voting as a single class, or by the board of directors.

Right to Call Meetings; Shareholder Proposals and Director Nominations

The certificate of formation provides that special shareholder meetings may be called by the holders of not less than 50% of all of the shares entitled to vote at the proposed meeting or by the other persons or holders authorized to call special shareholder meetings by the bylaws.

The bylaws provide that special meetings may be called only by the Chief Executive Officer, by a majority of the total number of directors on the board of directors if there were no vacancies, or by the request of holders of record of not less than one-fifth of the voting power of all shares entitled to vote at the meeting (a “Special Meeting Request”). If the Special Meeting Request is in proper form, the Secretary will call a special meeting of shareholders within 120 days of the request. To be in proper form, a Special Meeting Request must meet the criteria set forth in the bylaws, including the furnishing of written information similar to that required for shareholder proposals as summarized below, and an agreement to provide notice of dispositions of shares prior to the record date of the meeting (which could result in a cancellation of the special meeting if the one-fifth requirement is no longer met).

The bylaws also include provisions as to the requirements for shareholder proposals at annual meetings and director nominations. The Chief Executive Officer, the board or directors and any shareholder who is entitled to vote at the meeting and is a shareholder of record both at the time of a proposal or nomination and at the time of the meeting, may bring a matter before the meeting or submit a director nomination if such shareholder complies with the notice procedures set forth in the bylaws. These generally include: timely delivery of the proposal or nomination and furnishing of written information about the proposal or nominee (including a nominee questionnaire); identification of the shareholder or nominee and the shareholder’s or nominee’s holdings or short positions in the Company’s securities and in derivatives and other securities related to the Company; disclosure of any arrangements that involve voting or indicate a direct or indirect financial or other interest in the matter to be voted on, the Company or its competitors; disclosure of relationships between the shareholder and such nominee; disclosure of any litigation involving such shareholder or nominee relating to the Company and recent transactions with the Company or its competitors; disclosure of discussions of matters proposed to be brought before the meeting with other shareholders; a statement as to whether the shareholder intends to engage in a solicitation with respect to matters proposed to be brought before the meeting and whether the shareholder intends to deliver a proxy statement or form of proxy to shareholders; and furnishing of any other information required to be disclosed in a proxy statement relating to such proposal or nomination and certain other specified information.

Quorum and Voting at Shareholders Meetings

The certificate of formation and bylaws provide that a majority of the voting power of all shares entitled to vote that are present or represented at the meeting is a quorum, but in no event shall a quorum consist of the holders of less than one-third (1/3) of the shares entitled to vote and represented at such meeting. The TBOC and the certificate of formation provide for specified votes for certain actions as described elsewhere in this summary. The bylaws provide that, other than with respect to the election of directors, the act of a shareholders meeting is the vote of a majority of the voting power of shares entitled to vote on the matter and present or represented at the meeting if a quorum is present, unless the vote of a greater number is required by law or the certificate of formation.

Election of Directors

The bylaws provide that directors are elected by a plurality of the votes cast by shareholders entitled to vote in the election of directors present or represented at the meeting at which a quorum is present.

Removal of Directors

The bylaws provide that a director may be removed only for cause and by a majority of the voting power of all the shares then entitled to be voted in the election of directors.

Forum Selection

The bylaws contain a provision which provides that, unless the Company consents in writing to an alternate forum, the exclusive forum for (i) derivative actions by or in the right of the Company, (ii) actions asserting a claim for breach of fiduciary duty owed to the Company or its shareholders by any director, officer or employee of the Company, (iii) actions asserting a claim arising pursuant to a provision of the TBOC or certificate of formation or bylaws, (iv) actions to interpret, apply, enforce or determine the validity of the certificate of formation or bylaws, or (v) actions asserting a claim governed by the internal affairs doctrine, is the state district courts of Dallas County, Texas, or, if they do not have jurisdiction, the United States District Court for the Northern District of Texas, Dallas Division.

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The foregoing description of the Company’s capital stock does not purport to be complete and is qualified in its entirety by reference to the certificate of formation and the bylaws, copies of which are filed as exhibits to the Company’s Current Report on Form 8-K filed on April 23, 2018, and which are hereby incorporated by reference, as well as to the relevant provisions of Texas law, including the TBOC.