STOCK PURCHASE AGREEMENT

Exhibit 1.2

STOCK PURCHASE AGREEMENT

This STOCK PURCHASE AGREEMENT (this “Agreement”) is dated as of November 4, 2013, by and among PS Business Parks, Inc., a California corporation (the “Issuer”), and Public Storage, a Maryland real estate investment trust (the “Purchaser”).

W I T N E S S E T H:

WHEREAS, the Issuer has informed the Purchaser that it intends, subject to favorable market conditions and the satisfaction of the terms and conditions which shall be set forth in an underwriting agreement (the “Underwriting Agreement”) substantially in the form attached hereto as Annex I, with the underwriter to be named therein (the “Underwriter”), to make an offering to the public (the “Offering”) of up to 1,495,000 shares (the “Shares”) of common stock, par value $0.01 per share, of the Issuer (the “Common Stock”), consisting of an offering of 1,300,000 Shares together with an overallotment option of 195,000 Shares (the “Overallotment Option”), at a price to be mutually agreed between the Issuer and the Underwriter (the “Offering Price”); and

WHEREAS, subject to the consummation of the Issuer’s agreement to issue and sell the Shares to the Underwriter upon the satisfaction of the terms and conditions set forth in the Underwriting Agreement, the Purchaser desires to purchase up to 950,000 shares of Common Stock (the “Subject Shares”), at the Offering Price and the Issuer desires to issue and sell such shares to the Purchaser;

WHEREAS, if the size of the Offering is increased or decreased, the number of Shares to be acquired by the Purchaser will be increased or decreased proportionately so that Public Storage acquires 38.85% of the aggregate total shares sold in the Offering and to Public Storage;

NOW THEREFORE, in consideration of the premises and of the mutual agreements, covenants and provisions herein contained and for good and valuable consideration, the receipt of which is hereby acknowledged, the parties hereto agree as follows:

ARTICLE I

PURCHASE AND SALE

1.1 Purchase and Sale of Subject Shares. Subject to (a) the terms and conditions set forth in this Agreement and (b) the consummation of the Issuer’s agreement to issue and sell the Shares to the Underwriter upon the satisfaction of the terms and conditions set forth in the Underwriting Agreement (the “Offering Closing”), the Issuer agrees to issue the Subject Shares, and the Purchaser agrees to purchase the Subject Shares for $79.25 per share (the “Subject Shares Purchase Price”); provided that if the size of the Offering is increased or decreased, the number of Shares to be acquired by the Purchaser will be increased or decreased proportionately so that Public Storage acquires 38.85% of the aggregate total shares of Common Stock sold in the Offering and to Public Storage.

1.2 Closing. Subject to the terms and conditions of this Agreement and the occurrence of the Closing, the closing of the purchase and sale of the Subject Shares (the “Closing”) shall take place on the date of the Offering Closing at the offices of the Issuer or at such other place as the applicable parties to such closing shall agree in writing.

1.3 Delivery at Closing. At the Closing, (a) the Purchaser shall deliver to the Issuer the Subject Shares Purchase Price by wire transfer of immediately available funds to an account designated by the Issuer in writing by 10:00 a.m., and (b) the Issuer shall deliver certificates representing the Subject Shares to the Purchaser.

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ARTICLE II

REPRESENTATIONS AND WARRANTIES OF THE ISSUER

The Issuer represents and warrants to the Purchaser as follows:

2.1 Formation and Good Standing. The Issuer is a corporation duly incorporated, validly existing and in good standing under the jurisdiction and laws of the State of California.

2.2 Authorization and Validity of Agreements. The Issuer has all requisite power and authority to execute and deliver this Agreement, to perform its obligations hereunder and to consummate the transactions contemplated hereby. The execution and delivery of this Agreement, the performance by the Issuer of its obligations hereunder and the consummation of the transactions contemplated hereby have been duly authorized by all requisite corporate action of the Issuer. This Agreement constitutes a legal, valid and binding obligation of the Issuer, enforceable against the Issuer in accordance with its respective terms.

2.3 No Conflicts; Consents. The execution, delivery and performance of this Agreement by the Issuer and the consummation by the Issuer of the transactions contemplated hereby do not and will not conflict with, contravene, result in a violation or breach of or default under (with or without the giving of notice or the lapse of time, or both), permit any party to terminate, amend or accelerate the provisions of, or result in the imposition of any claim, lien, pledge, deed of trust, option, charge, security interest, hypothecation, encumbrance, right of first offer, voting trust, proxy, right of third parties or other restriction or limitation of any nature whatsoever (each, a “Lien”), or any obligation to create any Lien, upon any of the property or assets of the Issuer under (a) any contract, agreement, indenture, letter of credit, mortgage, security agreement, pledge agreement, deed of trust, bond, note, guarantee, surety obligation, warranty, license, franchise, permit, power of attorney, lease, instrument or other agreement (each, a “Contract”) to which the Issuer is a party or by which any of its property or assets may be bound or (b) any provision of the organizational document of the Issuer.

ARTICLE III

REPRESENTATIONS AND WARRANTIES OF THE PURCHASER

The Purchaser represents and warrants to the Issuer as follows:

3.1 Formation and Good Standing. The Purchaser is a real estate investment trust duly organized, validly existing and in good standing under the jurisdiction and laws of the State of Maryland.

3.2 Authorization and Validity of Agreements. The Purchaser has all requisite power and authority to execute and deliver this Agreement, to perform its obligations hereunder and to consummate the transactions contemplated hereby. The execution and delivery of this Agreement, the performance by the Purchaser of its obligations hereunder and the consummation of the transactions contemplated hereby have been duly authorized by all requisite corporate action of the Purchaser. This Agreement constitutes a legal, valid and binding obligation of the Purchaser, enforceable against the Purchaser in accordance with its respective terms.

3.3 No Conflicts; Consents. The execution, delivery and performance of this Agreement by the Purchaser and the consummation by the Purchaser of the transactions contemplated hereby do not and will not conflict with, contravene, result in a violation or breach of or default under (with or without the giving of notice or the lapse of time, or both), permit any party to terminate, amend or accelerate the provisions of, or result in the imposition of any Lien (or any obligation to create any Lien) upon any of the property or assets of the Purchaser under (a) any Contract to which the Purchaser is a party or by which any of its property or assets may be bound or (b) any provision of the organizational document of the Purchaser.

3.4 Investment Purpose; Accredited Purchaser; Access to Information.

(a) The Purchaser hereby acknowledges that the Subject Shares have not been registered under the Securities Act of 1933, as amended (the “Securities Act”), and may not be offered or sold except pursuant to registration or to an exemption from the registration requirements of the Securities Act and that the certificates evidencing the Subject Shares will bear a legend to that effect. The Subject Shares to be acquired by the Purchaser pursuant to this Agreement are being acquired for its own account and with no intention of distributing or reselling the Subject Shares or any part thereof in any transaction that would be in violation of

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the securities laws of the United States, any state of the United States or any foreign jurisdiction. The Purchaser further agrees that it has not entered and prior to the Closing will not enter into any Contract with respect to the distribution, sale, transfer or delivery of the Subject Shares.

(b) The Purchaser is an “accredited investor” as such term is defined in Section 2(15) of the Securities Act and within the meaning of Rule 501 of Regulation D under the Securities Act, as presently in effect.

(c) The Purchaser is sufficiently experienced in financial and business matters to be capable of evaluating the merits and risks involved in purchasing the Subject Shares and to make an informed decision relating thereto. The Purchaser has been furnished with the materials relating to the business, operations, financial condition, assets, liabilities of the Issuer and other matters relevant to the Purchaser’s investment in the Subject Shares, which have been requested by the Purchaser. The Purchaser has had adequate opportunity to ask questions of, and receive answers from, the officers, employees, agents, accountants, and representatives of the Issuer concerning the business, operations, financial condition, assets, liabilities of the Issuer and all other matters relevant to its investment in the Subject Shares.

ARTICLE IV

COVENANTS

4.1 No Purchases in Offering. The Purchaser agrees that purchases hereunder are in lieu of participating in the Offering. The Purchaser further agrees not to purchase Shares directly or indirectly in the Offering.

4.2 Further Assurances. Each party hereto shall execute and deliver such instruments and take such other actions prior to or after the Closing as any other party may reasonably request in order to carry out the intent of this Agreement, including without limitation obtaining any required consents or approvals from third parties.

ARTICLE V

CONDITIONS PRECEDENT TO THE OBLIGATIONS

5.1 Mutual Conditions. The obligations of the Issuer and the Purchaser to consummate the purchase and sale of the Subject Shares contemplated hereby are subject to the following conditions: (a) the occurrence of the Offering Closing, (b) the absence of any order, decree, judgment or injunction of a court of competent jurisdiction or other governmental or regulatory authority precluding the consummation of the purchase and sale of the Subject Shares contemplated hereby, and (c) there shall not have been any action taken or any statute, rule or regulation enacted, promulgated or deemed applicable to, the purchase and sale of the Subject Shares contemplated hereby by any court, governmental agency or regulatory or administrative authority that makes consummation of such transactions illegal.

5.2 Conditions to the Obligations of the Issuer. The obligations of the Issuer under this Agreement to consummate the issuance and sale of the Subject Shares contemplated hereby are subject to the fulfillment (or waiver by the Issuer) of the conditions that (a) the representations and warranties of the Purchaser contained in or made pursuant to this Agreement shall be deemed to have been made again at and as of the Closing and shall then be true and accurate, and (b) the Purchaser shall have performed and complied in all material respects with all agreements required by this Agreement to be performed or complied with by it prior to or at the Closing.

5.3 Conditions to the Obligations of the Purchaser. The obligations of the Purchaser under this Agreement to consummate the purchase and sale of the Subject Shares contemplated hereby are subject to the fulfillment (or waiver in writing by the Purchaser) of the condition that (a) all representations and warranties of the Issuer shall be deemed to have been made again at and as of the Closing and shall then be true and accurate, and (b) the Issuer shall have performed and complied in all material respects with all agreements required by this Agreement to be performed or complied with by it prior to or at the Closing.

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ARTICLE VI

MISCELLANEOUS

6.1 Termination. This Agreement shall be terminated prior to the consummation of the transactions contemplated hereby if, prior to the consummation of the Offering Closing, the Underwriting Agreement is terminated pursuant to its terms. In the event of any termination of this Agreement, this Agreement shall become void and have no effect, without any liability to any person in respect hereof on the part of any party hereto, except for any liability resulting from such party’s breach of this Agreement prior to such termination.

6.2 Survival. Each of the representations and warranties contained in this Agreement shall survive indefinitely. Each of the covenants contained in this Agreement shall survive the Closing until performed in accordance with their terms.

6.3 Amendments; Waivers. The provisions of this Agreement may not be amended or modified except by a writing signed by each of the parties. No waiver of any term or condition hereof or obligation hereunder shall be valid unless made in writing and signed by the party to which performance is due.

6.4 Severability of Provisions. Each provision of this Agreement shall be considered severable and if for any reason any provision or provisions herein are determined to be invalid, unenforceable or illegal under any existing or future law, such invalidity, unenforceability or illegality shall not impair the operation of or affect those portions of this Agreement which are valid, enforceable and legal.

6.5 Governing Law. This Agreement shall be governed by and construed in accordance with the laws of the State of New York, without giving effect to any conflict of laws principles thereof that would cause the application of the laws of another jurisdiction.

6.6 Waiver of Trial By Jury. TO THE EXTENT PERMITTED BY APPLICABLE LAW, EACH PARTY HERETO IRREVOCABLY WAIVES ALL RIGHT OF TRIAL BY JURY IN ANY ACTION, PROCEEDING OR COUNTERCLAIM, ARISING OUT OF OR IN CONNECTION WITH THIS AGREEMENT OR ANY MATTER ARISING HEREUNDER.

6.7 Remedies and Waivers. No delay or omission on the part of any Party to this Agreement in exercising any right, power or remedy provided by law or under this agreement shall (i) impair such right, power or remedy; or (ii) operate as a waiver thereof. The single or partial exercise of any right, power or remedy provided by law or under this Agreement shall not preclude any other or further exercise of any other right, power or remedy. The rights, powers and remedies provided in this Agreement are cumulative and not exclusive of any rights, powers and remedies provided by law.

6.8 Notices. All notices, requests, demands, waivers and other communications to be given by either party hereunder shall be in writing and shall be (i) mailed by first-class, registered or certified mail, postage prepaid, (ii) sent by hand delivery or reputable overnight delivery service or (iii) transmitted by fax (provided that a copy is also sent by reputable overnight delivery service) addressed to the Secretary of the Issuer or the Secretary of the Purchaser, as applicable, in each case at 701 Western Avenue, Glendale, California 91201, or such other address as may be specified in writing to the other party hereto. All such notices, requests, demands, waivers and other communications shall be deemed to have been given and received (i) if by personal delivery or fax, on the day of such delivery, (ii) if by first-class, registered or certified mail, on the fifth business day after the mailing thereof, or (iii) if by reputable overnight delivery service, on the day delivered.

6.9 Execution in Counterparts. This Agreement may be executed in any number of counterparts, each of which shall be deemed an original, but all such counterparts shall together constitute but one and the same instrument.

6.10 Headings. The Article and Section headings contained herein are for the convenience of the parties only and shall not affect the construction or interpretation of this Agreement.

6.11 Entire Agreement. This Agreement, including the Exhibits hereto, contains the entire understanding of the parties with respect to the subject matter hereof, and supersedes all prior agreements and understandings, both written and oral, among the parties with respect to the subject matter hereof.

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IN WITNESS WHEREOF, the parties have executed and delivered this Agreement as of the date first written above.

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Annex I

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