Document:

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                                                 $25,000,000.00Exhibit 10.6

                             ARCH CAPITAL GROUP LTD.

                           Restricted Share Agreement

     THIS AGREEMENT, dated on November 19, 2001, between Arch Capital Group Ltd.
(the "Company"), a Bermuda company, and Robert Clements (the "Executive").

     WHEREAS, the Executive has been granted the following award as compensation
for services to be rendered;

     NOW, THEREFORE, in consideration of the premises and mutual covenants
contained herein, the parties hereto agree as follows.

     1. Award of Shares. The Executive is hereby awarded 21,472 shares of
restricted common stock of the Company (the "Award"), subject to the terms and
conditions herein set forth. This Award shall be rescinded if it is not approved
by shareholders prior to the first anniversary hereof.

     2. Terms and Conditions. It is understood and agreed that the Award
evidenced hereby is subject to the following additional terms and conditions:

     (a) Vesting of Award. Subject to Section 2(b) below and the other terms and
conditions of this Agreement, this Award shall become vested in five equal
annual installments, beginning on the first anniversary of October 23, 2001.
Notwithstanding the foregoing, if the service of the Executive as Chairman of
the Board of the Company is terminated by the Company or is not continued by the
Company for any reason, or the Executive's service terminates due to his death
or Permanent Disability, then the Award shall become immediately vested in full
upon such termination of service. "Permanent Disability" means those
circumstances where the Executive is unable to continue to perform the usual
customary duties of his assigned job for a period of six (6) months in any
twelve (12) month period because of physical, mental or emotional incapacity
resulting from injury, sickness or disease. Any questions as to the existence of
a Permanent Disability shall be determined by a qualified, independent physician
selected by the Company and approved by the Executive (which approval shall not
be unreasonably withheld). The determination of any such physician shall be
final and conclusive for all purposes of this Agreement.

     (b) Termination of Service; Forfeiture of Unvested Shares. Except as
otherwise set forth in Section 2(a) above, in the event the Executive terminates
his service with the Company (other than due to his death or Permanent
Disability or the failure of the Company to continue his service) prior to the
date of vesting of an installment of the Award, the unvested installments shall
be forfeited by the Executive and become the property of the Company. For
purposes of this Agreement, service with any of the Company's wholly owned
subsidiaries shall be considered to be service with the Company.

<PAGE>
                                      -2-

     (c) Certificates. Each certificate issued in respect of an Award made
hereunder shall be dated the date hereof and deposited with the Company, or its
designee, together with, if requested by the Company, a stock power executed in
blank by the Executive, and shall bear a legend disclosing the restrictions on
transferability imposed on such Award by this Agreement (the "Restrictive
Legend"). Upon the vesting of the Award pursuant to Section 2(a) hereof, the
certificates evidencing such vested Shares, not bearing the Restrictive Legend,
shall be delivered to the Executive.

     (d) Rights of a Stockholder. Prior to the time an Award is fully vested
hereunder, except as set forth in Section 2(e) below, the Executive shall have
no right to transfer, pledge, hypothecate or otherwise encumber such Award.
Beginning on the date hereof and during such period, the Executive shall have
all other rights of a stockholder, including, but not limited to, the right to
vote and to receive dividends at the time paid on such Award.

     (e) Transferability. Except as set forth below, prior to vesting this Award
shall not be transferable by the Executive except by will or the laws of descent
and distribution. Notwithstanding the foregoing, if the Board of Directors
provides its consent (which consent shall not be unreasonably withheld), the
Award (or any part thereof) may be transferred by the Executive to members of
his or her "immediate family" or to a trust or other entity established for the
exclusive benefit of solely one or more members of the Executive's "immediate
family" or the Executive. Any Award held by the transferee will continue to be
subject to the same terms and conditions that were applicable to the Award
immediately prior to the transfer, except that the Award will be transferable by
the transferee only by will or the laws of descent and distribution. For
purposes hereof, "immediate family" means the Executive's children,
stepchildren, grandchildren, great grandchildren, parents, stepparents,
grandparents, spouse, siblings (including half brothers and sisters), in-laws,
and relationships arising because of legal adoption.

     3. Noncompetition. The Executive acknowledges that during his service with
the Company, he will become familiar with trade secrets and other confidential
information concerning the Company and that his services will be of special,
unique and extraordinary value to the Company. In addition, the Executive hereby
agrees that, in the event his service with the Company is terminated by the
Company prior to the fifth anniversary of October 23, 2001, during the period
ending on the later of the fifth anniversary of October 23, 2001 or one year
following the date of his termination by the Company, he will not, without the
Company's written consent, directly or indirectly manage, participate in, or
render services for any business competing with the businesses of the Company or
its subsidiaries as such businesses exist or are in process as of the date of
termination, within any geographical area in which the Company or its
subsidiaries engage in such businesses.

     4. Enforcement. If, at the enforcement of Section 3, a court holds that the
duration, scope or area restrictions stated herein are unreasonable under
circumstances then existing, the parties agree that the maximum duration, scope
or area reasonable

<PAGE>
                                      -3-

under such circumstances will be substituted for the stated duration, scope or
area and that the court will be permitted to revise the restrictions contained
in Section 3 to cover the maximum duration, scope and area permitted by law.

     5. Transfer of Shares. The vested shares delivered hereunder, or any
interest therein, may be sold, assigned, pledged, hypothecated, encumbered, or
transferred or disposed of in any other manner, in whole or in part, only in
compliance with the terms, conditions and restrictions as set forth in the
governing instruments of the Company, applicable United States federal and state
securities laws or any other applicable laws or regulations and the terms and
conditions hereof.

     6. Antidilution. In the event that the Board of Directors of the Company
shall determine that any dividend in shares, recapitalization, share split,
reverse split, reorganization, merger, consolidation, spin-off, combination,
repurchase, or share exchange, or other similar corporate transaction or event,
affects the Company common stock such that an adjustment is appropriate in order
to prevent dilution or enlargement of the rights of the Executive hereunder,
then the Board of Directors of the Company shall make such equitable changes or
adjustments as are appropriate and adjust any or all of the number and kind of
shares, other securities or other consideration issued or issuable in respect of
this Award.

     7. Expenses of Issuance of Shares. The issuance of stock certificates
hereunder shall be without charge to the Executive. The Company shall pay, and
indemnify the Executive from and against any issuance, stamp or documentary
taxes (other than transfer taxes) or charges imposed by any governmental body,
agency or official (other than income taxes) or by reason of the issuance of
shares hereunder.

     8. References. References herein to rights and obligations of the Executive
shall apply, where appropriate, to the Executive's legal representative or
estate without regard to whether specific reference to such legal representative
or estate is contained in a particular provision of this Agreement.

     9. Notices. Any notice required or permitted to be given under this
Agreement shall be in writing and shall be deemed to have been given when
delivered personally or by courier, or sent by certified or registered mail,
postage prepaid, return receipt requested, duly addressed to the party concerned
at the address indicated below or to such changed address as such party may
subsequently by similar process give notice of:

<PAGE>
                                      -4-

     If to the Company:

     Arch Capital Group Ltd.
     Executive Offices:
     20 Horseneck Lane
     Greenwich, CT  06830
     Attn.: Secretary

     If to the Executive: To the last address given to the Company by the
                          Executive in the manner set forth in this Section 9.

     10. Governing Law. This Agreement shall be governed by and construed in
accordance with the laws of Bermuda, without giving effect to principles of
conflict of laws.

     11. Entire Agreement. This Agreement constitutes the entire agreement among
the parties relating to the subject matter hereof, and any previous agreement or
understanding among the parties with respect thereto is superseded by this
Agreement.

     12. Counterparts. This Agreement may be executed in two counterparts, each
of which shall constitute one and the same instrument.

<PAGE>
                                      -5-

     IN WITNESS WHEREOF, the undersigned have executed this Agreement on the
date first above written.

                              ARCH CAPITAL GROUP LTD.

                              By:    /s/ Peter A. Appel
                                     -------------------------------------
                                     Name:  Peter A. Appel
                                     Title:  President and Chief Executive
                                                Officer

                              /s/ Robert Clements
                              --------------------------------------------
                                           Robert Clements

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