<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 JUNE 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            (IRS 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 common stock outstanding as of August 10, 1998 was
65,261,029.



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


<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-9)

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 second quarter of 1998, UAM issued an aggregate of 9,188
          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 price of the warrants was $22.66.

          Also, during the second quarter of 1998, UAM issued an aggregate of
          239,320 shares of its Common Stock in reliance on Section 4(2) of the
          Act to certain executives of Integra Capital Management Corporation
          and Integra Capital Financial Corporation in exchange for an aggregate
          of 239,320 Exchangeable Preferred Shares in such corporations
          originally issued in connection with the acquisition of an equity
          interest in such corporations by UAM. On April 29, 1998, UAM filed a
          registration statement on Form S-3 to register such shares of its
          Common Stock for resale.

Item 3.   Defaults Upon Senior Securities.  None

Item 4.   Submission of Matters to a Vote of Security Holders.
          On May 21, 1998, the Company held its Annual Meeting of Stockholders
          at which each of Harold J. Baxter, Francis Finlay, Robert J.
          Greenebaum, Charles E. Haldeman, Jr., Beverly L. Hamilton, George E.
          Handtmann, III, Bryant M. Hanley, Jr., Jay O. Light, Norton H. Reamer,
          David I. Russell, Philip Scaturro, John A. Shane and Barbara S. Thomas
          were elected as directors to serve until the next Annual Meeting of
          Stockholders. Each of the directors were elected with the following
          votes: Mr. Baxter, 59,519,123 votes cast for and 261,905 votes
          withholding authority; Mr. Finlay, 59,523,643 votes cast for and
          257,385 votes withholding authority; Mr. Greenebaum, 59,449,090 votes
          cast for and 331,938 votes withholding authority; Mr. Haldeman,
          59,524,743 votes cast for and 256,285 votes withholding


<PAGE>   3
          authority; Mrs. Hamilton, 59,522,375 votes cast for and 258,653 votes
          withholding authority; Mr. Handtmann, 59,526,143 votes cast for and
          254,885 votes withholding authority; Mr. Hanley, 59,526,543 votes cast
          for and 254,485 votes withholding authority; Mr. Light, 59,152,533
          votes cast for and 628,495 votes withholding authority; Mr. Reamer,
          59,523,186 votes cast for and 257,842 votes withholding authority; Mr.
          Russell, 59,115,233 votes cast for and 665,795 votes withholding
          authority; Mr. Scaturro, 59,525,883 votes cast for and 255,145 votes
          withholding authority; Mr. Shane, 59,222,413 votes cast for and
          558,615 votes withholding authority; and Mrs. Thomas, 59,520,563 votes
          cast for and 260,465 votes withholding authority.

          The Company's stockholders also approved the selection of
          PricewaterhouseCoopers LLP as independent accountants of the Company
          for the fiscal year ending December 31, 1998, with 59,323,249 votes
          cast for such approval, 361,548 votes cast against such approval,
          96,230 votes abstaining from such approval and one broker nonvote.

Item 5.   Other Information.  None

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

          (a)  Exhibit 10.1 - First Amendment dated as of June 23, 1998 to Note
                              Purchase Agreement dated as of August 1, 1995.

               Exhibit 11   - Calculation of Earnings Per Share (Page F-10).

               Exhibit 27   - Financial Data Schedule.

          (b)  There have been no reports on Form 8-K filed by the Company
               during the quarter ended June 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


August 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                  Six Months Ended
                                                   June 30,                            June 30,
                                        ------------------------------      ------------------------------
                                            1998              1997              1998              1997
                                        ------------      ------------      ------------      ------------
<S>                                     <C>               <C>               <C>               <C>         

Revenues                                $254,376,000      $219,572,000      $496,196,000      $435,094,000

Operating expenses:
     Compensation and related
        expenses                         125,163,000       107,041,000       244,717,000       212,113,000
     Amortization of cost assigned
        to contracts acquired             30,812,000        25,662,000        57,645,000        50,574,000
     Other operating expenses             46,355,000        35,842,000        91,418,000        70,928,000
                                        ------------      ------------      ------------      ------------
                                         202,330,000       168,545,000       393,780,000       333,615,000
                                        ------------      ------------      ------------      ------------
Operating income                          52,046,000        51,027,000       102,416,000       101,479,000
                                        ------------      ------------      ------------      ------------
Non-operating expenses:
     Interest expense, net                12,476,000         8,445,000        23,313,000        16,362,000
     Other amortization                      905,000           571,000         1,803,000         1,052,000
                                        ------------      ------------      ------------      ------------
                                          13,381,000         9,016,000        25,116,000        17,414,000
                                        ------------      ------------      ------------      ------------
Income before income tax expense          38,665,000        42,011,000        77,300,000        84,065,000
Income tax expense                        16,548,000        17,981,000        33,085,000        35,980,000
                                        ------------      ------------      ------------      ------------
Net income                              $ 22,117,000      $ 24,030,000      $ 44,215,000      $ 48,085,000
                                        ============      ============      ============      ============

Basic earnings per share                $        .33      $        .34      $        .64      $        .69
Diluted earnings per share              $        .32      $        .33      $        .62      $        .66
Dividends declared per share            $        .20      $       .185      $        .40      $        .37
                                        ============      ============      ============      ============
</TABLE>














See Notes to Condensed Consolidated Financial Statements.



                                      F-1
<PAGE>   5

                       UNITED ASSET MANAGEMENT CORPORATION

                      CONDENSED CONSOLIDATED BALANCE SHEET

<TABLE>
<CAPTION>

                                                         June 30,           December 31,
                                                           1998                 1997
                                                      --------------       --------------
                                                        (Unaudited)
<S>                                                   <C>                  <C> 

Assets
Current assets:
    Cash and cash equivalents                         $  132,874,000       $  173,638,000  
    Investment advisory fees receivable                  167,019,000          180,921,000  
    Other current assets                                  13,124,000           11,863,000
                                                      --------------       --------------  
Total current assets                                     313,017,000          366,422,000  
Fixed assets, net                                         44,559,000           41,110,000  
Cost assigned to contracts acquired, net               1,000,174,000        1,018,172,000  
Other assets                                             107,539,000           87,796,000  
                                                      --------------       --------------
Total assets                                          $1,465,289,000       $1,513,500,000  
                                                      ==============       ==============  
Liabilities and Stockholders' Equity                                                       
Current liabilities:                                                                       
    Accounts payable and accrued expenses             $  107,735,000       $  118,249,000  
    Accrued compensation                                 104,540,000          143,633,000  
    Current portion of notes payable                              --              137,000
                                                      --------------       --------------  
Total current liabilities                                212,275,000          262,019,000  
Senior notes payable                                     622,200,000          514,843,000  
Subordinated notes payable                               212,419,000          258,412,000  
Deferred income taxes                                     32,089,000           20,074,000
                                                      --------------       --------------  
Total liabilities                                      1,078,983,000        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                       359,617,000          357,239,000  
    Retained earnings                                    139,803,000          133,291,000  
    Accumulated other comprehensive income                (7,502,000)          (4,369,000) 
                                                      --------------       --------------
                                                         492,621,000          486,864,000  
    Less treasury shares at cost                        (106,315,000)         (28,712,000) 
                                                      --------------       --------------
Total stockholders' equity                               386,306,000          458,152,000  
                                                      --------------       --------------
Total liabilities and stockholders' equity            $1,465,289,000       $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                Six Months Ended
                                                                        June 30,                          June 30,
                                                             -----------------------------     -------------------------------
                                                                 1998             1997             1998              1997
                                                             ------------     ------------     -------------     -------------
<S>                                                          <C>              <C>              <C>               <C> 
Cash flow from (used in) operating activities:
    Net income                                               $ 22,117,000     $ 24,030,000     $  44,215,000     $  48,085,000
    Adjustments to reconcile net income to net cash
        flow from operating activities:
        Amortization of cost assigned to contracts
           acquired                                            30,812,000       25,662,000        57,645,000        50,574,000
        Depreciation                                            3,386,000        2,459,000         6,458,000         4,835,000
        Amortization of goodwill and other                        844,000          571,000         2,483,000         1,052,000
                                                             ------------     ------------     -------------     -------------
    Net income plus amortization and depreciation              57,159,000       52,722,000       110,801,000       104,546,000
    Changes in assets and liabilities:
        Decrease (increase) in investment advisory
           fees receivable                                     (3,744,000)      (1,684,000)       14,854,000         4,191,000
        Decrease (increase) in other current assets            (2,118,000)         209,000        (3,052,000)          912,000
        Increase (decrease) in accounts payable and
           accrued expenses                                      (820,000)       9,837,000       (14,483,000)       (4,200,000)
        Increase (decrease) in accrued compensation            25,049,000       19,718,000       (39,061,000)      (26,064,000)
        Increase (decrease) in deferred income taxes            1,547,000         (603,000)        2,293,000        (1,844,000)
                                                             ------------     ------------     -------------     -------------
Net cash flow from operating activities                        77,073,000       80,199,000        71,352,000        77,541,000
                                                             ------------     ------------     -------------     -------------
Cash flow used in investing activities:
    Cash additions to cost assigned to contracts acquired      (6,278,000)     (67,949,000)      (29,161,000)     (110,882,000)
    Change in other assets                                     (5,913,000)      (8,113,000)      (22,791,000)      (11,420,000)
                                                             ------------     ------------     -------------     -------------
Net cash flow used in investing activities                    (12,191,000)     (76,062,000)      (51,952,000)     (122,302,000)
                                                             ------------     ------------     -------------     -------------
Cash flow from (used in) financing activities:
    Purchase of treasury shares                               (79,093,000)     (25,286,000)     (129,381,000)      (34,829,000)
    Additions to (reductions in) notes payable, net            31,405,000         (352,000)       79,189,000       (10,515,000)
    Issuance or reissuance of equity securities                 4,379,000        8,539,000        17,274,000        18,704,000
    Dividends paid                                            (13,792,000)     (12,988,000)      (27,680,000)      (24,691,000)
                                                             ------------     ------------     -------------     -------------
Net cash flow used in financing activities                    (57,101,000)     (30,087,000)      (60,598,000)      (51,331,000)
                                                             ------------     ------------     -------------     -------------
Effect of foreign exchange rate changes on cash flow              627,000          398,000           434,000          (682,000)
                                                             ------------     ------------     -------------     -------------
Net increase (decrease) in cash and cash equivalents            8,408,000      (25,552,000)      (40,764,000)      (96,774,000)
Cash and cash equivalents at beginning of period              124,466,000      177,177,000       173,638,000       248,399,000
                                                             ------------     ------------     -------------     -------------
Cash and cash equivalents at end of period                   $132,874,000     $151,625,000     $ 132,874,000     $ 151,625,000
                                                             ============     ============     =============     =============

</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 June 30, 1998 and their results of
operations and cash flows for the three- and six-month periods ended June 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 $55,189,000 and
$48,731,000 at June 30, 1998 and December 31, 1997, respectively. The
accumulated amortization of cost assigned to contracts acquired was $801,020,000
and $743,795,000 at June 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-month period ended June 30,
1998, the Company repurchased 3,059,400 shares of its common stock at a cost of
$79,093,000. For the six months ended June 30, 1998, common stock repurchases
totaled 5,063,500 shares at a cost of $129,381,000. During the three- and
six-month periods ended June 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:

<TABLE>
<CAPTION>
                                                 Three Months        Six Months
                                                    Ended               Ended
                                                June 30, 1998      June 30, 1998
                                                -------------      -------------
            <S>                                   <C>               <C>        

           Subordinated notes extinguished        $  208,000        $ 7,179,000
           Cash proceeds received                 $3,569,000        $14,869,000
           Shares issued                                  --                 --
           Treasury shares reissued                  449,760          2,094,670

</TABLE>


         As of June 30, 1998, the Company held 4,058,378 treasury shares.
Warrants for the purchase of 8,877,000 shares and stock options for the purchase
of 8,368,000 shares were outstanding at weighted average exercise prices of
$23.35 and $22.49, respectively.



                                      F-4
<PAGE>   8

Note 4

         During the quarter ended June 30, 1998, the Company reached an
agreement to sell Analytic*TSA International, Inc., and also reached an
agreement to sell and subsequently sold Heitman Properties Limited, a
wholly-owned subsidiary of Heitman Financial Limited. In connection with the
above transactions, the Company reevaluated certain deferred tax assets
associated therewith. In addition, the Company received life insurance proceeds
as a result of the death of an executive. These events in aggregate did not have
a material effect on the Company's consolidated results of operations.

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 six-month
periods ended June 30, 1998 are set forth below:

<TABLE>
<CAPTION>
                                                          Three Months       Six Months
                                                              Ended            Ended
                                                         June 30, 1998     June 30, 1998
                                                         -------------     -------------
         <S>                                              <C>               <C>        

         Net income                                       $22,117,000       $44,215,000
         Other comprehensive income -
             foreign currency translation adjustment       (3,611,000)       (3,133,000)
                                                          -----------       -----------
         Comprehensive income                             $18,506,000       $41,082,000
                                                          ===========       ===========
</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 $210.1 billion as of June 30, 1998,
compared to $213.9 billion under management on March 31, 1998. The net $3.8
billion change in assets under management during the quarter resulted from
investment gains of $500 million and negative client cash flow of $4.3 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 68% of the Company's total assets as of June 30, 1998.
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
six-month periods ended June 30, 1998. 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 JUNE 30, 1998
                                   COMPARED TO
                        THREE MONTHS ENDED JUNE 30, 1997

         Revenues increased 16% to $254,376,000 for the three months ended June
30, 1998, from $219,572,000 for the second quarter 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. 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 20% to $171,518,000 from $142,883,000 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 20% to $30,812,000
from $25,662,000 primarily as a result of the acquisitions discussed above as
well as the recording of additional purchase price commitments associated with
prior-year acquisitions.

         Interest expense increased to $14,563,000 from $10,365,000 primarily
due to the increase in the Company's average debt levels as well as an increase
in the Company's average borrowing rates.

         Income before income tax expense was $38,665,000 compared to
$42,011,000 in 1997, reflecting the circumstances described above. The
Company's annual effective tax rate approximately 43% for both of the
three-month periods ended June 30, 1998 and 1997.

         Net income was $22,117,000 compared to $24,030,000 reflecting the net
results of the events discussed above. Diluted earnings per share were $.32 for
the second quarter of 1998 compared to $.33 in the second 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 $.44 in the second quarter of 1998 from $.35 in 1997 and Operating Cash Flow
increased to $57,159,000 in the second quarter of 1998 from $52,722,000 in 1997
primarily due to the circumstances discussed above.





                                      F-7
<PAGE>   11

                                OPERATING RESULTS

                         SIX MONTHS ENDED JUNE 30, 1998
                                   COMPARED TO
                         SIX MONTHS ENDED JUNE 30, 1997

         Revenues increased 14% to $496,196,000 for the six months ended June
30, 1998, from $435,094,000 for the first six 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. 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 19% to $336,135,000 from $283,041,000 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 14% to $57,645,000
from $50,574,000 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 $26,692,000 from $20,139,000 primarily
due to the increase in the Company's average debt levels as well as an increase
in the Company's average borrowing rates.

         Income before income tax expense was $77,300,000 compared to
$84,065,000 in 1997, reflecting the circumstances described above. Income tax
expense was $33,085,000 for the six months ended June 30, 1998, including the
effects of reevaluating certain deferred tax assets related to the sale of
certain operations. Income tax expense for the six months ended June 30, 1997
was $35,980,000. The Company's annual effective tax rate approximated 43% for
both of the six-month periods ended June 30, 1998 and 1997.

         Net income was $44,215,000 compared to $48,085,000 reflecting the net
results of the events discussed above. Diluted earnings per share were $.62 for
the six months ended June 30, 1998 compared to $.66 for the six months ended
June 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 $.81 for the six months ended June 30, 1998 from $.69 in 1997,
primarily due to the circumstances discussed above.





                                      F-8
<PAGE>   12

         CHANGES IN FINANCIAL CONDITION; LIQUIDITY AND CAPITAL RESOURCES


         The Company generated $57,159,000 and $110,801,000 of Operating Cash
Flow for the three- and six-month periods ended June 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 June 30, 1998, the
Company had $277,800,000 available under its $750,000,000 Reducing Revolving
Credit Agreement.

         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.


                           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.

         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 to the Company's Annual Report on Form 10-K for
the year ended December 31, 1997 filed with the Securities and Exchange
Commission. 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-9
<PAGE>   13


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


<TABLE>
<CAPTION>
---------------------------------------------------------------------------------------------------------------------------
                                                For the Three Months Ended June 30,     For the Six Months Ended June 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 six-month periods 
  ended June 30, 1998 
Basic Earnings per Share 
Income available to common shareholders        $22,117,000    67,636,000    $.33      $44,215,000    68,586,000      $.64 
                                                                            ====                                     ====
                                                                                                                        
Effect of Dilutive Securities (1)                       --     2,382,000                       --     2,364,000           
                                               -----------    ----------              -----------    ----------
Diluted Earnings per Share                                                                                              
Income available to common                                                                                              
  shareholders + assumed conversions           $22,117,000    70,018,000    $.32      $44,215,000    70,950,000      $.62
                                               ===========    ==========    ====      ===========    ==========      ====
================================================================================      ===================================
For the three- and six-month periods                                                                                    
  ended June 30, 1997                                                                                                   
Basic Earnings per Share                                                                                                
Income available to common shareholders        $24,030,000    69,865,000    $.34      $48,085,000    69,600,000      $.69
                                                                            ====                                     ====
                                                                                                                        
Effect of Dilutive Securities (2)                       --     3,145,000                       --     3,644,000          
                                               -----------    ----------              -----------    ----------

Diluted Earnings per Share                                                                                              
Income available to common                                                                                              
  shareholders + assumed conversions           $24,030,000    73,010,000    $.33      $48,085,000    73,244,000      $.66
                                               ===========    ==========    ====      ===========    ==========      ====
================================================================================      ===================================
                                               
</TABLE>


(1)  Options on 1,647,000 and 1,731,000 shares of common stock and warrants on
     1,521,000 and 1,526,000 shares of common stock were outstanding during the
     three- and six-month periods ended June 30, 1998, respectively, but were
     not included in computing diluted earnings per share because their effects
     were antidilutive.

(2)  Options on 1,271,000 and 717,000 shares of common stock and warrants on
     957,000 and 833,000 shares of common stock were outstanding during the
     three- and six-month periods ended June 30, 1997, respectively, but were
     not included in computing diluted earnings per share because their effects
     were antidilutive.



                                      F-10