BURNHAM FUND INC
N-30D, 1998-08-20
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<PAGE>

                                 [BURNHAM LOGO]

                                                                  August 7, 1998
Dear Shareholders:

We are pleased to present to you the Semi-Annual Report of the Burnham Fund for
1998.

BURNHAM FUND SEMI ANNUAL DATA
- -----------------------------

On June 30, 1998 The Burnham Fund's net asset value per share for Class A, B and
C shares was $32.84, $33.68 and $32.88, which represent increases for the first
six months of 16.4%, 16.0% and 15.9%, respectively.



SECOND QUARTER MARKET REVIEW OF 1998
- ------------------------------------

At the close of the second quarter, the S&P 500 Index* ("S&P 500") returned
3.3%, and 17.7% for the first half of the year. This compares favorably with
your Fund which returned 4.4% and 16.4%, respectively for the corresponding
periods. The markets were volatile during the second quarter period, and
investor wariness about issues overseas has continued to work its way into the
averages as the third quarter progresses. During the second quarter, the Asian
crisis continued to deepen: Indonesia's rioting continued, and surprise
underground nuclear testing in India and Pakistan rattled emerging markets. The
US economy, however, still shows a vigorous picture. Within our borders
construction spending, and consumer spending, as evidenced by comparable store
sales growth is strong. For the second quarter, the Commerce Department
indicates GDP rose about 1.4%, generally in line with analysts' expectations,
although down substantially from previous reports. Some economists predicted
that the 10-week UAW strike against General Motors alone impacted GDP by 0.50%.
However, as expected, U.S. exports have slowed due to slowdowns in Asia and
Europe, and the strong U.S. dollar. Earnings reports for the second quarter have
been disparate; according to Donaldson Lufkin & Jenrette, 60% of companies in
the S&P 500 have reported positive earnings growth.


The S&P 500 should report earnings growth of 3% year over year. Companies which
operate domestically have had few negative surprises. The Asian crisis has
impacted some companies with financial interests overseas in varying degrees:
Motorola, Boeing, Caterpillar and others, particularly smaller-capitalization
issues, have suffered weak earnings derived from that region. On the positive
side, some of these companies have been able to secure operating facilities at
lower rates, which has positive implications for profitability looking forward.
In the U.S., unemployment and wage inflation rates remain low, and the CPI
remains at an annualized growth rate of 1.7%. The Federal Reserve has kept
interest rates at current levels, watching the domestic economy in the face of
international weakness.

The Burnham Fund's industry representations shifted during the second quarter
due to market performance and selected purchases and sales. Energy equities were
the fourth largest component of the portfolio, vs. second at the end of the
first quarter. Oil Services dropped to the tenth position. During the quarter,
the Fund eliminated or reduced positions in certain companies because of
anticipated or realized weakness due to Asian or other factors. Examples of such
reductions include (with other specific factors noted): Johnson & Johnson,
Tiffany & Co., ThermoElectron, Charles Schwab (price war in on-line and discount
trading negatively impacting profit margins), Royal Dutch Petroleum, Hewlett
Packard, Vornado Realty and Tenneco. The Fund sold its long-standing position in
Monsanto in the month after the announcement of its merger with American Home
Products. The stock had reached our price objective, trading at a valuation
accorded to a pharmaceutical concern. New positions to the Fund included Mellon
Bank (we believe the stock is attractively valued and the com-

* These indices are unmanaged and includes dividends reinvested.





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<PAGE>

[BURNHAM LOGO]

pany is an acquisition candidate), Ralston Purina (a mature, well managed
producer of batteries and pet/agricultural products), Delta Airlines (an
attractively priced, reorganizing concern) and Qwest Communications (a
communications service company focusing on local markets.) The Fund added to
positions in, among others, Cisco, Chrysler, Ford and Estee Lauder.

Merger, acquisition and consolidation activities continued unabated in the
second and early weeks of the third quarters of 1998. Mellon Bank successfully
rebuffed a hostile offer from the Bank of New York, Monsanto agreed to merge
with American Home Products, Chrysler to be acquired by Daimler Benz, and GTE to
merge with Bell Atlantic. In the cases of Monsanto and GTE, investors, including
your fund's investment committee, were disappointed in the terms of the mergers.
The combinations were not viewed favorably by analysts as to price terms to
shareholders and near term earnings per share growth. We view the mergers as
long term strategic moves, dampening earnings growth for as much as two years.

OUTLOOK
- -------
The investment environment through the second quarter validated many of the
investment themes we have discussed in our letters for the last three years. We
have stated that this market has been fueled by many converging events:

        A technology and communications revolution that tends to smooth out the
        business cycle, improve corporate management and planning, and expand
        profit margins and bottom line earnings

        Continued low inflation and stable interest rates

        Elimination of the federal deficit

        The government's encouraging individual investing through lowering
        capital gains taxes and liberalizing retirement programs

        Record breaking inflows of tax deferred and discretionary investment
        into mutual funds from systematic investment programs and other
        retirement vehicles

        Increased level of corporate merger and acquisition activity as
        companies seek new distribution avenues both in the United States and
        abroad

        A shrinking supply of common stock from accelerating corporate stock
        buyback activity (which exceeds the market value of new stock coming to
        market from IPOs)

The markets, however, have been distracted yet again by the impact of the Asian
crisis on selected companies. As of the end of the second quarter, the S&P 500
stood at 25x 1998 earnings estimates, 5.8x book value, and had a dividend yield
of 1.3%. Since the close of the quarter, the market has corrected approximately
9% to a multiple of 21x 1998 earnings (as of August 4). On August 4, the index
of leading indicators showed a drop for the second month in a row. When this
occurs, analysts often interpret this as a signal that the economy is slowing.
This problem will last for several years while political and economic changes
take root in the Pacific region, particularly Japan and Indonesia. In the
meantime, we believe that Asia will cause the US economy in aggregate to slow
slightly, but it may also extend the business cycle further. GDP growth may
moderate, CPI may stay low, and the Fed will be unlikely to raise interest
rates. Adding to the current uncertainty is also the growing scandal surrounding
President Clinton, which may also continue

                                        2




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                                                                  [BURNHAM LOGO]


into next year. Finally, some analysts are concerned that the Year 2000 "bug"
and the adoption of the Euro may also cause a moderate decline in earnings
growth due to extensive resources dedicated to software programming and errors
associated with antiquated information systems.

Nevertheless, we continue to hold a positive view toward equities for the
balance of the year. We favor companies with earnings growth potential of at
least 15% to 20% per year for three to five years, product leadership,
innovative management with a shareholder-value orientation, superior financial
underpinnings, and a healthy dividend history (when pertinent). We also search
for companies whose stock is undervalued relative to its past, or those which
may benefit from restructuring actions. Most importantly, at this time we look
for predominantly liquid, large-capitalization companies with relatively little
or no exposure to Asia, or where the exposure is well understood. We are also
monitoring Year 2000 issues as they affect our investments, and to the extent to
which companies in the Fund are on track with compliance.

Portfolio Manager Jon Burnham continues his monthly appearances on CNBC, CNN/fn
and Bloomberg. If you would like to be notified by fax of his appearances
beforehand, please call our toll free number, 1-800-874-FUND and we would be
happy to include you on our fax broadcast of his schedule.

We appreciate your confidence in the Burnham Fund.

Very truly yours,

I. W. Burnham                                 Jon M. Burnham
I. W. Burnham, II                             Jon M. Burnham,
Chairman                                          President &
                                            Portfolio Manager

                       Cumulative Performance Comparison
<TABLE>
<CAPTION>
                                              Cumulative % Change                 Average Annualized % Change
                                      --------------------------------------  --------------------------------
                                       YTD     1 yr    3 yr    5 yr    10 yr   1 yr    3 yr    5 yr    10 yr
                                       ----    ----    ----    ----    -----   ----    ----    ----    ----
<S>                                   <C>     <C>     <C>     <C>     <C>     <C>     <C>     <C>     <C>    
Dow Jones Industrial Average          14.14%  18.68%  27.76%  23.35%  18.72%  18.68%  108.61% 185.60% 456.44%
Standard & Poor's 500 Index           17.70%  30.14%  30.22%  23.06%  18.55%  30.14%  120.82% 182.20% 448.32%
Morningstar Large Cap Blend Average   14.64%  25.80%  25.80%  19.48%  16.18%  25.80%   99.08% 143.54% 347.85%
Morningstar Growth & Income Average   12.86%  24.06%  25.37%  19.32%  15.67%  24.06%   97.07% 141.81% 328.79%
</TABLE>

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, 1998 were 25.86%, 16.66% and
13.78%, respectively. Such performance assuming the imposition of the Class A
shares' maximum 5% sales charge for the same periods would have been 17.57%,
19.47% and 13.20%, respectively. For Class B and C shares, average total return
for the one year period ended June 30, 1998 and life of class total return for
the period October 18, 1993 (inception date) to June 30, 1998 were 24.77% and
24.85% and 15.57% and 15.83%, respectively. Class B shares bear a maximum
contingent deferred sales charge at a rate of 5% if they are redeemed within the
first six years of purchase. Such performance assuming the imposition of the
contingent deferred sales charge of 4% for the one year period ended June 30,
1998 and life of class were 20.77% and 15.57%, respectively. Class C shares bear
a maximum contingent deferred sales charge at a rate of 1% if they are redeemed
within the first year of purchase.

                                        3





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[BURNHAM LOGO]

                             INVESTMENT PERSPECTIVE

    Equity Portfolio Distribution
      by Industry Classification
            June 30, 1998
<TABLE>
<CAPTION>
                                                 % Total
                                            Equity Portfolio
                                            ----------------
<S>                                               <C>
Financial Services ...............                11.4%
Computer Products & Software .....                10.2%
Banking ..........................                10.0%
Energy--Oil & Gas ................                 9.3%
Pharmaceuticals ..................                 8.3%
Real Estate Investment Trusts ....                 5.8%
Telecommunications Equipment .....                 5.6%
Automotive .......................                 5.2%
Telecommunication Network Services                 5.2%
Oil Drillers .....................                 3.9%
Personal Care Products ...........                 3.5%
Other ............................                21.6%
                                                -------
Total Equities ...................              100.00%
                                                =======
</TABLE>

 Total Portfolio Distribution by Asset Class
                June 30, 1998


                   [GRAPH]



Top 25% Portfolio Holdings
(excluding short-term investments)
June 30, 1998

<TABLE>
<CAPTION>
                                 Number of                % of
                                  Shares       Value    Net Assets
                                   -----       -----    ----------
<S>                               <C>       <C>            <C>
Travelers Group Inc ..........    120,000   $ 7,275,000    4.66%
The Bank of New York Co., Inc.    100,000   $ 6,068,750    3.89%
Lucent Technologies Inc. .....     70,000   $ 5,823,125    3.73%
Pfizer Inc. ..................     50,000   $ 5,434,375    3.48%
Exxon Corporation ............     70,000   $ 4,991,875    3.20%
American Express Co. .........     40,000   $ 4,560,000    2.92%
Microsoft Corp. ..............     40,000   $ 4,336,250    2.78%
Ford Motor Co. ...............     70,000   $ 4,130,000    2.65%
                                             ----------   ------
Top 25% Portfolio Holdings ...              $42,619,375   27.31%
                                             ==========   ======
</TABLE>

<PAGE>
[GRAPH]

<TABLE>
<CAPTION>
                 DOLLAR
  DATE            VALUE
- ---------        -------
<S>              <C>
  6/16/75         10,000
     8/75          9,514
    11/75          9,911
     2/76         10,998
     5/76         11,137
     8/76         11,434
    11/76         11,527
     2/77         11,437
     5/77         11,340
     8/77         11,546
    11/77         11,716
     2/78         11,070
     5/78         12,491
     8/78         13,899
    11/78         12,808
     2/79         13,346
     5/79         13,947
     8/79         15,796
    11/79         15,968
     2/80         17,622
     5/80         17,277
     8/80         19,143
    11/80         22,509
     2/81         21,202
     5/81         22,741
     8/81         20,551
    11/81         21,766
     2/82         20,375
     5/82         20,740
     8/82         22,122
    11/82         25,502
     2/83         27,130
     5/83         28,910
     8/83         28,750
    11/83         29,500
     2/84         28,077
     5/84         27,394
     8/84         30,463
    11/84         30,724
     2/85         33,209
     5/85         35,844
     8/85         36,285
    11/85         39,481
     2/86         44,533
     5/86         48,822
     8/86         50,708
    11/86         50,564
     2/87         56,170
     5/87         56,567
     8/87         61,493
    11/87         51,604
     2/88         57,209
     5/88         56,377
     8/88         57,468
    11/88         59,568
     2/89         62,375
     5/89         66,812
     8/89         70,974
    11/89         71,089
     2/90         70,280
     5/90         72,539
     8/90         69,839
    11/90         71,459
     2/91         75,301
     5/91         78,044
     8/91         79,325
    11/91         79,354
     2/92         86,673
     5/92         85,384
     8/92         87,127
    11/92         89,836
     2/93         93,453
     5/93         95,724
     8/93        100,595
    11/93         98,794
     2/94         99,703
     5/94         96,689
     8/94        100,244
    11/94         98,016
     2/95        102,777
     5/95        109,211
     8/95        114,164
    11/95        119,438
     2/96        127,075
     5/96        131,894
     8/96        127,870
    11/96        146,166
     2/97        149,787
     5/97        159,374
     8/97        171,146
    11/97        176,690
     2/98        191,141
     6/98        209,439
</TABLE>

*  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 ended June 30, 1998

<TABLE>
<CAPTION>
<S>                    <C>
One Year .........     25.86%
Five Years .......     16.66%
Ten Years ........     13.78%
Fifteen Years.....     13.93%
Twenty Years......     15.19%
</TABLE>



                                        4







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                                                                  [BURNHAM LOGO]

                            STATEMENT OF NET ASSETS

<TABLE>
<CAPTION>

                                              Number of                Value
                                               Shares                 (Note 1) 
- --------------------------------------------------------------------------------
<S>                                           <C>                  <C>
COMMON STOCKS                          89.31%
Aerospace                               2.22%
  Boeing Co............................         20,000             $   891,250
  General Motors Corp., Class H .......         30,000               1,413,750
  Gulfstream Aerospace Corp. ..........         25,000               1,162,500
                                                                   -----------
                                                                     3,467,500
                                                                   -----------
AUTOMOTIVE                              4.82%
  Chrysler Corp........................         60,000               3,382,500
  Ford Motor Company ..................         70,000               4,130,000
                                                                   -----------
                                                                     7,512,500
                                                                   -----------
BANKING                                 9.20%
  The Bank of New York Co., Inc.........      100,000                6,068,750
  Chase Manhattan Bank .................       20,000                1,510,000
  Citicorp .............................       15,000                2,238,750
  Fleet Financial Group Inc. ...........       25,000                2,087,500
  Mellon Bank Corp. ....................       35,000                2,436,875
                                                                   -----------
                                                                    14,341,875
                                                                   -----------

COMPUTER PRODUCTS &
 SOFTWARE                              9.45%
  Cisco Systems Inc. ..................       35,000(a)             3,223,281
  International Business Machines Corp.       25,000                2,870,312
  Microsoft Corp. .....................       40,000(a)             4,336,250
  Phoenix Technologies Ltd. ...........       80,000(a)             1,015,000
  Safeguard Scientifics Inc. ..........       25,000(a)             1,042,188
  Siebel Systems Inc. .................       70,000(a)             2,253,125
                                                                  -----------
                                                                   14,740,156
                                                                  -----------
CONGLOMERATES                          0.92%
  Textron Inc. ........................       20,000               1,433,750
                                                                 -----------
CONSUMER PRODUCTS                      2.87%
  Blyth Industries Inc. ...............       25,000(a)              831,250
  General Electric Co. ................       40,000               3,640,000
                                                                 -----------
                                                                   4,471,250
                                                                 -----------
DOMESTIC AIRLINES                      0.83%
  Delta Airlines, Inc. ................      10,000               1,292,500
                                                                -----------
ENERGY--OIL AND GAS                    8.51%
  Amoco Corp. .........................      40,000               1,665,000
  British Petroleum PLC ADS ...........      20,000               1,765,000
  Exxon Corporation ...................      70,000               4,991,875
  Mobil Corporation ...................      40,000               3,065,000
  Texaco Inc. .........................      30,000               1,790,625
                                                                -----------
                                                                 13,277,500
                                                                -----------
ENGINEERING/INDUSTRIAL
PRODUCTION                            0.06%
  Thermolyte Corp.....................       10,000(ab)             100,000
                                                                -----------
FINANCIAL SERVICES                   10.48%
  American Express Co. ...............       40,000             $ 4,560,000
  Associates First Capital Corp.......       28,104               2,160,495
  Franklin Resources Group ...........       25,000               1,350,000
  Travelers Group Inc. ...............      120,000               7,275,000
  Webster Financial Corporation ......       30,000                 997,500
                                                                -----------
                                                                 16,342,995
                                                                -----------
FOOD PRODUCTS                         0.75%
  Ralston Purina Co...................      10,000               1,168,125
                                                               -----------
HEALTHCARE FACILITIES                 1.33%
  Rehabcare Group Inc.................      85,000(a)            2,071,875
                                                               -----------
HOTELS & GAMING                       0.41%
  Mirage Resorts Inc..................      30,000(a)              639,375
                                                               -----------
INSURANCE                             2.35%
  Allstate ...........................      40,000               3,662,500
                                                               -----------
MEDIA BROADCASTING                    0.81%
  CBS Corporation ....................      40,000               1,270,000
                                                               -----------
MEDICAL SUPPLIES                      0.82%
  Medtronic Inc.......................      20,000               1,275,000
                                                               -----------
OIL DRILLING                          3.56%
  Diamond Offshore Drilling Inc.......     100,000               4,000,000
  Transocean Offshore Inc.............      35,000               1,557,500
                                                               -----------
                                                                 5,557,500
                                                               -----------
PASSSENGER CRUISE LINES              0.16%
  Royal Olympic Cruise Lines ........       25,000(a)              250,781
                                                               -----------
PASTA PRODUCER                       1.67%
  American Italian Pasta Co. ........       70,000               2,607,500
                                                               -----------
PERSONAL CARE PRODUCTS               3.27%
  Estee Lauder Inc. .................       15,000               1,742,188
  Gillette Co. ......................       40,000               2,267,500
  Procter & Gamble Corp. ............       12,000               1,092,750
                                                               -----------
                                                                 5,102,438
                                                               -----------
PHARMACEUTICALS                      7.63%
  Merck & Co. .......................       25,000               3,343,750
  Pfizer Inc. .......................       50,000               5,434,375
  Warner Lambert Inc. ...............       45,000               3,121,875
                                                               -----------
                                                                11,900,000
                                                               -----------
REAL ESTATE INVESTMENT
   TRUSTS                           5.32%
  Chateau Communities Inc. ..........      40,000               1,150,000
  Developers Diversified Realty Corp.      30,000               1,175,625
  Franchise Finance Corp. ...........      80,000               2,075,000
  Golf Trust  of America ............      45,000               1,546,875
  Meditrust SBI .....................      84,000               2,346,750
                                                              -----------
                                                                8,294,250
                                                              -----------
</TABLE>
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[BURNHAM LOGO]

                            STATEMENT OF NET ASSETS

<TABLE>
<CAPTION>
                                        Number of Shares
                                          or Principal             Value
                                             Amount               (Note 1)
- --------------------------------------------------------------------------------
<S>                                           <C>                  <C>
SEMICONDUCTORS                       1.90%
  Intel Corp. .......................        40,000             $ 2,963,750
                                                                -----------
TELECOMMUNICATION
   EQUIPMENT                         5.19%
  ECI Telecom Ltd. ..................        60,000               2,272,500
  Lucent Technologies Inc. ..........        70,000               5,823,125
                                                                -----------
                                                                  8,095,625
                                                                -----------
TELECOMMUNICATIONS NETWORK
   AND SERVICES                     4.78%
  Ericcson (L.M.) Telefon "B" ADS ...        50,000               1,434,375
  GTE Corp. .........................        40,000               2,225,000
  Qwest Communication International .        40,000(a)            1,395,000
  SBC Communications Inc. ...........        60,000               2,400,000
                                                                -----------
                                                                  7,454,375
                                                                -----------
  TOTAL COMMON STOCKS
    (cost: $78,967,208)..............                           139,293,120
                                                                -----------
CONVERTIBLE PREFERRED
   SECURITIES                         2.96%
ENTERTAINMENT                         0.33%
  Metromedia International
  Group, 7.25% cum. conv.............       10,000                 515,000
                                                               -----------
PASSENGER CRUISE LINES               1.61%
  Royal Caribbean Cruises,
   conv. Preferred Cl. `A'...........       20,000               2,520,000
                                                               -----------
UTILITIES                            1.02%
   AES Trust I, conv. Preferred
    Series `A'.......................        6,000                 468,000
   AES Trust II, $2.75 conv. Preferred
    Series `B' TECONS ...............       20,000               1,116,250
                                                               -----------
                                                                 1,584,250
                                                               -----------
  TOTAL CONVERTIBLE PREFERRED
   SECURITIES  (cost: $2,912,400) ...                            4,619,250
                                                               -----------
CONVERTIBLE BONDS                    0.78%
DATA PROCESSING                      0.78%
  Adaptec, Inc. 4.75% sub. deb.
   conv. 2/1/04......................  $1,000,000                 760,000
  Data General Corp., 6% sub. deb.
   conv. 5/15/04.....................     500,000                 462,500
                                                             ------------
TOTAL CONVERTIBLE BONDS
  (cost: $1,271,000).................                           1,222,500
                                                             ------------
</TABLE>

<TABLE>
<CAPTION>
                                        PRINCIPAL
                                         AMOUNT/              VALUE
                                      CALL OPTIONS           (NOTE 1)
- --------------------------------------------------------------------------------
<S>                                 <C>                    <C>
CORPORATE BONDS                     0.84%
HOTELS                              0.84%
  Marriott Corp., 9 3/8% deb. 6/15/07  $1,265,000          $   1,301,053
                                                           -------------
  TOTAL CORPORATE BONDS
    (cost: $1,273,606)..............                           1,301,053
                                                           -------------
COMMERCIAL PAPER                   6.55%
  American Express Credit Corp.,
   5.75% 07/01/98 ..................   3,310,000              3,310,000
  Associates First Capital Corp.,
   5.90% 07/01/98 ..................   5,620,000              5,620,000
  General Electric Capital Corp., 
    5.60% 07/01/98 .................   1,280,000              1,280,000
                                                          -------------
TOTAL COMMERCIAL PAPER
   (cost: $10,210,000) .............                         10,210,000
                                                          -------------
TOTAL INVESTMENTS IN SECURITIES
    (cost: $94,634,214) ............                        156,645,923
                                                          -------------
CALL OPTIONS WRITTEN                 (0.11%)
  Intel Corp., @ 100 expiring
   October, 1998 ...................   100 calls               (85,000)
  Lucent Technologies Inc. @ 70
   expiring July, 1998 .............   100                     (85,000)
                                                          -------------
  TOTAL CALL OPTIONS WRITTEN
   (premium received: $102,946).....                          (170,000)
                                                          -------------
TOTAL INVESTMENTS
   (cost: $94,531,268)               100.33%                156,475,923
CASH AND OTHER ASSETS,
  LESS LIABILITIES                    (0.33%)                  (510,190)
                                    --------              -------------
NET ASSETS                           100.00%               $155,965,733
                                    ========              =============
- --------------------------------------------------------------------------------

</TABLE>

(a)    Non-income producing security.

(b)    A unit consisting of one share of common stock of Thermolyte Corporation
       and one redemption right.

(c)    "TECONS" are term convertible securities with a liquidation amount of $50
       per security and are convertible into common stock of the AES
       Corporation.


FEDERAL INCOME TAX BASIS OF INVESTMENT SECURITIES
- -------------------------------------------------

     For Federal Tax purposes, the tax basis of investment securities owned at
June 30, 1998 was $94,531,268. The aggregate gross unrealized Appreciation for
all securities in which there was an excess of value over tax cost was
$62,459,447 and aggregate gross unrealized depreciation for all securities in
which there was excess of tax cost over value was $514,792.

                                        6





<PAGE>
 
<PAGE>

                                                                  [BURNHAM LOGO]

                      STATEMENT OF ASSETS AND LIABILITIES
                           June 30, 1998 (Unaudited)

- --------------------------------------------------------------------------------
<TABLE>

<S>                                                                      <C>    
ASSETS:
  Investment in securities, at value (identified
    cost: $94,634,214)(Note 1) ..............................       $156,645,923
  Cash in bank ..............................................                331
  Dividends and interest receivable .........................            179,511
  Receivable for capital stock sold .........................             19,911
  Receivable from investment advisor ........................                782
  Prepaid Expenses ..........................................             26,662
                                                                    ------------
    Total assets ............................................        156,873,120
                                                                    ------------
LIABILITIES:
  Payable for capital stock redeemed .........................               266
  Payable for investment securities purchased ................           450,600
  Payable for investment advisory fees (Note 6) ..............            77,352
  Payable for distribution and
    service fees (Note 7) ....................................            32,430
  Payable for options written
    (proceeds received: $102,946) ............................           170,000
  Accrued expenses and other payables ........................           176,739
                                                                    ------------
     Total liabilities .......................................           907,387
                                                                    ------------
NET ASSETS ....................................................     $155,965,733
                                                                    ============
CLASS A SHARES
NET ASSET VALUE AND REDEMPTION PRICE PER SHARE
  (NOTE 2): ($153,414,869/4,671,789 shares
  outstanding) ...............................................      $      32.84
                                                                    ============
CALCULATION OF MAXIMUM OFFERING PRICE
SALES CHARGE - 5% OF PUBLIC OFFERING PRICE:
  (NOTE 2): ($32.84 net asset value plus 5.0%
  of public offering price) ...................................     $      34.57
                                                                    ============
CLASS B SHARES
NET ASSET VALUE AND OFFERING PRICE PER SHARE:
  (NOTE 2): ($2,270,310/67,412 shares
  outstanding) ................................................     $      33.68
                                                                    ============
CLASS C SHARES
NET ASSET VALUE AND OFFERING PRICE PER SHARE:
  (NOTE 2): ($280,554/8,533.945 shares
  of capital stock outstanding) ...............................     $      32.88
                                                                    ============
Redemption price per share varies with the
length of time Class B and C shares
are held. (Note 7)

NET ASSETS CONSISTED OF:
  Capital paid-in ............................................      $ 86,932,990
  Undistributed net investment
    income ...................................................           287,928
  Accumulated net realized gains
    on investments ...........................................         6,800,160
  Net unrealized appreciation of
    investments ..............................................        61,944,655
                                                                    ------------
                                                                    $155,965,733
                                                                    ============
</TABLE>


                            STATEMENT OF OPERATIONS
                   Six months ended June 30, 1998 (Unaudited)
- --------------------------------------------------------------------------------
<TABLE>
<S>                                                           <C>    
INVESTMENT INCOME:
 INCOME:
  Dividends ....................................              $  1,187,318
  Interest .....................................                   336,156
                                                              ------------
Total income .....................................               1,523,474
                                                              ------------
EXPENSES:
  Investment advisory fees (Note 6) ..............                 453,923
  Distribution fee (Class A)(Note 7) .............                 109,735
  Distribution fee (Class B)(Note 7) .............                   7,251
  Distribution fee (Class C)(Note 7) .............                     648
  Service fees (Class B & C)(Note 7) .............                   2,632
  Transfer agent fees ............................                  98,854
  Professional fees ..............................                  81,450
  Reports to shareholders ........................                  25,340
  Directors' fees and expenses ...................                  42,563
  Custodian fees .................................                  24,797
  Registration fees and expenses .................                  18,002
  Insurance expense ..............................                  26,456
  Miscellaneous expense ..........................                   9,744
                                                              ------------
   Total expenses before reimbursement............                 901,395

   Less: Expenses voluntarily reimbursed
    by Investment Adviser (Note 6)................                     (50)
                                                              ------------
   Total expenses after reimbursement.............                 901,345
                                                              ------------
   Net investment income .........................                 622,129
                                                              ------------
NET REALIZED AND UNREALIZED GAIN ON INVESTMENTS:
  Realized gain from securities and options
   transactions (excluding short-term
    money market instruments)
     Proceeds from sales ........... $ 40,239,107
     Cost of securities sold........  (33,581,775)
                                     ------------
  Net realized gain from securities and options
    transactions ................................                6,657,332
                                                              ------------
Increase in unrealized appreciation
  of investments
   Beginning of period ............. $ 46,975,277
   End of period ...................   61,944,655
                                     ------------
 Increase in unrealized appreciation ............               14,969,378
                                                              ------------
Net realized and unrealized gain
        on investments .........................                21,626,710
                                                              ------------
Net increase in net assets resulting
        from operations ........................              $ 22,248,839
                                                              ============

</TABLE>

                       See notes to financial statements.

                                        7





<PAGE>
 
<PAGE>

[BURNHAM LOGO]

                       STATEMENT OF CHANGES IN NET ASSETS
                                   (Unaudited)

<TABLE>
<CAPTION>

                                               SIX MONTHS ENDED       YEAR ENDED
                                                   JUNE 30,          DECEMBER 31,
                                                     1998               1997
- --------------------------------------------------------------------------------
<S>                                            <C>                <C>          
INCREASE IN NET ASSETS:
  FROM OPERATIONS:
   Net investment income ............          $     622,129      $   2,087,255
   Net realized gain from
     security and option
     transactions ...................              6,657,332          7,595,669
Increase in unrealized
 appreciation of investments.........             14,969,378         18,745,136
                                               -------------      -------------
 Net increase in net assets
  resulting from operations .........             22,248,839         28,428,060
                                               -------------      -------------
DISTRIBUTIONS TO SHAREHOLDERS
  (NOTE 1):
  From net investment income:
   Class A Shares ...................               (924,002)        (2,041,644)
   Class B Shares ...................                 (3,373)           (12,430)
   Class C Shares ...................                   (361)              (122)
  From realized gains from security
   and option transactions:
   Class A Shares ...................             (7,404,378)        (5,310,408)
   Class B Shares ...................                (85,433)           (45,808)
   Class C Shares ...................                 (5,196)              (152)
                                               -------------      -------------
    Total distributions to
      shareholders ..................             (8,422,743)        (7,410,564)
                                               -------------      -------------
CAPITAL SHARE TRANSACTIONS
  (NOTE 2):
  Net proceeds from sale
   of shares ........................              2,609,319          2,286,944
  Net asset value of shares issued 
   to shareholders in
     reinvestment of dividends ......              7,392,717          6,428,892
                                               -------------      -------------
                                                  10,002,036          8,715,836
Cost of shares redeemed .............             (6,013,631)       (10,050,186)
                                               -------------      -------------
Increase/Decrease in net assets
  derived from capital share
    transactions ....................             3,988,405         (1,334,350)
                                              -------------      -------------
Increase in net
  assets for the period .............            17,814,501         19,683,146
                                              -------------      -------------
NET ASSETS:
  Beginning of period ...............           138,151,232        118,468,086
                                              -------------      -------------
  End of period (including
    undistributed net investment
    income of $287,928 and
    $593,535, respectively) .........         $ 155,965,733      $ 138,151,232
                                              =============      =============

</TABLE>

                        See notes to financial statements



                          NOTES TO FINANCIAL STATEMENTS
                            June 30, 1998 (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 management
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 for more
than six years. Class C shares are sold with a contingent deferred sales charge
of 1.0%, 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. Federal income taxes - It is the Fund's intent 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.


D. Option Writing - When the Fund writes a covered call option the amount
received is included in the Statement of





                                        8




<PAGE>
 
<PAGE>

                                                                  [BURNHAM LOGO]


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 gains (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 are increased by the
amount originally received and the resulting gain or loss is recorded by the
Fund.

Transaction in written options for the six months ended June 30, 1998 were as
follows:

<TABLE>
<CAPTION>

                                                           NUMBER OF OPTIONS       PREMIUMS
                                                           ---------------------------------
<S>                                                        <C>                     <C>
Options written at December 31, 1997 .....................         -0-                   -0-
Options written ..........................................         300             $ 160,045
Options cancelled in closing purchase
transactions .............................................        (100)              (57,099)
                                                             ---------             ---------
Options outstanding ......................................         200             $ 102,946
                                                             =========             =========

</TABLE>

The cost of canceling options in closing transactions was $24,775 resulting in a
net realized capital gain of $32,324.

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.

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.

G. Management's Use of Estimates - The preparation of financial statements in
conformity with generally accepted accounting principles requires management to
make estimates and assumptions that affect the reported amounts of assets and
liabilities at the date of the financial statements and the reported amounts of
income and expenses during the reporting period. Actual results could differ
from those estimates.

NOTE 2 -- CAPITAL STOCK

At June 30, 1998, 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, 1998, Class D shares were not issued.

Transactions in capital stock for the six months ended June 30, 1998 and year
ended 1997 for Class A, B and C shares were as follows:

<TABLE>
<CAPTION>

                                          SIX MONTHS
                                             ENDED                      YEAR ENDED
                                         JUNE 30, 1998                      1997
                                         -----------------------------------------

<S>                                           <C>                          <C>   

CLASS A SHARES
Shares sold ............................      67,223                       70,028
Shares issued to shareholders
  in reinvestment of distributions .....     257,041                      256,708
                                            --------                     --------
                                             324,264                      326,736

Shares redeemed ........................    (193,978)                    (363,191)
                                            --------                     --------
Net increase (decrease) ................     130,286                      (36,455)
                                            ========                     ========
CLASS B SHARES
Shares sold ............................      12,097                       11,773
Shares issued to shareholders
  in reinvestment of distributions .....       3,047                        2,280
                                            --------                     --------
                                              15,144                       14,053
Shares redeemed ........................        (145)                      (1,130)
                                            --------                     --------
Net increase ...........................      14,999                       12,923
                                            ========                     ========
CLASS C SHARES
Shares sold ............................       5,151                        3,071
Shares issued to shareholders
  in reinvestment of distributions .....         195                           10
                                            --------                     --------
                                               5,346                        3,081
Shares redeemed ........................        --                            (25)
                                            --------                     --------
Net increase ...........................       5,346                        3,056
                                            ========                     ========

</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, 1998 were:

<TABLE>
<CAPTION>

                                                                      PROCEEDS
                                             COST OF                  FROM SALES
                                            PURCHASES               OR MATURITIES
                                          --------------------------------------

<S>                                       <C>                       <C>         
Short-term money
  market instruments ................     $966,563,797              $965,760,797
Common stocks and other
  securities ........................     $ 33,857,222              $ 40,239,107


</TABLE>

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. A secondary market
exists for certain privately placed securities. At June 30, 1998, the Fund held
a restricted security with a value aggregating $100,000, representing less than
0.1% of the Fund's net assets. Currently, a market does not exist for the
security listed below:

                                        9





<PAGE>
 
<PAGE>

[BURNHAM LOGO]


<TABLE>
<CAPTION>

Units       Company               Acquired         Cost            Value
- -------------------------------------------------------------------------
<S>        <C>                   <C>             <C>             <C>
10,000     Thermolyte Corp.      03/16/1995      $100,000        $100,000

</TABLE>

This security has been valued in good faith by management.

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. There were no financial
instruments with off-balance sheet risk at the end of the year owned by the
Fund.

NOTE 6 -- INVESTMENT ADVISORY FEES AND OTHER TRANSACTIONS

Burnham Asset Management Corporation, 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, 1998, the Fund incurred fees
in the amount of $453,923. 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 C shares $50.

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, subject to certain NASD sales expense limitations
on 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, 1998, Class A, B and C shares incurred fees of
$109,735, $7,251, and $648, 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, 1998 were
$2,416 and $216, respectively. For the six months ended June 30, 1998, the
Distributor earned $42,234 in brokerage commissions from Fund transactions and
$8,859 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 Class A 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 shareholder'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
is paid to the Distributor. For the six months ended June 30, 1998, there were
$78 in CDSC 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.

                                       10





<PAGE>
 
<PAGE>



NOTE 8 -- DIVIDENDS AND DISTRIBUTIONS SUBSEQUENT TO END OF REPORTING PERIOD

The Fund announced a per-share distribution to shareholders of record June 30,
1998. The distribution had an ex-dividend date of July 1, 1998 and was payable
July 9, 1998.


The distribution was as follows:

<TABLE>
<CAPTION>

                                      CLASS A
- ----------------------------------------------
<S>                                     <C>  
From net investment income              $0.06
From long-term capital gains              --
                                        -----
Total distributions paid                $0.06
                                        =====

</TABLE>


NOTE 9 -- Financial Highlights

<TABLE>
<CAPTION>

                                               Six months
                                                ended                                    Class A Shares
                                                June 30,        -------------------------------------------------------------------
                                                 1998            1997           1996           1995           1994           1993
- ------------------------------------------------------------------------------------------------------------------------------------

<S>                                      <C>               <C>            <C>            <C>            <C>            <C>       
Net Asset Value,
  Beginning of Period                    $      30.04      $    25.65     $    23.19     $    19.88     $    21.86     $    21.95
                                         -------------------------------------------------------------------------------------------
                                           
INCOME FROM INVESTMENT OPERATIONS 
                                           
Net Investment Income                            0.13            0.45           0.51           0.71           0.75           0.81



Net Gains or Losses on Securities          
  (both realized and unrealized)                 4.50            5.54           3.36           3.91          (1.15)          1.11
                                         -------------------------------------------------------------------------------------------
                                           
Total from Investment Operations                 4.63            5.99           3.87           4.62          (0.40)          1.92

                                           
LESS DISTRIBUTIONS                         

Dividends (from net investment income)          (0.20)          (0.44)         (0.55)         (0.75)         (0.87)         (0.90)

                                           

Distributions from Capital Gains (from     
  securities and options transactions)          (1.63)          (1.16)         (0.86)         (0.56)         (0.71)         (1.11)
                                         -------------------------------------------------------------------------------------------
                                           
Total Distributions                             (1.83)          (1.60)         (1.41)         (1.31)         (1.58)         (2.01)
                                         -------------------------------------------------------------------------------------------
                                           
Net Asset Value, End of Period             $    32.84      $    30.04     $    25.65     $    23.19     $    19.88     $    21.86
                                         ===========================================================================================
                                           
Total Return                                    16.38%          24.74%         17.60%         24.45%         (1.77%)         9.35%
                                         -------------------------------------------------------------------------------------------
                                           
RATIOS/SUPPLEMENTAL DATA                   

Net Assets (in $millions), End of Period       153.4           136.4          117.4          112.0          101.8          118.5
                                         -------------------------------------------------------------------------------------------
                                           
Ratio of Expenses (net)                    
  to Average Net Assets [1]                      1.2%*           1.1%           1.3%           1.5%           1.5%           1.5%
                                         -------------------------------------------------------------------------------------------
                                           
Ratio of Net Income to Average Net Assets        0.9%*           1.6%           2.1%           3.3%           3.7%           3.7%
                                         -------------------------------------------------------------------------------------------
                                           
Average Commission Rate***                    $0.0670        $0.0749         $.0726            -.-            -.-            -.-

                                           
Portfolio Turnover Rate                          64.5%           59.4%          61.5%          78.3%          87.9%          54.1%
                                         -------------------------------------------------------------------------------------------


<CAPTION>
                                               Six months
                                                 ended                              Class B Shares
                                                June 30,        ----------------------------------------------------------
                                                 1998              1997       1996        1995        1994      1993*'DD'
- --------------------------------------------------------------------------------------------------------------------------

<S>                                          <C>             <C>         <C>          <C>         <C>         <C>
Net Asset Value,

Beginning of Period                          $     30.75    $     26.31   $   23.45   $   19.94   $   21.84   $   22.17
                                         ---------------------------------------------------------------------------------
INCOME FROM INVESTMENT OPERATIONS

Net Investment Income                              (0.01)          0.13        0.21        0.41        0.49        0.13

Net Gains or Losses on Securities
  (both realized and unrealized)                    4.63           5.75        3.69        4.10       (1.04)      (0.46)
                                         ---------------------------------------------------------------------------------
<PAGE>

Total from Investment Operations                    4.62           5.88        3.90        4.51       (0.55)      (0.33)

LESS DISTRIBUTIONS

Dividends (from net investment income)             (0.06)         (0.28)      (0.18)      (0.44)      (0.64)       0.0

Distributions from Capital Gains (from
  securities and options transactions)             (1.63)         (1.16)      (0.86)      (0.56)      (0.71)       0.0
                                         ---------------------------------------------------------------------------------
Total Distributions                                (1.69)         (1.44)      (1.04)      (1.00)      (1.35)       0.0
                                         ---------------------------------------------------------------------------------
Net Asset Value, End of Period               $     33.68    $     30.75   $   26.31   $   23.45   $   19.94   $   21.84
                                         =================================================================================
Total Return                                       15.90%         23.60%      17.34%      23.54%      (2.52%)     (1.49%)
                                         ---------------------------------------------------------------------------------
RATIOS/SUPPLEMENTAL DATA

Net Assets (in $millions), End of Period            2.3            1.6         1.0         0.6         0.3         0.2
                                         ---------------------------------------------------------------------------------
Ratio of Expenses (net)
  to Average Net Assets [1]                         2.0%+          2.0%        2.1%        2.2%        2.3%        2.2%'D'
                                         ---------------------------------------------------------------------------------
Ratio of Net Income to Average Net Assets        --                0.7%        1.3%        2.5%        2.9%        3.9%'D'
                                         ---------------------------------------------------------------------------------
Average Commission Rate***                   $      0.0670  $      0.0749 $ 0.0726         -.-         -.-        -.-

Portfolio Turnover Rate                            64.5%          59.4%       61.5%       78.3%       87.9%       54.1%
                                         ---------------------------------------------------------------------------------


<CAPTION>
                                               Six months
                                                ended                                    Class C Shares
                                                June 30,        --------------------------------------------------------------
                                                 1998            1997           1996           1995       1994       1993
- ------------------------------------------------------------------------------------------------------------------------------
<S>                                      <C>               <C>            <C>            <C>            <C>            <C>
Net Asset Value,

Beginning of Period                          $     30.09    $     25.69   $     23.10    $   19.89    $   21.87    $   22.17
                                             ---------------------------------------------------------------------------------
INCOME FROM INVESTMENT OPERATIONS

Net Investment Income                              (0.04)          0.13          0.29         0.54         0.72         0.15

Net Gains or Losses on Securities
  (both realized and unrealized)                    4.56           5.62          3.37         3.91        (1.15)       (0.45)
                                             ---------------------------------------------------------------------------------

Total from Investment Operations                    4.52           5.75          3.66         4.45        (0.43)       (0.30)

LESS DISTRIBUTIONS

Dividends (from net investment income)             (0.10)         (0.19)        (0.21)       (0.68)       (0.84)        0.0

Distributions from Capital Gains (from
  securities and options transactions)             (1.63)         (1.16)        (0.86)       (0.56)       (0.71)        0.0
                                             ---------------------------------------------------------------------------------

Total Distributions                                (1.73)         (1.35)        (1.07)       (1.24)       (1.55)        0.0
                                             ---------------------------------------------------------------------------------

Net Asset Value, End of Period               $     32.88    $     30.09   $     25.69    $   23.10    $   19.89    $   21.87
                                             =================================================================================

Total Return                                       15.94%         23.59%        16.56%       23.51%       (1.95%)      (1.35%)
                                             ---------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA

Net Assets (in $millions), End of Period            0.3            0.1           0.0**        0.0**        0.0**        0.0**
                                             ---------------------------------------------------------------------------------

Ratio of Expenses (net)
  to Average Net Assets [1]                         2.0%'D'        2.0%          2.2%         2.3%         1.5%         1.5%'D'
                                             ---------------------------------------------------------------------------------

Ratio of Net Income to Average Net Assets        --                0.5%          1.2%         2.5%         3.6%         3.5%'D'
                                             ---------------------------------------------------------------------------------

Average Commission Rate***                   $      0.0670  $      0.0749 $       .0726       -.-          -.-          -.-

Portfolio Turnover Rate                            64.5%          59.4%         61.5%        78.3%        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.

***  Disclosure effective for fiscal year 1996 and all periods thereafter.

[1]  Had the Investment Adviser not agreed to reimburse Class C shares for
     expenses in excess of the expense limitation described in Note 6, the
     ratios of expenses to average net assets for the six months ended June 30,
     1998 and years ended December 31, 1997, 1996, 1995 and 1994 would have been
     2.0%, 2.5%, 2.5%, 2.5% and 2.5%, respectively, for Class C shares.





<PAGE>
 
<PAGE>

OFFICERS OF THE FUND
I.W. Burnham, II Chairman
Jon M. Burnham, President
     and Chief Executive Officer
Michael E. Barna, Executive Vice President
     Chief Financial Officer, Treasurer and Secretary
Debra B. Hyman, Executive Vice President
Ronald M. Geffen, Vice President
Frank A. Passantino, Vice President and
     Assistant Secretary
Louis S. Rosenthal, Vice President


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

SERVICING AGENT
Boston Financial Data Services, Inc.
2 Heritage Drive
North Quincy, Massachusetts 02171


http://www.burnhamfunds.com


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, 1998




- --------------------------------------------------------------------------------
                        CONTINUITY            KNOWLEDGE



                              [BURNHAM FUND LOGO]



                          GROWTH                INCOME
- --------------------------------------------------------------------------------






BURNHAM Securities Inc.
PRINCIPAL DISTRIBUTOR





                          STATEMENT OF DIFFERENCES
                          ------------------------

  The dagger symbol shall be expressed as................................ 'D'
  The double dagger symbol shall be expressed as......................... 'DD'





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