Exhibit 10.5

                                                                  EXECUTION COPY

                             ARCH CAPITAL GROUP LTD.
                                20 Horseneck Lane
                               Greenwich, CT 06830

                                                               November 20, 2001

<TABLE>
<CAPTION>
<S>                                                         <C>
Farallon Capital Partners, L.P.                             Warburg Pincus Private Equity VIII, L.P.
Farallon Capital Institutional Partners II, L.P.            Warburg Pincus International Partners, L.P.
Farallon Capital Institutional Partners III, L.P.           Warburg Pincus Netherlands International
RR Capital Partners, L.P. (collectively, the                         Partners I, C.V.
"Farallon Purchasers" and, individually, a                  Warburg Pincus Netherlands International
"Farallon Purchaser")                                                Partners II, C.V.
c/o Farallon Capital Management, L.L.C.                     (collectively, "Warburg")
One Maritime Plaza, Suite 1325                              466 Lexington Avenue
San Francisco, CA  94111                                    New York, NY  10017
Telephone:  (415) 421-2132
Facsimile:   (415) 421-2133                                 HFCP IV (Bermuda), L.P. ("H&F")
                                                            c/o Hellman & Friedman LLC
                                                            One Maritime Plaza
                                                            Suite 1200
                                                            San Francisco, CA  94111
</TABLE>

Ladies and Gentlemen:

     This letter agreement (this "Agreement") confirms the agreement reached
today among each of the parties signatories hereto regarding the participation
of the Farallon Purchasers in the purchase of a portion of the Securities, as
contemplated by, and on the terms set forth in, this Agreement and the
Subscription Agreement dated as of October 24, 2001, as amended (the
"Subscription Agreement") by and among Arch Capital Group Ltd. ("Arch"), Warburg
and H&F (the "Original Signatories"), and certain other matters in connection
therewith. Capitalized terms used herein without definition shall have the
meanings ascribed to such terms in the Subscription Agreement.

     1. Investment by Farallon Purchasers. H&F hereby assigns, without recourse
or warranty by it, to the Farallon Purchasers the right, and obligation, to
purchase an aggregate of $25,000,000 of the Securities (in the respective
amounts set forth on Schedule 1 hereto) on the terms and conditions set forth in
the Subscription Agreement (except as explicitly modified hereby), each Farallon
Purchaser as a Purchaser (as defined in the Subscription Agreement). Each
Farallon Purchaser acknowledges that its investment will be required to be made
on the Closing Date, simultaneously with the investments being made by the
Original Signatories. Each Farallon Purchaser shall become a "Purchaser" under
the Subscription Agreement and an "Investor" under the Shareholders Agreement
(solely for purposes of Sec-


<PAGE>
                                      -2-


tions 3.4, 5.1, 5.2 and 5.3 and Articles II, IV and VIII thereof, and the
provisions implementing the provisions described in paragraph 2 below); provided
that:

          (a) Warburg and H&F shall jointly have the sole right (on behalf of
     themselves and all other Purchasers) to make any and all determinations
     with respect to, or to take any and all actions necessary to effectuate the
     provisions of, Section B of the Subscription Agreement (including the right
     to approve any amendment or acceleration of, or to waive compliance by Arch
     with, any of the terms thereof), provided that the consequences of such
     determinations and actions by Warburg and H&F do not apply differently to
     the Farallon Purchasers than to Warburg and H&F (or, if they apply
     differently, it is because of differences in the treatment of Warburg and
     H&F as opposed to other Purchasers existing in the Subscription Agreement
     (as modified by this Agreement) and such differences are not made more
     adverse to the Farallon Purchasers or more favorable to Warburg and H&F as
     a result of such determination or action);

          (b) Warburg and H&F shall have the sole right to determine whether
     each condition for the Purchasers contained in Section C of the
     Subscription Agreement is satisfied;

          (c) the failure of the conditions set forth in Section C.2 of the
     Subscription Agreement due to any breach by a Farallon Purchaser of any
     representation, warranty or covenant shall not affect the obligation of the
     Company to sell the Securities on the Closing Date to either Warburg or
     H & F;

          (d) the Farallon Purchasers shall be subject to Section D.1 and D.2 of
     the Subscription Agreement, including the covenants thereunder;

          (e) the Farallon Purchasers shall have no rights (including no right
     to consent to any action proposed to be taken by Arch under, or any right
     to waive compliance by Arch with, any covenant or agreement) as a
     "Purchaser" under Section D.4 of the Subscription Agreement, it being
     acknowledged that the Farallon Purchasers shall, however, have the
     obligations of a "Purchaser" under Sections D.4(d), (g) and (i) thereof;
     provided that any information provided to the Company pursuant to Section
     D.4(g) shall be held confidentially and not used for any purpose other than
     as set forth in Section D.4(g);

          (f) the Farallon Purchasers shall not be considered an "original
     signatory" to the Subscription Agreement for purposes of Section E.6
     thereof, provided that no amendment, modification or waiver of Section E of
     the Subscription Agreement shall affect the Farallon Purchasers differently
     than Warburg and H&F (or, if they affect them differently, it is because of
     differences in the treatment of


<PAGE>
                                      -3-


     Warburg and H&F as opposed to other Purchasers existing in the Subscription
     Agreement (as modified by this Agreement) and such differences are not made
     more adverse to the Farallon Purchasers or more favorable to Warburg and
     H&F as a result of such determination or action);

          (g) no consent of the Farallon Purchasers shall be required to effect
     any modification or amendment to the Subscription Agreement (including,
     without limitation, Schedules A and B, and Exhibits I, II and III thereto),
     unless such amendment or modification affects the Farallon Purchasers
     differently than Warburg and H&F (or, if they affect them differently, it
     is because of differences in the treatment of Warburg and H&F as opposed to
     other Purchasers existing in the Subscription Agreement (as modified by
     this Agreement) and such differences are not made more adverse to the
     Farallon Purchasers or more favorable to Warburg and H&F as a result of
     such determination or action);

          (h) the Farallon Purchasers shall have no rights under Section F.2,
     and no right to assign under Section F.4 of the Subscription Agreement
     (except that a Farallon Purchaser may assign its rights and obligations
     under the Subscription Agreement to (i) any person or entity that directly
     or indirectly through one or more intermediaries controls, or is controlled
     by or under common control with, such Farallon Purchaser or (ii) an entity
     over which such Farallon Purchaser has management rights, in each case so
     long as such transferee becomes a party to, and bound by, this Agreement,
     Amendment No. 1 to the Subscription Agreement and the Shareholders
     Agreement (a "Permitted Transferee")); and

          (i) for the avoidance of doubt, each Farallon Purchaser shall become a
     party to the Shareholders Agreement as an "Investor" solely for purposes of
     Sections 3.4, 5.1, 5.2 and 5.3 and Articles II, IV and VIII thereof and the
     provisions thereof implementing the provisions of paragraph 2 below; it
     being further understood that Warburg and H&F can consent on behalf of all
     other Investors to (A) any amendment or modification whatsoever of the
     Sections of the Shareholders Agreement that do not apply to the Farallon
     Purchasers and (B) any amendment or modification of the Sections of the
     Shareholders Agreement that do apply to the Farallon Purchasers, so long as
     in the case of clause (B), such amendment or modification does not affect
     the Farallon Purchasers differently than Warburg and H&F (or, if they
     affect them differently, it is because of differences in the treatment of
     Warburg and H&F as opposed to other Purchasers existing in the Subscription
     Agreement or the Shareholders Agreement (as modified by this Agreement) and
     such differences are not made more adverse to the Farallon Purchaser or
     more favorable to Warburg and H&F as a result of such determination or
     action).


<PAGE>
                                      -4-


     2. Registration; Tag-Along.

     Arch, the Original Signatories and the Farallon Purchasers agree that the
Shareholders Agreement will be amended and restated to provide that (and once so
amended and restated, the Shareholders Agreement shall govern with respect to
the matters covered by this Section 2):

          (a) if a Farallon Purchaser exercises its right under Section 4.3
     thereof, any cutback pursuant to Section 4.4 thereof will treat the
     Farallon Purchaser at least as favorably as Warburg and H&F (i.e., the
     Farallon Purchaser will have priority under clause (b), and not under
     clause (c), thereof);

          (b) the Farallon Purchasers will have the rights of a Tag-Along
     Investor, under Section 5.1 thereof to participate ratably on the basis of
     securities owned in a Third Party Sale (excluding any sale or distribution
     described in the last sentence of Section 5.1 of the Shareholders
     Agreement) on the same terms as a Selling Investor (but for the avoidance
     of doubt, not have the obligations of a Selling Investor under Section 5.1
     thereof); provided that (1) each Investor participating in a transaction
     under Section 5.1 shall only be responsible for its pro rata portion of any
     indemnification (except in respect of representations specifically relating
     to such Investor) and (2) that in the event that Warburg is a Selling
     Investor, the Farallon Purchasers shall only be permitted to elect to
     participate as a Tag-Along Investor if H&F so elects;

          (c) the Farallon Purchasers shall be subject to the restrictions of
     Section 5.2 of the Shareholders Agreement with respect to the Securities
     acquired by them under the Subscription Agreement and any securities
     acquired in respect thereof, to the same extent that Warburg and H&F are
     restricted with respect to the Securities acquired by them under the
     Subscription Agreement and any securities acquired in respect thereof.

"Tag-Along Investor," "Third Party Sale and "Selling Investor" have the meanings
given to them in the Shareholders Agreement and to the extent necessary the term
"Tag-Along Investor" shall be deemed to include more than one party.

     3. Further Assurances. Subject to the terms and conditions of this
Agreement, each of the parties hereto agrees to use its reasonable best efforts
to take, or cause to be taken, all action, and to do, or cause to be done, all
things necessary or desirable under applicable legal requirements, to consummate
and make effective the transactions contemplated by this Agreement. If at any
time after the Closing Date, any further action is necessary or desirable to
carry out the purposes of this Agreement, the parties hereto shall use their
reasonable best efforts to take or cause to be taken all such necessary or
desirable action and execute, and


<PAGE>
                                      -5-


deliver and file, or cause to be executed, delivered and filed, all necessary or
desirable documentation. The Farallon Purchasers agree (to the full extent of
their current or future ownership of securities of Arch) to vote in favor of all
matters to be submitted to shareholders of Arch in connection with the foregoing
or the transactions contemplated by the Subscription Agreement (and the grants
of any shares or options contemplated thereby or in connection therewith). Each
of the parties will consult with each other with respect to the issuance of any
press release or public announcement with respect to the foregoing.

     4. Notices. All notices or other communications given or made hereunder
shall be validly given or made if in writing and delivered by facsimile
transmission or in person at, or mailed by registered or certified mail, return
receipt requested, postage prepaid, to, the addresses (and shall be deemed
effective at the time of receipt thereof):

     (a) If to Arch:

         Arch Capital Group Ltd.
         20 Horseneck Lane
         Greenwich, CT  06830
         Attention:  Peter Appel, President and Chief Executive Officer
         Facsimile:  (203) 861-7240

     (b) If to the Farallon Purchasers:

         c/o Farallon Capital Management, L.L.C.
         One Maritime Plaza, Suite 1325
         San Francisco, CA  94111
         Telephone:  (415) 421-2132
         Facsimile:   (415) 421-2133
         Attention:  Mark Wehrly and Sarah Aitcheson

or to such other address as the party to whom notice is to be given may have
previously furnished notice in writing to the other in the manner set forth
above. A notice hereunder shall not be deemed given until copies thereof are
given as contemplated above. Notices to all other parties hereto shall be given
in accordance with the Subscription Agreement.

     5. Entire Agreement; Amendment. This Agreement, together with the
Subscription Agreement, Amendment No. 1 to the Subscription Agreement (including
the exhibits thereto) and the Shareholders Agreement, contain all of the terms
agreed upon by the parties with respect to the subject matter hereof. This
Agreement may be amended or the provisions thereof waived only by a written
instrument signed by the party against whom enforcement of any waiver, change,
modification, extension or discharge is sought.


<PAGE>
                                      -6-


     6. Headings. The headings of the sections of this Agreement are inserted
for convenience only and shall not constitute a part hereof.

     7. Assignment. This Agreement and all of the provisions hereof shall be
binding upon and inure to the benefit of the parties hereto and their respective
permitted assigns, but neither this Agreement nor any of the rights, interests
or obligations hereunder shall be assigned by any party without the prior
written consent of the other party; provided that this Agreement may be assigned
by a Purchaser consistent with an assignment in accordance with Section F.4 of
the Subscription Agreement and Section 1(h) hereof, so long as the assignee
executes an agreement in the form of this Agreement.

     8. Severability. In the event that any provision or any part of this
Agreement is held to be illegal, invalid or unenforceable, such illegality,
invalidity or unenforceability shall not effect the validity or enforceability
of any other provision or part thereof.

     9. Governing Law. This Agreement shall be governed in all respects,
including validity, interpretation and effect, by the substantive laws of the
State of New York, without giving effect to principles of conflicts of laws.

     10. Counterparts. This Agreement and any instrument delivered in connection
herewith may be executed in any number of counterparts with the same effect as
if the signatures on all counterparts are upon the same instrument.

                            [Signature pages follow]




<PAGE>
                                      -7-


     Please confirm that the foregoing is in accordance with your understanding
by signing and returning to us the duplicate enclosed copy of this Agreement.

                                   Very truly yours,


                                   ARCH CAPITAL GROUP LTD.

                                   By:  /s/ Louis T. Petrillo
                                        ---------------------------------------
                                            Name:  Louis T. Petrillo
                                            Title:  Senior Vice President and
                                                    General Counsel

Agreed to and Accepted
As of the Date First Above Written:

FARALLON CAPITAL PARTNERS, L.P.

By:      Farallon Partners, L.L.C.,
         its General Partner

By:  /s/ Monica R. Landry
     ---------------------------------------
           Name:  Monica R. Landry
           Title:    Managing Member

FARALLON CAPITAL INSTITUTIONAL
PARTNERS II, L.P.

By:      Farallon Partners, L.L.C.,
         its General Partner

By:  /s/ Monica R. Landry
     ---------------------------------------
         Name:  Monica R. Landry
         Title:    Managing Member


<PAGE>
                                      -8-


FARALLON CAPITAL INSTITUTIONAL
PARTNERS III, L.P.

By:      Farallon Partners, L.L.C.,
         its General Partner

By:  /s/ Monica R. Landry
     ---------------------------------------
         Name:  Monica R. Landry
         Title:    Managing Member

RR CAPITAL PARTNERS, L.P.

By:      Farallon Partners, L.L.C.,
         its General Partner

By:  /s/ Monica R. Landry
     ---------------------------------------
         Name:  Monica R. Landry
         Title:    Managing Member

Notice Information for Farallon Capital Partners, L.P.,
Farallon Capital Institutional Partners II, L.P.,
Farallon Capital Institutional Partners III, L.P. and
RR Capital Partners, L.P.:

c/o Farallon Capital Management, L.L.C.
One Maritime Plaza
Suite 1325
San Francisco, CA  94111
Attention:  Mark Wehrly and Sarah Aitcheson
Telephone:  (415) 421-2132
Facsimile:  (415) 421-2133



<PAGE>
                                      -9-


Acknowledged:

HFCP IV (BERMUDA), L.P.

By:      H&F Investors IV (Bermuda), L.P.,
         its General Partner

         By:  H&F Corporate Investors IV (Bermuda) Ltd.,
              its General Partner

By:      /s/ David R. Tunnell
         -----------------------------------
         Name:  David R. Tunnell
         Title:    Authorized Signatory

WARBURG PINCUS PRIVATE EQUITY VIII,
         L.P.
WARBURG PINCUS INTERNATIONAL
         PARTNERS, L.P.
WARBURG PINCUS NETHERLANDS
         INTERNATIONAL PARTNERS I, C.V.
WARBURG PINCUS NETHERLANDS
         INTERNATIONAL PARTNERS II, C.V.

By:      Warburg, Pincus & Co.,
         its General Partner

By:      /s/ Kewsong Lee
         -----------------------------------
         Name:  Kewsong Lee
         Title:    Partner



<PAGE>


                                   SCHEDULE 1
                                   ----------


                                                                   Amount
                        Assignee                            Assigned to Assignee
                        --------                            --------------------

Farallon Capital Partners, L.P.                                $17,363,247.95

Farallon Capital Institutional Partners II, L.P.                $3,971,282.15

Farallon Capital Institutional Partners III, L.P.               $3,156,495.67

RR Capital Partners, L.P.                                         $508,974.23
                                                               ==============
         Total                                                 $25,000,000.00