<PAGE>

                                                                   Exhibit 10.13


         ============================================================




                            ANTI-DILUTION AGREEMENT

                                    between

                              CBRE HOLDING, INC.

                                      and

                    CREDIT SUISSE FIRST BOSTON CORPORATION

                           Dated as of July 20, 2001



         ============================================================
<PAGE>

<TABLE>
<CAPTION>
                                             TABLE OF CONTENTS/1/
                                             --------------------
                                                                                                         Page
                                                                                                         ----
<S>                                                                                                      <C>
SECTION 1.     Authorization of Shares.................................................................     1
SECTION 2.     Payment of Taxes........................................................................     1
SECTION 3.     Obtaining Stock Exchange Listings.......................................................     1
SECTION 4.     Adjustment of Number of Shares..........................................................     1
SECTION 5.     Fractional Interests....................................................................     8
SECTION 6.     Adjustment Right Notices to Holders.....................................................     9
SECTION 7.     Notices to Company and Holders..........................................................     9
SECTION 8.     Supplements and Amendments..............................................................     9
SECTION 9.     Successors.............................................................................     10
SECTION 10.    Termination............................................................................     10
SECTION 11.    Governing Law..........................................................................     10
SECTION 12.    Benefits of this Agreement.............................................................     10
SECTION 13.    Counterparts...........................................................................     10
</TABLE>
___________________________
/1/  This Table of Contents does not constitute a part of this Agreement or have
     any bearing upon the interpretation of any of its terms or provisions.
<PAGE>

          ANTI-DILUTION AGREEMENT (the "Anti-Dilution Agreement" or this
                                        -----------------------
"Agreement") dated as of July 20, 2001 (the "Issue Date") by and between CBRE
----------                                   ----------
Holding, Inc., a Delaware corporation (the "Company"), and Credit Suisse First
                                            -------
Boston Corporation (together with their successors and assigns, the "Holders").
                                                                     -------

          Terms defined in the Purchase Agreement (the "Purchase Agreement")
                                                        ------------------
dated June 29, 2001 between the Company and Credit Suisse First Boston
Corporation (the "Purchaser") unless defined herein are used as therein defined.
                  ---------

          WHEREAS, pursuant to the Purchase Agreement and the Commitment Letter
(as described in the Purchase Agreement) the Company proposes to issue shares of
Class A common stock (the "Class A Common Stock") representing 2.867% of the
                           --------------------
fully diluted common equity of the Company (which is the sum of (i) the total
number of shares of common stock of the Company of any class or series (the
"Common Stock) and (ii) the total number of shares of Common Stock into which
-------------
securities of the Company are convertible or for which securities of the Company
are exercisable and outstanding on the Issue Date), in connection with a private
placement of the Company's 16% Senior Notes Due July 20, 2011;

          NOW, THEREFORE, in consideration of the promises and the mutual
agreements herein set forth, the parties hereto agree as follows:

          SECTION 1.  Authorization of Shares. The Company covenants that all
                      -----------------------
shares of Common Stock issued and paid for as provided in the Purchase Agreement
(together with any shares of Common Stock issued upon exercise of the Adjustment
Right provided in this Agreement, the "Shares") will, upon issue, be fully paid,
                                       ------
nonassessable, free of preemptive rights and free from all taxes, liens, charges
and security interests with respect to the issue thereof.

          SECTION 2.  Payment of Taxes. The Company will pay all documentary
                      ----------------
stamp taxes attributable to the initial issuance of Shares.

          SECTION 3.  Obtaining Stock Exchange Listings. The Company will from
                      ---------------------------------
time to time take all action which may be necessary so that the Shares will be
listed on the principal securities exchanges and markets (including any
automated quotation market) within the United States of America, if any, on
which other shares of Common Stock are then listed.

          SECTION 4.  Adjustment of Number of Shares. In the event an adjustment
                      ------------------------------
is required under the terms of this Section 4, each Holder of Shares shall have
the right (the "Adjustment Right") to purchase, at a price equal to their par
                ----------------
value, any or all of that number of shares of Class A Common Stock determined
pursuant to the formulas set out in this Section 4. For purposes of this Section
4 only, "Common Stock" means shares now or hereafter
<PAGE>

authorized of any class of Common Stock and any other stock of the Company,
however designated, that has the right (subject to any prior rights of any class
or series of preferred stock) to participate in any distribution of the assets
or earnings of the Company without preference or limit as to per share amount.
Any securities acquired by a Holder of Shares pursuant to the adjustment
provisions set forth below shall constitute Shares for all purposes of this
Agreement (including, without limitation, this Section 4). For all purposes of
this Agreement, shares of Class A Common Stock and shares of Class B Common
Stock shall be deemed to have the same value.

          (a)  Adjustment for Common Stock Issue.
               ---------------------------------

          If the Company issues shares of Common Stock for a consideration per
share less than the current market price per share on the date the Company fixes
the offering price of such additional shares, the number of Shares held by a
Holder of Shares upon exercise in full of such Holder's Adjustment Right shall
be determined in accordance with the following formula:

                                  N' = N x A
                                          ---
                                         O + P
                                             -
                                             M

where:
       N'=    the adjusted number of Shares which would be held by such
              Holder upon exercise in full of such Holder's Adjustment Right.

       N =    the then current number of Shares held by such Holder.

       O =    the number of shares of Common Stock outstanding on a fully
              diluted basis immediately prior to the issuance of such additional
              shares.

       P =    the aggregate consideration received for the issuance of such
              additional shares.

       M =    the current market price per share of Common Stock on the date
              of sale of such additional shares.

       A =    the number of shares of Common Stock outstanding on a fully
              diluted basis immediately prior to the issuance of such
              additional shares, plus the number of shares issued in
              connection with such issuance.

              The adjustment shall be made successively whenever any such
issuance is made, and shall become effective immediately after such issuance.

                                      -2-
<PAGE>

          This subsection (a) does not apply to:

     (1)  the conversion or exchange of options, warrants or other securities
          convertible or exchangeable for Common Stock,

     (2)  Common Stock issued to shareholders of any person which merges into
          the Company, or with a subsidiary of the Company, in connection with
          the acquisition of such person or otherwise issued in consideration of
          the Company's or any of its subsidiaries' acquisition of another
          person or business,

     (3)  Common Stock issued in a bona fide public offering pursuant to a firm
          commitment underwriting,

     (4)  Common Stock issued to the Holders,

     (5)  Common Stock issued pursuant to employee stock purchase programs
          meeting the requirements of (S) 423 of the Internal Revenue Code of
          1986, as amended, and

     (6)  Common Stock issued to all holders of Common Stock in connection with
          any stock split, stock dividend or other recapitalization of the
          Company.

     (b)  Adjustment for Convertible Securities Issue.
          -------------------------------------------

          If the Company issues any options, warrants or other securities
convertible into or exchangeable for Common Stock (including stock fund units
issued under employee plans of the Company or any of its subsidiaries) for a
consideration per share of Common Stock initially deliverable upon conversion or
exchange of such securities less than the current market price per share on the
date of issuance of such securities, the number of Shares held by a Holder of
Shares upon exercise in full of such Holder's Adjustment Right shall be
determined in accordance with the following formula:

                                        N' = N  x O + D
                                                 -------
                                                 O + P
                                                    ----
                                                   M x C

where:

      N' =  the adjusted number of Shares which would be held by such Holder
            upon exercise in full of such Holder's Adjustment Right.

      N =   the then current number of Shares held by such Holder.

                                      -3-
<PAGE>

      O =   the number of shares of Common Stock outstanding on a fully diluted
            basis immediately prior to the issuance of such securities.

      P =   the aggregate consideration received for the issuance of such
            securities.

      M =   the current market price per share of Common Stock on the date of
            sale of such securities.

      D =   the maximum number of shares of Common Stock deliverable upon
            conversion or in exchange for such securities at the initial
            conversion or exchange rate.

      C =   the maximum number of shares of Common Stock into which one share of
            each such security is convertible into.

            The adjustment shall be made successively whenever any such issuance
is made, and shall become effective immediately after such issuance.

            If all of the Common Stock deliverable upon conversion, exercise or
exchange of such securities have not been issued when such securities are no
longer outstanding, then the number of shares issuable upon exercise of future
Adjustment Rights shall be reduced, pro rata for all the Holders, in an amount
equal to the difference between (x) the number of Shares issuable upon exercise
of the Adjustment Right resulting from the issuance of such options, warrants or
other convertible or exchangeable securities and (y) the number of Shares which
would then be issuable had the adjustment upon the issuance of such options,
warrants or other convertible or exchangeable securities been made on the basis
of the actual number of shares of Common Stock issued upon conversion, exercise
or exchange of such securities.

            This subsection (b) does not apply to:

            (1)  convertible securities issued to shareholders of any person
      which merges into the Company, or with a subsidiary of the Company, in
      connection with the acquisition of such person or otherwise issued in
      consideration of the Company's or any of its subsidiaries' acquisition of
      another person or business,

            (2)  convertible securities issued in a bona fide public offering
      pursuant to a firm commitment underwriting,

            (3)  convertible securities issued to the Holders, and

            (4)  convertible securities issued to all holders of Common Stock in
      connection with any stock split, stock dividend or other recapitalization
      of the Company.

                                      -4-
<PAGE>

          (c)  Current Market Price.
               --------------------

          In subsections (a) and (b) of this Section 4, the current market price
per share of Common Stock on any date is the average of the Quoted Prices of the
Common Stock for 30 consecutive trading days commencing 45 trading days before
the date in question.  The "Quoted Price" of the Common Stock is the last
                            ------------
reported sales price of the Common Stock on a securities exchange if the Common
Stock is then listed on a securities exchange, which shall be for consolidated
trading if applicable to such exchange, the last reported sales price of the
Common Stock as reported by Nasdaq, National Market System or, if neither so
reported or listed, the last reported bid price of the Common Stock.  In the
absence of one or more such quotations, the Board of Directors of the Company
shall determine the current market price (i) based on the most recently
completed arm's-length transaction between the Company and a person other than
an Affiliate of the Company and the closing of which occurs on such date or
shall have occurred within the six months preceding such date; provided,
                                                               --------
however, that the issuance and sale of the Shares at an implied price of $16.0
-------
per share pursuant to the Purchase Agreement shall be deemed to have been an
arm's-length transaction between the Company and a person other than an
Affiliate of the Company, (ii) if no such transaction shall have occurred on
such date or within such six-month period, the value of the security most
recently determined as of a date within the six months preceding such date by
Houlihan Lokey Howard & Zukin Financial Advisors, Inc., or another nationally
recognized investment banking firm or appraisal firm which is not an Affiliate
of the Company (an "Independent Financial Advisor") or (iii) if neither clause
                    -----------------------------
(i) nor (ii) is applicable, the value of the security determined as of such date
by an Independent Financial Advisor.  For purposes of stock options, the current
market price per share of any class of Common Stock issuable upon exercise of
such options shall be determined (x) prior to the first bona fide public
offering of Common Stock, by the board of directors of the Company in good faith
and (y) after the first bona fide public offering of Common Stock, by reference
to the Quoted Price of Common Stock on the trading day immediately preceding the
date of grant or issuance of such option.

          (d)  Consideration Received.
               ----------------------

          For purposes of any computation respecting consideration received
pursuant to subsections (a) and (b) of this Section 4, the following shall
apply:

          (1)  in the case of the issuance of shares of Common Stock for cash,
     the consideration shall be the amount of such cash, provided, however, that
                                                         --------  -------
     in no case shall any deduction be made for any commissions, discounts or
     other expenses incurred by the Company for any underwriting of the issue or
     otherwise in connection therewith;

          (2)  in the case of the issuance of shares of Common Stock for a
     consideration in whole or in part other than cash, the consideration other
     than cash shall be

                                      -5-
<PAGE>

     deemed to be the fair market value thereof as determined in good faith by
     the Board of Directors (irrespective of the accounting treatment thereof),
     whose determination shall be described in a resolution of the Board of
     Directors; and

           (3)  in the case of the issuance of options, warrants or other
     securities convertible into or exchangeable for shares, the aggregate
     consideration received therefor shall be deemed to be the consideration
     received by the Company for the issuance of such securities plus the
     additional minimum consideration, if any, to be received by the Company
     upon the exercise or conversion or exchange thereof (the consideration in
     each case to be determined in the same manner as provided in clauses (1)
     and (2) of this subsection).

           (e)  If CB Richard Ellis Services, Inc. issues any shares of capital
stock upon the exercise of stock options outstanding on the Issue Date (other
than shares of capital stock issued to the Company or any of its wholly-owned
Restricted Subsidiaries (as defined in the indenture governing the 16% senior
notes Due July 20, 2011 of the Company issued in connection with the Shares)),
the number of Shares held by a Holder of Shares upon exercise in full of such
Holder's Adjustment Right shall be determined in accordance with the following
formula:

                               N' = N x  100
                                        -----
                                        100-A

where:

     N' =  the adjusted number of Shares which would be held by such Holder upon
           exercise in full of such Holder's Adjustment Right.

     N =   the then current number of Shares held by such Holder.

     A =   the percentage of the total capital stock of CB Richard Ellis
           Services, Inc. issued to persons or entities other than the Company
           or a wholly-owned Restricted Subsidiary of the Company upon the
           exercise of such stock options outstanding on the Issue Date.

           The adjustment shall be made successively whenever any such issuance
is made, and shall become effective immediately after such issuance.

           (f)  When De Minimis Adjustment May Be Deferred.
                ------------------------------------------

           No adjustment in the number of Shares need be made unless the
adjustment would require an increase or decrease of at least 1% in the number of
Shares held by each

                                      -6-
<PAGE>

Holder. Any adjustments that are not made shall be carried forward and taken
into account in any subsequent adjustment.

          All calculations under this Section shall be made to the nearest
1/100th of a share.

          (g)  Notice of Adjustment.
               --------------------

          Whenever the number of Shares may be adjusted, the Company shall
provide notice to the Holder as set forth in Section 6  hereof.

          (h)  No Dilution or Impairment.
               -------------------------

          If any event shall occur as to which the provisions of this Section 4
are not strictly applicable but the failure to make any adjustment would
adversely affect the Adjustment Rights represented by the Shares in accordance
with the essential intent and principles of this Section, then, in each such
case, the Company shall appoint an investment banking firm of recognized
national standing, or any other financial expert that does not (or whose
directors, officers, employees, affiliates or stockholders do not) have a direct
or material indirect financial interest in the Company or any of its
subsidiaries, who has not been, and, at the time it is called upon to give
independent financial advice to the Company, is not (and none of its directors,
officers, employees, affiliates or stockholders are) a promoter, director or
officer of the Company or any of its subsidiaries, which shall give their
opinion upon the adjustment, if any, on a basis consistent with the essential
intent and principles established in this Section 4, necessary to preserve,
without dilution, the rights of the Holders of the Shares.  Upon receipt of such
opinion, the Company will promptly mail a copy thereof to the Holders of the
Shares and shall make the adjustments described therein.

          The Company will not, by amendment of its certificate of incorporation
or through any consolidation, merger, reorganization, transfer of assets,
dissolution, issue or sale of securities or any other voluntary action, avoid or
seek to avoid the observance or performance of any of the terms of this
Agreement, but will at all times in good faith assist in the carrying out of all
such terms and in the taking of all such action as may be necessary or
appropriate in order to protect the rights of the Holders of the Shares under
this Agreement.  Without limiting the generality of the foregoing, the Company
(1) will take all such action as may be necessary or appropriate in order that
the Company may validly and legally issue fully paid and nonassessable shares of
Common Stock from time to time outstanding and (2) will not take any action
which results in any adjustment of the number of Shares if the total number of
Shares issuable after the action, would exceed the total number of Shares or
shares of Common Stock, as the case may be, then authorized by the Company's
certificate of incorporation and available for the purposes of issue.

                                      -7-
<PAGE>

          (i)  Reorganization of Company.
               -------------------------

          If the Company consolidates or merges with or into, or transfers or
leases all or substantially all its assets to, any person, and in connection
with such transaction the Holders receive common stock of another entity or
options, warrants or other securities convertible into or exchangeable for
common stock of another entity, then upon consummation of such transaction the
Adjustment Right shall automatically become applicable to the common stock of
such other entity.  Concurrently with the consummation of such transaction, the
corporation formed by or surviving any such consolidation or merger if other
than the Company, or the person to which such sale or conveyance shall have been
made, shall enter into a supplemental Agreement so providing and further
providing for adjustments which shall be as nearly equivalent as may be
practical to the adjustments provided for in this Agreement.  The successor
company shall mail to Holders of Shares a notice describing the supplemental
Agreement.

          If the issuer of securities deliverable upon exercise of Adjustment
Rights under the supplemental Agreement is an affiliate of the formed,
surviving, transferee or lessee corporation, that issuer shall join in the
supplemental Agreement.

          If this subsection (i) applies, subsections (a) and (b) of this
Section 4 do not apply.

          (j)  Exercise of Adjustment Right.
               ----------------------------

          In the event that a Holder of Shares is granted an Adjustment Right
pursuant to this Section 4, such Holder shall have 30 days from the later of the
date of any action requiring an adjustment and the date notice of such action is
provided pursuant to Section 6 hereof to exercise such Adjustment Right.  Any
Adjustment Right may be exercised by delivery of a written notice to the
Company, together with a certified check payable to the order of the Company in
an amount equal to the aggregate par value of the additional Shares to be issued
to such Holder pursuant to its exercise of the Adjustment Right.  Such notice
shall contain customary private placement representations and warranties in form
reasonably satisfactory to the Company.  Upon delivery of such Notice and such
payment, the Company shall promptly cause the additional Shares to be issued and
delivered to such Holder or to another person or address specified in writing by
such Holder.

          SECTION 5.  Fractional Interests.  Any Adjustment Rights may be
                      --------------------
exercised in full or in part; provided, however, that the Company shall not be
                              --------  -------
required to issue fractional Shares on the exercise of Adjustment Rights. If
more than one Adjustment Right shall be exercised at the same time by the same
Holder, the number of full Shares which shall be issuable upon the exercise
thereof shall be computed on the basis of the aggregate number of Shares
purchasable on exercise of the Adjustment Rights so requested to be exercised.
If any fraction

                                      -8-
<PAGE>

of a Share would, except for the provisions of this Section 5, be issuable on
the exercise of any Adjustment Rights (or specified portion thereof), the
Company shall pay an amount in cash equal to the product of (i) such fraction of
an Adjustment Right Share and (ii) the current market price of a share of Common
Stock.

          SECTION 6.  Adjustment Right Notices to Holders.  Upon any event
                      -----------------------------------
which may require adjustment of the number of Shares pursuant to Section 4, the
Company shall promptly thereafter (i) obtain a certificate which includes the
report of a firm of independent public accountants of recognized standing
selected by the Board of Directors of the Company (who may be the regular
auditors of the Company) setting forth the number of shares of Class A Common
Stock issuable upon exercise of the Adjustment Right in respect of each Share
and setting forth in reasonable detail the method of calculation and the facts
upon which such calculations are based, which certificate shall be conclusive
evidence of the correctness of the matters set forth therein, and (ii) cause to
be given to each of the registered Holders of the Shares at his or her address
appearing on the share register written notice of such adjustments by first-
class mail, postage prepaid, together with a copy of the certificate described
in clause (i) above.

          SECTION 7.  Notices to Company and Holders.  Any notice or demand
                      ------------------------------
authorized by this Agreement to be given or made by the registered holder of any
Share to or on the Company shall be sufficiently given or made when and if
deposited in the mail, first class or registered, postage prepaid, addressed to
the office of the Company expressly designated by the Company at its office for
purposes of this Agreement (until the Holders are otherwise notified in
accordance with this Section by the Company), as follows:

               CBRE Holding Inc.
               909 Montgomery Street
               San Francisco, CA  94133
               Facsimile:  415-434-3130
               Attention:  Chief Financial Officer

          Any notice pursuant to this Agreement to be given by the Company to
the registered holder(s) of any Share shall be sufficiently given when and if
deposited in the mail, first class or registered, postage prepaid, addressed
(until the Company is otherwise notified in accordance with this Section by such
holder) to such holder at the address appearing on the share register of the
Company.

          SECTION 8.  Supplements and Amendments.  The Company may from time to
                      --------------------------
time supplement or amend this Agreement with the written consent of Holders of a
majority of the then outstanding Shares.

                                      -9-
<PAGE>

          SECTION 9.  Successors.  All the covenants and provisions of this
                      ----------
Agreement by or for the benefit of the Company and the Holders shall bind and
inure to the benefit of their respective successors and assigns hereunder.

          SECTION 10. Termination.  This Agreement shall terminate on July 20,
                      -----------
2011 and, with respect to any Share, shall terminate at such time as such Share
has been transferred pursuant to a registration statement filed with the
Securities and Exchange Commission or pursuant to Rule 144 (or any successor
provision) of the Securities Act of 1933, as amended (at which time such share
of Common Stock shall cease to be a "Share" under this Agreement).

          SECTION 11. Governing Law.  THIS AGREEMENT SHALL BE GOVERNED BY, AND
                      -------------
CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

          SECTION 12. Benefits of this Agreement.  Nothing in this Agreement
                      --------------------------
shall be construed to give to any person or corporation other than the Company
and the registered holders of the Shares any legal or equitable right, remedy or
claim under this Agreement; but this Agreement shall be for the sole and
exclusive benefit of the Company and the registered holders of the Shares.
Nothing herein shall prohibit or limit the Company from entering into an
agreement providing holders of securities which may hereafter be issued by the
Company with such registration rights exercisable at such time or times and in
such manner as the Board of Directors shall deem in the best interests of the
Company so long as the performance by the Company of its obligations under such
other agreement will not cause the Company to breach its obligations hereunder
to the Holders.

          SECTION 13. Counterparts.  This Agreement may be executed in any
                      ------------
number of counterparts and each of such counterparts shall for all purposes be
deemed to be an original, and all such counterparts shall together constitute
but one and the same instrument.

                                      -10-
<PAGE>

          IN WITNESS WHEREOF, the parties hereto have caused this Agreement to
be duly executed, as of the day and year first above written.

                                      CBRE HOLDING, INC.


                                      By: __________________________________
                                          Name:
                                          Title:



                                      CREDIT SUISSE FIRST BOSTON CORPORATION


                                      By: __________________________________
                                          Name:
                                          Title: