<PAGE>   1

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

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 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, 1998 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 of the registrant's common stock outstanding as of
November 9, 1998 was 63,448,820.


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


<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-11)

Item 3.  Quantitative and Qualitative Disclosures About Market Risk. Not
         Applicable.

                                     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 1998, UAM issued an aggregate of 85,799
         shares of its Common Stock in reliance on Section 4(2) of the
         Securities Act of 1933, as amended (the Act), to certain executives of
         its subsidiaries upon the exercise of warrants originally issued in
         connection with the acquisition of such subsidiaries by UAM. The
         exercise prices of the warrants ranged from $14.50 to $17.50 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 - $250,000,000 Note Purchase Agreement dated as of 
                              August 12, 1998.
               Exhibit 10.2 - Undertaking to Furnish Copies of Omitted Exhibits 
                              and Schedules to $250,000,000 Note Purchase 
                              Agreement dated as of August 12, 1998.
               Exhibit 10.3 - Amendment No. 1 to Amended and Restated Credit 
                              Agreement dated as of August 12, 1998.
               Exhibit 11   - Calculation of Earnings Per Share (Page F-12).
               Exhibit 27   - Financial Data Schedule.
               Exhibit 99.1 - Risk Factors.


<PAGE>   3


         (b)  There have been no reports on Form 8-K filed by the Company
              during the quarter ended September 30, 1998.

                                   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 12, 1998                            /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

                      CONSOLIDATED STATEMENT OF OPERATIONS
                                   (Unaudited)
<TABLE>
<CAPTION>

-----------------------------------------------------------------------------------------------------------------------------------
                                                  Three Months Ended                                  Nine Months Ended
                                                     September 30,                                      September 30,
                                             1998                    1997                      1998                     1997
------------------------------------------------------------------------------------------------------------------------------------
<S>                                       <C>                     <C>                       <C>                      <C>        
Revenues                                 $226,745,000            $241,710,000              $722,941,000             $676,804,000
------------------------------------------------------------------------------------------------------------------------------------
Operating expenses:
      Compensation and related
         expenses                         108,023,000             119,183,000               352,740,000              331,296,000
      Amortization of cost assigned
         to contracts acquired             28,473,000              27,775,000                86,118,000               78,349,000
      Other operating expenses             43,094,000              43,677,000               134,512,000              114,605,000
------------------------------------------------------------------------------------------------------------------------------------
                                          179,590,000             190,635,000               573,370,000              524,250,000
------------------------------------------------------------------------------------------------------------------------------------
Operating income                           47,155,000              51,075,000               149,571,000              152,554,000
------------------------------------------------------------------------------------------------------------------------------------
Non-operating expenses:
      Interest expense, net                14,802,000               9,839,000                38,115,000               26,201,000
      Other amortization                    1,319,000                 543,000                 3,122,000                1,595,000
------------------------------------------------------------------------------------------------------------------------------------
                                           16,121,000              10,382,000                41,237,000               27,796,000
------------------------------------------------------------------------------------------------------------------------------------
Income before income tax expense           31,034,000              40,693,000               108,334,000              124,758,000
Income tax expense                         13,281,000              17,467,000                46,366,000               53,447,000
------------------------------------------------------------------------------------------------------------------------------------
Net income                               $ 17,753,000            $ 23,226,000              $ 61,968,000             $ 71,311,000
====================================================================================================================================
Basic earnings per share                 $        .27            $        .33              $        .92             $       1.02
Diluted earnings per share               $        .27            $        .32              $        .89             $        .97
====================================================================================================================================
Dividends declared per share             $        .20            $        .20              $        .60             $        .57
====================================================================================================================================
</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,
                                                          1998                          1997
                                                      (Unaudited)
---------------------------------------------------------------------------------------------------
<S>                                                   <C>                           <C>          
Assets
Current assets:
     Cash and cash equivalents                      $   164,097,000               $   173,638,000
     Investment advisory fees receivable                154,772,000                   180,921,000
     Other current assets                                 9,644,000                    11,863,000
---------------------------------------------------------------------------------------------------
Total current assets                                    328,513,000                   366,422,000
Fixed assets, net                                        42,876,000                    41,110,000
Cost assigned to contracts acquired, net                968,614,000                 1,018,172,000
Other assets                                            122,278,000                    87,796,000
---------------------------------------------------------------------------------------------------
Total assets                                        $ 1,462,281,000               $ 1,513,500,000
===================================================================================================
Liabilities and Stockholders' Equity
Current liabilities:
     Accounts payable and accrued expenses          $   106,478,000               $   118,249,000
     Accrued compensation                               120,810,000                   143,633,000
     Current portion of notes payable                             -                       137,000
---------------------------------------------------------------------------------------------------
Total current liabilities                               227,288,000                   262,019,000
Senior notes payable                                    672,150,000                   514,843,000
Subordinated notes payable                              210,700,000                   258,412,000
Deferred income taxes                                    32,178,000                    20,074,000
---------------------------------------------------------------------------------------------------
Total liabilities                                     1,142,316,000                 1,055,348,000
---------------------------------------------------------------------------------------------------

Commitments and contingencies
Stockholders' equity:
     Common stock, par value $.01 per share                 703,000                       703,000
     Capital in excess of par value                     360,546,000                   357,239,000
     Retained earnings                                  142,160,000                   133,291,000
     Accumulated other comprehensive income             (10,908,000)                   (4,369,000)
--------------------------------------------------------------------------------------------------
                                                        492,501,000                   486,864,000
     Less treasury shares at cost                      (172,536,000)                  (28,712,000)
--------------------------------------------------------------------------------------------------
Total stockholders' equity                              319,965,000                   458,152,000
---------------------------------------------------------------------------------------------------
Total liabilities and stockholders' equity          $ 1,462,281,000               $ 1,513,500,000
==================================================================================================

</TABLE>

See Notes to Condensed Consolidated Financial Statements.


                                      F-2


<PAGE>   6




                       UNITED ASSET MANAGEMENT CORPORATION

                 CONDENSED CONSOLIDATED STATEMENT OF CASH FLOWS
                                   (Unaudited)
<TABLE>
<CAPTION>
-----------------------------------------------------------------------------------------------------------------------------------
                                                                        Three Months Ended                 Nine Months Ended
                                                                            September 30,                    September 30,
                                                                       1998             1997            1998               1997
------------------------------------------------------------------------------------------------------------------------------------
<S>                                                               <C>              <C>             <C>              <C>          
Cash flow from (used in) operating activities:
  Net income                                                      $ 17,753,000     $ 23,226,000    $  61,968,000    $  71,311,000
  Adjustments to reconcile net income to net cash flow
       from operating activities:
       Amortization of cost assigned to contracts acquired          28,473,000       27,775,000       86,118,000       78,349,000
       Depreciation                                                  3,359,000        2,670,000        9,817,000        7,505,000
       Amortization of goodwill and other                            1,658,000          543,000        4,141,000        1,595,000
------------------------------------------------------------------------------------------------------------------------------------
  Net income plus amortization and depreciation                     51,243,000       54,214,000      162,044,000      158,760,000
  Changes in assets and liabilities:
       Decrease (increase) in investment advisory fees receivable   11,411,000      (14,708,000)      26,265,000      (10,517,000)
       Decrease (increase) in other current assets                   5,662,000         (198,000)       2,610,000          714,000
       Decrease in accounts payable and accrued expenses            (3,083,000)      (2,161,000)     (17,566,000)      (6,361,000)
       Increase (decrease) in accrued compensation                  17,596,000       27,251,000      (21,465,000)       1,187,000
       Increase (decrease) in deferred income taxes                   (373,000)       2,179,000        1,920,000          335,000
------------------------------------------------------------------------------------------------------------------------------------
Net cash flow from operating activities                             82,456,000       66,577,000      153,808,000      144,118,000
------------------------------------------------------------------------------------------------------------------------------------
Cash flow used in investing activities:
  Cash additions to cost assigned to contracts acquired               (417,000)     (47,395,000)     (29,578,000)    (158,277,000)
  Change in other assets                                           (15,856,000)      (1,962,000)     (38,647,000)     (13,382,000)
------------------------------------------------------------------------------------------------------------------------------------
Net cash flow used in investing activities                         (16,273,000)     (49,357,000)     (68,225,000)    (171,659,000)
------------------------------------------------------------------------------------------------------------------------------------
Cash flow from (used in) financing activities:
  Purchase of treasury shares                                      (76,171,000)     (19,935,000)    (205,552,000)     (54,764,000)
  Additions to notes payable, net                                   47,974,000       25,098,000      127,163,000       14,583,000
  Issuance or reissuance of equity securities                        6,549,000        4,370,000       23,823,000       23,074,000
  Dividends paid                                                   (13,269,000)     (12,959,000)     (40,949,000)     (37,650,000)
------------------------------------------------------------------------------------------------------------------------------------
Net cash flow used in financing activities                         (34,917,000)      (3,426,000)     (95,515,000)     (54,757,000)
------------------------------------------------------------------------------------------------------------------------------------
Effect of foreign exchange rate changes on cash flow                   (43,000)      (1,115,000)         391,000       (1,797,000)
------------------------------------------------------------------------------------------------------------------------------------
Net increase (decrease) in cash and cash equivalents                31,223,000       12,679,000       (9,541,000)     (84,095,000)
Cash and cash equivalents at beginning of period                   132,874,000      151,625,000      173,638,000      248,399,000
------------------------------------------------------------------------------------------------------------------------------------
Cash and cash equivalents at end of period                        $164,097,000     $164,304,000    $ 164,097,000    $ 164,304,000
====================================================================================================================================
</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, 1998 and their results of
operations and cash flows for the three- and nine-month periods ended September
30, 1998 and 1997. These Financial Statements should be read in conjunction with
the Company's Annual Report on Form 10-K for the year ended December 31, 1997.

Note 2

     Accumulated depreciation of fixed assets was $58,548,000 and $48,731,000 at
September 30, 1998 and December 31, 1997, respectively. The accumulated
amortization of cost assigned to contracts acquired was $829,493,000 and
$743,795,000 at September 30, 1998 and December 31, 1997, 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. During the three- and nine-month periods ended
September 30, 1998, the Company repurchased 3,038,500 and 8,102,000 shares of
its common stock at a cost of $76,171,000 and $205,552,000, respectively,
including certain shares repurchased under the terms of the Company's systematic
program. During the three- and nine-month periods ended September 30, 1998,
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:

                                           Three Months          Nine Months
                                              Ended                 Ended
                                       September 30, 1998     September 30, 1998
                                       ------------------     ------------------

     Subordinated notes extinguished       $1,393,000            $ 8,572,000
     Cash proceeds received                $5,878,000            $20,747,000
     Shares issued                                  -                      -
     Treasury shares reissued                 384,311              2,478,981


     As of September 30, 1998, the Company held 6,712,567 treasury shares.
Warrants for the purchase of 8,791,000 shares and stock options for the purchase
of 8,368,000 shares were outstanding at weighted average exercise prices of
$23.42 and $22.55, respectively.


                                      F-4


<PAGE>   8


Note 4

     In August 1998, the Company issued an aggregate of $250,000,000 of
fixed-rate long-term senior secured notes to institutional investors. Principal
payments on the notes are due over periods beginning in 2002 and ending in 2008
and bear interest at fixed rates ranging from 8.52% to 8.72%. Under the terms of
the private placement, the Company is required to meet certain financial
covenants including cash flow and debt ratios. The notes outstanding under this
facility are secured by the stock of the Company's subsidiaries.

Note 5

     Statement of Financial Accounting Standards No. 130, Reporting
Comprehensive Income (FAS 130), became effective for annual periods beginning
after December 15, 1997 and establishes standards for reporting and displaying
comprehensive income and its components in a full set of financial statements.
FAS 130 requires only additional reporting in the consolidated financial
statements and does not affect the Company's financial position or results of
operations. The components of comprehensive income for the three- and nine-month
periods ended September 30, 1998 are set forth below:
<TABLE>
<CAPTION>
                                                     Three Months           Nine Months
                                                        Ended                  Ended
                                                 September 30, 1998     September 30, 1998
                                                 ------------------     ------------------
<S>                                                 <C>                    <C>        
     Net income                                     $17,753,000            $61,968,000
     Other comprehensive income -
       foreign currency translation adjustment       (3,406,000)            (6,539,000)
                                                    -----------            -----------
     Comprehensive income                           $14,347,000            $55,429,000
                                                    ===========            ===========
</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 institutional and other clients.
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
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 $183.2 billion as of September 30, 1998,
compared to $210.1 billion under management on June 30, 1998. During the
quarter, market performance subtracted $20.7 billion from assets under
management and net client cash flow reduced these assets by $6.2 billion.


                                      F-5


<PAGE>   9


AMORTIZATION OF COST ASSIGNED TO CONTRACTS ACQUIRED AND OPERATING CASH FLOW (NET
INCOME PLUS AMORTIZATION AND DEPRECIATION)

     Cost assigned to contracts acquired, net of accumulated amortization,
represented approximately 66% of the Company's total assets as of September 30,
1998. Amortization of cost assigned to contracts acquired, which is a noncash
charge, represented 16% and 15% of the Company's operating expenses for the
three- and nine-month periods ended September 30, 1998, respectively. 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.

     Although the contracts acquired are typically terminable on 30-days notice,
analyses conducted by independent consultants retained by UAM and the experience
of UAM's firms to date have indicated that: 1) contracts are usually relatively
long-lived; 2) the duration of contracts can be reasonably estimated; and 3) the
value of the cost assigned to contracts acquired can be estimated based on the
present value of its projected income stream.

     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.

     When actual terminations differ from the statistical patterns developed, or
upon the occurrence of certain other events, the Company updates the lifing
analyses discussed above. 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. The Company regularly performs reviews for potential impairment
of the value of contracts. 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.

     For purposes of this discussion, Operating Cash Flow is defined as net
income plus amortization and depreciation, as reflected in the Company's
Condensed Consolidated Statement of Cash Flows. Management uses Operating Cash
Flow not to the exclusion of net income, but rather as an additional important
measure of the Company's performance.


                                      F-6


<PAGE>   10


                                OPERATING RESULTS

                      THREE MONTHS ENDED SEPTEMBER 30, 1998
                                   COMPARED TO
                      THREE MONTHS ENDED SEPTEMBER 30, 1997

     Revenues were $226,745,000 for the three months ended September 30, 1998
compared to $241,710,000 for the third quarter of 1997. Revenues declined due to
the effect of negative net client cash flow as well as the effect of Heitman
Financial Ltd. selling its non-retail property management operation during the
third quarter of 1998. Partially offsetting this decrease were acquisition
activity and the impact of market performance which generated higher fee
revenues. The revenues of Lincluden Management Limited and Integra Capital
Management Corporation, acquired September 4, 1997 and January 6, 1998,
respectively, have been included since their acquisition dates.

     Compensation and related expenses together with other operating expenses
were $151,117,000 compared to $162,860,000 in 1997, primarily reflecting lower
operating expenses and compensation earned by employees of existing affiliated
firms in accordance with revenue sharing plans, partially offset by the impact
of the acquisitions discussed above. Amortization of cost assigned to contracts
acquired increased to $28,473,000 from $27,775,000 primarily as a result of the
acquisitions discussed above as well as the recording of additional purchase
price commitments associated with prior-year acquisitions, partially offset by a
reduction in the value of intangible assets recorded in the fourth quarter of
1997.

     Interest expense increased to $16,765,000 from $11,389,000. The Company's
average debt levels increased due to the amount of stock repurchased as well as
acquisition activity. In addition, the Company completed its $250,000,000
private placement this quarter, creating longer term fixed-rate debt with higher
interest rates.

     Income before income tax expense was $31,034,000 compared to $40,693,000 in
1997, reflecting the circumstances described above. The Company's annual
effective tax rate approximated 43% for both of the three-month periods ended
September 30, 1998 and 1997.

     Net income was $17,753,000 compared to $23,226,000 reflecting the net
results of the events discussed above. Diluted earnings per share were $.27 for
the third quarter of 1998 compared to $.32 in the third quarter of 1997,
reflecting the effect of the Company's common stock repurchased and the
Company's lower average stock price, partially offset 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. Amortization of cost assigned to contracts acquired per share increased
to $.43 in the third quarter of 1998 from $.38 in 1997. Operating Cash Flow was
$51,243,000 in the third quarter of 1998 compared to $54,214,000 in 1997 due to
the circumstances discussed above.


                                      F-7


<PAGE>   11


                                OPERATING RESULTS

                      NINE MONTHS ENDED SEPTEMBER 30, 1998
                                   COMPARED TO
                      NINE MONTHS ENDED SEPTEMBER 30, 1997

     Revenues increased 7% to $722,941,000 for the nine months ended September
30, 1998, from $676,804,000 for the first nine months of 1997. This increase is
the result of rising securities markets, particularly in North America and
Europe, the impact of acquisitions and life insurance proceeds received as a
result of the death of an executive, partially offset by the effect of negative
net client cash flow and Heitman Financial Ltd. selling its non-retail property
management operation. The revenues of Pacific Financial Research, Inc., Thomson
Horstmann & Bryant, Inc., Lincluden Management Limited and Integra Capital
Management Corporation acquired May 29, 1997, June 6, 1997, September 4, 1997
and January 6, 1998, respectively, have been included since their acquisition
dates.

     Compensation and related expenses together with other operating expenses
increased 9% to $487,252,000 from $445,901,000, primarily reflecting higher
operating expenses and compensation earned by employees of existing and newly
acquired affiliated firms in accordance with revenue sharing plans. Amortization
of cost assigned to contracts acquired increased 10% to $86,118,000 from
$78,349,000 primarily as a result of the acquisitions discussed above as well as
the recording of additional purchase price commitments associated with prior
year acquisitions, partially offset by a reduction in the value of intangible
assets recorded in the fourth quarter of 1997.

     Interest expense increased to $43,457,000 from $31,530,000 primarily due to
the increase in the Company's average debt levels, resulting from stock
repurchases and acquisition activity, as well as an increase in the Company's
average borrowing rates.

     Income before income tax expense was $108,334,000 compared to $124,758,000
in 1997, reflecting the circumstances described above. Income tax expense was
$46,366,000 for the nine months ended September 30, 1998, including the effects
of reevaluating certain deferred tax assets related to the sale of certain
operations. Income tax expense for the nine months ended September 30, 1997 was
$53,447,000. The Company's annual effective tax rate approximated 43% for both
of the nine-month periods ended September 30, 1998 and 1997.

     Net income was $61,968,000 compared to $71,311,000 reflecting the net
results of the events discussed above. Diluted earnings per share were $.89 for
the nine months ended September 30, 1998 compared to $.97 for the nine months
ended September 30, 1997, reflecting the effect of the Company's common stock
repurchased and the Company's lower average stock price, partially offset 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. Amortization of cost assigned to contracts acquired per
share increased to $1.24 for the nine months ended September 30, 1998 from $1.07
in 1997 primarily due to the circumstances discussed above.


                                      F-8


<PAGE>   12


        CHANGES IN FINANCIAL CONDITION; LIQUIDITY AND CAPITAL RESOURCES

     The Company generated $51,243,000 and $162,044,000 of Operating Cash Flow
for the three- and nine-month periods ended September 30, 1998. This Operating
Cash Flow and additional borrowings under the Company's line of credit were
primarily used to finance the cash portion of acquisition activity, 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, 1998,
the Company had $477,850,000 available under its $750,000,000 Reducing Revolving
Credit Agreement.

     In August 1998, the Company issued an aggregate of $250,000,000 of
fixed-rate long-term senior secured notes to institutional investors. Principal
payments on the notes are due over periods beginning in 2002 and ending in 2008
and bear interest at fixed rates ranging from 8.52% to 8.72%. Under the terms of
the private placement, the Company is required to meet certain financial
covenants including cash flow and debt ratios. The notes outstanding under this
facility are secured by the stock of the Company's subsidiaries.

     Management believes that the Company's existing capital, together with
Operating Cash Flow 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 acquire additional investment management
firms, to fund commitments due or potentially due to former owners of affiliated
firms, to repurchase shares of the Company's common stock and to pay shareholder
dividends.

     Increases or decreases in interest rates affect UAM's costs of operations
chiefly through increasing or decreasing 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 SYSTEMS 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 has retained a consulting firm since 1997 to help develop and
implement a program to assess its Year 2000 readiness. An inventory of the
Company's computer hardware and software programs, as well as surveys conducted
of all of its software and hardware vendors have substantially been completed.
As part of this program, the Company is in the process of testing, modifying,
upgrading or replacing its computer software applications and systems and seeks
to be Year 2000 compliant by June 30, 1999.


                                      F-9


<PAGE>   13
     The Company is also addressing Year 2000 issues related to non-information
technology (non-IT) systems, including embedded software and equipment (e.g.
elevators, telephone systems, etc.), and addressing the compliance of key
business partners. The Company has substantially completed an assessment of its
non-IT providers and is in the process of gaining assurances that they will be
Year 2000 compliant, and seeks to have these assurances by June 30, 1999. 

     The Company is in the process of developing contingency plans in the event
that the IT or non-IT systems of the Company or any of its key service providers
are not Year 2000 compliant by the end of 1999. The contingency plans, which are
expected to be completed by the end of 1999, will address how to mitigate risks
associated with the worst reasonably likely failures of systems at critical
dates in both the short term and the long term. Any Year 2000 compliance problem
of the Company, any of its affiliated firms, any of its vendors and 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.

     To date, the Company and its affiliates have incurred expenses in the
amount of approximately $800,000 and expect to incur an additional $900,000
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 agreements and do not
affect the share of revenues retained by the Company. The total cost associated
with becoming Year 2000 compliant 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 discuss their Year 2000 readiness in Forms ADV-Y2K or BD-Y2K which will be
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.

     On January 1, 1999, 11 European Union member states will adopt the "Euro"
as their common national currency. This currency will replace existing national
currencies in all participating countries over a period ending July 1, 2002.
During this period, both the Euro and existing national currencies will be
accepted. The Company is currently assessing the potential impact of the Euro
conversion on its systems and does not expect any costs incurred to have a
material adverse effect on the Company's consolidated financial position, its
consolidated results of operations or its consolidated cash flows.

                           FORWARD-LOOKING STATEMENTS

     Certain statements within this Form 10-Q constitute "forward-looking
statements" within the meaning of the Private Securities Litigation Reform Act
of 1995. The words or phrases "can be," "expects," "may affect," "may depend," "
believes," "estimate," "project" and similar words and phrases are intended to
identify such forward-looking statements.


                                      F-10


<PAGE>   14


     Such forward-looking statements involve known and unknown risks,
uncertainties and other factors, which may cause the actual results,
performances or achievements of the Company to be materially different from any
future results, performances or achievements expressed or implied by such
forward-looking statements. Some of these risks, uncertainties and other factors
are: changes in domestic and foreign economic and market conditions, effects of
client cash flow, impairment of acquired client contracts, competition in the
investment management industry, and other factors as more thoroughly identified
and explained in Exhibit 99.1 which is being filed with the Securities and
Exchange Commission as part of this Form 10-Q. Because of such risks,
uncertainties and other factors, the Company cautions each person receiving such
forward-looking statements not to place undue reliance on any such statements.
All such forward-looking statements are current only as of the date and time
they are made. The Company has no obligation, and will not undertake, to release
publicly any revisions to such forward-looking statements (for example, to
reflect events or circumstances occurring after the date and time such
statements were made; or to reflect events or circumstances that were not
anticipated at the date and time such statements were made).



                                      F-11

<PAGE>   15


                       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, 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 (1)                         -       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
                                                ===========      ==========      ====      ===========      ==========      =====
                                                                                                                        
=====================================================================================      ========================================
For the three- and nine-month periods ended                                                                             
      September 30, 1997                                                                                                
                                                                                                                        
Basic Earnings per Share                                                                                                
Income available to common                                                                                              
      shareholders                              $23,226,000      69,794,000      $.33      $71,311,000      69,988,000      $1.02
                                                                                 ====                                       =====
                                                                                                                        
Effect of Dilutive Securities (2)                         -       3,106,000                          -       3,465,000  
                                                -----------      ----------                -----------      ----------  
                                                                                                                        
Diluted Earnings per Share                                                                                              
Income available to common                                                                                              
      shareholders + assumed conversions        $23,226,000      72,900,000      $.32      $71,311,000      73,453,000      $ .97
                                                ===========      ==========      ====      ===========      ==========      =====
                                                                                                                        
=====================================================================================      ========================================
</TABLE>
(1)  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.
(2)  Options on 521,000 and 652,000 shares of common stock and warrants on
     1,047,000 and 904,000 shares of common stock were outstanding during the
     three- and nine-month periods ended September 30, 1997, respectively, but
     were not included in computing diluted earnings per share because their
     effects were antidilutive.




                                     F-12