Exhibit 4.2

ARCH CAPITAL GROUP (U.S.) INC.,
as Issuer,

ARCH CAPITAL GROUP LTD,
as Guarantor

and

THE BANK OF NEW YORK MELLON,
as Trustee

FIRST SUPPLEMENTAL INDENTURE

Dated December 13, 2013

5.144% Senior Notes due 2043

FIRST SUPPLEMENTAL INDENTURE, dated December 13, 2013, between Arch Capital Group (U.S.) Inc., a Delaware corporation (herein called the “Company”), Arch Capital Group Ltd., a Bermuda company (herein called the “Guarantor”), and The Bank of New York Mellon, a New York banking corporation, as trustee hereunder (herein called the “Trustee”).

RECITALS OF THE COMPANY

The Company, the Guarantor and the Trustee entered into an Indenture dated as of December 13, 2013 (the “Original Indenture”), pursuant to which senior unsecured debentures, notes or other evidences of indebtedness of the Company (the “Securities”), which may be convertible into or exchangeable for any securities of any Person (including the Company), may be issued in one or more series from time to time.

Section 3.01 of the Original Indenture permits the terms of any series of Securities to be established in an indenture supplemental to the Original Indenture.

Section 9.01 of the Original Indenture provides that a supplemental indenture may be entered into by the Company, the Guarantor and the Trustee without the consent of any Holders of the Securities for certain purposes stated therein.

The Company and the Guarantor have requested the Trustee to join with each of them in the execution and delivery of this First Supplemental Indenture in order to supplement the Original Indenture by, among other things, establishing certain terms of a series of Securities to be known as the Company’s “5.144% Senior Notes due 2043” (the “Notes”), to be fully and unconditionally guaranteed by the Guarantor and adding certain provisions thereof for the benefit of the Holders of the Notes.

The Company has furnished the Trustee with a duly authorized and executed Company Order dated December 13, 2013 authorizing the execution of this First Supplemental Indenture and the issuance of the Notes. Such Company Order is sometimes referred to herein as the “Authentication Order.”

All things necessary to make this First Supplemental Indenture a valid agreement of the Company, the Guarantor and the Trustee and a valid supplement to the Original Indenture have been done.

NOW, THEREFORE, THIS FIRST SUPPLEMENTAL INDENTURE WITNESSETH:

For and in consideration of the premises and the purchase of the Notes to be issued hereunder by Holders thereof, the Company, the Guarantor and the Trustee mutually

covenant and agree, for the equal and proportionate benefit of the respective Holders from time to time of the Notes, as follows:

ARTICLE ONE

DEFINITIONS AND OTHER PROVISIONS
OF GENERAL APPLICATION

SECTION 1.1. Definitions.

The Original Indenture together with this First Supplemental Indenture are hereinafter sometimes collectively referred to as the “Indenture.” For the avoidance of doubt, references to any “Section” of the “Indenture” refer to such Section of the Original Indenture as supplemented and amended by this First Supplemental Indenture. All capitalized terms which are used herein and not otherwise defined herein are defined in the Original Indenture and are used herein with the same meanings as in the Original Indenture. If a capitalized term is defined in the Original Indenture and this First Supplemental Indenture, the definition in this First Supplemental Indenture shall apply to the Notes.

For all purposes of this First Supplemental Indenture, except as otherwise expressly provided or unless the context otherwise requires:

(1) the terms defined in this article have the meanings assigned to them in this article and include the plural as well as the singular;

(2) all other terms used herein which are defined in the Trust Indenture Act, either directly or by reference therein, have the meanings assigned to them therein;

(3) all accounting terms not otherwise defined herein have the meanings assigned to them in accordance with generally accepted accounting principles in the United States, and, except as otherwise herein expressly provided, the term “generally accepted accounting principles” with respect to any computation required or permitted hereunder shall mean such accounting principles as are generally accepted at the date of such computation;

(4) the words “herein,” “hereof” and “hereunder” and other words of similar import refer to this Indenture as a whole and not to any particular article, section or other subdivision; and

(5) all references used herein to the male gender shall include the female gender.

ARTICLE TWO

SECURITIES FORMS

SECTION 2.1. Creation of the Notes; Designations.

In accordance with Section 3.01 of the Original Indenture, the Company hereby creates the Notes as a series of its Securities issued pursuant to the Indenture. The Notes shall be known and designated as the “5.144% Senior Notes due 2043” of the Company.

SECTION 2.2. Forms Generally.

The Notes, the Trustee’s certificate of authentication and the Guarantee shall be in the forms set forth in Exhibit I attached hereto, with such appropriate insertions, omissions, substitutions and other variations as are required or permitted by the Indenture and may have such letters, numbers or other marks of identification and such legends or endorsements placed thereon as may be required to comply with the rules of any securities exchange or as may, consistently herewith, be determined by the officers executing such Notes or the Guarantee, as applicable, as evidenced by their execution of the Notes and the Guarantee. Any portion of the text of any Note may be set forth on the reverse thereof, with an appropriate reference thereto on the face of the Note.

The Notes and the Guarantee shall be printed, lithographed or engraved or produced by any combination of these methods or may be produced in any other manner, all as determined by the officers of the Company executing such Notes or the Guarantee, as applicable, as evidenced by their manual execution of such Notes and the Guarantee.

SECTION 2.3. Ranking.

The Notes will represent the Company’s direct, unsecured obligations and will rank equally with all the Company’s current and future unsecured and unsubordinated indebtedness. The Guarantee will represent the Guarantor’s direct, unsecured senior obligation and will rank equally with all similar guarantee agreements issued by the Guarantor as direct, unsecured senior obligations.

ARTICLE THREE

GENERAL TERMS AND CONDITIONS OF THE NOTES

SECTION 3.1. Title and Terms of Notes.

(a) The aggregate principal amount of Notes which shall be authenticated and delivered on December 13, 2013 (the “Issue Date”) under the Indenture shall be $500,000,000 (and which shall initially be in the form of a Global Security); provided, however, that the Company from time to time, without giving notice to or seeking the consent of the Holders of the Notes, may issue additional senior notes in any amount having the same ranking and the same interest rate, interest payment dates, maturity and other terms as the Notes, except for the issue price, the issue date and, in some cases, the first interest payment date; any additional senior notes having such similar terms shall be authenticated by the Trustee upon receipt of a Company Order to that effect, and when so authenticated, will constitute “Notes” for all purposes of the Indenture and will (together with all other Notes issued under the Indenture) constitute a single series of Securities under the Indenture. The Notes will be issued only in fully registered form without coupons in denominations of $2,000 and any whole multiple of $1,000.

(b) The principal amount of the Notes is due and payable in full on November 1, 2043, unless earlier redeemed.

(c) The Notes shall bear interest at the rate of 5.144% per annum (computed on the basis of a 360-day year comprised of twelve 30-day months) from the Issue Date or from the most recent Interest Payment Date to which interest has been paid or duly provided for to maturity or early redemption; and interest will be payable semi-annually on May 1 and November 1 of each year, commencing May 1, 2014, to the Persons in whose name such Notes were registered at the close of business on the preceding April 15 or October 15, respectively.

(d) Principal of and interest on the Notes shall be payable in accordance with Sections 1.13, 3.07 and 10.01 of the Original Indenture.

(e) Other than as provided in Articles Four or Five of this First Supplemental Indenture, the Notes shall not be redeemable.

(f) The Notes shall not be entitled to the benefits of a sinking fund.

(g) The Notes shall not be convertible into any other securities.

(h) Section 4.04 of the Original Indenture shall apply to the Notes.

(i) The Company initially appoints the Trustee as Registrar and Paying Agent with respect to the Notes until such time as the Trustee has resigned or a successor has been appointed.

(j) The Company shall pay principal of, premium, if any, and interest on the Notes in money of the United States of America that at the time of payment is legal tender for payment of public and private debts.

(k) A Holder may transfer or exchange Notes only in accordance with the Indenture. Upon any transfer or exchange, the Registrar and the Trustee may require a Holder, among other things, to furnish appropriate endorsements or transfer documents. No service charge shall be made for any registration of transfer or exchange, but the Company or the Trustee may require the payment of a sum sufficient to cover any tax or other governmental charge that may be imposed in connection therewith.

ARTICLE FOUR

SPECIAL REDEMPTION

SECTION 4.1. Special Mandatory Redemption.

If (i) the Purchase Agreements are terminated on any date prior to June 30, 2014, (ii) the Company publicly announces on any date prior to June 30, 2014 that the Acquisition will not be pursued or (iii) the Acquisition is not consummated prior to June 30, 2014 (the earliest of any such date, a ‘‘Trigger Date’’), then the Company shall redeem the Notes on the Special Mandatory Redemption Date at a special mandatory redemption price equal to 101% of the aggregate principal amount of the Notes (the “Special Mandatory Redemption Price”), plus accrued and unpaid interest on the Notes from the Issue Date, or the most recent Interest Payment Date, whichever is later, to, but excluding, the Special Mandatory Redemption Date. Notwithstanding the foregoing, interest on the Notes for which the Interest Payment Date is on or before the Special Mandatory Redemption Date, shall be payable on such Interest Payment Date to the holder of such Notes at the close of business on the preceding Regular Record Date.

SECTION 4.2. Special Redemption Definitions.

As used in this Article Four, the following terms shall have the respective meanings set forth below:

“Purchase Agreements” mean, collectively, (i) the Asset Purchase Agreement, dated as of February 7, 2013 and amended as of May 31, 2013, and as further amended,

supplemented and/or restated from time to time, by and among the Company, Arch U.S. MI Services Inc., a Delaware corporation, the Receiver of PMI Mortgage Insurance Co. in Rehabilitation (the “Receiver”), on behalf of PMI Mortgage Insurance Co., an Arizona stock insurance corporation (“PMI”), and (ii) the CMG Stock Purchase Agreement, dated as of February 7, 2013 and amended as of May 31, 2013, and as further amended, supplemented and/or restated from time to time, by and among the Company, Arch U.S. MI Holdings Inc., a Delaware corporation, the Receiver, on behalf of PMI, CMFG Life Insurance Company, formerly known as CUNA Mutual Insurance Society, an Iowa corporation, and CMG Mortgage Insurance Company, a Wisconsin insurance company.

“Acquisition” means the transaction contemplated by the Purchase Agreements.

“Special Mandatory Redemption Date” means the tenth Business Day following the Trigger Date.

SECTION 4.3. Special Mandatory Redemption Procedures.

The Company shall give notice of a special mandatory redemption pursuant to Section 4.1 to be transmitted by first-class mail, postage prepaid, to each Holder of the Notes at its address appearing in the Security Register, with a copy to the Trustee, no later than five Business Days after the occurrence of a Trigger Date. Any notice which is mailed in the manner herein provided shall be conclusively presumed to have been duly given, whether or not such Holder receives the notice. Failure to give notice by mail, or any defect in the notice to any such Holder in respect of any Notes, shall not affect the validity of the proceedings for the special mandatory redemption of any other Notes.

Such notice shall state:

(1) the Special Mandatory Redemption Date;

(2) the Special Mandatory Redemption Price and any accrued interest;

(3) that on the Special Mandatory Redemption Date the Special Mandatory Redemption Price and any accrued interest will become due and payable upon each Note and that interest on the Notes will cease to accrue on and after said date;

(4) the place or places where the Notes are to be surrendered for payment of the Special Mandatory Redemption Price and any accrued interest; and

(5) the CUSIP number and, if applicable, the ISIN number, of the Notes.

Notice of a special mandatory redemption having been given as aforesaid, the Notes so to be redeemed shall, on the Special Mandatory Redemption Date, become due and payable at the Special Mandatory Redemption Price therein specified together with accrued interest thereon. If funds sufficient to pay the Special Mandatory Redemption Price of all Notes to be redeemed on the Special Mandatory Redemption Date, and any accrued interest, in accordance with the Section 4.1 are deposited with the Paying Agent on or before the Special Mandatory Redemption Date, the Notes shall cease to bear interest on and after the Special Mandatory Redemption Date, and all rights under the Notes shall terminate.

Upon surrender of the Notes for a special mandatory redemption in accordance with said notice, such Notes shall be paid by the Company at the Special Mandatory Redemption Price, together with accrued interest to the Special Mandatory Redemption Date.

If any Notes called for a special mandatory redemption shall not be so paid upon surrender thereof for redemption, the principal (and premium, if any) shall, until paid, bear interest from the Special Mandatory Redemption Date at the rate prescribed therefor in the Notes.

ARTICLE FIVE

OPTIONAL REDEMPTION

SECTION 5.1. Optional Redemption.

The Notes will be redeemable, in whole at any time or in part from time to time, at the Company’s option, at a Redemption Price equal to accrued and unpaid interest on the principal amount being redeemed to the Redemption Date plus the greater of: (A) 100% of the principal amount of the Notes to be redeemed, and (B) the sum of the present values of the remaining scheduled payments of principal and interest on the Notes to be redeemed (not including any portion of such payments of interest accrued to the date of redemption) discounted to the date of redemption on a semiannual basis (assuming a 360-day year consisting of twelve 30-day months) at the Treasury Rate, plus 20 basis points. Interest on the Notes for which the Redemption Date is after a Regular Record Date and before the following Interest Payment Date, shall be payable to the holder of such Notes at the close of business on the Regular Record Date.

SECTION 5.2. Optional Redemption Definitions.

As used in this Article Five, the following terms shall have the respective meanings set forth below:

“Treasury Rate” means, for any Redemption Date, the rate per year equal to the semi-annual equivalent yield to maturity of the Comparable Treasury Issue, assuming a price for the Comparable Treasury Issue (expressed as a percentage of its principal amount) equal to the Comparable Treasury Price for the Redemption Date.

“Comparable Treasury Issue” means the United States Treasury security selected by an Independent Investment Banker as having a maturity comparable to the remaining term of the Notes being redeemed that would be utilized, at the time of selection and in accordance with customary financial practice, in pricing new issues of corporate notes of comparable maturity to the remaining term of such Notes.

“Independent Investment Banker” means one of the Reference Treasury Dealers appointed by the Company after consultation with the Trustee.

“Comparable Treasury Price” means, for any Redemption Date, (1) the average of the Reference Treasury Dealer Quotations for the Redemption Date, after excluding the highest and lowest Reference Treasury Dealer Quotations for that Redemption Date, or (B) if the Independent Investment Banker obtains fewer than four Reference Treasury Dealer Quotations, the average of all the Reference Treasury Dealer Quotations obtained.

“Reference Treasury Dealer Quotations” means, for each Reference Treasury Dealer and any Redemption Date, the average, as determined by the Independent Investment Banker, of the bid and asked prices for the Comparable Treasury Issue (expressed in each case as a percentage of its principal amount) quoted in writing to the Independent Investment Banker by the Reference Treasury Dealer at 5:00 p.m., New York City time, on the third Business Day preceding the Redemption Date for the Notes being redeemed.

“Reference Treasury Dealer” means (1)(i) each of J.P. Morgan Securities LLC and Merrill Lynch, Pierce, Fenner & Smith Incorporated and their respective successors and (ii) a primary U.S. government securities dealer in the United State (a “Primary Treasury Dealer”) selected by Wells Fargo Securities, LLC or its successor; provided, however, that if any of the foregoing ceases to be or refuses to act as a Primary Treasury Dealer, the Company will appoint another Primary Treasury Dealer as a substitute and (2) any other Primary Treasury Dealers selected by the Company.

SECTION 5.3. Optional Redemption Procedures.

The provisions of Article Eleven of the Original Indenture shall apply in the case of a redemption pursuant to this Article Five.

ARTICLE SIX

COVENANTS

SECTION 6.1. Covenants.

(a) The Notes shall be entitled to the benefit of each of the covenants in Article Ten of the Original Indenture and the following additional covenants (which shall be deemed to be provisions of the Original Indenture, when referred to as a provision of the Original Indenture, shall be identified by reference to the Section number that is set forth immediately preceding the covenant):

“SECTION 10.07. Limitation on Liens on Stock of Designated Subsidiaries.

Neither the Company nor the Guarantor shall, nor shall either the Company or the Guarantor permit any Designated Subsidiary to, create, assume, incur or guarantee any indebtedness for money borrowed that is evidenced by notes, debentures, bonds or similar negotiable instruments, which is secured by any mortgage, pledge, lien, security interest or other encumbrance (each, a “Lien”) upon any shares of Capital Stock of any Designated Subsidiary (whether such shares of stock are now owned or hereafter acquired) without providing concurrently for the Notes to be secured equally and ratably with such indebtedness (it being understood that such security interest in favor of the Holders of the Notes shall be automatically released if the Liens securing the other indebtedness are for any reason released) for at least the time period such other indebtedness is so secured.

SECTION 10.08. Limitation on the Disposition of Stock of Designated Subsidiaries.

So long as any Notes are Outstanding, the Guarantor will not, nor will the Guarantor permit any Designated Subsidiary to, issue, sell, assign, transfer or otherwise dispose of any shares of Capital Stock of any Designated Subsidiary (other than to the Company, the Guarantor or another Designated Subsidiary) unless, after giving effect to any such issuance, sale, assignment, transfer or other disposal, the Guarantor and its Designated Subsidiaries, would own, directly or indirectly, 80% or more of the shares of Capital Stock of such Designated Subsidiary and the consideration received is at least equal to the fair market value of the Capital Stock so disposed of or issued, as the case may be, as set forth or stated in a Board Resolution adopted in good faith; provided, however, the foregoing shall not apply to (i) any grant of a Lien or any sale, transfer or other disposition resulting from any foreclosure or similar proceeding with respect to a Lien, (ii) the sale, transfer, disposition or issuance of directors’ qualifying

shares or similar securities, (iii) any issuance, sale, assignment, transfer or disposition of securities required by any law, regulation or order of any court, or governmental or insurance regulatory authority, unless any such order was requested by the Company, the Guarantor or any of the Designated Subsidiaries, or (iv) any such sale, transfer or disposition pursuant to any agreement or contractual arrangement between the Company or the Guarantor and any of its security holders in effect on the date the Notes are first issued.”

(b) For purposes only of the Notes and Sections 10.07 and 10.08 of the Original Indenture, the following terms shall have the following meanings:

“Capital Stock” of any Person means any and all shares, interests, rights to purchase, warrants, options, participations or other equivalents of or interests in (however designated) equity of such person, including Preferred Stock, in each case, which are entitled to vote in the election of directors, member or general partners or other similar managing body, as applicable, but excluding any debt securities convertible into or other securities convertible into such equity; provided, however, that preferred shares or other similar securities issued in the ordinary course of business by any of the Company’s Subsidiaries in connection with their “rent-a-captive” business shall not be deemed capital stock for purposes of the covenants described herein.

“Designated Subsidiary” means any present or future consolidated Subsidiary of the Guarantor, the assets of which constitute at least 20% of the Guarantor’s consolidated assets; provided, however, that (i) in the event Liens of the type described in Section 10.07 are placed on the Capital Stock of more than one of the Guarantor’s Subsidiaries in one transaction or in a series of related transactions and such Subsidiaries, when taken together as a whole, constitute at least 20% of the Guarantor’s consolidated assets, each such Subsidiary shall be deemed to be a “Designated Subsidiary” for purposes such transaction or transactions, as the case may be, and (ii) in the event of a sale, transfer or other disposition of the type described in Section 10.08 of any shares of Capital Stock of more than one of the Guarantor’s Subsidiaries in one transaction or in a series of related transactions and such Subsidiaries, when taken together as a whole, constitute at least 20% of the Guarantor’s consolidated assets, each such Subsidiary shall be deemed to be a “Designated Subsidiary” for purposes of transaction or transactions, as the case may be.

“Lien” shall have the meaning set forth in Section 10.07 hereof.

(c) For purposes of the Indenture and the Notes, Section 10.04 of the Original Indenture is hereby amended in its entirety and replaced with the following:

“SECTION 10.04. Corporate Existence.

Except as otherwise permitted under Article Eight, the Company and the Guarantor will each do or cause to be done all things necessary to preserve and keep in full force and effect its corporate existence and material rights (charter and statutory) and franchises; provided, however, that neither the Company nor the Guarantor will be required to preserve any such right or franchise if the Company’s Board of Directors or the Guarantor’s Board of Directors, as the case may be, or senior management of the Company or the Guarantor, as the case may be, determine that the preservation thereof is no longer desirable in the conduct of the business of the Company or the Guarantor, as the case may be, and that the loss thereof is not disadvantageous in any material respect to the Holders.”

ARTICLE SEVEN

SUCCESSOR CORPORATION

SECTION 7.1. When Company or Guarantor May Merge or Transfer Assets.

For purposes of the Indenture and the Notes, Section 8.01 of the Original Indenture is hereby amended in its entirety and replaced with the following:

“SECTION 8.01: When Company or Guarantor May Merge or Transfer Assets.

The Guarantor shall not, and shall not permit the Company to, consolidate or amalgamate with or merge with or into any other Person (other than a Subsidiary) or convey, transfer, sell or lease the properties and assets of the Company substantially as an entirety to any Person (other than a Subsidiary), or permit any Person to consolidate with or merge into the Guarantor or the Company, as the case may be, unless:

(1) either (a) the Guarantor or the Company, as the case may be, shall be the surviving Person or (b) the surviving Person (if other than the Guarantor or the Company, as the case may be) shall (1) be a corporation or limited liability company organized and existing under the laws of the United States of America, any state thereof, the District of Columbia, Bermuda, the Cayman Islands or any country or state which, on the date of this Indenture or on the date of such transaction, is a member of the Organization for Economic Co-operation and Development and (2) expressly assume, by an indenture supplemental hereto, executed and delivered to the Trustee, in form reasonably satisfactory to the Trustee, all of the obligations of the Guarantor or the Company, as the case may be, under the Securities or the Guarantee, as applicable, and this Indenture;

(2) immediately after giving effect to such transaction, no Event of Default, and no event that, after notice or lapse of time or both, would become an Event of Default, shall have occurred and be continuing; and

(3) the Guarantor or the Company, as the case may be, shall have delivered to the Trustee an Officers’ Certificate and an Opinion of Counsel, each stating that such consolidation, merger, conveyance, transfer, sale or lease and, if a supplemental indenture is required in connection with such transaction, such supplemental indenture, comply with this Section 8.01 and that all conditions precedent herein provided for relating to such transaction have been satisfied.

The surviving Person of such transaction shall succeed to, and be substituted for, and may exercise every right and power of, the Guarantor or the Company, as the case may be, under this Indenture with the same effect as if such successor had been named as the Guarantor or the Company, as the case may be, herein; and thereafter, the Guarantor or the Company, as the case may be, shall be discharged from all obligations and covenants under this Indenture and the Securities or the Guarantee, as the case may be. Subject to Section 9.03, the Company, the Trustee and the successor Person shall enter into a supplemental indenture to evidence the succession and substitution of such successor Person and such discharge and release of the Guarantor or the Company, as the case may be.”

ARTICLE EIGHT

EVENTS OF DEFAULT

SECTION 8.1. Events of Default.

Section 5.01 of the Original Indenture is, for purposes of the Indenture and the Notes, hereby amended to add the following clauses (8) through (10):

“(8) default by the Company or the Guarantor, as the case may be, in the payment when due of the principal or premium, if any, of any bond, debenture, note or other evidence of its indebtedness, in each case for money borrowed, or in the payment of principal or premium, if any, under any mortgage, indenture, agreement or instrument under which there may be issued or by which there may be secured or evidenced any of the indebtedness of the Company or the Guarantor, as the case may be, for money borrowed, which default for payment of principal or premium, if any, is in an aggregate amount exceeding $50.0 million, if such default shall continue unremedied or unwaived for more than 60 days after the expiration of any grace period or extension of the time for payment applicable thereto; or

(9) default by the Company or the Guarantor, as the case may be, under any instrument or instruments under which there is or may be secured or evidenced any of the indebtedness of the Company or the Guarantor, as the case may be (other than the Notes or the Guarantee), having an outstanding principal amount of $50.0 million or more, individually or in the aggregate, that has caused the holders thereof to declare such indebtedness to be due and payable prior to its stated maturity, unless such declaration has been rescinded or cured within 60 days; or

(10) failure within 60 days to pay, bond or otherwise discharge any uninsured judgment against the Company or the Guarantor, as the case may be, or court order for the payment of money by the Company or the Guarantor, as the case may be, in each case, in excess of $50.0 million, which is not stayed on appeal or is not otherwise being appropriately contested in good faith.”

ARTICLE NINE

MISCELLANEOUS

SECTION 9.1. Effect of First Supplemental Indenture.

(a) This First Supplemental Indenture is a supplemental indenture within the meaning of Section 9.01 of the Original Indenture, and the Original Indenture shall be read together with this First Supplemental Indenture and shall have the same effect over the Notes, in the same manner as if the provisions of the Original Indenture and this First Supplemental Indenture were contained in the same instrument.

(b) In all other respects, the Original Indenture is confirmed by the parties hereto as supplemented by the terms of this First Supplemental Indenture.

SECTION 9.2. Effect of Headings.

The Article and Section headings herein are for convenience only and shall not affect the construction hereof.

SECTION 9.3. Successors and Assigns.

All covenants and agreements in this First Supplemental Indenture by the Company, the Guarantor, the Trustee and the Holders shall bind their successors and assigns, whether so expressed or not.

SECTION 9.4. Severability Clause.

In case any provision in this First Supplemental Indenture, in the Notes or in the Guarantee shall be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby.

SECTION 9.5. Benefits of First Supplemental Indenture.

Nothing in this First Supplemental Indenture, in the Notes or in the Guarantee, express or implied, shall give to any Person, other than the parties hereto, any benefit or any legal or equitable right, remedy or claim under this First Supplemental Indenture.

SECTION 9.6. Conflict.

In the event that there is a conflict or inconsistency between the Original Indenture and this First Supplemental Indenture, the provisions of this First Supplemental Indenture shall control; provided, however, if any provision hereof limits, qualifies or conflicts with another provision herein or in the Original Indenture, in either case, which is required or deemed to be included in this Indenture by any of the provisions of the Trust Indenture Act, such required or deemed provision shall control.

SECTION 9.7. Governing Law.

THIS FIRST SUPPLEMENTAL INDENTURE, THE NOTES AND THE GUARANTEE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.

SECTION 9.8. Trustee.

The Trustee shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this First Supplemental Indenture or for or in respect of the recitals contained herein, all of which are made solely by the Company or the Guarantor, as the case may be.

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

IN WITNESS WHEREOF, the parties hereto have caused this First Supplemental Indenture to be duly executed on the date and year first written above.

ARCH CAPITAL GROUP (U.S.) INC.,
as Issuer.


By:	/s/ Thomas J. Ahern
	Name:	Thomas J. Ahern
	Title:	Senior Vice President & Chief Financial Officer


ARCH CAPITAL GROUP LTD.,
as Guarantor


By:	/s/ Mark D. Lyons
	Name:	Mark D. Lyons
	Title:	Executive Vice President & Chief Financial Officer


THE BANK OF NEW YORK MELLON,
	as Trustee


By:	/s/ Michelle Drinkard
	Name:	Michelle Drinkard
	Title:	Vice President

First Supplemental Indenture Signature Page

EXHIBIT I

[INSERT GLOBAL SECURITY LEGEND, IF APPROPRIATE - UNLESS THIS CERTIFICATE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY TRUST COMPANY, A NEW YORK CORPORATION (“DTC”), TO ARCH CAPITAL GROUP (U.S.) INC. OR ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT, AND ANY CERTIFICATE ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR IN SUCH OTHER NAME AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC (AND SUCH PAYMENT IS MADE TO CEDE & CO. OR TO SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC), ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR OTHERWISE BY OR TO ANY PERSON IS WRONGFUL INASMUCH AS THE REGISTERED OWNER, CEDE & CO., HAS AN INTEREST HEREIN.

UNLESS AND UNTIL THIS CERTIFICATE IS EXCHANGED IN WHOLE OR IN PART FOR NOTES IN CERTIFICATED FORM, THIS CERTIFICATE MAY NOT BE TRANSFERRED EXCEPT AS A WHOLE BY DTC TO A NOMINEE THEREOF OR BY A NOMINEE THEREOF TO DTC OR ANOTHER NOMINEE OF DTC OR BY DTC OR ANY SUCH NOMINEE TO A SUCCESSOR OF DTC OR A NOMINEE OF SUCH SUCCESSOR.]

ARCH CAPITAL GROUP (U.S.) INC.
5.144% SENIOR NOTE DUE 2043

No.

Principal Amount $

CUSIP No. 03938JAA7

ARCH CAPITAL GROUP (U.S.) INC., a Delaware corporation, for value received, promises to pay to , or registered assigns, the principal sum of United States Dollars (US$ ) on November 1, 2043.

Interest Payment Dates: May 1 and November 1.

Regular Record Dates: April 15 and October 15.

Additional provisions of this Note are set forth on the other side of this Note.

IN WITNESS WHEREOF, the Company has caused this instrument to be duly executed.

	ARCH CAPITAL GROUP (U.S.) INC.


	By:
		Name:
		Title:

TRUSTEE’S CERTIFICATE OF AUTHENTICATION

This is one of the Notes of the series designated therein referred to in the within-mentioned Indenture.

Dated:

	THE BANK OF NEW YORK MELLON,
	as Trustee

	By:
		Authorized Officer

Signature Page to Note-

For value received, Arch Capital Group Ltd. hereby unconditionally guarantees on an unsecured, unsubordinated basis to the holder of the Notes represented by this Security the payment of principal of (and premium, if any) and interest on the Security upon which this Guarantee is endorsed in the amounts and at the times when due and payable whether by declaration thereof, or otherwise, and interest on the overdue principal of (and premium, if any) and interest on such Notes, if lawful, and the payment or performance of all other obligations of the Company under the Indenture or the Notes, to the holder of such Notes and the Trustee, all in accordance with and subject to the terms and limitations of such Notes and Article Thirteen of the Indenture. This Guarantee will not become effective until the Trustee duly executes the certificate of authentication on this Security. This Guarantee shall be governed by and construed in accordance with the laws of the State of New York.

Dated:

	ARCH CAPITAL GROUP LTD.


	By:
		Name:
		Title:

Signature Page to Guarantee Endorsement-

(Reverse of Note)

5.144% Senior Note due 2043

1. Interest

Arch Capital Group (U.S.) Inc., a Delaware corporation (such corporation, and its successors and assigns under the Indenture hereinafter referred to, being herein called the “Company”), for value received, promises to pay interest on the principal amount of this Note (the “Note”) at the rate of 5.144% per annum. The Company shall pay interest semiannually on May 1 and November 1 of each year, commencing May 1, 2014. Interest on the Note shall accrue from the most recent date to which interest has been paid or duly provided for or, if no interest has been paid or duly provided for, from December 13, 2013 until the principal hereof is due. Interest shall be computed on the basis of a 360-day year comprised of twelve 30-day months. The Company shall pay interest on overdue principal at the rate borne by the Note, and it shall pay interest on overdue installments of interest at the same rate to the extent lawful.

2. Method of Payment

The Company shall pay interest on the Note (except defaulted interest, which shall be paid pursuant to Section 3.07 of the Original Indenture) to the Persons who are registered Holders at the close of business on the April 15 or October 15 next preceding the Interest Payment Date even if Notes are canceled after the record date and on or before the Interest Payment Date. The Company shall pay principal, premium, if any, and interest in money of the United States of America that at the time of payment is legal tender for payment of public and private debts. Payment of principal (and premium, if any) and interest in respect of Notes represented by a Global Security will be made by wire transfer of immediately available funds to the accounts specified by the Depository. Payments of principal (and premium, if any) and interest in respect of a certificated Note may be made, at the option of the Company, either by wire transfer in immediately available funds to the accounts specified by registered Holders as of the relevant record dates or (subject to collection) by check mailed to the address of the registered Holders as of the relevant record dates or at the specified offices of any Paying Agent. Payment of principal in respect of a certificated Note will only be made against presentation and, provided that payment is made in full, surrender of the appropriate certificate at the specified offices of any Paying Agent.

3. Paying Agent and Registrar

Initially, THE BANK OF NEW YORK MELLON, a New York banking corporation (the “Trustee”), will act as Paying Agent and Registrar with respect to the Notes. The Company may appoint and change any Paying Agent or Registrar without notice. The Company may act as Paying Agent or Registrar.

4. Indenture

The Company issued the Notes under an Indenture dated as of December 13, 2013, between the Company, ARCH CAPITAL GROUP LTD., a Bermuda company (such company, and its successors and assigns under the Indenture hereinafter referred to, being herein called the “Guarantor”), and the Trustee (the “Original Indenture”), as supplemented by a First Supplemental Indenture dated December 13, 2013, between the Company, the Guarantor and the Trustee, which collectively constitutes the indenture governing the Securities (the “Indenture”). The terms of the Notes include those stated in the Indenture and those made part of the Indenture by reference to the Trust Indenture Act of 1939, as amended as in effect on the date of the Indenture (the “TIA”). The Notes include all terms and provisions of the Indenture, and Holders are referred to the Indenture and the TIA for a statement of such terms and provisions. This Security is one of a series of Securities designated as the 5.144% Senior Notes due 2043 of the Company (the “Notes”). Capitalized terms used herein have the same meanings given in the Indenture unless otherwise indicated.

The aggregate principal amount at maturity of the Notes which may be authenticated and delivered under the Indenture shall be unlimited. In addition, the aggregate principal amount of Securities of any class or series which may be authenticated and delivered under the Indenture shall be unlimited, provided that such Securities shall rank equally with the Notes.

5. Certain Covenants

The Indenture imposes certain limitations on the ability of each of the Company, the Guarantor and the Designated Subsidiaries to, among other things, create or incur Liens and to sell or otherwise dispose of Designated Subsidiaries. The Indenture also imposes limitations on the ability of the Company and the Guarantor to consolidate or amalgamate with or merge into any other Person or convey, transfer, sell or lease its property or assets substantially as an entirety to any Person.

6. Special Redemption

If (i) the Purchase Agreements are terminated on any date prior to June 30, 2014, (ii) the Company publicly announces on any date prior to June 30, 2014 that the Acqui-sition will not be pursued or (iii) the Acquisition is not consummated prior to June 30, 2014 (the earliest of any such date, a ‘‘Trigger Date’’), then the Company shall redeem the Notes on the Special Mandatory Redemption Date at a special mandatory redemption price equal to 101% of the aggregate principal amount of the Notes (the “Special Mandatory Redemption Price”), plus accrued and unpaid interest on the Notes from the Issue Date, or the most recent Interest Payment Date, whichever is later, to, but excluding, the Special Mandatory Redemp-tion Date. Notwithstanding the foregoing, interest on the Notes for which the Interest Pay-ment Date is on or before the Special Mandatory Redemption Date, shall be payable on such Interest Payment Date to the holder of such Notes at the close of business on the preceding Regular Record Date.

As used in this Section 6, the following terms shall have the respective meanings set forth below:

“Purchase Agreements” mean, collectively, (i) the Asset Purchase Agreement, dated as of February 7, 2013 and amended as of May 31, 2013, and as further amended, supplemented and/or restated from time to time, by and among the Company, Arch U.S. MI Services Inc., a Delaware corporation, the Receiver of PMI Mortgage Insurance Co. in Rehabilitation (the “Receiver”), on behalf of PMI Mortgage Insurance Co., an Arizona stock insurance corporation (“PMI”), and (ii) the CMG Stock Purchase Agreement, dated as of February 7, 2013 and amended as of May 31, 2013, and as further amended, supplemented and/or restated from time to time, by and among the Company, Arch U.S. MI Holdings Inc., a Delaware corporation, the Receiver, on behalf of PMI, CMFG Life Insurance Company, formerly known as CUNA Mutual Insurance Society, an Iowa corporation, and CMG Mortgage Insurance Company, a Wisconsin insurance company.

“Acquisition” means the transaction contemplated by the Purchase Agree-ments.

“Special Mandatory Redemption Date” means the tenth Business Day fol-lowing the Trigger Date.

7. Notice of Special Mandatory Redemption

The Company shall cause notice of a special mandatory redemption pursuant to Section 4.1 of the First Supplemental Indenture and Section 6 hereof to be mailed by first-class mail, postage prepaid, to each Holder of the Notes at its address appearing on the Security Register, with a copy to the Trustee, no later than five Business Days after the occurrence of a Trigger Date. Such notice shall state, among other things, the Special Mandatory Redemption Date, the Special Mandatory Redemption Price and any accrued interest. If money sufficient to pay the Special Mandatory Redemption Price of all Notes to be redeemed on the Special Mandatory Redemption Date, and any accrued interest, in accordance with the Section 4.1 of the First Supplemental Indenture and Section 6 hereof are deposited with the Paying Agent on or before the Special Mandatory Redemption Date, the Notes shall cease to bear interest on and after the Special Mandatory Redemption Date, and all rights under the Notes shall terminate.

8. Optional Redemption

twelve 30-day months) at the Treasury Rate, plus 20 basis points. Interest on the Notes for which the Redemption Date is after a Regular Record Date and before the following Interest Payment Date, shall be payable to the holder of such Notes at the close of business on the Regular Record Date.

As used in this Section 8, the following terms shall have the respective meanings set forth below:

“Independent Investment Banker” means one of the Reference Treasury Dealers appointed by the Company after consultation with the Trustee.

The provisions of Article Eleven of the Original Indenture shall apply in the case of a redemption pursuant to Article Five of the Supplemental Indenture and this Section 8.

9. Notice of Optional Redemption

Notice of optional redemption will be mailed by first-class mail, postage prepaid, at least 30 days but not more than 60 days before the Redemption Date to each Holder of Notes to be redeemed at such Holder’s registered address. Notes in denominations larger than $2,000 may be redeemed in part but only in whole multiples of $1,000. If money sufficient to pay the Redemption Price of and accrued and unpaid interest, including premium, if any, on all Notes (or portions thereof) to be redeemed on the Redemption Date is deposited with the Paying Agent on or before the Redemption Date and certain other conditions are satisfied, on and after such date interest ceases to accrue on such Notes (or such portions thereof) called for redemption.

10. Sinking Fund

The Notes will not be entitled to the benefit of any sinking fund.

11. Denominations; Transfer; Exchange

The Notes are in fully registered form without coupons in denominations of $2,000 and any whole multiple of $1,000. A Holder may transfer or exchange Notes in accordance with the Indenture. Upon any transfer or exchange, the Registrar and the Trustee may require a Holder, among other things, to furnish appropriate endorsements or transfer documents. No service charge shall be made for any registration of transfer or exchange, but the Company or the Trustee may require the payment of a sum sufficient to cover any tax or other governmental charge that may be imposed in connection therewith permitted by the Indenture.

12. Persons Deemed Owners

The registered Holder of this Note may be treated as the owner of it for all purposes.

13. Discharge and Defeasance

Subject to certain conditions and limitations set forth in the Indenture, the Company may terminate some of or all its obligations under the Notes and the Indenture (or elect to have the some or all of the obligations of the Guarantor under the Guarantee and Indenture terminated) if the Company deposits with the Trustee money or U.S. Government Obligations for the payment of principal of, premium, if any, and interest, on, the Notes to redemption or maturity, as the case may be.

14. Amendment, Waiver

Subject to certain exceptions set forth in the Indenture, (i) the Indenture and the terms of the Notes may be amended with the written consent of the Holders of not less than a majority in aggregate principal amount of the Notes and (ii) any default may be waived

with the written consent of the Holders of at least a majority in principal amount of the Outstanding Securities of such series affected. Subject to certain exceptions set forth in the Indenture, without the consent of any Holder, the Company, the Guarantor and the Trustee may amend the Indenture, the Notes or the Guarantee, so long as such changes do not materially and adversely affect the interests of the Holder, (a) to cure any ambiguity, omission, defect or inconsistency; (b) to make any change that does not adversely affect the rights of any Holder in any material respect; (c) to provide for successors to the Company or the Guarantor; (d) to provide any security for or additional guarantees of the Notes; (e) to add Events of Default with respect to the Notes; (f) to add additional covenants or to surrender any right or power conferred upon the Company or the Guarantor, as the case may be, by the Indenture; (g) to comply with the requirements of the Commission in order to effect or maintain the qualification of the Indenture under the TIA; (h) to provide for uncertificated Notes in addition to certificated Notes; (i) to change or eliminate any of the provisions of the Indenture, provided that such change or elimination shall become effective only when there are no Securities of a prior series outstanding that are entitled to the benefit of such provision; (j) to establish the form or terms of Securities or the related Guarantees as permitted by the Indenture; and (k) to evidence and provide for the acceptance of appointment under the Indenture by a successor Trustee with respect to the Securities of one or more series and to add to or change any of the provisions of the Indenture as shall be necessary to provide for or facilitate the administration of the trusts under the Indenture by more than one Trustee, pursuant to the Indenture.

15. Defaults and Remedies

If an Event of Default, other than an Event of Default described in Section 5.01(5) or 5.01(6) of the Original Indenture, with respect to the Notes shall have occurred and be continuing, the Trustee or the Holders of at least 25% in aggregate principal amount of the Notes then Outstanding, by notice in writing to the Company and the Guarantor (and to the Trustee if given by the Holders of the Notes), will be entitled to declare all unpaid principal of and accrued interest on the Notes then Outstanding to be due and payable immediately. In the case of an Event of Default described in Section 5.01(5) or 5.01(6) of the Original Indenture, all unpaid principal of and accrued interest on all Notes then outstanding shall be due and payable immediately without any declaration or other act on the part of the Trustee or the Holders of any Notes. Such declaration of acceleration may be annulled and past defaults (except, unless theretofore cured, a default in payment of principal of, premium, if any, interest on the Notes) may be waived by the Holders of a majority in principal amount of the Notes then outstanding upon the conditions provided in the Indenture.

16. Trustee Dealings with the Company and the Guarantor

Subject to certain limitations imposed by the TIA, the Trustee under the Indenture, in its individual or any other capacity, may become the owner or pledgee of Note or Securities of other series and may otherwise deal with and collect obligations owed to it by the Company, the Guarantor or their respective Affiliates and, subject to the Indenture, may otherwise deal with the Company or the Guarantor, as the case may be, with the same rights it would have if it were not Trustee.

17. No Recourse Against Others

No incorporator, shareholder, officer or director, as such, of the Company or the Guarantor, as the case may be, shall have any liability for any obligations, covenants or agreements of the Company under the Notes or the Indenture or the Guarantor under the Guarantee of the Indenture, or for any claim based thereon or otherwise in respect thereof. By accepting a Note, each Holder expressly waives and releases all such liability. The waiver and release are a condition of, and part of the consideration for, the execution of the Indenture and the issuance of the Notes and the Guarantee.

18. Authentication

This Note shall not be valid until an authorized signatory of the Trustee manually signs the certificate of authentication on the other side of this Note.

19. Abbreviations

Customary abbreviations may be used in the name of a Holder or an assignee, such as TEN COM (=tenants in common), TEN ENT (=tenants by the entireties), JT TEN (=joint tenants with rights of survivorship and not as tenants in common), CUST (=custodian), and U/G/M/A (=Uniform Gift to Minors Act).

20. Governing Law

THE INDENTURE, THIS NOTE AND THE GUARANTEE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.

21. CUSIP Number

Pursuant to a recommendation promulgated by the Committee on Uniform Security Identification Procedures, the Company has caused the CUSIP number to be printed on this Note and has directed the Trustee to use the CUSIP number in notices of redemption as a convenience to Holders. No representation is made as to the accuracy of such number either as printed on this Note or as contained in any notice of redemption and reliance may be placed only on the other identification numbers placed thereon.

The Company will furnish to any Holder of Notes upon written request and without charge to the Holder a copy of the Indenture and a copy of this Note.

ASSIGNMENT FORM

To assign this Note , fill in the form below:

I or we assign and transfer this Security to


(Print or type assignee’s name, address and zip code)


(Insert assignee’s soc. sec. or tax I.D. No.)

and irrevocably appoint agent to transfer this Note on the books of the Company. The agent may substitute another to act for him.


Sign exactly as your name appears on the other side of this Note.

SCHEDULE OF INCREASES OR DECREASES IN GLOBAL SECURITY

The initial principal amount of this Global Security is $ . The following increases or decreases in this Global Security have been made:

Date of Exchange	Amount of decrease in Principal Amount of this Global Security	Amount of increase in Principal Amount of this Global Security	Principal amount of this Global Security following such decrease or increase	Signature of authorized signatory of Trustee or Securities Custodian

Your Signature: