BURNHAM FUND INC
N-30D, 1995-08-29
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<PAGE>
                                  BURNHAM
                                   Fund
 
                                                                  August 8, 1995
 
Dear Shareholder:
 
     We  are pleased to present to you  the Second Quarter Report of The Burnham
Fund Inc. for 1995.
 
     On June 30, 1995, the Fund's net asset value per share for Class A, B and C
shares was $21.39,  $21.56 and $21.39,  respectively, which represent  increases
for  the second quarter  of 1995 of  6.85%, 6.57% and  6.79%, respectively (with
dividends reinvested but without the imposition  of the maximum 5% sales  charge
for  Class A shares).  In the same  period, the unmanaged  Standard & Poor's 500
Index rose 9.53% (with dividends  reinvested) and the unmanaged Lehman  Brothers
Government/Corporate Bond Index increased 6.48%.
 
     The  Burnham Fund  paid dividends in  respect of  its Class A,  Class B and
Class C shares for the second quarter on July 11, 1995 to shareholders of record
on June 30, 1995. The distribution of $0.20, $0.15 and $0.19 per Class A, B &  C
share, respectively, consisted entirely of net investment income.
 
     At  June  30, the  Fund's asset  allocation  was as  follows: 64.6%  of the
portfolio was invested in  common and preferred stocks;  31.0% of the  portfolio
was  invested  in  corporate  bonds;  2.8%  of  the  portfolio  was  invested in
convertible corporate  bonds;  and  the  remaining 1.6%  of  the  portfolio  was
invested in cash and cash equivalents.
 
     This  past period has been one of the most spectacular bull markets we have
witnessed. The continuation of the stock market's strength in the second quarter
of 1995  is  attributable,  in our  view,  to  a number  of  factors.  First,  a
multi-month  string of weak economic releases  confirmed the consensus view that
the economy had indeed slowed down from  the brisk pace of first half 1994.  The
bond  markets rose  as managers correctly  anticipated that  the Federal Reserve
Board would reduce  interest rates. This  move occurred in  early July.  Second,
corporations  in the S&P 500 showed operating  earnings growth in excess of 20%.
This encouraged analysts to raise  estimates  -- perhaps  too high based on  the
accompanying  economic  view  that the  economy  was indeed  weakening  and that
second-half 1995 earnings comparisons versus  1994 would prove to be  difficult.
Third,  talk in Washington, D.C. that  focused on fiscal restraint led investors
to believe  that the  government would  be  more successful  in its  efforts  at
deficit reduction.
 
     In  keeping with  our positive  long-term views  of the  equity markets, we
reduced our fixed income position by selling some of our shorter duration  bonds
and  adding to or  purchasing stocks of  companies we believe  to be undervalued
relative to  their industry,  and  which show  strong sustainable  earnings  and
rising dividends or exhibit exceptional growth prospects. We added funds to some
of  our longer standing  positions such as  McDonald's, Phoenix Technologies and
Motorola. We moved profits from some  of our petroleum holdings and initiated  a
new position in Chevron. We reduced or elimi-
 
                                       1
 
<PAGE>

BURNHAM
 Fund

nated  some positions due to sharp price appreciation, lackluster performance or
deteriorating  fundamentals.  We  initiated  positions  in  Xerox  Corp.,  Apple
Computer,  Microsoft  and  Humana.  Our  equity  position  currently  stands  at
approximately 66% of total net assets.
 
     While we are positive on our long-term  views  of  the  equity  markets, we
believe that  the second half of the year may be volatile.  The  factors  stated
above that led to such  buoyant returns  in the  first  half may  in the  second
half  cause caution. Recession fears have abated, but now the markets will focus
on economic strength  and  the  possibility  of  reheated  inflation.  Investors
will question whether the Federal  Reserve  will loosen interest rates  again --
we believe  it will,  but not until the fall or perhaps later. Reported earnings
may fall short of analysts' unrealistically  high expectations,  as in  the case
of Intel  and Microsoft, and profit taking on very small earnings shortfalls may
be swift. The worsening  Bosnia  conflict may  bring an increased  U.S. presence
overseas which may cause investor  concern on  our shores.  We believe  that any
such downturns are an  opportunity to add  to positions.  We are confident  that
U.S. industry's  return  to global  competitiveness will  achieve  longer  term,
sustainable economic growth.
 
     We thank you for your continued confidence in The Burnham Fund.
 
Very sincerely yours,
I.W. BURNHAM
I.W. Burnham, II, President
 
* The  performance data quoted represents past performance and is not indicative
  of future  performance.  The  investment  return and  principal  value  of  an
  investment  will fluctuate so that an investor's shares, when redeemed, may be
  worth more or less than their original cost. Average total return for Class  A
  shares, assuming the reinvestment of dividends and excluding the maximum sales
  charge for the one, five and ten year periods ended June 30, 1995 were 16.41%,
  8.98%  and 11.75%, respectively.  Such performance assuming  the imposition of
  the Class A shares's maximum 5% sales  charge for the same periods would  have
  been 10.59%, 7.87% and 11.18%, respectively. For Class B and C shares, average
  total  return for the  one year period ended  June 30, 1995  and life of class
  total return for  the period  October 18, 1993  (inception date)  to June  30,
  1995, were 15.24% and 16.70%, and 4.61% and 5.34%, respectively.
 
Cumulative Performance Comparison
The Burnham Fund vs. Broad Market Indices
 
<TABLE>
<CAPTION>
                                                     Cumulative % Change           Average Annualized % Change
                                                ------------------------------    ------------------------------
                                                10 Years    5 Years    3 Years    10 Years    5 Years    3 Years
                                                --------    -------    -------    --------    -------    -------
 
<S>                                             <C>         <C>        <C>        <C>         <C>        <C>
The Burnham Fund.............................    203.77%     53.74%     32.10%      11.75%      8.98%      9.72%
Standard & Poor's 500 Index
  (with dividends reinvested)................    293.16%     74.84%     44.60%      14.67%     11.82%     13.08%
Lehman Brothers Government/Corporate
  Bond Index.................................    158.15%     58.06%     25.60%       9.95%      9.59%      7.89%
</TABLE>
 
                                       2
 
<PAGE>
                                                                    BURNHAM
                                                                      Fund

                             INVESTMENT PERSPECTIVE
                         Equity Portfolio Distribution
                           by Industry Classification
                                 June 30, 1995
 
<TABLE>
<CAPTION>
                                             % Total
                                         Equity Portfolio
                                         ----------------
 
<S>                                      <C>
Energy -- Oil & Gas...................         14.20%
Pharmaceuticals.......................         11.87%
Telephone Companies...................          7.67%
Communications Services...............          6.94%
Banking...............................          6.08%
Semiconductors........................          5.28%
Utilities.............................          4.61%
Hotels................................          4.51%
Computers & Software..................          4.03%
Real Estate...........................          3.64%
Others................................         31.17%
                                         ----------------
Total Equities........................        100.00%
                                         ----------------
                                         ----------------
</TABLE>
 
                  Total Portfolio Distribution by Asset Class
                                 June 30, 1995
 
                  [SEE APPENDIX TO GRAPHIC AND IMAGE MATERIAL]
 
Top 25% Portfolio Holdings
June 30, 1995
 
<TABLE>
<CAPTION>
                                                    Number of Shares/       % of
                                                    Principal Amount        Value       Net Assets
                                                    -----------------    -----------    ----------
 
<S>                                                 <C>                  <C>            <C>
Exxon Corporation................................           45,000       $ 3,178,125       2.97%
Motorola, Inc....................................           35,000       $ 2,349,375       2.20%
Texaco Capital Inc., 8.65% nts. 1/30/98..........      $ 2,000,000       $ 2,117,785       1.98%
Ford Motor Credit Corp., 8% nts. 10/1/96.........      $ 2,000,000       $ 2,043,140       1.91%
The Bank of New York Co., Inc.,
  7.5% conv. sub. deb. 8/15/01...................      $ 1,000,000       $ 2,040,000       1.91%
Caremark International Inc.......................          100,000       $ 2,000,000       1.87%
SBC Communications Inc...........................           40,000       $ 1,905,000       1.78%
AT&T Corp........................................           35,000       $ 1,859,375       1.74%
Mobil Corp.......................................           19,000       $ 1,824,000       1.70%
Georgia Pacific Corp.............................           20,000       $ 1,735,000       1.62%
Bell Atlantic Corp...............................           30,000       $ 1,680,000       1.57%
Chrysler Corp....................................           35,000       $ 1,675,625       1.57%
Amoco Oil Co.....................................           25,000       $ 1,665,625       1.56%
US West Inc......................................           40,000       $ 1,665,000       1.56%
                                                                         -----------    ----------
Total Top 25% Portfolio Holdings.................                        $27,738,050      25.94%
                                                                         -----------    ----------
                                                                         -----------    ----------
</TABLE>
 
                               Cumulative Return
                     of a Hypothetical $10,000 Investment*
                         from inception (June 16, 1975)
                             through June 30, 1995
 
                   [SEE APPENDIX TO GRAPHIC AND IMAGE MATERIAL]
 
* All  performance analyses shown herein represent  past performance and are not
  indicative of future performance. All dividends and distributions from  income
  and  capital  gains have  been  continually reinvested.  Performance  does not
  include the imposition of the maximum  5% sales charge. Performance for  other
  classes  of the Fund will be greater or  less than the data shown in the graph
  and tables based on differences in sales charges and fees paid by shareholders
  investment in the different classes of the Fund.
 
                                        
                          Average Annual Total Return
                          Period ending June 30, 1995
 
<TABLE>
<S>                         <C>
One Year.................   16.41%
Five Years...............    8.98%
Ten Years................   11.75%
Fifteen Years............   12.97%
Twenty Years.............   12.58%
</TABLE>
 
                                       3
 
<PAGE>
BURNHAM
 Fund

                            STATEMENT OF NET ASSETS
                                 June 30, 1995
                                  (Unaudited)
 
<TABLE>
<CAPTION>
                                                Number of       Value
                                                 Shares        (Note 1)
                                                ---------    ------------
 
<S>                               <C>           <C>          <C>
COMMON STOCKS                           64.01%
AEROSPACE                                1.09%
  Textron, Inc...............................     20,000     $  1,162,500
                                                             ------------
ALUMINUM PRODUCTION                      1.17%
  Aluminum Company of America................     25,000        1,253,125
                                                             ------------
AUTOMOTIVE                               1.57%
  Chrysler Corp..............................     35,000        1,675,625
                                                             ------------
BAKED GOODS & SNACK FOODS                0.37%
  Flowers Industries Inc.....................     20,000          395,000
                                                             ------------
BANKING                                  3.90%
  Citicorp...................................     20,000        1,157,500
  Home Financial Corp........................     50,000          709,375
  Mellon Bank Corp...........................     30,000        1,248,750
  Morgan (J.P.) & Co., Inc...................     15,000        1,051,875
                                                             ------------
                                                                4,167,500
                                                             ------------
BUILDING PRODUCTS                        1.20%
  Manville Corp..............................     50,000 a        687,500
  USG Corp...................................     25,000 a        593,750
                                                             ------------
                                                                1,281,250
                                                             ------------
COMMUNICATIONS SERVICES                  4.44%
  AT&T Corp..................................     35,000        1,859,375
  ECI Telecom Ltd............................     60,000          825,000
  GTE Corp...................................     40,000        1,365,000
  TeleCommunications Inc. Cl. A..............     30,000 a        703,125
                                                             ------------
                                                                4,752,500
                                                             ------------
COMPUTERS & SOFTWARE                     2.58%
  Apple Computer Inc.........................     25,000        1,162,500
  Microsoft Corp.............................     10,000 a        903,750
  Phoenix Technologies Ltd...................     65,000 a        698,750
                                                             ------------
                                                                2,765,000
                                                             ------------
CONSUMER PRODUCTS                        0.79%
  General Electric Co........................     15,000          845,625
                                                             ------------
DATA PROCESSING SYSTEMS                  0.91%
  EMC Corp...................................     40,000 a        970,000
                                                             ------------
ENERGY -- OIL AND GAS                    9.09%
  Amoco Oil Co...............................     25,000        1,665,625
  Chevron Corp...............................     25,000        1,165,625
  Exxon Corporation..........................     45,000        3,178,125
  Hugoton Energy Corp........................     30,000 a        255,000
  Mobil Corporation..........................     19,000        1,824,000
  Texaco Inc.................................     25,000        1,640,625
                                                             ------------
                                                                9,729,000
                                                             ------------
ELECTRICAL CONNECTORS                    0.79%
  AMP Inc....................................     20,000     $    845,000
                                                             ------------
ENGINEERING/INDUSTRIAL PRODUCTION        1.50%
  Thermo Electron Corp.......................     37,500 a      1,509,375
  Thermolyte Corp. (Note 4)..................     10,000 a        100,000
                                                             ------------
                                                                1,609,375
                                                             ------------
FOOD CHAINS                              1.28%
  McDonald's Corp............................     20,000        1,369,375
                                                             ------------
FOREST PRODUCTS                          1.62%
  Georgia Pacific Corp.......................     20,000        1,735,000
                                                             ------------
HEALTH & PERSONAL CARE PRODUCTS          0.00%
  Cooper Development Co......................      1,260 a          3,780
                                                             ------------
HEALTHCARE REIT                          1.28%
  Meditrust SBI..............................     40,000        1,365,000
                                                             ------------
HOTELS                                  2.89%
  Hilton Hotels Corp.........................     22,500        1,580,625
  Marriott International Inc.................     25,000          896,875
  Mirage Resorts Inc.........................     20,000 a        612,500
                                                             ------------
                                                                3,090,000
                                                             ------------
INSURANCE                                0.97%
  Allstate Corp..............................     35,000        1,036,875
                                                             ------------
MEDICAL SUPPLIES                         0.18%
  PLC Systems Inc............................     20,000 a        196,250
                                                             ------------
MINING                                   0.78%
  Homestake Mining...........................     50,000          825,000
                                                             ------------
OFFICE EQUIPMENT                         1.32%
  Xerox Corp.................................     12,000        1,407,000
                                                             ------------
PHARMACEUTICALS                          7.60%
  American Home Products Corp................     20,000        1,547,500
  Bristol Myers Squibb Co....................     20,000        1,362,500
  Caremark International Inc.................    100,000        2,000,000
  Humana Inc.................................     10,000          176,250
  Merck & Co., Inc...........................     25,000        1,225,000
  Pall Corp..................................     30,000          667,500
  Pfizer Inc.................................     12,500        1,154,687
                                                             ------------
                                                                8,133,437
                                                             ------------
PHOTO PRODUCTS & SERVICES                1.13%
  Eastman Kodak Co...........................     20,000        1,212,500
                                                             ------------
REAL ESTATE REIT                         2.33%
  Franchise Finance Corp. of America.........     57,600        1,238,400
  National Golf Properties...................     60,000        1,260,000
                                                             ------------
                                                                2,498,400
                                                             ------------
</TABLE>
                     See notes to financial statements.

                                    4

<PAGE>
                                                                    BURNHAM
                                                                      Fund

                    STATEMENT OF NET ASSETS (Continued)
                               June 30, 1995
                                (Unaudited)
<TABLE>
<CAPTION>
                                                Number of
                                           Shares, Put Options,  Value
                                           or Principal Amount  (Note 1)
                                           -------------------  --------
<S>                                    <C>      <C>          <C>
COMMON STOCKS (CONCLUDED)
Semiconductors                           3.38%
  Intel Corp.................................     20,000       $1,266,250
  Motorola, Inc..............................     35,000        2,349,375
                                                             ------------
                                                                3,615,625
                                                             ------------
SPECIALTY CHEMICALS                      0.68%
  Morton International Inc...................     25,000          731,250
                                                             ------------
TELEPHONE COMPANIES                      4.91%
  Bell Atlantic Corp.........................     30,000        1,680,000
  SBC Communications Inc.....................     40,000        1,905,000
  US West Inc................................     40,000        1,665,000
                                                             ------------
                                                                5,250,000
                                                             ------------
TRAVEL RELATED & FINANCIAL SERVICES      1.31%
  American Express Co........................     40,000        1,405,000
                                                             ------------
UTILITIES                                2.95%
  Northeast Utilities........................     50,000        1,125,000
  Puget Sound Power & Light..................     40,000          915,000
  Southern Co................................     50,000        1,118,750
                                                             ------------
                                                                3,158,750
                                                             ------------
TOTAL COMMON STOCKS (COST: $60,081,652)......                  68,484,742
                                                             ------------
  Put Options                            0.01%
  Standard & Poor's 100 July 1995 @ 470......   100 puts a          2,500
  Standard & Poor's 100 July 1995 @ 475......    50 puts a          1,250
  Standard & Poor's 100 July 1995 @ 485......    50 puts a          2,500
  Standard & Poor's 100 Aug. 1995 @ 490......    50 puts a          9,688
                                                             ------------
TOTAL PUT OPTIONS (COST: $217,654)...........                      15,938
                                                             ------------
CONVERTIBLE PREFERRED STOCK              0.53%
  Storage Technology Corp. $3.50 cum. conv.
    pfd......................................     10,000          570,000
                                                             ------------
  TOTAL CONVERTIBLE PREFERRED STOCK (COST:
    $480,800)................................                     570,000
                                                             ------------
CORPORATE CONVERTIBLE BONDS              2.83%
BANKING                                  1.91%
  The Bank of New York Company, Inc.,   7 1/2%
    conv. sub. deb. 8/15/01.................. $1,000,000        2,040,000
                                                             ------------
STEEL                                    0.43%
  USX Corp., 7% conv. sub. deb. 6/15/17......    500,000          460,000
                                                             ------------
UTILITIES                                0.49%
  Consolidated Natural Gas Co., 7 1/4% conv.
    sub. deb. 12/15/15.......................    500,000          522,500
                                                             ------------
  TOTAL CORPORATE CONVERTIBLE BONDS (COST:
    $1,971,250)..............................                   3,022,500
                                                             ------------

<CAPTION>
                                               Principal         Value
                                                 Amount          Note 1
                                               ---------         ------
CORPORATE BONDS                         31.03%
BANKING                                  1.93%
  Chase Manhattan Corp., 7 7/8% sub. notes
    8/01/04..................................  $1,000,000      $1,023,812
  Morgan (J.P.) & Co., Inc., 7 5/8% sub. notes
    11/15/98.................................   1,000,000       1,040,788
                                                             ------------
                                                                2,064,600
                                                             ------------
BROADCASTING                             0.49%
  Ackerley Communications, Inc., 10 3/4% sr.
    secured notes 'Series A' 10/01/03........     500,000         527,500
                                                             ------------
BUILDING PRODUCTS                        1.86%
  USG Corp., 8% sr. notes 12/15/96...........     500,000         498,750
  USG Corp., 8% sr. notes 3/15/97............   1,500,000       1,496,250
                                                             ------------
                                                                1,995,000
                                                             ------------
CHEMICALS                                1.38%
  duPont (E.I.) de Nemours & Co., 6% notes
    12/01/01.................................   1,000,000         971,250
  duPont (E.I.) de Nemours & Co., 6 3/4%
    notes 10/15/02...........................     500,000         503,056
                                                             ------------
                                                                1,474,306
                                                             ------------
COMMUNICATION SERVICES                   0.94%
  Storer Communications Inc., 10% deb.
    5/15/03..................................   1,000,000       1,005,000
                                                             ------------
CONSUMER PRODUCTS                        0.95%
  General Electric Corp., 7 7/8% notes
    5/01/96..................................   1,000,000       1,015,699
                                                             ------------
ENERGY -- OIL & GAS                      0.88%
  Maxus Energy Corp., 9 3/8% notes 11/01/03..   1,000,000         945,000
                                                             ------------
FINANCIAL SERVICES                      11.11%
  Exxon Capital Corp., 7% gtd. notes
    4/15/96..................................   1,000,000       1,013,772
  Ford Motor Credit Corp., 8% notes
    10/01/96.................................   2,000,000       2,043,140
  Ford Motor Credit Corp., 9 1/4% notes
    6/15/98..................................   1,000,000       1,075,680
  General Electric Capital Corp., 8% notes
    1/15/98..................................   1,000,000       1,039,315
  GMAC Corp., 7.65% notes 2/04/97............     400,000         407,755
  GMAC Corp., 7 3/4% notes 4/15/97...........   1,000,000       1,014,975

</TABLE>
                     See notes to financial statements.

                                    5

<PAGE>
BURNHAM
 Fund

                    STATEMENT OF NET ASSETS (Concluded)
                               June 30, 1995
                                (Unaudited)
<TABLE>
<CAPTION>
                                                Principal        Value
                                                 Amount         (Note 1)
                                                ---------       --------
<S>                                    <C>      <C>          <C>
CORPORATE BONDS (CONTINUED)
GMAC Corp., 7 3/4% notes 1/15/99.............  $1,000,000      $1,037,345
  MGM Grand Hotel Finance Corp., 11 3/4% gtd.
    notes 5/01/99............................   1,000,000       1,082,500
  Texaco Capital Inc., 9% gtd. notes
    11/15/97.................................   1,000,000       1,051,250
  Texaco Capital Corp., 8.65% 1/30/98........   2,000,000       2,117,785
                                                             ------------
                                                               11,883,517
                                                             ------------
FOOD & BEVERAGE                          0.47%
  Spreckles Industries Inc., 11 1/2% sr. sec.
    notes 9/01/00............................     500,000         507,500
                                                             ------------
FOOD & TOBACCO                           1.97%
  Philip Morris Companies Inc., 9 1/4%
    12/01/97.................................   1,000,000       1,064,986
  RJR Nabisco, 8% notes 1/15/00..............   1,000,000       1,045,000
                                                             ------------
                                                                2,109,986
                                                             ------------
HOTELS                                   2.28%
  Marriott Corp., 9 5/8% sr. notes 'B' 2/01/96.   525,000         525,846
  Marriott Corp., 8 1/8% sr. notes 'C'
    12/01/96.................................     450,000         442,980
  Marriott Corp., 8 7/8% sr. notes 'D' 5/01/97.   115,000         114,288
  Marriott Corp., 9 7/8% sr. notes 'E'
    11/01/97.................................     850,000         849,576
  Marriott Corp., 9 3/8% deb. 6/15/07........     500,000         510,282
                                                             ------------
                                                                2,442,972
                                                             ------------
PAPER PRODUCTS                           1.74%
  Kimberly Clark Corp. 9% notes 8/01/00......     700,000         778,800
  Riverwood International Corp., 10 3/4% sr.
    notes II 6/15/00.........................     500,000         540,000

  Riverwood International Corp., 10 3/4% sr.
    notes 6/15/00............................     500,000         540,000
                                                             ------------
                                                                1,858,800
                                                             ------------
PHARMACEUTICALS                          1.98%
  Johnson & Johnson, 7 3/8% euronotes 11/09/97. 1,000,000       1,030,625
  Lilly (Eli) & Co., 8 1/8% notes 12/01/01..... 1,000,000       1,082,471
                                                             ------------
                                                                2,113,096
                                                             ------------
TELEPHONE COMPANIES                      2.57%
  Bell South TeleCommunications Inc., 6 1/4%
    notes 5/15/03............................  $1,000,000      $  978,747
  GTE California Inc., 6 1/4% 1/15/98........   1,000,000       1,001,043
  Southwestern Bell Corp., 8.30% notes
    6/01/96..................................     750,000         764,209
                                                             ------------
                                                                2,743,999
                                                             ------------
UTILITIES                                0.48%
  AES Corp., 9 3/4% sr. sub. notes 6/15/00...     500,000         510,000
                                                             ------------
  TOTAL CORPORATE BONDS (COST:
    $32,413,424).............................                  33,196,975
COMMERCIAL PAPER                         1.14%
  Associates Corp. of NA, 5.93% 7/03/95......   1,219,000       1,219,000
                                                             ------------
  TOTAL COMMERCIAL PAPER (COST:
    $1,219,000)..............................                   1,219,000
                                                             ------------
TOTAL INVESTMENTS (COST: $96,383,780)   99.55%                106,509,155
CASH AND OTHER ASSETS, LESS LIABILITIES  0.45                     481,156
                                       ------                ------------
NET ASSETS                             100.00%               $106,990,311
                                       ------                ------------
                                       ------                ------------
</TABLE>
 
a Non-income producing security.
 
Federal Income Tax Basis of Investment
Securities
 
     For Federal income  tax purposes,  the tax basis  of investment  securities
owned  at  June  30,  1995  was  $96,510,156.  The  aggregate  gross  unrealized
appreciation for all securities in which there  was an excess of value over  tax
cost  was  $10,941,204  and  aggregate  gross  unrealized  depreciation  for all
securities in which there was excess of tax cost over value was $942,205.
 
                       See notes to financial statements.

                                       6
<PAGE>
                                                                    BURNHAM
                                                                      Fund

                      STATEMENT OF ASSETS AND LIABILITIES
                                 June 30, 1995
                                  (Unaudited)
- --------------------------------------------------------------------------------
 
<TABLE>
<S>                                                                                                  <C>
ASSETS:
     Investment in securities, at value (identified cost: $98,383,780) (Note 1)...................   $106,509,155
     Receivable for investments sold..............................................................      3,619,382
     Dividends and interest receivable............................................................        851,850
     Receivable for capital stock sold............................................................         28,666
     Prepaid expenses.............................................................................         52,609
     Receivable from investment adviser...........................................................          4,771
                                                                                                     ------------
          Total assets............................................................................    111,066,433
                                                                                                     ------------
LIABILITIES:
     Bank overdraft...............................................................................        121,668
     Payable for investment securities purchased..................................................      3,691,854
     Payable for capital stock redeemed...........................................................         31,625
     Accrued expenses and other payables..........................................................        230,975
                                                                                                     ------------
          Total liabilities.......................................................................      4,076,122
                                                                                                     ------------
NET ASSETS........................................................................................   $106,990,311
                                                                                                     ------------
                                                                                                     ------------
CLASS A SHARES
Net asset value and redemption price per share
  (Note 2): ($106,447,513/4,977,458 shares outstanding)...........................................   $      21.39
                                                                                                     ------------
                                                                                                     ------------
Calculation of Maximum Offering Price
Sales charge -- 5% of public offering price:(Note 2): ($21.39 net asset value plus 5.0% of public
  offering price).................................................................................   $      22.52
                                                                                                     ------------
                                                                                                     ------------
CLASS B SHARES
Net asset value and offering price per share:
  (Note 2): ($540,147/25,047.598 shares outstanding)..............................................   $      21.56
                                                                                                     ------------
                                                                                                     ------------
CLASS C SHARES
Net asset value and offering price per share:
  (Note 2): ($2,651/123.944 shares of capital stock outstanding)..................................   $      21.39
                                                                                                     ------------
                                                                                                     ------------
Redemption price per share varies with the length of time Class B and C shares are held. (Note 5)
Net assets consisted of:
     Capital paid-in..............................................................................   $ 93,343,012
     Undistributed net investment income..........................................................        946,076
     Accumulated net realized gains on investments................................................      2,575,848
     Net unrealized appreciation of investments...................................................     10,125,375
                                                                                                     ------------
                                                                                                     $106,990,311
                                                                                                     ------------
                                                                                                     ------------
</TABLE>
 
                            STATEMENT OF OPERATIONS
                     For the six months ended June 30, 1995
                                  (Unaudited)
- --------------------------------------------------------------------------------
 
<TABLE>
<S>                                                                             <C>              <C>
INVESTMENT INCOME:
     Income:
          Dividends.............................................................................    $    921,742
          Interest..............................................................................       1,772,870
                                                                                                    ------------
               Total income.....................................................................       2,694,612
                                                                                                    ------------
     Expenses:
          Investment advisory fees (Note 6).....................................................         318,773
          Distribution fee (Class A) (Note 7)...................................................         127,813
          Distribution fee (Class B) (Note 7)...................................................           1,595
          Distribution fee (Class C) (Note 7)...................................................               4
          Service fees (Class B & C) (Note 7)...................................................             537
          Transfer agent fees...................................................................          98,176
          Professional fees.....................................................................         129,745
          Reports to shareholders...............................................................          23,380
          Directors' fees and expenses..........................................................          33,400
          Custodian fees........................................................................          23,790
          Registration fees and expenses........................................................          33,095
          Miscellaneous expense.................................................................          36,433
                                                                                                    ------------
               Total expenses before reimbursement..............................................         826,741
                                                                                                    ------------
               Less: Expenses voluntarily reimbursed by Investment Adviser (Note 4).............          (4,755)
                                                                                                    ------------
               Total expenses after reimbursement...............................................         821,986
                                                                                                    ------------
                    Net investment income.......................................................       1,872,626
                                                                                                    ------------
NET REALIZED AND UNREALIZED LOSS ON INVESTMENTS:
     Realized gain from securities and options transactions (excluding short-term
      money market instruments)
          Proceeds from sales...................................................   $ 53,357,645
          Cost of securities sold...............................................    (50,699,074)
                                                                                    -----------
          Net realized gain from securities and
               options transactions.............................................                       2,658,571
                                                                                                    ------------
     Increase in unrealized appreciation of investments
          Beginning of period...................................................   $  2,231,529
          End of period.........................................................     10,125,375
                                                                                    -----------
          Increase in unrealized appreciation...................................................       7,893,846
                                                                                                    ------------
     Net realized and unrealized gain on investments............................................      10,552,417
                                                                                                    ------------
     Net increase in net assets resulting from operations.......................................     $12,425,043
                                                                                                    ------------
                                                                                                    ------------
</TABLE>
                       See notes to financial statements.
 
                                       7
 
<PAGE>
BURNHAM
 Fund

                       STATEMENT OF CHANGES IN NET ASSETS
                                  (Unaudited)
 
<TABLE>
<CAPTION>
                                                                                 Six Months            Year
                                                                                    ended              ended
                                                                                June 30, 1995    December 31, 1994
- -------------------------------------------------------------------------------------------------------------------
 
<S>                                                                             <C>              <C>
Increase (Decrease) in net assets:
  From operations:
     Net investment income...................................................   $   1,872,626      $   3,970,955
     Net realized gain from security and option transactions.................       2,658,571          3,854,723
     Increase (Decrease) in unrealized appreciation of investments...........       7,893,846        (10,028,824)
                                                                                -------------    -----------------
          Net increase (decrease) in net assets resulting from operations....      12,425,043         (2,203,146)
                                                                                -------------    -----------------
Distributions to shareholders
  (Note 1):
  From net investment income:
     Class A Shares..........................................................      (2,045,595)        (4,681,668)
     Class B Shares..........................................................          (4,876)            (7,380)
     Class C Shares..........................................................             (48)               (96)
  From realized gains from security and option transactions:
       Class A Shares........................................................      (2,611,673)        (3,806,005)
       Class B Shares........................................................          (8,696)            (7,594)
       Class C Shares........................................................             (60)               (79)
                                                                                -------------    -----------------
          Total distributions to shareholders................................      (4,670,948)        (8,502,822)
                                                                                -------------    -----------------
Capital share transactions
  (Note 2):
  Net proceeds from sale of shares...........................................         714,835          2,874,828
  Net asset value of shares issued to shareholders in reinvestment of
     dividends...............................................................       4,044,720          7,340,553
                                                                                -------------    -----------------
                                                                                    4,759,555         10,215,381
  Cost of shares redeemed....................................................      (7,674,969)       (15,991,754)
                                                                                -------------    -----------------
  Decrease in net assets derived from capital share transactions.............      (2,915,414)        (5,776,373)
                                                                                -------------    -----------------
  Increase (Decrease) in net assets for the period...........................       4,838,681        (16,482,341)
                                                                                -------------    -----------------
Net Assets:
  Beginning of period........................................................     102,151,630        118,633,971
                                                                                -------------    -----------------
  End of period (including undistributed net investment income of $946,076
     and $1,123,969, respectively)...........................................   $ 106,990,311      $ 102,151,630
                                                                                -------------    -----------------
                                                                                -------------    -----------------
</TABLE>
                       See notes to financial statements.

                         NOTES TO FINANCIAL STATEMENTS
                                 June 30, 1995
                                  (unaudited)
- --------------------------------------------------------------------------------
 
NOTE 1  -- Significant Accounting Policies
 
The Burnham Fund Inc. ('Fund') is registered under the Investment Company Act of
1940, as  amended  (the '1940  Act'),  as  a  diversified,  open-end  investment
company.
 
The  Fund  offers  three classes  of  shares. Class  A  shares are  sold  with a
front-end sales charge of up to 5.0%. Class B shares are sold with a  contingent
deferred  sales charge of  5.0% which declines  to zero for  purchases held more
than six years. Class C shares are sold with a contingent deferred sales  charge
of 1%, which declines to zero if held for more than one year.
 
The  following  is a  summary  of significant  accounting  policies consistently
followed by  the  Fund in  the  preparation  of its  financial  statements.  The
policies are in conformity with generally accepted accounting principles.
 

A.  Security  valuation  --  Investments in  securities  traded,  or  in options
purchased, on a  national securities exchange  are valued at  the last  reported
sales  price  on the  primary  exchange on  which they  are  traded on  the last
business day of  the period.  Securities traded in  the over-the-counter  market
(including securities listed on exchanges whose primary market is believed to be
over-the-counter)  and listed securities for which  no sale was reported on that
date are valued  at the mean  between the  last reported bid  and asked  prices.
Short-term  money market instruments which have a  maturity of more than 60 days
are valued at prices based on market quotations for securities of similar  type,
yield and maturity. Short-term money market instruments which have a maturity of
60 days or less are valued at amortized cost which approximates value.
 
B.  Repurchase  agreements  --  Securities  held  as  collateral  for repurchase
agreements are held by the Federal Reserve Bank and are designated as being held
for the Fund's  behalf by its  custodian under the  book-entry system. The  Fund
monitors  the adequacy of the collateral  (U.S. Government securities) daily and
can require the seller to provide additional collateral in the event the  market
value  of the securities pledged  falls below 102% of  the carrying value of the
repurchase agreement.
 
C. Option Writing  -- When the  Fund writes  a covered call  option, the  amount
received  is included in the Statement of 

                                        8 
<PAGE>
                                                                    BURNHAM
                                                                      Fund

                           NOTES TO FINANCIAL STATEMENTS
                                  June 30, 1995
                                   (Unaudited)

Assets and Liabilities as an asset and an equivalent  liability.  The  liability
is subsequently  marked to  market  to reflect  the current value  of the option
written. When a call option expires or when the  Fund   enters  into  a  closing
purchase transaction, the Fund will recognize  a gain  (or loss)  without regard
to any unrealized gain or loss on the underlying  security. When  a call  option
is  exercised, the  proceeds from  the delivery of  the underlying  security are
increased  by the  amount originally received and  the resulting gain or loss is
recorded by the Fund.
 
Transactions in written options for the six  months ended June 30, 1995 were  as
follows:
 
<TABLE>
<CAPTION>
                                                                                            Number of
                                                                                             Options     Premiums
                                                                                            ---------    ---------
 
<S>                                                                                         <C>          <C>
Options written at December 31, 1994.....................................................       -0-      $     -0-
Options written..........................................................................       (20)       (29,299)
Options cancelled in closing purchase transactions.......................................        20         29,299
                                                                                            ---------    ---------
Options outstanding at June 30, 1995.....................................................       -0-      $     -0-
                                                                                            ---------    ---------
                                                                                            ---------    ---------
</TABLE>
 
The  cost of cancelling options in closing transactions was $38,200 resulting in
a net realized capital loss of $8,001.
 
D. Federal income taxes  -- It is the  Fund's policy to qualify  each year as  a
'regulated  investment company' under Subchapter M of the Internal Revenue Code.
By so qualifying, the Fund  will not be subject to  Federal income taxes to  the
extent  that  its  net investment  income  and  net realized  capital  gains are
distributed.
 
E. Other -- Security transactions are  accounted for on the date the  securities
are  purchased or  sold. Interest  income is recorded  on the  accrual basis and
dividend  income  on  the  ex-dividend  date.  Dividends  and  distributions  to
shareholders  are recorded on  the ex-dividend dates.  The Fund may periodically
make reclassifications among certain of its capital accounts as a result of  the
timing  and characteristics  of certain  income and  capital gains distributions
determined annually in accordance with Federal tax regulations which may  differ
from  generally accepted  accounting principles. During  1995, the  Fund has not
made classifications of undistributed net  investment income or accumulated  net
realized gains.
 
F. Expenses -- Expenses that are attributable to a specific class of shares will
be charged to that class. Fund-level expenses will be allocated daily based upon
the  relative percentage of net assets of each class of shares as they relate to
the Fund.
 
NOTE 2  -- Capital Stock
 
     At June 30, 1995, there were 40,000,000 shares of capital stock ($0.10  par
value)  authorized, divided  into four  classes designated Class  A, B,  C and D
shares. At June 30, 1995, Class D shares were not issued.
 

     Transactions in capital stock  for the six months  ended June 30, 1995  and
for  the  year ended  December 31,  1994 for  Class A,  B and  C shares  were as
follows:
 
<TABLE>
<CAPTION>
                                                                                   Six months ended     Year ended
                                                                                    June 30, 1995      Dec. 31, 1994
                                                                                   ----------------    -------------
 
<S>                                                                                <C>                 <C>
CLASS A SHARES
Shares sold.....................................................................          28,022           130,430
Shares issued to shareholders in reinvestment of distributions..................         208,438           361,712
                                                                                   ----------------    -------------
                                                                                         236,460           492,142
Shares redeemed.................................................................        (379,929)         (790,191)
                                                                                   ----------------    -------------
Net decrease....................................................................        (143,469)         (298,049)
                                                                                   ----------------    -------------
                                                                                   ----------------    -------------
CLASS B SHARES
Shares sold.....................................................................           7,306             9,254
Shares issued to shareholders in reinvestment of distributions..................             693               748
                                                                                   ----------------    -------------
                                                                                           7,999            10,002
Shares redeemed.................................................................              (2)             (254)
                                                                                   ----------------    -------------
Net increase....................................................................           7,997             9,748
                                                                                   ----------------    -------------
                                                                                   ----------------    -------------
CLASS C SHARES
Shares sold.....................................................................              -0-               -0-
Shares issued to shareholders in reinvestment of distributions..................               5                 9
                                                                                   ----------------    -------------
                                                                                               5                 9
Shares redeemed.................................................................              -0-               -0-
                                                                                   ----------------    -------------
Net increase....................................................................               5                 9
                                                                                   ----------------    -------------
                                                                                   ----------------    -------------
</TABLE>
 
NOTE 3  -- Purchase and Sales of Securities
 
     The aggregate cost of purchases and  the proceeds from sales of  securities
or maturities for the six months ended June 30, 1995 were:
 
<TABLE>
<CAPTION>
                                                                                  Cost of       Proceeds from sales
                                                                                 purchases         or maturities
                                                                                ------------    -------------------
 
<S>                                                                             <C>             <C>
Short-term money market instruments..........................................   $105,991,500       $ 104,772,500
Long-term U.S. government obligations........................................            -0-                 -0-
Common stocks and other securities...........................................     46,370,476          53,357,645
</TABLE>


                                        9

<PAGE>
BURNHAM
 Fund

                           NOTES TO FINANCIAL STATEMENTS
                                  June 30, 1995
                                   (Unaudited)

     For the six months ended June 30, 1995, the Fund had net realized losses of
$535,518 resulting from purchased option transactions.
 
NOTE 4 -- Restricted Securities
 
     A restricted security  is a security which has not been registered with the
U.S.  Securities and Exchange Commission pursuant to the Securities Act of 1933.
The Fund may purchase restricted securities through a private offering and  they
cannot  be  sold without  prior registration  under the  Securities Act  of 1933
unless such sale  is pursuant  to an  exemption therefrom.  Subsequent costs  of
registration  of such  securities are  borne by  the issuer.  A secondary market
exists for certain privately placed securities. At June 30, 1995, the Fund  held
restricted  securities with a  value aggregating $100,000,  representing 0.1% of
the Fund's net assets. Such securities are:
 
<TABLE>
<CAPTION>
Shares       Company       Acquired        Value        Cost
- ---------------------------------------------------------------
 
<S>        <C>            <C>            <C>          <C>
10,000     Thermolyte     03/10/1995      $100,000     $100,000
           Corp.
</TABLE>
 
NOTE 5 -- Off Balance Sheet Risk in Financial Instruments
 
     The Fund  may  from  time  to time  trade  in  financial  instruments  with
off-balance  sheet  risk in  the normal  course of  its investing  activities to
assist in managing exposure to various market risks. These financial instruments
include written as  well as  purchased options, and  may involve,  to a  varying
degree,  elements  of risk  in excess  of the  amounts recognized  for financial
statement purposes. The notional or contractual  amounts  of  these  instruments
represent  the  investment  the Fund  has in  particular  classes  of  financial
instruments  and  does   not  necessarily  represent  the   amounts  potentially
subject to  risk. The  measurement of  risks associated  with  these instruments
is meaningful only when all  related and offsetting transactions are considered.
A summary of obligations under these financial instuments at June 30, 1995 is as
follows:
 
<TABLE>
<CAPTION>
Expiration                        Number of            Security           Security      Net Unrealized
Date                              Contracts            Position             Type         Depreciation
- ------------------------------------------------------------------------------------------------------
 
<S>                               <C>            <C>                      <C>           <C>
July, 1995                         100 puts      S&P 100 puts @ 470           long         $ 81,803
July, 1995                          50 puts      S&P 100 puts @ 475           long           45,290
July, 1995                          50 puts      S&P 100 puts @ 485           long           42,786
July, 1995                          50 puts      S&P 100 puts @ 490           long           31,837
                                                                                        --------------
                                                                                           $201,716
                                                                                        --------------
                                                                                        --------------
</TABLE>
 
NOTE 6 -- Investment Advisory Fees and Other Transactions
 
     The Investment Adviser provides research and statistical services and makes
investment  recommendations to the Fund.  With its affiliate, Burnham Securities
Incorporated  (the  'Distributor'),  the  Investment  Adviser  supplies a  staff
trained   in  accounting   and  shareholder   services  to  aid  in  the  Fund's
administration and day-to-day operations.
 
     The  Investment Adviser receives an investment advisory fee paid monthly at
an annual rate  of 5/8 of 1% of the Fund's  average daily net  asset values.  In
addition,  if in  any year the  Fund's operating  expenses, including investment
advisory fees but  excluding interest, taxes  and brokerage commissions,  exceed
2.5% of the first $30 million of the Fund's average net assets, 2.0% of the next
$70 million and 1.5% of the remaining average net assets, the fees to be paid to
the  Investment Adviser will be reduced to  the extent that such expenses exceed
such limitation. For the six months ended June 30, 1995, the Fund incurred  fees
in  the amount of  $318,773. The advisory fees  and the expenses  of the Fund as
defined above did not  exceed the maximum  allowable limitation. The  Investment
Adviser  has voluntarily agreed to reimburse expenses of Class B and C shares in
order to limit such expenses to an  annual rate of 2.3% and 2.3%,  respectively.
Accordingly,  the Investment Adviser has reimbursed  Class B and C shares $2,183
and $2,572, respectively.
 
NOTE 7 -- Distribution Services Agreement
 
     The Distributor serves as  principal distributor of  Fund shares. The  Fund
has  adopted a Distribution Service Agreement (the 'Agreement') pursuant to Rule
12b-1 under the 1940 Act for Classes A, B and C shares. Under the agreement, the
Fund pays a  distribution fee to  the Distributor  at an annual  rate of  0.25%,
0.75%   and  0.75%,  respectively,  of  the  Fund's  average  daily  net  assets
attributable to each respective class. For  the six months ended June 30,  1995,
Class A, B and C shares incurred fees of $127,813, $1,595, and $4, respectively.
Class  B and C shares of the Fund will  also pay a service fee at an annual rate
of 0.25% of the average  daily net assets of Class  B and C shares. The  service
fee  will be used by the Distributor to compensate broker-dealers and other NASD
members for rendering continuing, ongoing service to Class B and C shareholders.
Service fees incurred for Class B and C shares for the six months ended June 30,
1995 was

                                       10
<PAGE>
                                                                    BURNHAM
                                                                      Fund

                           NOTES TO FINANCIAL STATEMENTS
                                  June 30, 1995
                                   (Unaudited)

$536  and  $1,  respectively.  For  the  six  months  ended  June 30, 1995,  the
Distributor  earned $118,306 in brokerage commissions from Fund transactions and
$6,096 in sales commissions from the distribution of Class A shares.
 
     A contingent  deferred sales  charge ('CDSC') at a  maximum rate  of 5%  is
imposed  on  Class B  shares  if an  investor redeems  within  six years  of the
purchase date. A CDSC is imposed on Class C shares at a rate of 1% if shares are
redeemed within 12 months from the date  of purchase. A CDSC will be imposed  on
the  proceeds of the  redemptions of shares purchased  aggregating $1 million or
more if they are redeemed within 24 months  of the end of the calendar month  of
their  purchase, in  an amount equal  to 1%  if the redemption  occurs within 12
months and .50 of 1% if the redemption occurs within the next 12 months. No CDSC
will be  imposed  on Class  A,  B and  C  shares derived  from  reinvestment  of
dividends  or  capital  gain distributions,  or  on amounts  which  represent an
increase in  the value  of  the share-holder's  account resulting  from  capital
appreciation    above   the    amount   paid    for   Class    A,   B    and   C
shares purchased during the CDSC period. Any sales charge imposed on redemptions
are paid to the Distributor. For the six months ended June 30, 1995, there  were
no charges paid to the Distributor.
 
     Certain  directors and  officers of the  Fund are  also directors, officers
and/or employees  of the  Investment  Adviser and/or  Distributor. None  of  the
directors  so affiliated received  compensation for his  services as director of
the Fund. Similarly, none of the Fund's officers received compensation from  the
Fund.
 



NOTE 8 -- Financial Highlights
<TABLE>
<CAPTION>
                                              Class A Shares                              Class B Shares
                         --------------------------------------------------------  -----------------------------
                           Six                                                       Six
                         months                         Year                       months            Year
                          ended                     ended Dec. 31,                  ended       ended Dec. 31,
                         6/30/1995   1994       1993     1992     1991     1990    6/30/1995   1994      1993*`DD'
                         -------    -------    -------  -------  -------  -------  -------    -------    -------
 
<S>                      <C>        <C>        <C>      <C>      <C>      <C>      <C>        <C>        <C>
Net Asset Value,
  Beginning of Period... $19.88     $ 21.86    $ 21.95  $ 22.16  $ 20.01  $ 23.62  $19.94     $ 21.84    $ 22.17
                         -------    -------    -------  -------  -------  -------  -------    -------    -------
Income from Investment
  Operations
Net Investment Income...   0.37        0.75       0.81     0.88     1.07     1.19    0.17        0.49       0.13
Net Gains or Losses on
  Securities (both
  realized and
  unrealized)...........   2.05       (1.15)      1.11     0.69     2.36    (1.62)   2.19       (1.04)     (0.46)
                         -------    -------    -------  -------  -------  -------  -------    -------    -------
Total from Investment
  Operations............   2.42       (0.40)      1.92     1.57     3.43    (0.43)   2.36       (0.55)     (0.33)
Less Distributions
Dividends (from net
  investment income)....  (0.40 )     (0.87)     (0.90)   (1.12)   (1.06)   (1.24)  (0.23 )     (0.64)       -0-
Distributions from
  Capital Gains (from
  securities and options
  transactions).........  (0.51 )     (0.71)     (1.11)   (0.66)   (0.22)   (1.94)  (0.51 )     (0.71)       -0-
                         -------    -------    -------  -------  -------  -------  -------    -------    -------
    Total
      Distributions.....  (0.91 )     (1.58)     (2.01)   (1.78)   (1.28)   (3.18)  (0.74 )     (1.35)       -0-
                         -------    -------    -------  -------  -------  -------  -------    -------    -------
Net Asset Value, End of
  Period................ $21.39     $ 19.88    $ 21.86  $ 21.95  $ 22.16  $ 20.01  $21.56     $ 19.94    $ 21.84
                         -------    -------    -------  -------  -------  -------  -------    -------    -------
                         -------    -------    -------  -------  -------  -------  -------    -------    -------
Total Return............  12.70 %     (1.77%)     9.35%    7.70%   17.98%   (1.76%)  12.24 %    (2.52%)    (1.49%)
                         -------    -------    -------  -------  -------  -------  -------    -------    -------
Ratios/Supplemental
  Data
Net Assets (in
  $millions), End of
  Period................  107.0       101.8      118.5    117.2    125.4    123.7     0.5         0.3        0.2
                         -------    -------    -------  -------  -------  -------  -------    -------    -------
Ratio of Expenses to
  Average Net Assets....    1.6 %`D'     1.5%      1.5%     1.2%     1.1%     1.2%    2.3 %`D'     2.3%      2.2%`D'
                         -------    -------    -------  -------  -------  -------  -------    -------    -------
Ratio of Net Income to
  Average Net Assets....    3.6 %`D'     3.7%      3.7%     4.1%     5.0%     5.6%    2.8 %`D'     2.9%      3.9%`D'
                         -------    -------    -------  -------  -------  -------  -------    -------    -------
Portfolio Turnover
  Rate..................   89.9 %`D'    87.9%     54.1%    68.5%   120.8%   107.4%   89.9 %`D'    87.9%     54.1%
                         -------    -------    -------  -------  -------  -------  -------    -------    -------
 
<CAPTION>
                                Class C Shares
                         -----------------------------
                           Six
                         months            Year
                          ended       ended Dec. 31,
                         6/30/1995   1994      1993*`DD'
                         -------    -------    -------
<S>                      <C>        <C>        <C>
Net Asset Value,
  Beginning of Period... $19.89     $ 21.87    $ 22.17
Income from Investment
  Operations
Net Investment Income...   0.35        0.72       0.15
Net Gains or Losses on
  Securities (both
  realized and
  unrealized)...........   2.06       (1.15)     (0.45)
                         -------    -------    -------
Total from Investment
  Operations............   2.41       (0.43)     (0.30)
Less Distributions
Dividends (from net
  investment income)....  (0.40 )     (0.84)       -0-
Distributions from
  Capital Gains (from
  securities and options
  transactions).........  (0.51 )     (0.71)       -0-
                         -------    -------    -------
    Total
      Distributions.....  (0.91 )     (1.55)       -0-
                         -------    -------    -------
Net Asset Value, End of
  Period................ $21.39     $ 19.89    $ 21.87
                         -------    -------    -------
                         -------    -------    -------
Total Return............  12.75 %     (1.95%)    (1.35%)
                         -------    -------    -------
Ratios/Supplemental
  Data
Net Assets (in
  $millions), End of
  Period................    0.0 **      0.0**      0.0**
                         -------    -------    -------
Ratio of Expenses to
  Average Net Assets....    1.7 %`D'     1.5%      1.5%`D'
                         -------    -------    -------
Ratio of Net Income to
  Average Net Assets....    3.5 %`D'     3.6%      3.5%`D'
                         -------    -------    -------
Portfolio Turnover
  Rate..................   89.9 %`D'    87.9%     54.1%
                         -------    -------    -------
</TABLE>
 
*  The  Fund commenced offering Class B shares and Class C shares on October 18,
   1993.
 
** Less than $100,000 of net assets.    `D' Annualized.    `DD' Based on average
   shares outstanding.
 
NOTE 9 -- Dividends and Distributions Subsequent to end of Reporting Period
 
The Fund announced a per-share distribution  to shareholders of record June  30,
1995.  The distribution has an ex-dividend date  of July 3, 1995 and was payable
July 11, 1995.
 
The distribution was as follows:
 
<TABLE>
<CAPTION>
                                                           CLASS   CLASS   CLASS
                                                             A       B       C
                                                          ------  ------  ------
 
<S>                                                      <C>     <C>     <C>
From net investment income................................ $0.20   $0.15   $0.19
                                                          ------  ------  ------
Total distributions paid.................................. $0.20   $0.15   $0.19
                                                          ------  ------  ------
                                                          ------  ------  ------
</TABLE>
 
                                      11
 
<PAGE>
OFFICERS OF THE FUND
 
I.W. Burnham, II President
  and Chief Executive Officer
Jon M. Burnham, Executive Vice President
Michael E. Barna, First Vice President
  Chief Financial Officer, Treasurer and Secretary
Ronald M. Geffen, Vice President
Debra B. Hyman, Vice President
Frank A. Passantino, Vice President and Assistant Secretary
Louis S. Rosenthal, Vice President
Leon C. Sunstein, Jr., Vice President
Mara D. Cohen, Assistant Treasurer
 
INVESTMENT ADVISER
 
Burnham Asset Management Corporation
1325 Avenue of the Americas
New York, New York 10019
 
DISTRIBUTOR
 
Burnham Securities Incorporated
1325 Avenue of the Americas
New York, New York 10019
Telephone: 1 (800) 874-FUND
 
CUSTODIAN AND TRANSFER AGENT
 
State Street Bank and Trust Company
225 Franklin Street
Boston, Massachusetts 02110
 
LEGAL COUNSEL
 
Skadden, Arps, Slate, Meagher & Flom
919 Third Avenue
New York, New York 10022
 
SERVICING AGENT
 
Boston Financial Data Services, Inc.
2 Heritage Drive
North Quincy, Massachusetts 02171
 
This report has been prepared for the information of shareholders of The Burnham
Fund Inc. and is not authorized for distribution to prospective investors unless
preceded or accompanied by an effective prospectus that includes information
regarding the Fund's objectives, policies, management, records and other
information.
 

Semi-Annual Report
June 30, 1995

CONTINUITY                      KNOWLEDGE
[PHOTOGRAPH OF CLOCK]           [PHOTOGRAPH OF CHESS PIECE]

                        [LOGO]
GROWTH                          INCOME
[PHOTOGRAPH OF STEPS]           [PHOTOGRAPH OF COINS]

Burnham Securities Inc.
PRINCIPAL DISTRBUTOR
 
<PAGE>
                     APPENDIX TO GRAPHIC AND IMAGE MATERIAL
 
Graph 1 Page 3 of Report 'Total Portfolio Distribution by Asset Class'
 
The pie chart sets out to describe  the asset allocation of The Burnham Fund  as
of  June 30, 1995. The  asset allocation is broken  out in the following manner:
Common stocks, Convertible preferred securities and Options  - 64%; Corporate  &
Convertible bonds  - 34%; Cash equivalents  - 2%.
 
Graph  2  Page  3  of  Report  'Cumulative  Return  of  a  Hypothetical  $10,000
Investment'
 
The  line  chart  describes  a  hypothetical  investment  of  $10,000  over  the
investment  period  June  16,  1975  (inception  date)  to  June  30,  1995. The
performance figures do not include the imposition of the maximum sales charge of
5%. All dividends  and distributions  from income  and capital  gains have  been
continually  reinvested. The performance in the graph represent past performance
and are not indicative of future performance. The performance at the end of  the
period reflects a total hypothetical value of $111,089 representing a cumulative
total return of 1,010.89% and an annualized compound rate of return of 12.73%.


                           STATEMENT OF DIFFERENCES
              The dagger shall be expressed as.............  'D'
              The double dagger shall be expressed as...... 'DD'





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