<PAGE>   1
                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                   FORM 10-Q

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

     FOR THE QUARTERLY PERIOD ENDED: MARCH 31, 1999

                                       OR

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

     FOR THE TRANSITION PERIOD FROM ................... TO....................

     COMMISSION FILE NUMBER: 0-27662

                               IPC HOLDINGS, LTD.
             (Exact name of registrant as specified in its charter)


               BERMUDA                              NOT APPLICABLE
   (State or other jurisdiction of                 (I.R.S. Employer
    incorporation or organization)               Identification No.)

   AMERICAN INTERNATIONAL BUILDING, 29 RICHMOND ROAD, PEMBROKE, HM 08, BERMUDA
                   (Address of principal executive offices)

                                 (441) 298-5100
              (Registrant's telephone number, including area code)


     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.  Yes . x..No ........


The number of outstanding common shares par value U.S. $0.01 per share of IPC
Holdings, Ltd., as of May 6, 1999, was 25,033,932.

                                 TOTAL PAGES 15
                        EXHIBIT INDEX LOCATED ON PAGE 13


                                       1


<PAGE>   2


                         PART I.  FINANCIAL INFORMATION

ITEM 1.  FINANCIAL STATEMENTS

                      IPC HOLDINGS, LTD. AND SUBSIDIARIES
                          CONSOLIDATED BALANCE SHEETS

(Expressed in thousands of United States dollars, except for per share amounts)



<TABLE>
<CAPTION>
                                                     As of             As of
                                                 March 31, 1999  December 31, 1998
                                                 --------------  -----------------
                                                  (unaudited)
<S>                                              <C>             <C>
ASSETS:
Fixed maturity investments:
Available for sale, at fair market value
(Amortized  cost 1999: $490,518; 1998:
$478,806)                                              $490,854           $484,863
Equity investments, available for sale (Cost
1999: $53,564;  1998: $69,268)                           75,611             94,152
Cash and cash equivalents                                57,521             20,966
Reinsurance balances receivable (Related party
1999: $8,855; 1998: $3,653)                              56,804             20,747
Funds held by reinsured companies                         2,434              2,434
Deferred premiums ceded                                   2,129                  0
Accrued investment income                                11,908             14,752
Deferred acquisition costs                                6,621              2,048
Prepaid expenses and other assets                         4,222              3,129
                                                 --------------  -----------------
TOTAL ASSETS                                           $708,104           $643,091
                                                 ==============  =================
LIABILITIES:
Reserve for losses and loss adjustment expenses        $ 58,129           $ 52,226
Unearned premiums                                        58,428             17,602
Reinsurance balances payable (Related party
1999: $231; 1998: $0)                                     2,311                  0
Deferred commissions                                        396                  0
Investments pending settlement                           16,027                  0
Accounts payable and accrued liabilities
(Related party 1999: $1,554; 1998: $1,689)                8,151              7,311
                                                 --------------  -----------------
TOTAL LIABILITIES                                       143,442             77,139
                                                 --------------  -----------------
SHAREHOLDERS' EQUITY:
Share capital (Common shares outstanding, par
value U.S.$0.01 - 1999: 25,033,932; 1998:
25,033,932 shares)                                          250                250
Additional paid-in capital                              299,833            299,833
Retained earnings                                       242,196            234,928
Accumulated other comprehensive income                   22,383             30,941
                                                 --------------  -----------------
TOTAL SHAREHOLDERS' EQUITY                              564,662            565,952
                                                 --------------  -----------------
TOTAL LIABILITIES AND SHAREHOLDERS' EQUITY             $708,104           $643,091
                                                 ==============  =================
</TABLE>

          See accompanying Notes to Consolidated Financial Statements

                                       2


<PAGE>   3





                      IPC HOLDINGS, LTD. AND SUBSIDIARIES
                       CONSOLIDATED STATEMENTS OF INCOME

(Expressed in thousands of United States dollars, except for per share amounts)



<TABLE>
<CAPTION>
                                                   Three months ended March 31,
                                                  ------------------------------
                                                       1999            1998
                                                  --------------  --------------
<S>                                               <C>             <C>
REVENUES:                                          (Unaudited)     (Unaudited)
Gross premiums written                               $   65,315      $   72,173
Premiums ceded                                           (2,839)              0
                                                  -------------   -------------
Net written premiums                                     62,476          72,173
Change in unearned premium reserve                      (38,698)        (43,229)
                                                  -------------   -------------
Net premiums earned                                      23,778          28,944
Net investment income                                     7,413           7,262
Realized gains (losses), net on investments               6,545           2,604
                                                  -------------   -------------
TOTAL REVENUES                                           37,736          38,810
                                                  =============   =============
EXPENSES:
Losses and loss adjustment expenses                      16,773           4,125
Acquisition costs, net                                    3,370           3,260
General and administrative expenses                       2,276           2,635
Exchange loss (gain)                                        101              (2)
                                                  -------------   -------------
TOTAL EXPENSES                                           22,520          10,018
                                                  -------------   -------------
NET INCOME                                           $   15,216      $   28,792
                                                  =============   =============
Basic net income per common share                    $     0.61      $     1.15
Diluted net income per common share                  $     0.58      $     1.08
Weighted average number of common share - basic      25,033,932      25,023,046
Weighted average number of common share -
diluted                                              26,172,696      26,697,683
</TABLE>

          See accompanying Notes to Consolidated Financial Statements

                                       3


<PAGE>   4


                      IPC HOLDINGS, LTD. AND SUBSIDIARIES
                     CONSOLIDATED STATEMENTS OF CASH FLOWS

               (Expressed in thousands of United States dollars)


<TABLE>
<CAPTION>
                                                         Three months ended March 31,
                                                        ------------------------------
                                                             1999            1998
                                                        --------------  --------------
<S>                                                     <C>             <C>
                                                         (unaudited)     (unaudited)
CASH FLOWS FROM OPERATING ACTIVITIES:
Net income                                                   $ 15,216        $ 28,792
Adjustments to reconcile net income to cash provided
 by operating activities:
Amortization of investment premium, net                           (17)            207
Realized (gains) losses, net on investments                    (6,545)         (2,604)
 Changes in, net:
 Reinsurance balances receivable                              (36,057)        (34,641)
 Funds held by reinsured companies                                  0          (2,427)
 Deferred premiums ceded                                       (2,129)              0
 Accrued investment income                                      2,844           2,657
 Deferred acquisition costs                                    (4,573)         (5,469)
 Prepaid expenses and other assets                             (1,093)         (1,287)
 Reserve for losses and loss adjustment expenses                5,903             320
 Unearned premiums                                             40,826          43,229
 Reinsurance balances payable                                   2,311               0
 Deferred commissions                                             396               0
 Accounts payable and accrued liabilities                         840           1,331
                                                        -------------   -------------
                                                               17,922          30,108
                                                        -------------   -------------
CASH FLOWS FROM INVESTING ACTIVITIES:
Purchase of fixed maturity investments                       (119,600)       (100,636)
Proceeds from sale of fixed maturity investments              103,687          79,044
Proceeds from maturities of fixed maturity investments         20,500           5,000
Purchases of equity investments                                (1,547)           (692)
Proceeds from sale of equity investments                       23,541          10,597
                                                        -------------   -------------
                                                               26,581          (6,687)
                                                        -------------   -------------
CASH FLOWS FROM FINANCING ACTIVITIES:
Additional share capital                                            0             300
Cash dividends paid to shareholders                            (7,948)        (27,975)
                                                        -------------   -------------
                                                               (7,948)        (27,675)
                                                        -------------   -------------
Net increase (decrease) in cash and cash equivalents           36,555          (4,254)
Cash and cash equivalents, beginning of period                 20,966           9,746
                                                        -------------   -------------
Cash and cash equivalents, end of period                     $ 57,521        $  5,492
                                                        =============   =============
</TABLE>

          See accompanying Notes to Consolidated Financial Statements

                                       4


<PAGE>   5


                      IPC HOLDINGS, LTD. AND SUBSIDIARIES
                CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME

               (Expressed in thousands of United States dollars)



<TABLE>
<CAPTION>
                                                                 Three months ended March 31,
                                                                ------------------------------
                                                                     1999            1998
                                                                --------------  --------------
<S>                                                             <C>             <C>
Net income                                                            $15,216         $28,792
                                                                -------------   -------------
Other comprehensive income:
Holding (losses ) gains, net on investments during period              (2,013)         12,246
Reclassification adjustment for (gains) losses included in
net income                                                             (6,545)         (2,604)
                                                                -------------   -------------
                                                                       (8,558)          9,642
                                                                -------------   -------------
Comprehensive income                                                  $ 6,658         $38,434
                                                                =============   =============
</TABLE>

          See accompanying Notes to Consolidated Financial Statements

                                       5


<PAGE>   6



                      IPC HOLDINGS, LTD. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

(Expressed in thousands of United States dollars, except for per share amounts)
                                  (unaudited)


1. GENERAL:

  The consolidated interim financial statements presented herein have been
  prepared on the basis of United States generally accepted accounting
  principles ("GAAP") and include the accounts of IPC Holdings, Ltd. (the
  "Company"), and its wholly-owned subsidiaries, IPCRe Limited ("IPCRe") and
  IPCRe Services Limited ("Services" and, together with the Company and IPCRe,
  "IPC").   In the opinion of management, these financial statements reflect
  all adjustments (consisting of normal recurring accruals) necessary for a
  fair presentation of the results of operations for the three month periods
  ended March 31, 1999 and 1998, respectively, the balance sheet at March 31,
  1999 and the cash flows for the three month periods ended March 31, 1999 and
  1998, respectively.  These interim consolidated financial statements should
  be read in conjunction with the audited consolidated financial statements for
  the year ended December 31, 1998.   The results of operations for any interim
  period are not necessarily indicative of results for the full year.

2.   DIVIDENDS:

  On February 28, 1999, the Directors declared a quarterly dividend of $0.3175
  per share, payable to shareholders of record on March 9, 1999.   Such
  dividends were paid March 25, 1999.

  On April 27, 1999, the Directors declared a quarterly dividend of $0.3175 per
  share, payable on June 24, 1999, to shareholders of record on June 8, 1999.

3.   NET INCOME PER SHARE:

  The Company has adopted Statement of Financial Accounting Standards No. 128,
  "Earnings per Share", which requires dual presentation of basic and diluted
  earnings per share.   Diluted net income per common share is computed by
  dividing net income by the weighted average number of shares of common stock
  and common stock equivalents outstanding during the year.   Stock options
  granted to a shareholder of the Company were considered common stock
  equivalents and were included in the number of weighted average shares
  outstanding using the treasury stock method.  Stock options granted to
  employees on February 15, 1996, July 25, 1996, January 2, 1997, January 2,
  1998 and January 5, 1999 were also considered common stock equivalents for
  the purpose of calculating diluted net income per common share.

4. ACCOUNTING FOR DERIVATIVES:

  The Financial Accounting Standards Board has also recently issued Statement
  of Financial Accounting Standard No. 133, "Accounting for Derivative
  Instruments and Hedging Activities," ("SFAS 133") which is effective for
  periods beginning after June 15, 1999.   Management does not expect the
  impact of the adoption of SFAS 133 on the Company's financial position or
  results of operations to be material.


5.   DEPOSIT ACCOUNTING:

  In October, 1998 the American Institute of Certified Public Accountants
  ("AICPA") issued Statement of Position 98-7, "Accounting for Insurance and
  Reinsurance Contracts that do not Transfer Insurance Risk", which is
  effective for fiscal years beginning after June 15, 1999.   IPCRe does not
  currently write or cede business which would be affected by this Statement.


                                       6


<PAGE>   7



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


  RESULTS OF OPERATIONS, QUARTERS ENDED MARCH 31, 1999 AND 1998

  In the quarters ended March 31, 1999 and 1998, IPCRe wrote gross premiums of
  $65.3 million and $72.2 million, respectively, a decrease of 9.5%. Written
  premiums were impacted by the following: rate reductions in the period,
  generally in the range of 10% but as high as 15 to 20% in some cases; program
  restructuring where ceding companies have consolidated; and the non-renewal of
  some contracts by IPCRe, where the rates and/or terms were considered
  unsatisfactory. These reductions, which totaled approximately $12.0 million,
  were partially offset by increased signings and additional business from
  existing clients, and selectively written business for new clients, which
  totaled approximately $4.0 million. Premiums were also boosted by
  reinstatement premiums from increased claim activity. Net premiums written
  were also impacted by IPCRe's first cession to its proportional reinsurance
  facility, which had the effect of reducing written premium by a further $2.8
  million. Premiums earned in the three months ended March 31, 1999 were $23.8
  million, compared to $28.9 million in the same period in 1998, a decrease of
  17.8%. This reduction is primarily due to the decrease in net premiums
  written.

  Net investment income was $7.4 million in the quarter ended March 31, 1999,
  compared to $7.3 million for the quarter ended March 31, 1998, an increase of
  2.1%. The increase arises from the average amount of invested assets being
  10.1% higher, offset by decreases in short term interest rates.

  Net realized gains from the sale of investments in the quarter ended March 31,
  1999 totaled $6.5 million, compared to $2.6 million in the corresponding
  period of 1998. Net realized gains and losses fluctuate from period to
  period, depending on the individual securities sold, as recommended by IPCRe's
  investment advisor.

  In the three months ended March 31, 1999, incurred losses were $16.8 million,
  compared to $4.1 million in the corresponding period of 1998. Claim activity
  in the three months ended March 31, 1999 included $6.3 million from the Rouge
  Industries steel mill explosion in Michigan, as well as losses from crop hail
  damage during 1998, storms which took place in Australia and Ireland in late
  December 1998, the winter storms which took place in the mid-west United
  States in January of this year, as well as some development from Hurricanes
  Georges and Mitch and Typhoon Vicki. IPC's loss and loss expense ratio (the
  ratio of losses and loss adjustment expenses to premiums earned) was 70.5% in
  the first quarter of 1999 compared to 14.2% in the corresponding period of
  1998.

  Acquisition costs incurred, which consist primarily of commissions and
  brokerage fees paid to intermediaries for the production of business, were
  $3.4 million for the quarter ended March 31, 1999, compared to $3.3 million in
  the same period of 1998. Certain contracts have been written with profit
  commission clauses or "no claims" bonuses, which return a portion of the net
  underwriting profits generated from those contracts as a commission to the
  insureds. This has resulted in an increase in the level of acquisition cost
  as a percentage of premiums earned. General and administrative expenses were
  $2.3 million in the quarter ended March 31, 1999, compared to the $2.6 million
  incurred in the corresponding period in 1998. IPC's expense ratio (the ratio
  of acquisition costs plus general and administrative expenses to premiums
  earned) was 23.8% for the quarter ended March 31, 1999 compared to 20.4% for
  the corresponding period in 1998.

  The following table summarizes the loss and loss expense ratio, expense ratio
  and combined ratio (sum of loss and loss expense ratio, plus expense ratio)
  for the quarters ended March 31, 1999 and 1998, respectively:

                                           Quarter ended March 31,
                                           1999              1998
                                           -----            -----
               Loss & loss expense ratio  70.5%              14.2%
               Expense ratio              23.8%              20.4%
               Combined ratio             94.3%              34.6%


  Net income for the quarter ended March 31, 1999 was $15.2 million, compared
  to $28.8 million for the corresponding period in 1998, a decrease of 47.2%.
  Excluding the effects of net realized gains and losses arising from the sale
  of investments, net operating income for the first quarter of 1999 was $8.7
  million, compared to $26.2 million for the first quarter of 1998, a decrease
  of 66.9%. The decrease is a result of the reduction of premium income,
  combined with increases in claims and expenses, as discussed above.


                                       7


<PAGE>   8


LIQUIDITY AND CAPITAL RESOURCES

  The Company is a holding company that conducts no reinsurance operations of
  its own.   The Company's cash flows are limited to distributions from IPCRe
  and Services by way of loans or dividends.   The dividends that IPCRe may pay
  are limited under Bermuda legislation and IPCRe's revolving credit facility.
  The Bermuda Insurance Act of 1978, and subsequent amendments thereto
  ("Bermuda regulations"), require IPCRe to maintain a minimum solvency margin
  and a minimum liquidity ratio.   The maximum dividend payable by IPCRe in
  accordance with Bermuda regulations as of January 1, 1999 was approximately
  $141 million.

  IPCRe's sources of funds consist of premiums written, investment income and
  proceeds from sales and redemptions of investments.   Cash is used primarily
  to pay losses and loss adjustment expenses, premiums retroceded, brokerage
  commissions, excise taxes, general and administrative expenses and dividends.
  The potential for a large catastrophe means that unpredictable and
  substantial payments may need to be made within relatively short periods of
  time.   Hence the Company's cash flows may fluctuate significantly from
  period to period.

  Cash flows from operating activities in the first three months of 1999 were
  $17.9 million compared to $30.1 million in the first three months of 1998,
  which represents a decrease of 40.5%.   The decrease arises primarily from
  the reduction in operating income, as noted above.

  Net cash flows generated from investing activities in the first three months
  of 1999 were $26.6 million.   In addition, $7.9 million were paid to
  shareholders in dividends on March 25, 1999.   Cash and cash equivalents
  increased by $36.6 million in the three months, resulting in a balance of
  $57.5 million at March 31, 1999.   At March 31, 1999, 50% of IPC's fixed
  maturity portfolio (based on market value) was held in cash, United States
  Treasury notes and in securities rated AAA, and 39% was held in securities
  rated AA.   The average modified duration of IPC's fixed maturity portfolio
  was 2.7 years.   IPC's portfolio does not contain any investments in real
  estate or mortgage loans. Management believes that IPCRe's $300 million
  revolving credit facility, and the relatively high quality of its investment
  portfolio, provides sufficient liquidity to meet IPC's cash demands.

  YEAR 2000 READINESS DISCLOSURE STATEMENT

       Certain computer programs use only the last two digits to refer to a
  year.   Therefore, these computer programs do not properly recognize the
  century in which a particular year occurs and may, for example, treat "00" as
  being the year 1900, instead of the year 2000.   These computer programs may
  be used in software applications or may be embedded in microprocessors used
  to control the operation of computer hardware and other devices.   If not
  corrected, many computer programs could fail or create erroneous results.
  This problem is commonly known as the "Y2K", "Millennium Bug" and/or "Year
  2000" issue and systems and equipment which use computer programs and
  microprocessors that do not have this problem are generally referred to as
  being "compliant".

       IPC's Critical Systems

       IPC believes that all of its critical systems, including its hardware
  and software, are currently compliant.  IPC's critical systems include those
  used in assessing underwriting risk, recording policy details, processing
  related premium and claims transactions and communicating with brokers who
  produce the business.   Following minor remedial work to some computer
  hardware and the upgrading of some software, a test programme was undertaken
  on these systems and the results were completed by September 30, 1998 and
  subjected to audit by technology consultants provided through American
  International Group, Inc. ("AIG").  Accordingly, while there can be no
  assurance that these systems will be free from failure, IPC believes that any
  failure will not result in material adverse impact on IPC's results of
  operations or financial condition.

       Third Party Dependencies

       IPC's Y2K compliance programme also includes a review of third party
  dependencies, which includes non-information technology areas, including
  office equipment, power supply, telecommunications and building
  infrastructure.

       Administrative Services

       IPC's day-to-day administrative services, including the provision of
  non-information technology, are performed by American International Company,
  Limited ("AICL"), a wholly-owned subsidiary of AIG, pursuant to an
  administrative services agreement (the "Administrative Services Agreement").
  Services and facilities provided pursuant to the Administrative Services
  Agreement include legal and accounting services, office space in Bermuda, the
  use of office equipment, electronic data services and other services required
  by IPC in the ordinary course of business.  IPC and AICL have worked jointly
  to ensure compliance of systems used in the processing of IPC's business and
  this work was successfully completed by September 30, 1998.


                                       8


<PAGE>   9


       In addition, AICL is monitoring progress towards compliance by
  significant third parties from whom IPC receives non-information technology
  services, such as the suppliers of electric power and local and long-distance
  telephone services.  In the event that such third parties are unable to
  achieve compliance, AICL has developed contingency plans, for example,
  independent power supply, which are designed to mitigate the effects of a
  failure on the part of such third parties to supply services.

       Accordingly, while there can be no assurance that these systems will be
  free from failure, IPC believes that any failure will not result in material
  adverse impact on IPC's results of operations or financial condition.

       Other Third Parties

       As of March 31, 1999, IPC has contacted other third parties, such as
  brokers and depository institutions, with whom IPC currently has a
  relationship which, in IPC's judgement, involves material Y2K compliance
  concerns, in order to establish their degree of compliance and/or their plans
  to become compliant prior to December 31, 1999.   Among other things, IPC's
  brokers collect, and maintain records of, premiums and claims and, as such,
  make payments into IPC's depository institutions.  Prior to June 30, 1999,
  IPC intends to develop contingency plans to mitigate the effects of failure
  of such third party systems on IPC's business operations.  There can be no
  assurance that the systems of such third parties will be timely converted,
  that IPC will be able to develop satisfactory contingency plans or that
  failure of such systems in any event would not have a material adverse effect
  on IPC's results of operations or financial condition.

       Costs

       The costs incurred by IPC up to March 31, 1999 in effecting Y2K
  compliance of its own systems are nominal and it is not anticipated that the
  future costs of IPC's Year 2000 evaluation and compliance implementation will
  be material.   In addition, AICL is responsible for the cost of compliance of
  the administrative services it supplies to IPC.  Therefore, assuming
  compliance has been achieved as aforesaid, it is not anticipated that the
  total costs incurred in relation to the Y2K issue will have a material
  adverse effect on IPC's results of operations.

       Policy Risks

       The extent of worldwide property damage (whether insured or uninsured)
  which could result from failure or malfunction of non-compliant systems is
  not known.   Many of the insurance markets around the world in which IPC's
  clients operate have not established a clear position on whether to include
  or exclude Y2K risk in policies available in those markets.   Although Y2K
  exclusion clauses have been produced by some individual companies and some
  insurance and reinsurance industry associations, to date they have not been
  applied in a uniform manner.   The Y2K issue is unique.   Therefore,
  notwithstanding the presence or absence of an exclusion of the Y2K risk in
  insurance or reinsurance policies, in the general absence of legal precedent,
  courts may determine, on a case-by-case basis, that coverage exists for
  property damage resulting from failure or malfunction of non-compliant
  systems.

       IPCRe is principally an excess of loss property catastrophe reinsurer.
  Currently, IPCRe's reinsurance policies do not specifically include Y2K as a
  covered event and IPCRe currently does not intend to provide specific
  coverage for losses arising from Y2K events.   However, in the future, it is
  possible that market forces could oblige IPCRe to provide such coverage, or
  that certain of IPCRe's policies could be held to cover such losses.   IPC
  carefully monitors the terms of policy renewals with respect to the extent
  that they oblige IPC to provide such coverage and, with respect to the
  January 1, 1999 renewals, declined certain business.   Regardless of IPCRe's
  intent not to provide specific coverage for losses arising from Y2K events
  and IPCRe's actions to avoid obligations to provide such coverage, if IPCRe
  is obliged to provide such coverage or its policies are held to cover such
  losses, there can be no assurance that such losses would not have a material
  adverse effect on IPCRe's future results of operations or financial
  condition, commencing in the year 2000.


                                       9


<PAGE>   10


  ITEM 3.  QUALITATIVE AND QUANTITATIVE DISCLOSURE ABOUT MARKET RISK

     IPCRe commissioned an independent Value at Risk analysis, to estimate the
maximum potential loss of fair value for each segment of market risk, as of
December 31, 1998.   There were no material changes to the composition of
IPCRe's investment portfolio during the quarter ended March 31, 1999.   The
equity element of the total portfolio was reduced from approximately 15% to 12%
in February, 1999, and the proceeds were used to purchase money-market
instruments.   In addition, there were no material changes to interest rates or
foreign exchange rates in the quarter.

Accordingly, management does not believe that there has been any material
change to the amount of market risk to which the  Company is exposed, in the
period from January 1 to March 31, 1999.

     NOTE ON FORWARD-LOOKING STATEMENTS

     This report contains certain forward-looking statements within the meaning
of Section 27A of the Securities Act of 1933, as amended, and Section 21E of
the Exchange Act.   Forward-looking statements are statements other than
historical information or statements of current condition.   Some
forward-looking statements may be identified by use of terms such as
"believes", "anticipates", "intends", or "expects".   These forward-looking
statements relate to Year 2000 issues and the effect of the future adoption of
accounting standards.   In light of the risks and uncertainties inherent in all
forward-looking statements, the inclusion of such statements in this report
should not be considered as a representation by the Company or any other person
that the objectives or plans of the Company will be achieved.   Numerous
factors could cause the Company's actual results to differ materially from
those in the forward-looking statements, including unanticipated consequences
of the Millennium bug with respect to IPC or third parties.


PART II-OTHER INFORMATION

  ITEM 1.       LEGAL PROCEEDINGS
                NONE

  ITEM 2.       CHANGES IN SECURITIES
                NONE

  ITEM 3.       DEFAULTS UPON SENIOR SECURITIES
                NONE

  ITEM 4.       SUBMISSION OF MATTERS TO A VOTE OF SECURITY-HOLDERS
                NONE

  ITEM 5.       OTHER INFORMATION
                NONE




                                       10


<PAGE>   11


ITEM 6.     EXHIBITS AND REPORTS ON FORM 8-K

            (a) Exhibits

            Unless otherwise indicated, exhibits are incorporated by reference
            to the corresponding numbered exhibits to the Company's 
            Registration Statement on Form S-1 incorporated by reference to the
            corresponding numbered (Registration No. 333-00088).

EXHIBIT
NUMBER      DESCRIPTION
------      -----------
 3.1        Memorandum of Association of the Company
 3.2        Amended and Restated Bye-laws of the Company
 3.3        Form of Memorandum of Increase of Share Capital
 11.1   *   Reconciliation of the numerator and denominator for 
            basic and diluted net income per common share ("EPS").
 27.1   *   Financial Data Schedule

        * Filed herewith

            (b) Reports on Form 8-K
            NONE


                                       11


<PAGE>   12



                               IPC HOLDINGS, LTD.

                                   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.



                                   IPC HOLDINGS, LTD.
                                     (REGISTRANT)





DATE  MAY 6, 1999              /s/ John P. Dowling
-----------------        -----------------------------------------------
                               JOHN P. DOWLING
                               PRESIDENT AND CHIEF EXECUTIVE OFFICER




DATE  MAY 6, 1999              /s/ John R. Weale
-----------------        -----------------------------------------------
                               JOHN R. WEALE
                               VICE PRESIDENT AND CHIEF FINANCIAL OFFICER






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                                 EXHIBIT INDEX




       Unless otherwise indicated, exhibits are incorporated by reference to
  the corresponding numbered exhibits to the Company's Registration Statement
  on Form S-1 (Registration No. 333-00088).


EXHIBIT
NUMBER         DESCRIPTION
-------        -----------
  3.1          Memorandum of Association of the Company
  3.2          Amended and Restated Bye-laws of the Company
  3.3          Form of Memorandum of Increase of Share Capital
  11.1   *     Reconciliation of the numerator and denominator for basic 
               and diluted net income per common share ("EPS")
  27.1   *     Financial Data Schedule

         * Filed herewith




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