<PAGE>
                                                                    EXHIBIT 10.6

                       SECOND AMENDMENT TO LOAN AGREEMENT


         THIS SECOND AMENDMENT TO LOAN AGREEMENT (this "Amendment") is made and
entered into as of June 6, 2001 by and among HCC INSURANCE HOLDINGS, INC., a
Delaware corporation (the "Borrower"); each of the Lenders which is a party to
the Loan Agreement (as defined below) (individually, a "Lender" and,
collectively, the "Lenders"), WELLS FARGO BANK TEXAS, NATIONAL ASSOCIATION,
Administrative Agent for the Lenders and Lead Arranger (in such capacity,
together with its successors in such capacity, the "Agent"), FIRST UNION
NATIONAL BANK, as Syndication Agent, BANK OF AMERICA, N.A., as Documentation
Agent, and THE BANK OF NEW YORK, as Senior Managing Agent.

                                    RECITALS

         A. The Borrower, the Lenders and the Agent executed and delivered that
certain Loan Agreement dated as of December 17, 1999. Said Loan Agreement, as
heretofore amended, is herein called the "Loan Agreement". Any capitalized term
used in this Amendment and not otherwise defined shall have the meaning ascribed
to it in the Loan Agreement.

         B. The Borrower, the Lenders and the Agent desire to amend the Loan
Agreement in certain respects.

         NOW, THEREFORE, in consideration of the premises and the mutual
agreements, representations and warranties herein set forth, and further good
and valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the Borrower, the Lenders and the Agent do hereby agree as
follows:

         SECTION 1. Amendments to Loan Agreement. Effective as of the date
hereof, the Loan Agreement is hereby amended as follows:

         (a) The definition of "Margin Percentage" set forth in Section 1.1 of
the Loan Agreement is hereby amended to read in its entirety as follows:

                  Margin Percentage means (i) on any day prior to July 1, 2001,
         0.750% and (ii) on and after July 1, 2001, the applicable per annum
         percentage set forth at the appropriate intersection in the table shown
         below, based on the Debt to Capitalization Ratio as of the last day of
         the most recently ended fiscal quarter of Borrower calculated by Agent
         as soon as practicable after receipt by Agent of all financial reports
         required under this Agreement with respect to such fiscal quarter
         (including a Compliance Certificate) (provided, however, that if the
         Margin Percentage is increased as a result of the reported Debt to
         Capitalization Ratio, such increase shall be retroactive to the date
         that Borrower was obligated to deliver such financial reports to Agent
         pursuant to the terms of this Agreement and provided further, however,
         that if the Margin Percentage is decreased as a result of the reported
         Debt to Capitalization Ratio, and such financial reports are delivered
         to Agent not more than ten (10) calendar days after the date required
         to be delivered pursuant to the terms of this Agreement, such decrease
         shall be retroactive to the date that Borrower was obligated to deliver
         such financial reports to Agent pursuant to the terms of this
         Agreement):


<PAGE>
<TABLE>
                      Debt to
                Capitalization Ratio                        Margin Percentage
                --------------------                        -----------------
<S>                                                         <C>
                Greater than or equal to
                0.250 to 1.000                                     1.150

                Greater than or equal to
                0.175 to 1.00 but less
                than 0.250 to 1.000                                0.950

                Less than 0.175 to 1.000                           0.750
</TABLE>
         (b) The definition of "Permitted Dividends" set forth in Section 1.1 of
the Loan Agreement is hereby amended to read in its entirety as follows:

                  Permitted Dividends means (i) dividends or distributions by a
         Subsidiary of Borrower to Borrower (or to another Subsidiary of
         Borrower) or redemption by a Subsidiary of any of its stock held by
         Borrower (or by another Subsidiary of Borrower), (ii) dividends paid in
         stock and stock splits and (iii) so long as no Default or Event of
         Default shall have occurred and be continuing (or would result
         therefrom), dividends or distributions by Borrower not exceeding, in
         the aggregate in any applicable fiscal year, $35,000,000. The dividends
         and distributions otherwise permitted under this definition shall be
         subject to the provisions of Section 8.15 hereof.

         (c) Section 2.2(a) of the Loan Agreement is hereby amended to read in
its entirety as follows:

                    (a) [INTENTIONALLY LEFT BLANK]

         (d) Section 2.3(a) of the Loan Agreement is hereby amended to read in
its entirety as follows:

               (a) Borrower shall pay to Agent for the account of each Revolving
          Loan Lender revolving loan commitment fees for the period from June 6,
          2001 to and including the Revolving Loan Termination Date at 0.15% per
          annum. Such revolving loan commitment fees shall be computed (on the
          basis of the actual number of days elapsed in a year composed of 365
          or 366 days, as the case may be) on each day and shall be based on the
          excess of (x) the aggregate amount of each Revolving Loan Lender's
          Commitment for such day over (y) the aggregate unpaid principal
          balance of such Lender's Note on such day. Accrued revolving loan
          commitment fees under this provision shall be payable in arrears on
          the Quarterly Dates prior to the Revolving Loan Termination Date and
          on the Revolving Loan Termination Date.

         (e) Section 7.2(h) of the Loan Agreement is hereby amended to read in
its entirety as follows:

                                       2

<PAGE>

               (h) within sixty (60) days after the end of each fiscal year,
          projections of the consolidated financial statements of Borrower and
          its Subsidiaries for the following fiscal year

         (f) Section 7.3(a)(ii) of the Loan Agreement is hereby amended to read
in its entirety as follows:

               (ii) Debt to Capitalization Ratio - a Debt to Capitalization
          Ratio of not greater than 30% at all times.

         (g) Section 7.3(b) of the Loan Agreement is hereby amended to read in
its entirety as follows:

               (b) Borrower will cause each of its Insurance Company
          Subsidiaries to maintain a Risk Based Capital Ratio of not less than
          200% as of the last day of each fiscal year. In addition, Borrower
          will cause the Insurance Company Subsidiaries to maintain, on a
          consolidated basis, a statutory surplus of not less than $300,000,000
          at all times.

         (h) Section 8.1(vii) of the Loan Agreement is hereby amended to read in
its entirety as follows:

               (vii) any unsecured Indebtedness of Borrower not to exceed, in
          the aggregate at any one time outstanding, $100,000,000 (to be
          increased on a dollar-for-dollar basis by any decrease of the
          Commitments from time to time from the levels in effect as of May 1,
          2001); provided, however, that $100,000,000 of such availability for
          borrowings shall be restricted to public debt offerings by Borrower;
          and

         (i) A new subsection (viii) is hereby added to Section 8.1, such new
subsection to read in its entirety as follows:

               (viii) any unsecured Indebtedness owing by a Subsidiary of
          Borrower to Borrower.

         (j) Section 8.5 of the Loan Agreement is hereby amended to read in its
entirety as follows:

               8.5 Disposition of Assets. Sell, convey or lease all or any part
          of its assets, except as permitted by Section 8.4 hereof and except
          for (a) sales of Inventory in the ordinary course of business, (b)
          transfers resulting from casualty or condemnation of property, (c)
          intercompany sales or transfers of goods, (d) any sale or other
          transfer of any property or assets not otherwise permitted hereunder
          provided that the net proceeds of all such sales and transfers shall
          not exceed, in the aggregate during any fiscal year of Borrower, five
          percent (5%) of the tangible assets of Borrower and its Subsidiaries,
          on a consolidated basis and determined in accordance with GAAP, (e)
          licenses or sublicenses of intellectual property and general
          intangibles and licenses, leases or subleases of other Property in the
          ordinary course of business and which do not materially interfere with
          the business or operation of any Obligor and which does not otherwise
          have a Material Adverse Effect, (f) sales/leaseback transactions
          (provided that Borrower and its

                                       3

<PAGE>

          Subsidiaries shall not, in the aggregate, consummate more than three
          (3) sales/leasebacks with respect to Property owned by Borrower or its
          Subsidiaries as of the Effective Date), and (g) sales of any
          investment assets (including, without limitation, stocks, bonds, cash
          equivalents, etc.) in the ordinary course of business. Prior to
          consummation of any single disposition providing for aggregate
          consideration in excess of $25,000,000, Borrower shall certify to
          Agent that no Default can reasonably be expected to arise by reason of
          such transaction. This Section shall be subject to the limitations set
          forth in Section 8.15 hereof.

         (k) Section 8.6 of the Loan Agreement is hereby amended to read in its
entirety as follows:

               8.6 Redemption, Dividends and Distributions. At any time: (a)
          redeem, retire or otherwise acquire, directly or indirectly, any
          equity interest in Borrower other than stock repurchases not
          exceeding, in the aggregate and on a cumulative basis from and after
          the Effective Date, $100,000,000 or (b) make any distributions of any
          Property or cash to the owner of any of the equity interests in
          Borrower or any of its Subsidiaries other than Permitted Dividends.

         (l) Section 8.12 of the Loan Agreement is hereby amended to read in its
entirety as follows:

               8.12 Acquisitions. Without the prior written consent of the
          Majority Lenders, acquire any real Property or any material personal
          Property (including any acquisition of equity interests in another
          Person other than an Obligor or, subject to the provisions of Section
          8.15 hereof, any other Subsidiary of Borrower as of the Effective
          Date) after the Effective Date from any Person other than an Obligor
          if the aggregate cash consideration for transactions would exceed
          twelve and one-half percent (12-1/2%) of the tangible assets of
          Borrower and its Subsidiaries, on a consolidated basis and determined
          in accordance with GAAP, in any fiscal year or if the aggregate
          consideration (cash or otherwise) for transactions would exceed
          twenty-five percent (25%) of the tangible assets of Borrower and its
          Subsidiaries, on a consolidated basis and determined in accordance
          with GAAP, in any fiscal year. Each such acquisition shall be subject
          to the provisions of Section 8.7 hereof. Notwithstanding anything to
          the contrary set forth in this Section, neither the Borrower nor any
          of its Subsidiaries may acquire any additional equity interests in and
          to the Second Tier Insurance Company Subsidiaries without the prior
          written consent of the Majority Lenders.

         SECTION 2. Reduction of Commitments. The Commitments of the respective
Lenders are hereby reduced to the amounts set forth on Exhibit A hereto.

         SECTION 3. Amendment Fee. No part of this Amendment shall become
effective until the Borrower shall have delivered to the Agent payment to each
Lender of a fee equal to 0.075% of such Lender's Commitment, as amended hereby.

         SECTION 4. Ratification. Except as expressly amended by this Amendment,
the Loan Agreement and the other Loan Documents shall remain in full force and
effect. None of the rights, title and interests existing and to exist under the
Loan Agreement are hereby released,

                                       4

<PAGE>

diminished or impaired, and the Borrower hereby reaffirms all covenants,
representations and warranties in the Loan Agreement (except such
representations and warranties which are, by their express terms, limited to a
prior date).

         SECTION 5. Expenses. The Borrower shall pay to the Agent all reasonable
fees and expenses of its respective legal counsel (pursuant to Section 11.3 of
the Loan Agreement) incurred in connection with the execution of this Amendment.

         SECTION 6. New Lenders. From and after the date hereof, Citicorp USA
and Southwest Bank of Texas, N.A. shall constitute "Lenders" under the Loan
Agreement and, by their execution hereof, Citicorp USA and Southwest Bank of
Texas, N.A. acknowledge and agree to the obligations arising therefrom.

         SECTION 7. Certifications. The Borrower hereby certifies that (a) no
material adverse change in the assets, liabilities, financial condition,
business or affairs of the Borrower has occurred since December 31, 2000 and (b)
no uncured Default or uncured Event of Default has occurred and is continuing or
will occur as a result of this Amendment.

         SECTION 8. Waiver/Consent. The Agent and the Lenders hereby waive any
Default or Event of Default which may exist as a result of the Borrower's
failure to comply with Section 8.1(vii) of the Loan Agreement for all periods
prior to the date of this Amendment. The waiver granted herein is given solely
for the express purpose stated herein and is not a waiver of any other provision
of the Loan Agreement or for any other period.

         SECTION 9. Miscellaneous. This Amendment (a) shall be binding upon and
inure to the benefit of the Borrower, the Lenders and the Agent and their
respective successors, assigns, receivers and trustees; (b) may be modified or
amended only by a writing signed by the required parties; (c) shall be governed
by and construed in accordance with the laws of the State of Texas and the
United States of America; (d) may be executed in several counterparts by the
parties hereto on separate counterparts, and each counterpart, when so executed
and delivered, shall constitute an original agreement, and all such separate
counterparts shall constitute but one and the same agreement and (e) together
with the other Loan Documents, embodies the entire agreement and understanding
between the parties with respect to the subject matter hereof and supersedes all
prior agreements, consents and understandings relating to such subject matter.
The headings herein shall be accorded no significance in interpreting this
Amendment.

             NOTICE PURSUANT TO TEX. BUS. & COMM. CODE SECTION 26.02

         THE LOAN AGREEMENT, AS AMENDED BY THIS AMENDMENT, AND ALL OTHER LOAN
DOCUMENTS EXECUTED BY ANY OF THE PARTIES PRIOR HERETO OR SUBSTANTIALLY
CONCURRENTLY HEREWITH CONSTITUTE A WRITTEN LOAN AGREEMENT WHICH REPRESENTS THE
FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF
PRIOR, CONTEMPORANEOUS OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE
NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.

                                       5

<PAGE>



         IN WITNESS WHEREOF, the Borrower, the Lenders and the Agent have caused
this Amendment to be signed by their respective duly authorized officers,
effective as of the date first above written.

Exhibit A -- Reduced Commitments

                                                  HCC INSURANCE HOLDINGS, INC.,
                                                  a Delaware corporation


                                                  By:  /s/ EDWARD H. ELLIS, JR.
                                                     ---------------------------
                                                       Edward H. Ellis, Jr.,
                                                       Senior Vice President
                                                       and Chief Financial
                                                       Officer

                                       6

<PAGE>



                                                WELLS FARGO BANK TEXAS, NATIONAL
                                                ASSOCIATION, as Administrative
                                                Agent and Lead Arranger and as a
                                                Lender


                                                By:   /s/  JONATHAN C. HOMEYER
                                                      --------------------------
                                                Name:      Jonathan C. Homeyer
                                                      --------------------------
                                                Title:     Vice President
                                                      --------------------------


                                       7

<PAGE>



                                                FIRST UNION NATIONAL BANK,
                                                as Syndication Agent and as a
                                                Lender


                                                By:     /s/  DANIEL J. NORTON
                                                      --------------------------
                                                Name:        Daniel J. Norton
                                                      --------------------------
                                                Title:       Director
                                                      --------------------------



                                       8


<PAGE>



                                                BANK OF AMERICA, N.A.,
                                                as Documentation Agent and as a
                                                Lender


                                                By:     /s/  LESLIE E. REED
                                                      --------------------------
                                                Name:        Leslie E. Reed
                                                      --------------------------
                                                Title:         Vice President
                                                      --------------------------



                                       9



<PAGE>



                                                THE BANK OF NEW YORK,
                                                as Senior Managing Agent and as
                                                a Lender


                                                By:     /s/  BENJAMIN L. BALKIND
                                                      --------------------------
                                                Name:        Benjamin L. Balkind
                                                      --------------------------
                                                Title:       Vice President
                                                      --------------------------







                                       10






<PAGE>



                                                CITICORP USA


                                                By:     /s/  WILLIAM J. CAVANAGH
                                                      --------------------------
                                                Name:        William J. Cavanagh
                                                      --------------------------
                                                Title:       Vice President
                                                      --------------------------



                                       11





<PAGE>



                                                SOUTHWEST BANK OF TEXAS, N.A.


                                                By:     /s/  BENNETT D. DOUGLAS
                                                      --------------------------
                                                Name:        Bennett D. Douglas
                                                      --------------------------
                                                Title:       SVP
                                                      --------------------------





                                       12







<PAGE>



         The undersigned hereby join in this Amendment to evidence their consent
to execution by Borrower of this Amendment, to confirm that each Loan Document
now or previously executed by the undersigned applies and shall continue to
apply to the Loan Agreement, as amended hereby, to acknowledge that without such
consent and confirmation, Lenders would not execute this Amendment and to join
in the notice pursuant to Tex. Bus. & Comm. Code Section 26.02 set forth above.

                                             AVEMCO CORPORATION, a Delaware
                                             corporation, NORTH AMERICAN SPECIAL
                                             RISK ASSOCIATES, INC., an Illinois
                                             corporation, LDG REINSURANCE
                                             CORPORATION, a Massachusetts
                                             corporation, HCC EMPLOYER SERVICES,
                                             INC., an Alabama corporation, HCC
                                             EMPLOYEE BENEFITS, INC., a Delaware
                                             corporation, HCC AVIATION INSURANCE
                                             GROUP, INC., a Texas corporation,
                                             HCC BENEFITS CORPORATION, a
                                             Delaware corporation, HCC
                                             INTERMEDIARIES, INC., a Texas
                                             corporation, HCC INTERMEDIATE
                                             HOLDINGS, INC., a Delaware
                                             corporation, THE CENTRIS GROUP,
                                             INC., a Delaware corporation, U.S.
                                             BENEFITS INSURANCE SERVICES, INC.,
                                             a California corporation, and U.S.
                                             HOLDINGS, INC., a Delaware
                                             corporation


                                             By:     /s/  EDWARD H. ELLIS, JR.
                                                --------------------------------
                                             Name:        Edward H. Ellis, Jr.
                                                  ------------------------------
                                             Title:       Senior Vice President
                                                   -----------------------------


                                       13
<PAGE>



                                    EXHIBIT A


<Table>
<S>                                                              <C>
Wells Fargo Bank Texas, National Association.....................$45,000,000

First Union National Bank........................................$40,000,000

Bank of America, N.A.............................................$40,000,000

The Bank of New York.............................................$35,000,000

Citicorp USA.....................................................$25,000,000

Southwest Bank of Texas, N.A.....................................$15,000,000
</Table>