Exhibit

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EXHIBIT 5.2

November 23, 2020

Arch Capital Group Ltd.
Waterloo House, Ground Floor
100 Pitts Bay Road
Pembroke HM 08
Bermuda

Arch Capital Group (U.S.) Inc.
Harborside Financial Center

300 Plaza Three, 3rd Floor

Jersey City, NJ 07311

Arch Capital Finance LLC

360 Hamilton Avenue, Suite 600

White Plains, NY 10601

Ladies and Gentlemen:

We have acted as special United States counsel to Arch Capital Group Ltd., a Bermuda exempted company (the “Company”), Arch Capital Group (U.S.) Inc., a Delaware corporation (“Arch US”) and Arch Capital Finance LLC (“Arch Finance” and, together with the Company and Arch US, the “Registrants”), in connection with:

1. the Registration Statement on Form S-3 (the “Registration Statement”) to be filed with the Securities and Exchange Commission (the “Commission”), pursuant to which (A) the Company proposes to issue and/or sell from time to time (i) Common Shares, par value U.S. $.0011 per share (the “Common Shares”), (ii) Preference Shares, par value U.S.$.01 per share (the “Preference Shares”), (iii) debt securities consisting of debentures, notes or other evidences of indebtedness representing unsecured, unsubordinated obligations of the Company (the “Senior Debt Securities”), (iv) debt securities consisting of debentures, notes or other evidences of indebtedness representing unsecured, subordinated obligations of the Company (the “Subordinated Debt Securities” and, together with the Senior Debt Securities, the “Debt Securities”), (v) depositary shares representing Common Shares or Preference Shares (the “Depositary Shares”), (vi) warrants to purchase Common Shares (the “Common Share Warrants”), (vii) warrants to purchase Preference Shares (the “Preference Share Warrants”), (viii) warrants to purchase Debt Securities (the “Debt Securities Warrants”), (ix) Common Share purchase contracts obligating the holders thereof to purchase from the Company, and the Company to sell to such holders, or obligating the Company to purchase from the holders thereof, and such holders to sell to the Company, at a future date, a specified number of Common Shares (the “Common Share Purchase Contracts”), (x) Common Share purchase units (the “Common Share Purchase Units”) consisting of one or more Common Share Purchase Contracts and any one or more of (a) debt or equity obligations of third parties, including,

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but not limited to U.S. Treasury securities, (b) Preference Shares, (c) Senior Debt Securities, (d) Subordinated Debt Securities, (e) Arch US Preferred Stock (as defined below), (f) Arch US Senior Debt Securities (as defined below), (g) Arch US Subordinated Debt Securities (as defined below) and (h) Arch Finance Senior Debt Securities (as defined below), (xi) guarantees of the Arch US Preferred Stock (the “Arch US Preferred Stock Guarantee”), (xii) guarantees of the Arch US Senior Debt Securities (the “Arch US Senior Debt Securities Guarantee”), (xiii) guarantees of the Arch US Subordinated Debt Securities (the “Arch US Subordinated Debt Securities Guarantee”) and (xiv) guarantees of the Arch Finance Senior Debt Securities (the “Arch Finance Senior Debt Securities Guarantee”); (B) Arch US proposes to issue and sell from time to time (i) Preferred Stock, par value U.S. $.01 per share (the “Arch US Preferred Stock”), which will have the benefit of the Arch US Preferred Stock Guarantee, (ii) debt securities consisting of debentures, notes or other evidences of indebtedness representing unsecured, unsubordinated obligations of Arch US (the “Arch US Senior Debt Securities”), which will have the benefit of the Arch US Senior Debt Securities Guarantee and (iii) debt securities consisting of debentures, notes or other evidences of indebtedness representing unsecured, subordinated obligations of Arch US (the “Arch US Subordinated Debt Securities”), which will have the benefit of the Arch US Subordinated Debt Securities Guarantee; (C) Arch Finance proposes to issue and sell from time to time debt securities consisting of debentures, notes or other evidences of indebtedness representing unsecured, unsubordinated obligations of Arch Finance (the “Arch Finance Senior Debt Securities”), which will have the benefit of the Arch Finance Senior Debt Securities Guarantee; and (D) selling shareholders may sell Common Shares from time to time;

2. the indenture, dated as of May 4, 2004 (the “Senior Debt Indenture”), between the Company and The Bank of New York Mellon, as successor trustee to JPMorgan Chase Bank, N.A. (the “Senior Debt Trustee”);

3. the form of indenture, to be dated on or about the date of first issuance of Subordinated Debt Securities thereunder (the “Subordinated Debt Indenture”), between the Company and a trustee to be named (the “Subordinated Debt Trustee”);

4. the indenture, dated as of December 13, 2013 (the “Arch US Senior Debt Indenture”), by and among Arch US, as issuer, the Company, as guarantor, and The Bank of New York Mellon, as trustee (in such capacity, the “Arch US Senior Debt Trustee”);

5. the form of indenture, to be dated on or about the dated of first issuance of Arch US Subordinated Debt Securities thereunder (the “Arch US Subordinated Debt Indenture”), by and among Arch US, as issuer, the Company, as guarantor, and a trustee to be named (the “Arch US Subordinated Debt Trustee”);

6. the indenture, dated as of December 8, 2016 (the “Arch Finance Senior Debt Indenture”), by and among Arch Finance, as issuer, the Company, as guarantor, and The Bank of New York Mellon, as trustee (in such capacity, the “Arch Finance Senior Debt Trustee”);

7. the form of Arch US Preferred Stock Guarantee;

8. the form of Arch US Senior Debt Securities Guarantee;

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9. the form of Arch US Subordinated Debt Securities Guarantee; and

10 the form of Arch Finance Senior Debt Securities Guarantee.

The Common Shares, the Preference Shares, the Senior Debt Securities, the Subordinated Debt Securities, the Depositary Shares, the Common Share Warrants, the Preference Share Warrants, the Debt Securities Warrants, the Common Share Purchase Contracts, the Common Share Purchase Units, the Arch US Preferred Stock, the Arch US Senior Debt Securities, the Arch US Subordinated Debt Securities, the Arch Finance Senior Debt Securities, the Arch US Preferred Stock Guarantee, the Arch US Senior Debt Securities Guarantee, the Arch US Subordinated Debt Securities Guarantee and the Arch Finance Senior Debt Securities Guarantee are referred to herein collectively as the “Offered Securities.” The Senior Debt Indenture, the Subordinated Debt Indenture, the Arch US Senior Debt Indenture, the Arch US Subordinated Debt Indenture and the Arch Finance Senior Debt Indenture are referred to herein collectively as the “Indentures.” The Arch US Senior Debt Securities Guarantee and the Arch US Subordinated Debt Securities Guarantee are referred to herein collectively as the “Arch US Debt Securities Guarantees.” The Offered Securities being registered under the Registration Statement may be offered on a continued or delayed basis pursuant to the provisions of Rule 415 of the Securities Act of 1933, as amended (the “Securities Act”).

In rendering the opinion set forth herein, we have examined originals, photocopies or conformed copies certified to our satisfaction of corporate records, agreements, instruments and documents of the Registrants, certificates of public officials and other certificates and opinions and have made such other investigations as we have deemed necessary in connection with the opinion set forth herein. In our examination, we have assumed (a) the due organization and valid existence of each of the Registrants, (b) the due authorization, execution, authentication and delivery by all persons of the Registration Statement and each of the documents related thereto, (c) that each of such parties has the legal power to act in the respective capacity or capacities in which he, she or it is to act thereunder, (d) the authenticity of all documents submitted to us as originals, (e) the conformity to the original documents of all documents submitted to us as copies and (f) the genuineness of all signatures on the Registration Statement and all documents submitted to us.

Based upon and subject to the foregoing and assuming that (i) the Registration Statement and any amendments thereto (including any post-effective amendments) will have become effective and comply with all applicable laws at the time the Offered Securities are offered or issued as contemplated by the Registration Statement, (ii) a prospectus supplement will have been prepared and filed with the Commission describing the Offered Securities offered thereby and will at all relevant times comply with all applicable laws, (iii) all Offered Securities will be issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement and the appropriate prospectus supplement, (iv) a definitive purchase, underwriting or similar agreement and any other necessary agreement with respect to any Offered Securities will have been duly authorized and validly executed and delivered by each applicable Registrant and the other party or parties thereto, (v) the applicable Indenture(s) will have been duly qualified under the Trust Indenture Act of 1939, as amended (the “TIA”), (vi) the applicable Arch US Debt Securities Guarantee(s) or Arch Finance Senior Debt Securities Guarantee will have been duly qualified under the TIA and (vii) any Offered Securities issuable upon conversion, exercise or exchange of any Offered Securities being offered or issued will be duly authorized, created and, if appropriate, reserved for issuance upon such conversion, exercise or exchange, we advise you that in our opinion:

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1. Insofar as the laws of the State of New York are applicable thereto, when (A) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary action to approve the issuance and terms of the Senior Debt Securities and related matters, (B) the terms of the Senior Debt Securities and their issuance and sale have been duly established in conformity with the Senior Debt Indenture and so as not to violate any applicable law, the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, (C) either a supplemental indenture has been duly authorized, executed and delivered by the Company and the Senior Debt Trustee or a securities resolution has been duly executed setting forth the terms of the Senior Debt Securities, in each case, in accordance with the Senior Debt Indenture and (D) the Senior Debt Securities, in the form established in accordance with the Senior Debt Indenture filed as an exhibit to the Registration Statement, have been duly executed and delivered by the Company and authenticated by the Senior Debt Trustee in accordance with the provisions of the Senior Debt Indenture and delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Senior Debt Securities will constitute valid and legally binding obligations of the Company, entitled to the benefits of the Senior Debt Indenture and enforceable against the Company in accordance with their terms, except that (a) the enforceability thereof may be subject to (i) bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance or other similar laws now or hereafter in effect relating to or affecting creditors' rights or remedies generally and (ii) general principles of equity and the discretion of the court before which any proceedings therefor may be brought (regardless of whether enforcement is sought in a proceeding at law or in equity) and (b) the enforceability of provisions imposing liquidated damages, penalties or an increase in interest rate upon the occurrence of certain events may be limited in certain circumstances ((a) and (b) collectively, the “Enforceability Exceptions”).

2. Insofar as the laws of the State of New York are applicable thereto, when (A) the execution of the Subordinated Debt Indenture has been duly authorized by the Company by appropriate action, (B) the Subordinated Debt Indenture, in the form filed as an exhibit to the Registration Statement, has been duly executed and delivered by the Company and the Subordinated Debt Trustee, (C) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary action to approve the issuance and terms of the Subordinated Debt Securities and related matters, (D) the terms of the Subordinated Debt Securities and their issuance and sale have been duly established in conformity with the Subordinated Debt Indenture and so as not to violate any applicable law, the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, (E) either a supplemental indenture has been duly authorized, executed and delivered by the Company and the Subordinated Debt Trustee or a securities resolution has been duly executed setting forth the terms of the Subordinated Debt Securities, in each case, in accordance with the Subordinated Debt Indenture and (F) the Subordinated Debt Securities, in the form established in accordance with the Subordinated Debt Indenture filed as an exhibit to the Registration Statement, have been duly executed and delivered by the Company and authenticated by the Subordinated Debt Trustee in accordance with the provisions of the Subordinated

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Debt Indenture and delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Subordinated Debt Securities will constitute valid and legally binding obligations of the Company, entitled to the benefits of the Subordinated Debt Indenture and enforceable against the Company in accordance with their terms, subject to the Enforceability Exceptions.

3. Insofar as the laws of the State of New York are applicable thereto, when (A) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of Arch US have taken all necessary action to approve the issuance and terms of the Arch US Senior Debt Securities and related matters, (B) the terms of the Arch US Senior Debt Securities and their issuance and sale have been duly established in conformity with the Arch US Senior Debt Indenture and so as not to violate any applicable law, the Amended and Restated Certificate of Incorporation or By-laws of Arch US or the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon Arch US or the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over Arch US or the Company, (C) either a supplemental indenture has been duly authorized, executed and delivered by Arch US, the Company and the Arch US Senior Debt Trustee or a securities resolution has been duly executed setting forth the terms of the Arch US Senior Debt Securities, in each case, in accordance with the Arch US Senior Debt Indenture and (D) the Arch US Senior Debt Securities, in the form established in accordance with the Arch US Senior Debt Indenture filed as an exhibit to the Registration Statement, have been duly executed and delivered by Arch US and authenticated by the Arch US Senior Debt Trustee in accordance with the provisions of the Arch US Senior Debt Indenture and delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Arch US Senior Debt Securities will constitute valid and legally binding obligations of Arch US, entitled to the benefits of the Arch US Senior Debt Indenture and enforceable against Arch US in accordance with their terms, subject to the Enforceability Exceptions.

4. Insofar as the laws of the State of New York are applicable thereto, when (A) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of Arch US and the Company have taken all necessary action to approve the issuance and terms of the Arch US Senior Debt Securities and the Arch US Senior Debt Securities Guarantee, respectively, and related matters, (B) the terms of the Arch US Senior Debt Securities and their issuance and sale and the terms of the Arch US Senior Debt Securities Guarantee have been duly established in conformity with the Arch US Senior Debt Indenture and so as not to violate any applicable law, the Amended and Restated Certificate of Incorporation or By-laws of Arch US or the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon Arch US or the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over Arch US or the Company, (C) either a supplemental indenture has been duly authorized, executed and delivered by Arch US, the Company and the Arch US Senior Debt Trustee or a securities resolution has been duly executed setting forth the terms of the Arch US Senior Debt Securities, in each case, in accordance with the Arch US Senior Debt Indenture, (D) the Arch US Senior Debt Securities, in the form established in accordance with the Arch US Senior Debt Indenture filed as an exhibit to the Registration Statement, have been duly executed and delivered by Arch US and authenticated by the Arch US Senior Debt

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Trustee in accordance with the provisions of the Arch US Senior Debt Indenture, (E) the Arch US Senior Debt Securities Guarantee, in the form included in the form of Arch US Senior Debt Indenture filed as an exhibit to the Registration Statement, has been duly executed and delivered by the Company and (F) the Arch US Senior Debt Securities are delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Arch US Senior Debt Securities Guarantee will constitute a valid and legally binding obligation of the Company, entitled to the benefits of the Arch US Senior Debt Indenture and enforceable against the Company in accordance with its terms, subject to the Enforceability Exceptions.

5. Insofar as the laws of the State of New York are applicable thereto, when (A) the execution of the Arch US Subordinated Debt Indenture has been duly authorized by Arch US by appropriate action, (B) the Arch US Subordinated Debt Indenture, in the form filed as an exhibit to the Registration Statement, has been duly executed and delivered by Arch US, the Company and the Arch US Subordinated Debt Trustee, (C) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of Arch US have taken all necessary action to approve the issuance and terms of the Arch US Subordinated Debt Securities and related matters, (D) the terms of the Arch US Subordinated Debt Securities and their issuance and sale have been duly established in conformity with the Arch US Subordinated Debt Indenture and so as not to violate any applicable law, the Amended and Restated Certificate of Incorporation or By-laws of Arch US or the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon Arch US or the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over Arch US or the Company, (E) either a supplemental indenture has been duly authorized, executed and delivered by Arch US, the Company and the Arch US Subordinated Debt Trustee or a securities resolution has been duly executed setting forth the terms of the Arch US Subordinated Debt Securities, in each case, in accordance with the Arch US Subordinated Debt Indenture and (F) the Arch US Subordinated Debt Securities, in the form established in accordance with the Arch US Subordinated Debt Indenture filed as an exhibit to the Registration Statement, have been duly executed and delivered by Arch US and authenticated by the Arch US Subordinated Debt Trustee in accordance with the provisions of the Arch US Subordinated Debt Indenture and delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Arch US Subordinated Debt Securities will constitute valid and legally binding obligations of Arch US, entitled to the benefits of the Arch US Subordinated Debt Indenture and enforceable against Arch US in accordance with their terms, subject to the Enforceability Exceptions.

6. Insofar as the laws of the State of New York are applicable thereto, when (A) the execution of the Arch US Subordinated Debt Indenture has been duly authorized by Arch US by appropriate action, (B) the Arch US Subordinated Debt Indenture, in the form filed as an exhibit to the Registration Statement, has been duly executed and delivered by Arch US, the Company and the Arch US Subordinated Debt Trustee, (C) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of Arch US and the Company have taken all necessary action to approve the issuance and terms of the Arch US Subordinated Debt Securities and the Arch US Subordinated Debt Securities Guarantee, respectively, and related matters, (D) the terms of the Arch US Subordinated Debt Securities and their issuance and sale and the terms of the Arch US Subordinated Debt Securities Guarantee have been duly established in conformity with the Arch US

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Subordinated Debt Indenture and so as not to violate any applicable law, the Amended and Restated Certificate of Incorporation or By-laws of Arch US or the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon Arch US or the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over Arch US or the Company, (E) either a supplemental indenture has been duly authorized, executed and delivered by Arch US, the Company and the Arch US Subordinated Debt Trustee or a securities resolution has been duly executed setting forth the terms of the Arch US Subordinated Debt Securities, in each case, in accordance with the Arch US Subordinated Debt Indenture, (F) the Arch US Subordinated Debt Securities, in the form established in accordance with the Arch US Subordinated Debt Indenture filed as an exhibit to the Registration Statement, have been duly executed and delivered by Arch US and authenticated by the Arch US Subordinated Debt Trustee in accordance with the provisions of the Arch US Subordinated Debt Indenture, (G) the Arch US Subordinated Debt Securities Guarantee, in the form included in the form of Arch US Subordinated Debt Indenture filed as an exhibit to the Registration Statement, has been duly executed and delivered by the Company and (H) the Arch US Subordinated Debt Securities are delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Arch US Subordinated Debt Securities Guarantee will constitute a valid and legally binding obligation of the Company, entitled to the benefits of the Arch US Subordinated Debt Indenture and enforceable against the Company in accordance with its terms, subject to the Enforceability Exceptions.

7. Insofar as the laws of the State of New York are applicable thereto, when (A) the board of managers, including any appropriate committee appointed thereby, and appropriate officers of Arch Finance have taken all necessary action to approve the issuance and terms of the Arch Finance Senior Debt Securities and related matters, (B) the terms of the Arch Finance Senior Debt Securities and their issuance and sale have been duly established in conformity with the Arch Finance Senior Debt Indenture and so as not to violate any applicable law, the Certificate of Formation or Limited Liability Company Agreement of Arch Finance or the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon Arch Finance or the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over Arch Finance or the Company, (C) either a supplemental indenture has been duly authorized, executed and delivered by Arch Finance, the Company and the Arch Finance Senior Debt Trustee or a securities resolution has been duly executed setting forth the terms of the Arch Finance Senior Debt Securities, in each case, in accordance with the Indenture and (D) the Arch Finance Senior Debt Securities, in the form established in accordance with the Arch Finance Senior Debt Indenture filed as an exhibit to the Registration Statement, have been duly executed and delivered by Arch Finance and authenticated by the Arch Finance Senior Debt Trustee in accordance with the provisions of the Arch Finance Senior Debt Indenture and delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Arch Finance Senior Debt Securities will constitute valid and legally binding obligations of Arch Finance, entitled to the benefits of the Arch Finance Senior Debt Indenture and enforceable against Arch Finance in accordance with their terms, subject to the Enforceability Exceptions.

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8. Insofar as the laws of the State of New York are applicable thereto, when (A) the board of managers, including any appropriate committee appointed thereby, and appropriate officers of Arch Finance and the Company have taken all necessary action to approve the issuance and terms of the Arch Finance Senior Debt Securities and the Arch Finance Senior Debt Securities Guarantee, respectively, and related matters, (B) the terms of the Arch Finance Senior Debt Securities and their issuance and sale and the terms of the Arch Finance Senior Debt Securities Guarantee have been duly established in conformity with the Arch Finance Senior Debt Indenture and so as not to violate any applicable law, the Certificate of Formation or Limited Liability Company Agreement of Arch Finance or the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon Arch Finance or the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over Arch Finance or the Company, (C) either a supplemental indenture has been duly authorized, executed and delivered by Arch Finance, the Company and the Arch Finance Senior Debt Trustee or a securities resolution has been duly executed setting forth the terms of the Arch Finance Senior Debt Securities, in each case, in accordance with the Indenture, (D) the Arch Finance Senior Debt Securities, in the form established in accordance with the Arch Finance Senior Debt Indenture filed as an exhibit to the Registration Statement, have been duly executed and delivered by Arch Finance and authenticated by the Arch Finance Senior Debt Trustee in accordance with the provisions of the Arch Finance Senior Debt Indenture, (E) the Arch Finance Senior Debt Securities Guarantee, in the form included in the Arch Finance Senior Debt Indenture filed as an exhibit to the Registration Statement, has been duly executed and delivered by the Company and (F) the Arch Finance Senior Debt Securities are delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Arch Finance Senior Debt Securities Guarantee will constitute a valid and legally binding obligation of the Company, entitled to the benefits of the Arch Finance Senior Debt Indenture and enforceable against the Company in accordance with its terms, subject to the Enforceability Exceptions.

9. Insofar as the General Corporation Law of the State of Delaware (the “DGCL”) is applicable thereto, when (A) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of Arch US have taken all necessary action to approve the issuance and terms of a series of Arch US Preferred Stock (including the powers, designations, preferences and relative, participating, optional or other rights, if any, thereof), the adoption of a Certificate of Designations (the “Certificate of Designations”) relating thereto in the form required by applicable law and related matters, (B) the terms of such series of Arch US Preferred Stock and the issuance and sale thereof have been duly established in accordance with Section 151 of the DGCL and in conformity with the Amended and Restated Certificate of Incorporation and By-laws of Arch US and so as not to violate any applicable law or the Memorandum of Association or Bye-Laws of the Company or result in a default under or breach of any agreement or instrument binding upon Arch US or the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over Arch US or the Company, (C) proper and valid filing with the Office of the Secretary of State of the State of Delaware of the Certificate of Designations has been made and (D) the shares of such series of Arch US Preferred Stock have been issued and delivered against payment therefor in an amount in excess of the par value thereof, as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, such shares of Arch US Preferred Stock will be validly issued, fully paid and non-assessable.

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10. Insofar as the DGCL or the laws of the State of New York are applicable thereto, when (A) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of Arch US have taken all necessary action to approve the issuance and terms of a series of Arch US Preferred Stock (including the powers, designations, preferences and relative, participating, optional or other rights, if any, thereof), the adoption of the Certificate of Designations relating thereto in the form required by applicable law and related matters, (B) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary action to approve the issuance and terms of the Arch US Preferred Stock Guarantee and related matters, (C) the terms of such series of Arch US Preferred Stock and the issuance and sale thereof have been duly established in accordance with Section 151 of the DGCL and in conformity with the Amended and Restated Certificate of Incorporation and By-laws of Arch US, (D) the terms of such series of Arch US Preferred Stock and the issuance and sale thereof and the terms of the Arch US Preferred Stock Guarantee have been duly established so as not to violate any applicable law or the Memorandum of Association or Bye-Laws of the Company or result in a default under or breach of any agreement or instrument binding upon Arch US or the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over Arch US or the Company, (E) proper and valid filing with the Office of the Secretary of State of the State of Delaware of the Certificate of Designations has been made, (F) the Arch US Preferred Stock Guarantee, in the form filed as an exhibit to the Registration Statement, has been duly executed and delivered by the Company and (G) the shares of such series of Arch US Preferred Stock have been issued and delivered against payment therefor in an amount in excess of the par value thereof, as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Arch US Preferred Stock Guarantee will constitute a valid and legally binding obligation of the Company, enforceable against the Company in accordance with its terms, subject to the Enforceability Exceptions.

11. Insofar as the laws of the State of New York are applicable thereto, when (A) the execution of the deposit agreement pursuant to which the Depositary Shares will be issued (the “Deposit Agreement”) has been duly authorized by the Company by appropriate action, (B) the Deposit Agreement has been duly executed and delivered by the Company and the depositary thereunder, (C) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary action to approve the issuance and terms of the Depositary Shares and related matters, (D) the terms of the Depositary Shares and their issuance and sale have been duly established in conformity with the Deposit Agreement and so as not to violate any applicable law, the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company and (E) the Depositary Shares, in the form included in the Deposit Agreement, have been duly executed and delivered by the Company and countersigned by the depositary thereunder in accordance with the provisions of the Deposit Agreement and delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Depositary Shares will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with its terms, subject to the Enforceability Exceptions.

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12. Insofar as the laws of the State of New York are applicable thereto, when (A) the execution of the warrant agreement pursuant to which the Common Share Warrants will be issued (the “Common Share Warrant Agreement”) has been duly authorized by the Company by appropriate action, (B) the Common Share Warrant Agreement has been duly executed and delivered by the Company and the warrant agent thereunder, (C) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary action to approve the issuance and terms of the Common Share Warrants and related matters, including, without limitation, any necessary reservation of Common Shares issuable upon exercise of the Common Share Warrants, (D) the terms of the Common Share Warrants and their issuance and sale have been duly established in conformity with the Common Share Warrant Agreement and so as not to violate any applicable law, the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company and (E) the Common Share Warrants, in the form included in the Common Share Warrant Agreement, have been duly executed and delivered by the Company and countersigned by the warrant agent thereunder in accordance with the provisions of the Common Share Warrant Agreement and delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Common Share Warrants will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with its terms, subject to the Enforceability Exceptions.

13. Insofar as the laws of the State of New York are applicable thereto, when (A) the execution of the warrant agreement pursuant to which the Preference Share Warrants will be issued (the “Preference Share Warrant Agreement”) has been duly authorized by the Company by appropriate action, (B) the Preference Share Warrant Agreement has been duly executed and delivered by the Company and the warrant agent thereunder, (C) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary action to approve the issuance and terms of the Preference Share Warrants and related matters, including, without limitation, any necessary reservation of Preference Shares issuable upon exercise of the Preference Share Warrants, (D) the terms of the Preference Share Warrants and their issuance and sale have been duly established in conformity with the Preference Share Warrant Agreement and so as not to violate any applicable law, the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company and (E) the Preference Share Warrants, in the form included in the Preference Share Warrant Agreement, have been duly executed and delivered by the Company and countersigned by the warrant agent thereunder in accordance with the provisions of the Preference Share Warrant Agreement and delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Preference Share Warrants will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with its terms, subject to the Enforceability Exceptions.

14. Insofar as the laws of the State of New York are applicable thereto, when (A) the execution of the warrant agreement pursuant to which the Debt Securities Warrants will be issued (the “Debt Securities Warrant Agreement”) has been duly authorized by the Company by appropriate

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action, (B) the Debt Securities Warrant Agreement has been duly executed and delivered by the Company and the warrant agent thereunder, (C) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary action to approve the issuance and terms of the Debt Securities Warrants and related matters, including, without limitation, any necessary reservation of Debt Securities issuable upon exercise of the Debt Securities Warrants, (D) the terms of the Debt Securities Warrants and their issuance and sale have been duly established in conformity with the Debt Securities Warrant Agreement and so as not to violate any applicable law, the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company and (E) the Debt Securities Warrants, in the form included in the Debt Securities Warrant Agreement, have been duly executed and delivered by the Company and countersigned by the warrant agent thereunder in accordance with the provisions of the Debt Securities Warrant Agreement and delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Debt Securities Warrants will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with its terms, subject to the Enforceability Exceptions.

15. Insofar as the laws of the State of New York are applicable thereto, when (A) the execution of the Common Share Purchase Contracts has been duly authorized by the Company and each counterparty thereunder by appropriate action, (B) the Common Share Purchase Contracts have been duly executed and delivered by the Company and the counterparty thereunder, (C) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary action to approve the issuance and terms of the Common Share Purchase Contracts and related matters, (D) the terms of the Common Share Purchase Contracts and their issuance and sale have been duly established so as not to violate any applicable law, the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company and (E) the Common Share Purchase Contracts, in an appropriate form, have been duly executed and delivered by the Company and countersigned by the counterparty thereunder and delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Common Share Purchase Contracts will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with its terms, subject to the Enforceability Exceptions.

16. Insofar as the laws of the State of New York are applicable thereto, when (A) the execution of the Common Share Purchase Units has been duly authorized by the Company and each counterparty thereunder by appropriate action, (B) the Common Share Purchase Units have been duly executed and delivered by the Company and the counterparty thereunder, (C) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary action to approve the issuance and terms of the Common Share Purchase Units and related matters, (D) the terms of the Common Share Purchase Units and their issuance and sale have been duly established so as not to violate any applicable law, the Memorandum of Association or Bye-Laws of the Company or result in default under or breach of any agreement or

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instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company and (E) the Common Share Purchase Units, in an appropriate form, have been duly executed and delivered by the Company and countersigned by the counterparty thereunder and delivered and paid for as contemplated by any applicable purchase or underwriting agreement and the Registration Statement, the Common Share Purchase Units will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with its terms, subject to the Enforceability Exceptions.

In giving our opinion, we are relying, without independent verification (A) as to all matters of fact, upon certificates and written statements of officers of the Registrants and (B) as to all matters of Bermuda law, on the opinion of Conyers Dill & Pearman, dated of even date herewith and filed as Exhibit 5.1 to the Registration Statement.

We are members of the Bar of the State of New York and do not purport to be experts in or to express any opinion concerning the laws of any jurisdictions other than the laws of the State of New York, the DGCL and the federal laws of the United States of America. In rendering the opinion set forth above, we express no opinion as to the laws of any jurisdictions other than the laws of the State of New York, the DGCL and the federal laws of the United States.

We hereby consent to the reference to our firm in the Registration Statement under the caption “Legal Matters” and to the inclusion of this opinion as an exhibit to the Registration Statement. Our consent to such reference does not constitute a consent under Section 7 of the Securities Act, as in consenting to such reference we have not certified any part of the Registration Statement and do not otherwise come within the categories of persons whose consent is required under Section 7 of the Securities Act or under the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Cahill Gordon & Reindel LLP

CAHILL GORDON & REINDEL LLP