Exhibit 10.3

                             ARCH CAPITAL GROUP LTD.

                            SHARE PURCHASE AGREEMENT

           THIS AGREEMENT, dated November 6, 2002, between Arch Capital Group
Ltd. (the "COMPANY"), a Bermuda company, and Robert Clements (the "EXECUTIVE");

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

          1.    On one or more Closing Dates (as defined below), the Executive
                agrees to sell, transfer and deliver to the Company, and the
                Company agrees to purchase from the Executive, the Shares (as
                defined below) for a purchase price equal to the outstanding
                principal balance under the promissory note, dated April 10,
                2002, from the Executive to Arch Capital Group (U.S.) Inc. (the
                "PURCHASE PRICE").

                For purposes hereof, (a) "SHARES" means an aggregate number of
                common shares, par value $0.01 per share (the "COMMON SHARES"),
                of the Company equal to the sum of the portion of the Purchase
                Price paid on each Closing Date divided by the higher of the
                average of the high and low sale prices of the Common Shares as
                reported on the Nasdaq National Market on (i) such Closing Date
                or (ii) the trading date immediately preceding such Closing
                Date, and (b) "CLOSING DATE" means one or more dates agreed upon
                by the parties, but in no event later than November 12, 2002.

          2.    This agreement shall be governed by and construed in accordance
                with the laws of Bermuda, without giving effect to principles of
                conflict of laws, and may be executed in two counterparts, each
                of which shall constitute one and the same instrument.

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

                                   ARCH CAPITAL GROUP LTD.


                                   By: /s/ JOHN D. VOLLARO
                                      -----------------------------------------
                                       Name:  John D. Vollaro
                                       Title: Executive Vice President and Chief
                                              Financial Officer


                                       /s/ ROBERT CLEMENTS
                                       ----------------------------------------
                                        Robert Clements