SUB-INVESTMENT ADVISORY AGREEMENT

Exhibit (g)(3)

SUB-INVESTMENT ADVISORY AGREEMENT

AGREEMENT dated June 10, 2013, among BlackRock Multi-Sector Income Trust, a Delaware statutory trust (the “Trust”), BlackRock Advisors, LLC, a Delaware limited liability company (the “Advisor”), and BlackRock (Singapore) Limited, a Singapore limited company (the “Sub-Advisor”).

WHEREAS, the Advisor has agreed to furnish investment advisory services to the Trust, a closed-end management investment company registered under the Investment Company Act of 1940, as amended (the “1940 Act”);

WHEREAS, the Advisor wishes to retain the Sub-Advisor to provide it with certain sub-advisory services as described below in connection with Advisor’s advisory activities on behalf of the Trust;

WHEREAS, the investment management agreement between the Advisor and the Trust, dated February 25, 2013 (such agreement or the most recent successor agreement between such parties relating to advisory services to the Trust is referred to herein as the “Advisory Agreement”), contemplates that the Advisor may appoint a sub-adviser to perform investment advisory services with respect to the Trust; and

WHEREAS, this Agreement has been approved in accordance with the provisions of the 1940 Act, and the Sub-Advisor is willing to furnish such services upon the terms and conditions herein set forth;

NOW, THEREFORE, in consideration of the mutual premises and covenants herein contained and other good and valuable consideration, the receipt of which is hereby acknowledged, it is agreed by and between the parties hereto as follows:

1.    Appointment. The Advisor hereby appoints the Sub-Advisor to act as sub-advisor with respect to the Trust and the Sub-Advisor accepts such appointment and agrees to render the services herein set forth for the compensation herein provided.

2.    Services of the Sub-Advisor. Subject to the succeeding provisions of this section, the oversight and supervision of the Advisor and the direction and control of the Board of Trustees of the Trust, the Sub-Advisor will perform certain of the day-to-day operations of the Trust, which may include one or more of the following services, at the request of the Advisor: (a) acting as investment advisor for and managing the investment and reinvestment of those assets of the Trust as the Advisor may from time to time request and in connection therewith have complete discretion in purchasing and selling such securities and other assets for the Trust and in voting, exercising consents and exercising all other rights appertaining to such securities and other assets on behalf of the Trust; (b) arranging, subject to the provisions of paragraph 3 hereof, for the purchase and sale of securities and other assets of the Trust; (c) providing investment research and credit analysis concerning the Trust’s investments, (d) assist the Advisor in determining what portion of the Trust’s assets will be invested in cash, cash equivalents and money market instruments, (e) placing orders for all purchases and sales of such investments made for the Trust, and (f) maintaining the books and records as are required to support the

Trust’s investment operations. At the request of the Advisor, the Sub-Advisor will also, subject to the oversight and supervision of the Advisor and the direction and control of the Board of Trustees of the Trust, provide to the Advisor or the Trust any of the facilities and equipment and perform any of the services described in Section 3 of the Advisory Agreement. In addition, the Sub-Advisor will keep the Trust and the Advisor informed of developments materially affecting the Trust and shall, on its own initiative, furnish to the Trust from time to time whatever information the Sub-Advisor believes appropriate for this purpose. The Sub-Advisor will periodically communicate to the Advisor, at such times as the Advisor may direct, information concerning the purchase and sale of securities for the Trust, including: (a) the name of the issuer, (b) the amount of the purchase or sale, (c) the name of the broker or dealer, if any, through which the purchase or sale is effected, (d) the CUSIP number of the instrument, if any, and (e) such other information as the Advisor may reasonably require for purposes of fulfilling its obligations to the Trust under the Advisory Agreement. The Sub-Advisor will provide the services rendered by it under this Agreement in accordance with the Trust’s investment objectives, policies and restrictions (as currently in effect and as they may be amended or supplemented from time to time) as stated in the Trust’s Prospectus and Statement of Additional Information and the resolutions of the Trust’s Board of Trustees.

3.    Covenants. (a) In the performance of its duties under this Agreement, the Sub-Advisor shall at all times conform to, and act in accordance with, any requirements imposed by: (i) the provisions of the 1940 Act and the Investment Advisers Act of 1940, as amended (the “Advisers Act”), and all applicable Rules and Regulations of the Securities and Exchange Commission (the “SEC”); (ii) any other applicable provision of law; (iii) the provisions of the Agreement and Declaration of Trust and By-Laws of the Trust, as such documents are amended from time to time; (iv) the investment objectives and policies of the Trust as set forth in its Registration Statement on Form N-2; and (v) any policies and determinations of the Board of Trustees of the Trust.

(b)    In addition, the Sub-Advisor will:

(i)    place orders either directly with the issuer or with any broker or dealer. Subject to the other provisions of this paragraph, in placing orders with brokers and dealers, the Sub-Advisor will attempt to obtain the best price and the most favorable execution of its orders. In placing orders, the Sub-Advisor will consider the experience and skill of the firm’s securities traders as well as the firm’s financial responsibility and administrative efficiency. Consistent with this obligation, the Sub-Advisor may select brokers on the basis of the research, statistical and pricing services they provide to the Trust and other clients of the Advisor or the Sub-Advisor. Information and research received from such brokers will be in addition to, and not in lieu of, the services required to be performed by the Sub-Advisor hereunder. A commission paid to such brokers may be higher than that which another qualified broker would have charged for effecting the same transaction, provided that the Sub-Advisor determines in good faith that such commission is reasonable in terms either of the transaction or the overall responsibility of the Advisor and the Sub-Advisor to the Trust and their other clients and that the total commissions paid by the Trust will be reasonable in relation to the benefits to the Trust over the long-term. In no instance, however, will the Trust’s securities be purchased from or sold to the Advisor, the Sub-Advisor or any affiliated person thereof,

except to the extent permitted by the SEC or by applicable law. Subject to the foregoing and the provisions of the 1940 Act, the Securities Exchange Act of 1934, as amended, and other applicable provisions of law, the Sub-Advisor may select brokers and dealers with which it or the Trust is affiliated;

(ii)    maintain books and records with respect to the Trust’s securities transactions and will render to the Advisor and the Trust’s Board of Trustees, such periodic and special reports as they may request;

(iii)    maintain a policy and practice of conducting its investment advisory services hereunder independently of the commercial banking operations of its affiliates. When the Sub-Advisor makes investment recommendations for the Trust, its investment advisory personnel will not inquire or take into consideration whether the issuer of securities proposed for purchase or sale for the Trust’s accounts are customers of the commercial department of its affiliates; and

(iv)    treat confidentially and as proprietary information of the Trust all records and other information relative to the Trust, and the Trust’s prior, current or potential shareholders, and will not use such records and information for any purpose other than performance of its responsibilities and duties hereunder, except after prior notification to and approval in writing by the Trust which approval shall not be unreasonably withheld and may not be withheld where the Sub-Advisor may be exposed to civil or criminal contempt proceedings for failure to comply, when requested to divulge such information by duly constituted authorities, or when so requested by the Trust.

4.    Services Not Exclusive. Nothing in this Agreement shall prevent the Sub-Advisor or any officer, employee or other affiliate thereof from acting as investment advisor for any other person, firm or corporation, or from engaging in any other lawful activity, and shall not in any way limit or restrict the Sub-Advisor or any of its officers, employees or agents from buying, selling or trading any securities for its or their own accounts or for the accounts of others for whom it or they may be acting; provided, however, that the Sub-Advisor will undertake no activities which, in its judgment, will adversely affect the performance of its obligations under this Agreement.

5.    Books and Records. In compliance with the requirements of Rule 31a-3 under the 1940 Act, the Sub-Advisor hereby agrees that all records which it maintains for the Trust are the property of the Trust as the case may be and further agrees to surrender promptly to the Trust, any such records upon the Trust’s request as the case may be. The Sub-Advisor further agrees to preserve for the periods prescribed by Rule 31a-2 under the 1940 Act the records required to be maintained by Rule 31a-1 under the 1940 Act (to the extent such books and records are not maintained by the Advisor).

6.    Agency Cross Transactions. From time to time, the Sub-Advisor or brokers or dealers affiliated with it may find themselves in a position to buy for certain of their brokerage clients (each an “Account”) securities which the Sub-Advisor’s investment advisory clients wish to sell, and to sell for certain of their brokerage clients securities which advisory clients wish to

buy. Where one of the parties is an advisory client, the Advisor or the affiliated broker or dealer cannot participate in this type of transaction (known as a cross transaction) on behalf of an advisory client and retain commissions from both parties to the transaction without the advisory client’s consent. This is because in a situation where the Sub-Advisor is making the investment decision (as opposed to a brokerage client who makes his own investment decisions), and the Sub-Advisor or an affiliate is receiving commissions from one or both sides of the transaction, there is a potential conflicting division of loyalties and responsibilities on the Sub-Advisor’s part regarding the advisory client. The SEC has adopted a rule under the Advisers Act which permits the Sub-Advisor or its affiliates to participate on behalf of an Account in agency cross transactions if the advisory client has given written consent in advance. By execution of this Agreement, the Trust authorizes the Sub-Advisor or its affiliates to participate in agency cross transactions involving an Account. The Trust may revoke its consent at any time by written notice to the Sub-Advisor.

7.    Expenses. During the term of this Agreement, the Sub-Advisor will bear all costs and expenses of its employees and any overhead incurred by the Sub-Advisor in connection with its duties hereunder; provided that the Board of Trustees of the Trust may approve reimbursement to the Sub-Advisor of the pro-rata portion of the salaries, bonuses, health insurance, retirement benefits and all similar employment costs for the time spent on the Trust’s operations (including, without limitation, compliance matters) (other than the provision of investment advice and administrative services required to be provided hereunder) of all personnel employed by the Sub-Advisor who devote substantial time to the Trust’s operations or the operations of other investment companies advised or sub-advised by the Sub-Advisor.

8.    Compensation.

(a)    For that portion of the Fund for which the Sub-Advisor acts as sub-adviser, the Advisor agrees to pay to the Sub-Advisor and the Sub-Advisor agrees to accept as full compensation for all services rendered by the Sub-Advisor pursuant to this Agreement, an annual fee in arrears in an amount equal to 46% of the management fees received by the Advisor from the Trust with respect to the average daily value of the Managed Assets of the Trust allocated to the Sub-Advisor.

(b)    For purposes of this Agreement, the Managed Assets of the Trust shall be calculated pursuant to the procedures adopted by resolutions of the Board of Trustees of the Trust for calculating the value of the Trust’s assets or delegating such calculations to third parties.

9.    Indemnity.

(a)    The Trust may, with the prior consent of the Board of Trustees of the Trust, including a majority of the trustees of the Trust that are not “interested persons” of the Trust (as defined in Section 2(a)(19) of the 1940 Act), indemnify the Sub-Advisor and each of the Sub-Advisor’s directors, officers, employees, agents, associates and controlling persons and the directors, partners, members, officers, employees and agents thereof (including any individual who serves at the Sub-Advisor’s request as director, officer, partner, member, trustee or the like of another entity) (each such person being an “Indemnitee”) against any liabilities and

expenses, including amounts paid in satisfaction of judgments, in compromise or as fines and penalties, and counsel fees (all as provided in accordance with applicable state law) reasonably incurred by such Indemnitee in connection with the defense or disposition of any action, suit or other proceeding, whether civil or criminal, before any court or administrative or investigative body in which such Indemnitee may be or may have been involved as a party or otherwise or with which such Indemnitee may be or may have been threatened, while acting in any capacity set forth herein or thereafter by reason of such Indemnitee having acted in any such capacity, except with respect to any matter as to which such Indemnitee shall have been adjudicated not to have acted in good faith in the reasonable belief that such Indemnitee’s action was in the best interest of the Trust and furthermore, in the case of any criminal proceeding, so long as such Indemnitee had no reasonable cause to believe that the conduct was unlawful; provided, however, that (1) no Indemnitee shall be indemnified hereunder against any liability to the Trust, the Trust’s shareholders or any expense of such Indemnitee arising by reason of (i) willful misfeasance, (ii) bad faith, (iii) gross negligence or (iv) reckless disregard of the duties involved in the conduct of such Indemnitee’s position (the conduct referred to in such clauses (i) through (iv) being sometimes referred to herein as “disabling conduct”), (2) as to any matter disposed of by settlement or a compromise payment by such Indemnitee, pursuant to a consent decree or otherwise, no indemnification either for said payment or for any other expenses shall be provided unless there has been a determination that such settlement or compromise is in the best interests of the Trust and that such Indemnitee appears to have acted in good faith in the reasonable belief that such Indemnitee’s action was in the best interest of the Trust and did not involve disabling conduct by such Indemnitee and (3) with respect to any action, suit or other proceeding voluntarily prosecuted by any Indemnitee as plaintiff, indemnification shall be mandatory only if the prosecution of such action, suit or other proceeding by such Indemnitee was authorized by a majority of the full Board of Trustees of the Trust, including a majority of the trustees of the Trust who are not “interested persons” of the Trust (as defined in Section 2(a)(19) of the 1940 Act).

(b)    The Trust shall make advance payments in connection with the expenses of defending any action with respect to which indemnification might be sought hereunder if the Trust receives a written affirmation of the Indemnitee’s good faith belief that the standard of conduct necessary for indemnification has been met and a written undertaking to reimburse the Trust unless it is subsequently determined that such Indemnitee is entitled to such indemnification and if the trustees of the Trust determine that the facts then known to them would not preclude indemnification. In addition, at least one of the following conditions must be met: (A) the Indemnitee shall provide a security for such Indemnitee-undertaking, (B) the Trust shall be insured against losses arising by reason of any unlawful advance, or (C) a majority of a quorum consisting of trustees of the Trust who are neither “interested persons” of the Trust (as defined in Section 2(a)(19) of the 0000 Xxx) nor parties to the proceeding (“Disinterested Non-Party Trustees”) or an independent legal counsel in a written opinion, shall determine, based on a review of readily available facts (as opposed to a full trial-type inquiry), that there is reason to believe that the Indemnitee ultimately will be found entitled to indemnification.

(c)    All determinations with respect to indemnification hereunder shall be made (1) by a final decision on the merits by a court or other body before whom the proceeding was brought that such Indemnitee is not liable by reason of disabling conduct, or (2) in the absence of such a decision, by (i) a majority vote of a quorum of the Disinterested Non-Party

Trustees of the Trust, or (ii) if such a quorum is not obtainable or even, if obtainable, if a majority vote of such quorum so directs, independent legal counsel in a written opinion. All determinations that advance payments in connection with the expense of defending any proceeding shall be authorized shall be made in accordance with the immediately preceding clause (2) above.

The rights accruing to any Indemnitee under these provisions shall not exclude any other right to which such Indemnitee may be lawfully entitled.

10.    Limitation on Liability.

(a)    The Sub-Advisor will not be liable for any error of judgment or mistake of law or for any loss suffered by the Advisor or by the Trust in connection with the performance of this Agreement, except a loss resulting from a breach of fiduciary duty with respect to the receipt of compensation for services or a loss resulting from willful misfeasance, bad faith or gross negligence on its part in the performance of its duties or from reckless disregard by it of its duties under this Agreement.

(b)    Notwithstanding anything to the contrary contained in this Agreement, the parties hereto acknowledge and agree that, as provided in Section 5.1 of Article V of the Agreement and Declaration of Trust, this Agreement is executed by the Trustees and/or officers of the Trust, not individually but as such Trustees and/or officers of the Trust, and the obligations hereunder are not binding upon any of the Trustees or Shareholders individually but bind only the estate of the Trust.

11.    Duration and Termination.

(a)    This Agreement shall become effective as of the date hereof and, unless sooner terminated with respect to the Trust as provided herein, shall continue in effect for a period of two years. Thereafter, if not terminated, this Agreement shall continue in effect with respect to the Trust for successive periods of 12 months, provided such continuance is specifically approved at least annually by both (a) the vote of a majority of the Trust’s Board of Trustees or a vote of a majority of the outstanding voting securities of the Trust at the time outstanding and entitled to vote and (b) by the vote of a majority of the Trustees, who are not parties to this Agreement or interested persons (as such term is defined in the 0000 Xxx) of any such party, cast in person at a meeting called for the purpose of voting on such approval.

(b)    Notwithstanding the foregoing, this Agreement may be terminated by the Trust or the Advisor at any time, without the payment of any penalty, upon giving the Sub-Advisor 60 days’ notice (which notice may be waived by the Sub-Advisor), provided that such termination by the Trust or the Advisor shall be directed or approved by the vote of a majority of the Trustees of the Trust in office at the time or by the vote of the holders of a majority of the voting securities of the Trust at the time outstanding and entitled to vote, or by the Sub-Advisor on 60 days’ written notice (which notice may be waived by the Trust and the Advisor), and will terminate automatically upon any termination of the Advisory Agreement between the Trust and the Advisor. This Agreement will also immediately terminate in the event of its assignment. (As used in this Agreement, the terms “majority of the outstanding voting securities,” “interested person” and “assignment” shall have the same meanings of such terms in the 1940 Act.)

12.    Notices. Any notice under this Agreement shall be in writing to the other party at such address as the other party may designate from time to time for the receipt of such notice and shall be deemed to be received on the earlier of the date actually received or on the fourth day after the postmark if such notice is mailed first class postage prepaid.

13.    Amendment of this Agreement. No provision of this Agreement may be changed, waived, discharged or terminated orally, but only by an instrument in writing signed by the party against which enforcement of the change, waiver, discharge or termination is sought. Any amendment of this Agreement shall be subject to the 1940 Act.

14.    Miscellaneous. The captions in this Agreement are included for convenience of reference only and in no way define or delimit any of the provisions hereof or otherwise affect their construction or effect. If any provision of this Agreement shall be held or made invalid by a court decision, statute, rule or otherwise, the remainder of this Agreement shall not be affected thereby. This Agreement shall be binding on, and shall inure to the benefit of the parties hereto and their respective successors.

15.    Governing Law. This Agreement shall be governed by and construed in accordance with the laws of the State of New York for contracts to be performed entirely therein without reference to choice of law principles thereof and in accordance with the applicable provisions of the 1940 Act.

16.    Counterparts. This Agreement may be executed in counterparts by the parties hereto, each of which shall constitute an original counterpart, and all of which, together, shall constitute one Agreement.

[Signature Page Follows]

IN WITNESS WHEREOF, the parties hereto have caused this instrument to be executed by their duly authorized officers designated below as of the day and year first above written.

BLACKROCK ADVISORS, LLC
By:		/s/ Xxxx X. Xxxxxxx
		Name: Xxxx X. Xxxxxxx
		Title: Managing Director
BLACKROCK (SINGAPORE) LIMITED
By:		/s/ Neeraj Seth
		Name: Neeraj Seth
		Title: Managing Director
BLACKROCK MULTI-SECTOR INCOME TRUST
By:		/s/ Xxxx Xxxxxxxxx
		Name: Xxxx Xxxxxxxxx
		Title: President

Signature Page to BlackRock (Singapore) Limited Sub-Investment Advisory Agreement