<PAGE>   1
================================================================================

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                    FORM 10-Q

       (MARK ONE)
 [X]   QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
       EXCHANGE ACT OF 1934

       FOR THE QUARTERLY PERIOD ENDED SEPTEMBER 30, 1999    OR

 [ ]   TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
       EXCHANGE ACT OF 1934

       FOR THE TRANSITION PERIOD FROM              TO


                          Commission file number 1-9215


                          -------------------------------

                       UNITED ASSET MANAGEMENT CORPORATION
             (Exact name of registrant as specified in its charter)

              DELAWARE                                04-2714625
  (State or other jurisdiction of        (I.R.S. Employer Identification Number)
   incorporation or organization)



                             ONE INTERNATIONAL PLACE
                           BOSTON, MASSACHUSETTS 02110
                    (Address of principal executive offices)

       Registrant's telephone number, including area code: (617) 330-8900

         Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.  X   Yes      No
                                          ---      ---

         The number of shares outstanding of the registrant's common stock as of
November 5, 1999 was 58,655,624.


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

<PAGE>   2


                                     PART I
                              FINANCIAL INFORMATION


Item 1.       Financial Statements. (Pages F-1 to F-5)

Item 2.       Management's Discussion and Analysis of Financial Condition and
              Results of Operations. (Pages F-5 to F-10)

Item 3.       Quantitative and Qualitative Disclosures About Market Risk.
              (Page F-10)

                                     PART II
                                OTHER INFORMATION

Item 1.       Legal Proceedings.
              The Company and certain of the Company's subsidiaries are subject
              to legal proceedings arising in the ordinary course of business.
              On the basis of information presently available and advice
              received from legal counsel, it is the opinion of management that
              the disposition or ultimate determination of such legal
              proceedings will not have a material adverse effect on the
              Company's consolidated financial position, its consolidated
              results of operations or its consolidated cash flows.

Item 2.       Changes in Securities.
              During the third quarter of 1999, UAM issued an aggregate of
              222,564 shares of its Common Stock upon the exercise of warrants.
              This issuance was exempt from registration under Section 4(2) of
              the Securities Act of 1933. UAM had originally issued the
              warrants, as consideration for the acquisition of one of its
              subsidiaries, to certain principals of that subsidiary. These
              principals subsequently assigned these warrants to an unaffiliated
              third party. The exercise price of these warrants was $16.50 per
              share.

Item 3.       Defaults Upon Senior Securities.  None

Item 4.       Submission of Matters to a Vote of Security Holders.  None

Item 5.       Other Information.  None

Item 6.       Exhibits and Reports on Form 8-K.

              (a)  Exhibit 10.1 - Forms of Agreements with Certain Employees.
                   Exhibit 11   - Calculation of Earnings Per Share (Page F-11).
                   Exhibit 27   - Financial Data Schedule.

              (b)  There have been no reports on Form 8-K filed by the
                   Company during the quarter ended September 30, 1999.


<PAGE>   3


                                   SIGNATURES

         Pursuant to the requirements of the Securities Exchange Act of 1934,
the registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.


                                            UNITED ASSET MANAGEMENT CORPORATION


November 9, 1999                            /s/  William H. Park
----------------------------------          ------------------------------------
(Date)                                      William H. Park
                                            Executive Vice President and
                                             Chief Financial Officer



<PAGE>   4

                          PART I. FINANCIAL INFORMATION

Item 1. Financial Statements

                       UNITED ASSET MANAGEMENT CORPORATION

                 CONDENSED CONSOLIDATED STATEMENT OF OPERATIONS
                                   (Unaudited)

<TABLE>
<CAPTION>


                                               Three Months Ended                 Nine Months Ended
                                                  September 30,                      September 30,
                                        ------------------------------      ------------------------------
                                             1999             1998              1999              1998
                                        ------------      ------------      ------------      ------------
<S>                                     <C>               <C>               <C>               <C>
Revenues                                $217,215,000      $226,745,000      $654,252,000      $722,941,000
                                        ------------      ------------      ------------      ------------
Operating expenses:
     Compensation and related
        expenses                         107,752,000       108,023,000       327,132,000       352,740,000
     Amortization of cost assigned
        to contracts acquired             26,218,000        28,473,000        78,813,000        86,118,000
     Other operating expenses             38,351,000        43,094,000       116,288,000       134,512,000
                                        ------------      ------------      ------------      ------------
                                         172,321,000       179,590,000       522,233,000       573,370,000
                                        ------------      ------------      ------------      ------------
Operating income                          44,894,000        47,155,000       132,019,000       149,571,000
                                        ------------      ------------      ------------      ------------
Non-operating expenses:
     Interest expense, net                16,164,000        14,802,000        48,500,000        38,115,000
     Other amortization                    1,182,000         1,319,000         3,525,000         3,122,000
                                        ------------      ------------      ------------      ------------
                                          17,346,000        16,121,000        52,025,000        41,237,000
                                        ------------      ------------      ------------      ------------
Income before income tax expense          27,548,000        31,034,000        79,994,000       108,334,000
Income tax expense                        11,794,000        13,281,000        34,238,000        46,366,000
                                        ------------      ------------      ------------      ------------
Net income                              $ 15,754,000      $ 17,753,000      $ 45,756,000      $ 61,968,000
                                        ============      ============      ============      ============
Basic earnings per share                $        .27      $        .27      $        .77      $        .92
Diluted earnings per share              $        .27      $        .27      $        .76      $        .89
Dividends declared per share            $        .20      $        .20      $        .60      $        .60
                                        ============      ============      ============      ============
</TABLE>

See Notes to Condensed Consolidated Financial Statements.

                                      F-1
<PAGE>   5

                      UNITED ASSET MANAGEMENT CORPORATION

                      CONDENSED CONSOLIDATED BALANCE SHEET

<TABLE>
<CAPTION>

                                                  September 30,         December 31,
                                                      1999                  1998
                                                  (Unaudited)
                                                 --------------        --------------
<S>                                             <C>                    <C>
Assets
Current assets:
  Cash and cash equivalents                      $  121,703,000        $  153,616,000
  Investment advisory fees receivable               161,942,000           169,061,000
  Other current assets                               10,945,000            12,419,000
                                                 --------------        --------------
Total current assets                                294,590,000           335,096,000
Fixed assets, net                                    38,569,000            42,148,000
Cost assigned to contracts acquired, net            864,093,000           931,815,000
Other assets                                        132,453,000           130,452,000
                                                 --------------        --------------
Total assets                                     $1,329,705,000        $1,439,511,000
                                                 ==============        ==============
Liabilities and Stockholders' Equity
Current liabilities:
  Accounts payable and accrued expenses          $  109,735,000        $  143,559,000
  Accrued compensation                               95,234,000           108,222,000
                                                 --------------        --------------
Total current liabilities                           204,969,000           251,781,000
Senior notes payable                                686,053,000           687,521,000
Subordinated notes payable                          191,851,000           202,840,000
Deferred income taxes                                27,042,000            27,525,000
                                                 --------------        --------------
Total liabilities                                 1,109,915,000         1,169,667,000
                                                 --------------        --------------
Commitments and contingencies
Stockholders' equity:
  Common stock, par value $.01 per share:               703,000               703,000
  Capital in excess of par value                    361,810,000           360,781,000
  Retained earnings                                 138,875,000           140,751,000
  Accumulated other comprehensive income             (7,245,000)          (10,132,000)
                                                 --------------        --------------
                                                    494,143,000           492,103,000
  Less treasury shares at cost                     (274,353,000)         (222,259,000)
                                                 --------------        --------------
Total stockholders' equity                          219,790,000           269,844,000
                                                 --------------        --------------
Total liabilities and stockholders' equity       $1,329,705,000        $1,439,511,000
                                                 ==============        ==============
</TABLE>

See Notes to Condensed Consolidated Financial Statements.

                                      F-2


<PAGE>   6


                       UNITED ASSET MANAGEMENT CORPORATION

                      CONSOLIDATED STATEMENT OF CASH FLOWS
                                  (Unaudited)

<TABLE>
<CAPTION>
                                                                     Three Months Ended               Nine Months Ended
                                                                        September 30,                    September 30,
                                                                -----------------------------     -----------------------------
                                                                    1999            1998              1999            1998
                                                                ------------     ------------     ------------     ------------
<S>                                                             <C>              <C>             <C>               <C>
Cash flow related to operating activities:
  Net income                                                    $ 15,754,000     $ 17,753,000     $ 45,756,000     $ 61,968,000
  Adjustments to reconcile net income to net cash flow
     from operating activities:
     Amortization of cost assigned to contracts acquired          26,218,000       28,473,000       78,813,000       86,118,000
     Depreciation                                                  3,446,000        3,359,000       11,162,000        9,817,000
     Amortization of goodwill and other                            1,991,000        1,658,000        5,952,000        4,141,000
                                                                ------------     ------------     ------------     ------------
  Net income plus amortization and depreciation                   47,409,000       51,243,000      141,683,000      162,044,000
  Changes in assets and liabilities:
     Decrease in investment advisory fees receivable               1,588,000       11,411,000        7,105,000       26,265,000
     Decrease in other current assets                              4,687,000        5,662,000        1,460,000        2,610,000
     Decrease in accounts payable and accrued expenses           (11,527,000)      (3,083,000)     (31,428,000)     (17,566,000)
     Increase (decrease) in accrued compensation                   9,951,000       17,596,000      (12,943,000)     (21,465,000)
     Increase (decrease) in deferred income taxes                 (2,776,000)        (373,000)      (4,352,000)       1,920,000
                                                                ------------     ------------     ------------     ------------
Net cash flow from operating activities                           49,332,000       82,456,000      101,525,000      153,808,000
                                                                ------------     ------------     ------------     ------------
Cash flow related to investing activities:
  Cash additions to cost assigned to contracts acquired                   --         (417,000)      (5,134,000)     (29,578,000)
  Change in other assets                                          (8,828,000)     (15,856,000)     (13,310,000)     (38,647,000)
                                                                ------------     ------------     ------------     ------------
Net cash flow used in investing activities                        (8,828,000)     (16,273,000)     (18,444,000)     (68,225,000)
                                                                ------------     ------------     ------------     ------------
Cash flow related to financing activities:
  Purchase of treasury shares                                             --      (76,171,000)     (88,095,000)    (205,552,000)
  Additions to (reductions in) notes payable, net                (32,947,000)      47,974,000       (9,196,000)     127,163,000
  Issuance or reissuance of equity securities                      4,834,000        6,549,000       18,576,000       23,823,000
  Dividends paid                                                 (11,768,000)     (13,269,000)     (35,954,000)     (40,949,000)
                                                                ------------     ------------     ------------     ------------
Net cash flow used in financing activities                       (39,881,000)     (34,917,000)    (114,669,000)     (95,515,000)
                                                                ------------     ------------     ------------     ------------
Effect of foreign exchange rate changes on cash flow               1,027,000          (43,000)        (325,000)         391,000
                                                                ------------     ------------     ------------     ------------
Net increase (decrease) in cash and cash equivalents               1,650,000       31,223,000      (31,913,000)      (9,541,000)
Cash and cash equivalents at beginning of period                 120,053,000      132,874,000      153,616,000      173,638,000
                                                                ------------     ------------     ------------     ------------
Cash and cash equivalents at end of period                      $121,703,000     $164,097,000     $121,703,000     $164,097,000
                                                                ============     ============     ============     ============
</TABLE>

See Notes to Condensed Consolidated Financial Statements.

                                      F-3
<PAGE>   7


                       UNITED ASSET MANAGEMENT CORPORATION

              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                                   (Unaudited)


Note 1

         In the opinion of management, the accompanying unaudited Condensed
Consolidated Financial Statements contain all adjustments, consisting only of
normal recurring accruals, necessary to present fairly the financial position of
the Company and its subsidiaries at September 30, 1999 and their results of
operations and cash flows for the three- and nine-month periods ended September
30, 1999 and 1998. These Financial Statements should be read in conjunction with
the Company's Annual Report on Form 10-K for the year ended December 31, 1998.

Note 2

         Accumulated depreciation of fixed assets was $66,371,000 and
$55,209,000 at September 30, 1999 and December 31, 1998, respectively. The
accumulated amortization of cost assigned to contracts acquired was $674,007,000
and $598,621,000 at September 30, 1999 and December 31, 1998, respectively.

Note 3

         The Company has a systematic program to repurchase shares of its common
stock to meet the requirements for future issuance of shares upon the exercise
of stock options and warrants. For the three- month period ended September 30,
1999, the Company did not repurchase any shares. For the nine-month period ended
September 30, 1999, the Company repurchased 3,800,800 shares of its common stock
at a cost of $88,095,000, including certain shares repurchased under the terms
of this program. During the three- and nine-month periods ended September 30,
1999, exercises of warrants and stock options, as well as the issuance of stock
to former owners of affiliates in connection with purchase price commitments
that came due, resulted in the Company extinguishing subordinated notes,
receiving cash proceeds and issuing stock as follows:

<TABLE>
<CAPTION>

                                          Three Months           Nine Months
                                              Ended                Ended
                                       September 30, 1999     September 30, 1999
                                       ------------------     ------------------
<S>                                        <C>                   <C>
Subordinated notes extinguished            $3,672,000            $ 9,987,000
Cash proceeds received                     $1,102,000            $13,839,000
Treasury shares reissued                      282,488              1,399,786
</TABLE>


         As of September 30, 1999, the Company held 11,193,893 treasury shares.
Warrants for the purchase of 7,793,000 shares and stock options for the purchase
of 8,515,000 shares were outstanding at weighted average exercise prices of
$24.17 and $22.75, respectively.

                                      F-4

<PAGE>   8


Note 4

         The components of comprehensive income for the three- and nine-month
periods ended September 30, 1999 and 1998, respectively, are set forth below:

<TABLE>
<CAPTION>

                                                    Three Months Ended                  Nine Months Ended
                                                        September 30,                      September 30,
                                              ------------------------------       -----------------------------
                                                   1999             1998              1999              1998
                                                   ----             ----              ----              ----
<S>                                           <C>                <C>               <C>              <C>
Net income:                                    $15,754,000       $17,753,000       $45,756,000       $61,968,000
Other comprehensive income, net:
     Foreign currency translation
         adjustment                              2,482,000        (3,406,000)        3,536,000        (6,539,000)
     Unrealized gain (loss) on
         marketable securities                     (40,000)               --           513,000                --
     Less:  reclassification adjustment
         for gains realized in net income               --                --        (1,162,000)               --
                                               -----------       -----------       -----------       -----------
Comprehensive income                           $18,196,000       $14,347,000       $48,643,000       $55,429,000
                                               ===========       ===========       ===========       ===========
</TABLE>


Note 5

         The Company operates in one business segment, that is, as investment
advisors, managing both domestic and international portfolios for corporate,
government and union benefit plans, mutual funds, individuals, endowments, and
foundations. Although each affiliated firm operates under its own name with its
own investment philosophy and approach, the firms' regulatory environments and
the economic characteristics of their products, services, client bases, and
manner of distribution are similar. Therefore, the affiliated firms are
aggregated as one business segment.

         Revenues and long-lived assets shown below are classified according to
the affiliate's geographic location. Revenues are derived primarily from fees
for investment advisory services provided to institutions, mutual funds, and
other investors. These fees are generally a function of the overall fee rate
charged to each account and the level of assets under management by the
affiliated firms.

<TABLE>
<CAPTION>

                                          Three Months Ended                     Nine Months Ended
                                             September 30,                         September 30,
                                    ------------------------------       -------------------------------
                                        1999              1998               1999               1998
                                        ----              ----               ----               ----
<S>                                 <C>               <C>                <C>                <C>
Domestic revenues                   $197,518,000      $205,727,000       $594,724,000       $657,929,000
Foreign revenues                    $ 19,697,000      $ 21,018,000       $ 59,528,000       $ 65,012,000
Domestic long-lived assets          $876,772,000      $961,912,000       $876,772,000       $961,912,000
Foreign long-lived assets           $158,343,000      $171,856,000       $158,343,000       $171,856,000
</TABLE>


Item 2.      MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
             AND RESULTS OF OPERATIONS

         The revenues of UAM's affiliated firms are derived primarily from fees
for investment advisory services provided to institutions, mutual funds and
other investors. Investment advisory fees are generally a function of the
overall fee rate charged to each account and the level of assets under
management by the


                                      F-5
<PAGE>   9

affiliated firms. A minor portion of revenues is generated when firms
consummate transactions for client portfolios. Assets under management can be
affected by the addition of new client accounts or client contributions to
existing accounts, withdrawals of assets from or terminations of client
accounts, and investment performance, which may depend on general market
conditions.

         UAM's assets under management were $193.6 billion as of September 30,
1999, compared to $205.9 billion under management on June 30, 1999. Market
performance subtracted $9.5 billion from UAM's assets under management,
reflecting a decline in equity markets in the United States during the 1999
third quarter, and net client cash flow reduced these assets by an additional
$2.6 billion during the period. The sale of an affiliate, Nelson, Benson &
Zellmer, Inc., subtracted approximately $200 million from the total.


               AMORTIZATION OF COST ASSIGNED TO CONTRACTS ACQUIRED

         Cost assigned to contracts acquired, net of accumulated amortization,
represented approximately 65% of the Company's total assets as of September 30,
1999. Amortization of cost assigned to contracts acquired, which is a noncash
charge, represented 15% of the Company's operating expenses for both the three-
and nine-month periods ended September 30, 1999. Recording the cost assigned to
contracts acquired as an asset, with the resulting amortization as an operating
expense, reflects the application of generally accepted accounting principles to
acquisitions by UAM of investment management firms in transactions accounted for
as purchases. The principal assets acquired are the investment advisory
contracts which evidence the firms' ongoing relationships with their clients.

         The cost assigned to contracts acquired is amortized on a straight-line
basis over the estimated weighted average useful life of the contracts of
individual firms acquired. These lives are estimated through statistical
analysis of historical patterns of terminations and the size and age of the
contracts acquired as of the acquisition date.

         The Company regularly performs reviews of estimated lives as well as
for potential impairment of the value of contracts. If the update indicates that
any of the estimates should be shortened, the remaining cost assigned to
contracts acquired will be amortized over the shorter life commencing in the
year in which the new estimate is determined. If the review indicates that the
carrying value of the contracts is impaired, the asset is adjusted to its
estimated fair value.

         Cost assigned to contracts acquired is amortized as an operating
expense. It does not, however, require the use of cash and therefore, management
believes that it is important to distinguish this expense from other operating
expenses in order to evaluate the performance of the Company. Amortization of
cost assigned to contracts acquired per share referred to below has been
calculated by dividing total amortization by the same number of shares used in
the diluted earnings-per-share calculation.


                                      F-6

<PAGE>   10



                                OPERATING RESULTS

                      THREE MONTHS ENDED SEPTEMBER 30, 1999
                                   COMPARED TO
                      THREE MONTHS ENDED SEPTEMBER 30, 1998

         Revenues were $217,215,000 for the three months ended September 30,
1999 compared to $226,745,000 for the third quarter of 1998. Revenues declined
due to the effect of negative net client cash flow, partially offset by the
impact of positive market performance over the past 12-month period which
generated higher fee revenues.

         Compensation and related expenses together with other operating
expenses were $146,103,000 compared to $151,117,000 in 1998, primarily
reflecting lower operating expenses and compensation earned by employees of
existing affiliated firms in accordance with revenue sharing plans. Amortization
of cost assigned to contracts acquired was $26,218,000 compared to $28,473,000
in 1998. The decrease was the result of various factors including certain cost
assigned to contracts acquired being fully amortized at the end of 1998,
partially offset by the recording of additional purchase price commitments
associated with prior-year acquisitions.

         Interest expense increased to $17,558,000 from $16,765,000 in 1998,
primarily due to the increase in the Company's debt level from stock repurchases
over the past 12 months.

         Income before income tax expense was $27,548,000 compared to
$31,034,000 in 1998, reflecting the circumstances described above. The Company's
annual effective tax rate approximated 43% for the three-month periods ended
September 30, 1999 and 1998.

         Net income was $15,754,000 compared to $17,753,000 in 1998, reflecting
the results of the events discussed above. Diluted earnings per share were $.27
for both the third quarter of 1999 and 1998. Diluted earnings per share were
affected by the impact of the issuance of shares of common stock and the
hypothetical exercise of warrants and stock options on the calculation of
earnings per share under the treasury stock method, and by the effect of the
Company's common stock repurchased over the past 12-month period and the
Company's lower average stock price. Amortization of cost assigned to contracts
acquired per share increased to $.44 in the third quarter of 1999 from $.43 in
1998. Net income plus amortization and depreciation was $47,409,000 in the third
quarter of 1999 compared to $51,243,000 in 1998, and EBITDA (earnings before
interest, taxes, depreciation and amortization) was $75,367,000 in the third
quarter of 1999 compared to $79,326,000 in 1998 due to the circumstances
discussed above. Management uses the last two statistics not to the exclusion of
net income, but rather as an additional important measure of the Company's
performance.


                                      F-7
<PAGE>   11

                      NINE MONTHS ENDED SEPTEMBER 30, 1999
                                   COMPARED TO
                      NINE MONTHS ENDED SEPTEMBER 30, 1998


         Revenues were $654,252,000 for the nine months ended September 30, 1999
compared to $722,941,000 for the first nine months of 1998. Revenues declined
due to the effect of negative net client cash flow, partially offset by the
impact of positive market performance which generated higher fee revenues.

         Compensation and related expenses together with other operating
expenses were $443,420,000 compared to $487,252,000 in 1998, primarily
reflecting lower operating expenses and compensation earned by employees of
existing affiliated firms in accordance with revenue sharing plans. Amortization
of cost assigned to contracts acquired was $78,813,000 compared to $86,118,000
in 1998. The decrease was the result of various factors including certain cost
assigned to contracts acquired being fully amortized at the end of 1998,
partially offset by the recording of additional purchase price commitments
associated with prior-year acquisitions.

         Interest expense increased to $52,577,000 from $43,457,000 in 1998,
primarily due to the increase in the Company's debt level resulting from stock
repurchases, as well as an increase in the Company's borrowing rates.

         Income before income tax expense was $79,994,000 compared to
$108,334,000 in 1998, reflecting the circumstances described above. The
Company's annual effective tax rate approximated 43% for the nine-month periods
ended September 30, 1999 and 1998.

         Net income was $45,756,000 compared to $61,968,000 reflecting the net
results of the events discussed above. Diluted earnings per share were $.76 for
the nine months ended September 30, 1999 compared to $.89 for the nine months
ended September 30, 1998. Diluted earnings per share were affected by the impact
of the issuance of shares of common stock and the hypothetical exercise of
warrants and stock options on the calculation of earnings per share under the
treasury stock method, and by the effect of the Company's common stock
repurchased over the past 12-month period and the Company's lower average stock
price. Amortization of cost assigned to contracts acquired per share increased
to $1.32 for the nine months ended September 30, 1999 from $1.24 in 1998,
primarily due to the circumstances discussed above. Net income plus amortization
and depreciation was $141,683,000 for the nine months ended September 30, 1999
compared to $162,044,000 in 1998, and EBITDA was $224,421,000 for the nine
months ended September 30, 1999 compared to $246,525,000 in 1998 due to the
circumstances discussed above.


         CHANGES IN FINANCIAL CONDITION; LIQUIDITY AND CAPITAL RESOURCES

         The Company's internally generated cash and additional borrowings under
the Company's line of credit were primarily used to repurchase shares of the
Company's common stock and to pay dividends to shareholders. The Company invests
its excess cash in deposits with major banks, money market funds or in
securities, principally commercial paper of companies with strong credit ratings
in diversified industries. As of September 30, 1999, the Company had drawn down
$283,000,000 leaving $467,000,000 available under its $750,000,000 Reducing
Revolving Credit Agreement.

         Management believes that the Company's existing capital, together with
internally generated cash and borrowings available under its revolving line of
credit, will provide the Company with sufficient resources to meet its present
and reasonably foreseeable future cash needs. Management expects that the
principal uses of financial resources will be to provide further support for
investing in the growth initiatives of existing affiliates, to repurchase shares
of the Company's common stock, to

                                      F-8
<PAGE>   12


pay shareholder dividends, to acquire additional investment management firms,
and to fund commitments due or potentially due to former owners of affiliated
firms.

         Increases or decreases in interest rates affect UAM's costs of
operations chiefly through raising or lowering the interest expense related to
the Company's variable-rate debt outstanding. To mitigate the risks associated
with increases in interest rates, UAM has entered into and plans to continue to
enter into interest-rate protection agreements. Rates of interest on the Senior
Notes and existing subordinated debt are fixed. Increases and decreases in
interest rates may also affect market prices of assets managed by the Company's
affiliated firms. Changes in such prices may affect the affiliated firms'
revenues, and therefore UAM's consolidated revenues.


                    YEAR 2000 AND OTHER SYSTEM-RELATED ISSUES

         The "Year 2000 issue" is the result of computer programs and other
electronic systems that use two digits rather than four to define the applicable
year. These programs and systems may not be able to process dates beyond 1999,
which may cause system failures or create erroneous results.

         The Company and its affiliates have retained a consulting firm since
1997 to help develop and implement a program to assess their Year 2000
readiness. The Company and its affiliates have substantially completed
inventories of their computer hardware and software programs, have conducted
surveys of all of their software and hardware vendors, and have substantially
completed the testing, modification, upgrading or replacement of their computer
software applications and systems.

         The Company and its affiliates are also addressing Year 2000 issues
related to non-information technology (non-IT) systems, including embedded
software and equipment (e.g. elevators, telephone systems, etc.). The Company
and its affiliates have substantially completed an assessment of its mission
critical non-IT systems and service providers and have gained assurances from
substantially all of their key service providers that they will be prepared for
Year 2000.

         The Company and its affiliates are also developing contingency plans in
the event that the IT or non-IT systems or any of their key service providers
are not substantially Year 2000 compliant by the end of 1999. The contingency
plans, which are substantially complete, address how to mitigate risks
associated with the worst reasonably likely failure of systems at critical dates
in both the short term and the long term. A major Year 2000 compliance problem
of the Company, any of its affiliated firms, any of its vendors, or any other
company with which it conducts business could have a material adverse effect on
the Company's consolidated financial position, consolidated results of
operations or consolidated cash flows.

         Through September 30, 1999, the Company and its affiliates have
incurred expenses of approximately $1,800,000 and expect to incur an additional
$350,000 related to this issue. These costs, which principally represent
consulting fees, are being expensed as incurred. The Company has performed, and
expects to continue to perform, modifications, upgrades and replacements of its
computer software applications and systems through the Company's ongoing
maintenance program. Therefore, the Company has not incurred, and does not
expect to incur, significant incremental expenses for such modifications,
upgrades and replacements. The Company does not segregate payroll or other
internal costs specifically devoted to its efforts to address Year 2000 issues,
but does not believe these costs to be significant. The expenses of the
Company's affiliated firms related to the Year 2000 issues are funded out of the
share of revenues that is reserved for the affiliates under revenue sharing


                                      F-9
<PAGE>   13

agreements and do not affect the share of revenues retained by the Company. The
total cost associated with preparing for the Year 2000 is not expected to be
material to the Company's consolidated financial position, consolidated results
of operations or consolidated cash flows.

         The Company's affiliates that are registered with the Securities and
Exchange Commission (SEC) as investment advisers or broker-dealers are required
to disclose their Year 2000 readiness in Forms ADV-Y2K or BD-Y2K which have been
filed with the SEC and made available to clients.

         The estimates and conclusions herein contain forward-looking statements
and are based on management's best estimates of future events. These statements
should be read in conjunction with the Company's disclosures under the heading
"Forward-Looking Statements" detailed below.


                           FORWARD-LOOKING STATEMENTS

         This Quarterly Report on Form 10-Q contains "forward-looking
statements." These statements include descriptions of UAM's operational plans,
expectations about future earnings and other results of operations, views of
future industry or market conditions, and other statements that include words
like "may," "expects," "believes," and "intends," and that describe opinions
about future events.

         Investors should not rely on these statements as though they were
guarantees. These statements are current only when they are made. UAM's
management has no obligation to revise or update these statements based on
future developments. Known and unknown risks may cause UAM's actual results and
performances to be materially different from those expressed or implied by these
statements. Some of these risks are that: most of UAM's revenues are based on
the market value of managed assets and, therefore, will rise and fall with
changes in the economy and financial markets; the investment management business
is highly competitive; the investment management business is susceptible to
internal shifts and frequently requires firms to adapt; and UAM's affiliated
firms depend significantly on key employees. These and other risk factors are
identified and more thoroughly explained in Exhibit 99.1 to UAM's Annual Report
on Form 10-K filed on March 25, 1999 with the SEC.


ITEM 3.      QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

         The information provided below updates that which was previously
presented in Item 7A, Quantitative and Qualitative Disclosures About Market
Risk, of the Company's Form 10-K for the year ended December 31, 1998.

         The Company had $283,000,000 outstanding under its $750,000,000
Reducing Revolving Credit Agreement (the Credit Agreement) as of September 30,
1999. Interest rates available for amounts outstanding under the Credit
Agreement are currently: prime, 1.875% over LIBOR or a money market bid option.
The effective interest rate on the outstanding borrowings at September 30, 1999
was 7.32% compared to 7.14% at September 30, 1998. In addition, an annual
commitment fee, payable on the daily average unused portion of the Credit
Agreement, is currently .375%.

         At September 30, 1998, the Company also had $191,851,000 of
subordinated notes outstanding which mature at various dates through March 2005
and have interest rates ranging from 5.5% to 7.5%.

                                      F-10

<PAGE>   14
                                                                      Exhibit 11

                       UNITED ASSET MANAGEMENT CORPORATION

                        CALCULATION OF EARNINGS PER SHARE
                    (In thousands, except per-share amounts)
                                   (Unaudited)

<TABLE>
<CAPTION>

                                             For the Three Months Ended September 30,     For the Nine Months Ended September 30,
                                            -----------------------------------------     ----------------------------------------
                                              Income         Shares         Per-Share       Income         Shares        Per-Share
                                            (Numerator)   (Denominator)       Amount      (Numerator)   (Denominator)     Amount
                                            -----------    ------------     ---------     -----------   -------------    ---------
<S>                                         <C>             <C>             <C>            <C>            <C>             <C>
For the three- and nine-month periods
 ended September 30, 1999
Basic Earnings per Share
Income available to common
     shareholders                           $15,754,000     58,916,000         $ .27       $45,756,000     59,457,000       $ .77
                                                                             =======                                      =======
Effect of Dilutive Securities (1)                    --        123,000                              --        367,000
                                            -----------     ----------                     -----------     ----------
Diluted Earnings per Share
Income available to common
     shareholders + assumed conversions     $15,754,000     59,039,000         $ .27       $45,756,000     59,824,000       $ .76
                                            ===========     ==========       =======       ===========     ==========     =======
====================================================================================================================================
For the three- and nine-month periods
 ended September 30, 1998
Basic Earnings per Share
Income available to common
     shareholders                           $17,753,000     64,950,000         $. 27       $61,968,000     67,230,000       $ .92
                                                                             =======                                      =======
Effect of Dilutive Securities (2)                    --      1,751,000                              --      2,160,000
                                            -----------     ----------                     -----------     ----------
Diluted Earnings per Share
Income available to common
     shareholders + assumed conversions     $17,753,000     66,701,000         $ .27       $61,968,000     69,390,000       $ .89
                                            ===========     ==========       =======       ===========     ==========     =======
====================================================================================================================================
</TABLE>


(1) Options on 6,713,000 and 5,217,000 shares of common stock and warrants on
    7,288,000 and 5,865,000 shares of common stock were outstanding during the
    three- and nine-month periods ended September 30, 1999, respectively, but
    were not included in computing diluted earnings per share because their
    effects were antidilutive.

(2) Options on 2,101,000 and 1,854,000 shares of common stock and warrants on
    1,520,000 and 1,524,000 shares of common stock were outstanding during the
    three- and nine-month periods ended September 30, 1998, respectively, but
    were not included in computing diluted earnings per share because their
    effects were antidilutive.

                                      F-11