VAN KAMPEN CONVERTIBLE SECURITIES FUND
N-30D, 1999-02-24
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<PAGE>   1
 
- ---------------------------------------------------------------
                    TABLE OF CONTENTS
 
<TABLE>
<S>                                               <C>
Letter to Shareholders...........................  1
Performance Results..............................  3
Glossary of Terms................................  4
Portfolio Management Review......................  5
Portfolio of Investments.........................  8
Statement of Assets and Liabilities.............. 13
Statement of Operations.......................... 14
Statement of Changes in Net Assets............... 15
Financial Highlights............................. 16
Notes to Financial Statements.................... 18
Report of Independent Accountants................ 22
Dividend Reinvestment Plan....................... 23
</TABLE>
 
VXS ANR 2/99
<PAGE>   2
 
                             LETTER TO SHAREHOLDERS
 
January 20, 1999
 
Dear Shareholder,
    The past decade has been a remarkable time for investors. Together, we've
witnessed one of the greatest bull markets in investment history, unprecedented
growth in mutual fund investing, and a surge in personal retirement planning.
The coming millennium promises to hold even more opportunities.
    To lead us into this new era of investing, Richard F. Powers III has joined
Van Kampen as Chairman and Chief Executive Officer. He comes to us from our
parent company, Morgan Stanley Dean Witter & Co., where he served as Executive
Vice President and Director of Marketing. He brings 27 years of experience in
the financial services industry, including an extensive background in product
management, strategic planning and brand development.
    Although former Chairman Don G. Powell retired on January 1, he will remain
active in the industry and the community. Mr. Powell plans to continue his
service as a member of the board of directors of the Investment Company
Institute, the leading mutual fund industry association, and he will remain a
trustee of your fund.
 
ECONOMIC OVERVIEW
    Despite a stormy year in the global economy, the United States ended 1998
with only a moderate slowdown in growth. The nation's gross domestic product, a
measure of economic health, grew 3.9 percent during the year, matching 1997's
growth rate and indicating that our nation's economy remains strong. A
continuation of low inflation--only a 1.6 percent increase in the consumer price
index over the last 12 months--also helped sustain the domestic economy and kept
inflation-adjusted interest rates attractive.
    Although the year ended on a positive note, the economic environment was
quite unsettled in the third quarter, with the Asian financial crisis
contributing to slowing corporate profits in the United States. Given the
uncertainty surrounding emerging market nations and the near-collapse of a major
U.S. hedge fund, the stock and bond markets experienced significant volatility
during this period. With instability as a backdrop, American and foreign
investors alike pursued a flight to quality--seeking the relative safety of
large-company stocks and government bonds.
    In the last few months of the year the global financial situation improved
in conjunction with the Federal Reserve's interest rate decreases. In response
to declining corporate profits and mounting international concerns, the Fed
lowered interest rates three times, with 0.25 percent cuts in September,
October, and November. These rate cuts, coupled with a wave of corporate mergers
and cost-cutting measures, lent the support needed to keep the economy growing.
Dozens of foreign central banks also reduced interest rates in an effort to
stimulate their economies. These actions gave a boost to investor confidence and
encouraged a return to a more diversified range of investments in the last few
months of the year.
 
                                                             Continued on page 2
 
                                        1
<PAGE>   3
 
MARKET REVIEW
    Despite bouts of volatility, the stock market experienced impressive returns
during 1998. Large-company stocks were responsible for much of this as investors
favored the perceived stability of established, high-quality companies. The Dow
Jones Industrial Average rose more than 16 percent during the year and hit a
record high of 9374 in November before falling back to more moderate levels.
Technology companies generally fared well during the year, with the
technology-heavy Nasdaq composite index up almost 40 percent for the year. On
the other hand, commodity-based stocks--especially those of oil
companies--suffered from declining commodity prices. Small-company stocks also
significantly underperformed the rest of the market, with the Russell 2000 index
actually losing 3.45 percent during the 12-month period.
 
OUTLOOK
    Our outlook for the domestic economy is positive, and we anticipate
continued low inflation and healthy economic growth. However, the aftereffects
of the global economic slowdown may continue to put pressure on corporate
earnings in the first half of the year. Internationally, we anticipate that low
interest rates and declining inflation will lead to improvements in troubled
areas such as Asia and Latin America. With the successful launch of the euro,
the new European transnational currency, we believe that many foreign markets
will become increasingly attractive in 1999.
    In the long term, we are optimistic that the stock market will continue its
record growth, although we could experience additional volatility in the months
ahead if concerns about high stock valuations and increasing earnings pressure
become more pronounced. Combined with growing questions about corporate and
government reactions to the Year 2000 computer problem, we could see an
increasingly cautious market by mid-year.
    Additional details about your fund, including a question-and-answer section
with your portfolio management team, are provided in this report. As always, we
are pleased to have the opportunity to share with you the progress of your
investment.
 
Sincerely,
 
 
[SIG]                                 
Richard F. Powers III                  

Chairman                               
Van Kampen Asset Management Inc.       

[SIG]
Dennis J. McDonnell

President
Van Kampen Asset Management Inc.


 
                                        2
<PAGE>   4
 
           PERFORMANCE RESULTS FOR THE PERIOD ENDED DECEMBER 31, 1998
 
                     VAN KAMPEN CONVERTIBLE SECURITIES FUND
                            NYSE TICKER SYMBOL--VXS
 
 TOTAL RETURNS
 
<TABLE>
<S>                                                          <C>
One-year total return based on market price(1).............    2.05%
One-year total return based on NAV(2)......................    5.90%
 
 DISTRIBUTION RATE

Distribution rate as a % of closing common stock
  price(3)...............................................      4.23%

 SHARE VALUATIONS
 
Net asset value...........................................   $ 23.87
Closing common stock price................................   $19.875
One-year high common stock price (04/06/98)...............   $24.750
One-year low common stock price (10/14/98)................   $17.375
</TABLE>
 
(1)Total return based on market price assumes an investment at the market price
at the beginning of the period indicated, reinvestment of all distributions for
the period in accordance with the Fund's dividend reinvestment plan, and sale of
all shares at the closing stock price at the end of the period indicated.
 
(2)Total return based on net asset value (NAV) assumes an investment at the
beginning of the period indicated, reinvestment of all distributions for the
period, and sale of all shares at the end of the period, all at NAV.
 
(3)Distribution rate represents the quarterly annualized distributions of the
Fund at the end of the period and not the earnings of the Fund.
 
See the Prior Performance section of the current prospectus. An investment
should be made with an understanding of the risks that an investment in equity
securities entails. These include the risk that the financial condition of the
Issuers of the securities in the portfolio, or the condition of the stock market
in general, may worsen and therefore, the value of Fund shares may decline. Past
performance does not guarantee future results. Investment return and net asset
value will fluctuate with market conditions. Market volatility may have
adversely affected fund performance since December 31, 1998. Fund shares, when
redeemed, may be worth more or less than their original cost.
 
                                        3
<PAGE>   5
 
                               GLOSSARY OF TERMS
 
BOND: A debt security issued by a government or corporation that pays a
    bondholder a stated rate of interest and repays the principal at the
    maturity date.
 
DOW JONES INDUSTRIAL AVERAGE: The oldest and most widely recognized stock market
    average, which reflects the performance of 30 actively traded stocks of
    well-established, blue-chip companies.
 
CONVERTIBLE SECURITY: A security that can be exchanged for common stock at the
    option of the security holder for a specified price or rate. Examples
    include convertible bonds and convertible preferred stock.
 
CREDIT RATING: An evaluation of an issuer's credit history and capability of
    repaying obligations. Standard & Poor's and Moody's Investors Service are
    two companies that assign bond ratings. Standard & Poor's ratings range from
    a high of AAA to a low of D, while Moody's ratings range from a high of Aaa
    to a low of C.
 
CREDIT SPREAD: Also called quality spread, the difference in yield between
    higher-quality issues (such as Treasury securities) and lower-quality
    issues. Normally, lower-quality issues provide higher yields to compensate
    investors for the additional credit risk.
 
FLIGHT TO QUALITY: The flow of funds toward safer investments in times of
    marketplace uncertainty or fear.
 
INVESTMENT GRADE: Securities rated BBB and above by Standard & Poor's or Baa and
    above by Moody's Investor Services. Bonds rated below BBB or Baa are
    noninvestment grade.
 
INFLATION: A persistent and measurable rise in the general level of prices.
    Inflation is widely measured by the Consumer Price Index, an economic
    indicator that measures the change in the cost of purchased goods and
    services.
 
FEDERAL RESERVE BOARD (THE FED): The governing body of the Federal Reserve
    System, which is the central bank system of the United States. Its
    policy-making committee, called the Federal Open Market Committee, meets
    eight times a year to establish monetary policy and monitor the economic
    pulse of the United States.
 
FUNDAMENTALS: Characteristics of a company, such as revenue growth, earnings
    growth, financial strength, market share, and quality of management.
 
NET ASSET VALUE (NAV): The value of a fund share, calculated by deducting a
    fund's liabilities from the total assets applicable to common shareholders
    in its portfolio and dividing this amount by the number of common shares
    outstanding.
 
VALUATION: The estimated or determined worth of a stock, based on financial
    measures such as the stock's current price relative to earnings, revenue,
    book value, and cash flow.
 
VOLATILITY: A measure of the fluctuation in the market price of a security. A
    security that is volatile has frequent and large swings in price.
 
                                        4
<PAGE>   6
 
                          PORTFOLIO MANAGEMENT REVIEW
 
                     VAN KAMPEN CONVERTIBLE SECURITIES FUND
 
We recently spoke to the management team of the Van Kampen Convertible
Securities Fund about the key events and economic forces that shaped the markets
during the past 12 months. The team includes Christine Drusch, portfolio
manager; Matthew Hart and David McLaughlin, portfolio comanagers; and Stephen L.
Boyd, chief investment officer for equity investments. The following excerpts
reflect their views on the Fund's performance during the 12 months ended
December 31, 1998.
 
 Q    THE STOCK MARKET WAS UP, DOWN, AND UP AGAIN IN 1998. CAN YOU DESCRIBE SOME
      OF THE FACTORS THAT AFFECTED THE MARKET DURING THE REPORTING PERIOD?

 A    The stock market performed extremely well through mid-July, when the Dow
      Jones Industrial Average set a then-record high. Trouble was on the
      horizon, however, as investors began to fear that Asian economic trouble
would spread throughout the world and hurt U.S. corporate profits. By August 31
the Dow had fallen 19 percent from its high. The Russell 2000 fell harder--by
October 8 this index of small-capitalization stocks was down 37 percent from its
April high. Meanwhile, credit spreads between BB-rated corporate bonds and U.S.
Treasuries widened during the year--indicating a "flight to quality," or
investor preference for government bonds and investment-grade securities issued
by large-cap companies.
    Inflation remained tame, prompting the Federal Reserve Board to lower
interest rates in September and then again in October and November. After the
second cut in interest rates, investor confidence began to improve. Companies
began to report better-than-expected third-quarter earnings, reminding investors
that the U.S. economy, though slowing, was still fundamentally solid. The
volatile stock market began to rise again, with the Dow briefly setting a new
record in November before declining moderately from its high by year-end.
 
 Q    HOW DID THE CONVERTIBLE SECURITIES MARKET RESPOND?

 A    The convertibles market is composed primarily of securities issued by
      small-cap companies and has an average credit rating of BB-. Therefore,
      convertibles were hurt both by the underperformance of small-cap stocks
and the widening of credit spreads. Fortunately, as investor confidence rose,
small caps did perform well during the year's final quarter, so convertibles
were able to make up most of the ground lost during the difficult period between
July and October. Accordingly, the Merrill Lynch Convertible Index returned 13.8
percent in the fourth quarter.

 Q    GIVEN THIS ENVIRONMENT, WHAT WAS YOUR STRATEGY FOR MANAGING THE FUND?

 A    We did not change our investment strategy in response to market
      conditions--we consistently manage the Fund for capital appreciation,
      current income, and
 
                                        5
<PAGE>   7
 
preservation of capital by investing primarily in convertible securities. In
seeking to meet this objective, we focus on growth companies and diversify
across market sectors.
    When selecting convertibles in which to invest, we first examine the equity
characteristics of the securities. We look for companies with improving
fundamentals, strong earnings growth, increasing market share, and attractive
valuations. After we have determined which companies represent what we believe
are attractive equity investments, we then examine the company's convertible
bonds to assess how likely they are to provide us with equity participation. If
it appears likely, we normally invest in the security.
 
 Q    WHAT SECTORS AND SPECIFIC HOLDINGS MOST HELPED THE FUND?

 A    Technology companies performed very well during the reporting period. At
      the beginning of the year, the Fund's technology weighting was just 7
      percent of the Fund. We gradually increased this weighting--eventually to
29 percent--as we realized the sector's fundamentals were improving.
    Beginning in July we added a sizeable position in semiconductor securities
because we believed that the companies would soon correct the inventory buildup
that had plagued the industry and had reduced revenue and earnings. These
companies began to perform well in the fourth quarter, and our investment in
them contributed to the Fund's outperformance of the Merrill Lynch Convertible
Index between October and December. Among the Fund's best performers in the
technology sector were SCI Systems (electronics manufacturer), Micron Technology
(computer and microchip manufacturer), Level One Communications (microchip
manufacturer), EMC (data storage company), and America Online (Internet service
provider).
    The combination of low inflation, low unemployment, and high consumer
spending helped increase the stock prices of retail companies. Retailers made up
a significant portion of the Fund's portfolio, benefiting the Fund's
performance. Some of the companies in this sector that particularly helped the
Fund were AnnTaylor (women's apparel), Staples (office supplies), and Home Depot
(home improvement products).
 
 Q    DID ANY SECTORS OR SPECIFIC HOLDINGS HURT THE FUND?

 A    Most financial companies performed very well in the first half of the
      year, but they encountered a particularly difficult third quarter because
      of exposure to emerging markets. Although we maintained a relatively small
weighting in financial companies, the Fund was nevertheless hurt by their poor
performance in the second half of 1998. Equitable Companies, Citigroup, and
Conseco were among the financial stocks that had a negative impact on the Fund.
    Despite the successes of most of our semiconductor holdings, our investment
in microchip manufacturer VLSI Technology didn't turn out as anticipated. In
mid-summer we decided to purchase VLSI's common stock at $14 per share because
we thought the company was attractively priced relative to its fundamentals. A
week later, however, the company announced unfavorable news about its earnings,
and the stock's value fell by
 
                                        6
<PAGE>   8
 
half shortly thereafter. In response to the new information and a reevaluation
of VLSI's future prospects, we sold our position at a loss.
    Many telecommunications companies were also hit hard by the third-quarter
market sell-off. These companies rely heavily on outside funding to finance
their growth, and investors were concerned that such funding would become more
expensive and difficult to obtain. The Fund owned securities in Smartalk,
Omnipoint, Nextlink, and Premiere Technologies, all of which had a negative
impact on the Fund's performance.
 
 Q    HOW DID THE FUND PERFORM DURING THE REPORTING PERIOD?

 A    For the 12 months ended December 31, 1998, the Fund generated a total
      return of 5.90 percent(2) at net asset value and 2.05 percent(1) at market
      price. The Fund's return reflects the change in market price per share on
the New York Stock Exchange from $21.125 on December 31, 1997, to $19.875 on
December 31, 1998, and dividends and capital gains totaling $1.8228 per share.
Please refer to the chart on page 3 for additional Fund performance results.

 Q    WHAT DO YOU SEE AHEAD FOR THE FUND FOR THE NEXT SIX MONTHS?

 A    We believe there are a number of uncertainties as we move into 1999.
      Sagging economies in Japan and Latin America will continue to affect
      markets worldwide, while easing consumer demand at home could slow the
U.S. economy. Credit spreads are still wide, reflecting investors' continued
cautiousness. This is not necessarily the best environment for convertible
securities. Convertibles are predominantly issued by small- and mid-cap
companies, investing in which usually carries a higher-than-average degree of
risk.
    On the plus side, small-cap stocks remain undervalued relative to large-cap
stocks, and small caps have typically outperformed during cyclical recoveries.
If the global economy stabilizes and the Fed can successfully sustain the U.S.
economy, the convertible market could benefit.
    Either way, we intend to continue with our strategy of investing in those
companies we believe offer the best combination of sound fundamentals and
potential for positive returns relative to the market. If a market decline does
occur, investors could benefit from the level of downside protection that
convertibles typically have offered relative to the broader equity market.
 
[SIG]
Christine Drusch

Portfolio Manager
 
[SIG]
David McLaughlin

Portfolio Comanager
 
[SIG]
Matthew Hart

Portfolio Comanager
 
[SIG]
Stephen L. Boyd

Chief Investment Officer
Equity Investments
 
                                                  Please see footnotes on page 3
 
                                        7
<PAGE>   9
 
                            PORTFOLIO OF INVESTMENTS
 
                               December 31, 1998
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
  Par
Amount
 (000)                      Description                    Coupon    Maturity  Market Value
- -------------------------------------------------------------------------------------------
<C>       <S>                                              <C>       <C>       <C>
          CONVERTIBLE DEBT  55.0%
          CONSUMER DISTRIBUTION  2.8%
$   850   Central Garden & Pet Co. ......................   6.000%   11/15/03  $   714,000
    530   Home Depot, Inc. ..............................   3.250    10/01/01    1,416,425
                                                                               -----------
                                                                                 2,130,425
                                                                               -----------
          CONSUMER DURABLES  1.0%
  1,690   Lennar Corp....................................       *    07/29/18      764,725
                                                                               -----------
          CONSUMER NON-DURABLES  0.9%
    850   Loews Corp. ...................................   3.125    09/15/07      682,125
                                                                               -----------
          CONSUMER SERVICES  5.6%
    370   Interim Services, Inc. ........................   4.500    06/01/05      334,388
  1,100   Jacor Communications, Inc., LYON...............       *    02/09/18      530,750
    600   Mail Well, Inc. ...............................   5.000    11/01/02      543,000
    880   Metamor Worldwide, Inc. .......................   2.940    08/15/04      688,600
  1,800   News America Holdings, Inc., LYON..............       *    03/11/13    1,035,000
    200   Omnicom Group, Inc. ...........................   4.250    01/03/07      381,000
    700   Personnel Group of America, Inc., 144A--Private
          Placement (a)..................................   5.750    07/01/04      813,750
                                                                               -----------
                                                                                 4,326,488
                                                                               -----------
          ENERGY  1.8%
    500   Conxus Communications, Inc., 144A--Private
          Placement (a)..................................   9.000    05/15/01      450,000
    310   Diamond Offshore Drilling, Inc. ...............   3.750    02/15/07      287,138
    698   Pennzoil Co. ..................................   4.950    08/15/08      684,040
                                                                               -----------
                                                                                 1,421,178
                                                                               -----------
          FINANCE  1.5%
STRYPES   Merrill Lynch & Co., Inc., 15,900 shares
          (Convertible into 24,462 CIBER, Inc. common
          shares)........................................   7.875    02/01/01      863,012
STRYPES   Merrill Lynch & Co., Inc., 5,500 shares
          (Convertible into Cox Communication common
          shares)........................................   6.000    06/01/99      313,538
                                                                               -----------
                                                                                 1,176,550
                                                                               -----------
          HEALTHCARE  8.0%
    850   Atrix Labs, Inc. 144A--Private Placement
          (a) ...........................................   7.000    12/01/04      612,000
    400   Elan Finance Corp., Ltd., LYON.................       *    12/14/18      226,250
    640   Fuisz Technologies, Ltd., 144A--Private
          Placement (a)..................................   7.000    10/15/04      691,200
    590   Genzyme Corp., 144A--Private Placement (a).....   5.250    06/01/05      842,225
    850   Healthsouth Corp., 144A--Private Placement
          (a)............................................   3.250    04/01/03      726,750
    450   Renal Treatment Centers, Inc. .................   5.625    07/15/06      540,563
  2,450   Roche Holdings, Inc., LYON, 144A--Private
          Placement (a)..................................       *    04/20/10    1,583,312
    270   Sunrise Assisted Living........................   5.500    06/15/02      405,000
    541   Total Renal Care Holdings, Inc., 144A--Private
          Placement (a)..................................   7.000    05/15/09      588,337
                                                                               -----------
                                                                                 6,215,637
                                                                               -----------
</TABLE>
 
                                               See Notes to Financial Statements
 
                                        8
<PAGE>   10
                      PORTFOLIO OF INVESTMENTS (CONTINUED)
 
                               December 31, 1998
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
  Par
Amount
 (000)                      Description                    Coupon    Maturity  Market Value
- -------------------------------------------------------------------------------------------
<C>       <S>                                              <C>       <C>       <C>
          PRODUCER MANUFACTURING  3.9%
$   370   Antec Corp., 144A--Private Placement (a).......   4.500%   05/15/03  $   364,450
    730   U. S. Filter Corp..............................   4.500    12/15/01      683,463
  1,980   WMX Technologies, Inc..........................   2.000    01/24/05    1,937,925
                                                                               -----------
                                                                                 2,985,838
                                                                               -----------
          TECHNOLOGY  26.6%
    930   Adaptec, Inc...................................   4.750    02/01/04      720,750
  1,470   Advanced Micro Devices, Inc....................   6.000    05/15/05    1,517,775
    750   Affiliated Computer Services, Inc.
          144A--Private Placement (a)....................   4.000    03/15/05      906,562
    190   America Online, Inc............................   4.000    11/15/02    1,072,074
    795   Amkor Technology, Inc..........................   5.750    05/01/03      791,025
    370   Automatic Data Processing, Inc., LYON..........       *    02/20/12      381,563
    500   Candescent Technologies Corp., 144A--Private
          Placement (a)..................................   7.000    05/01/03      450,000
  2,275   Comverse Technology, Inc., 144A--Private
          Placement (a)..................................   4.500    07/01/05    2,857,969
  1,340   DSC Communications Corp........................   7.000    08/01/04    1,405,325
    150   EMC Corp.......................................   3.250    03/15/02      562,875
  2,560   Hewlett Packard Co., LYON......................       *    10/14/17    1,424,000
    360   Kellstrom Industries, Inc......................   5.500    06/15/03      381,600
    365   Level One Communications, Inc..................   4.000    09/01/04      536,550
    580   May & Speh, Inc................................   5.250    04/01/03      971,500
    940   Micron Technology, Inc.........................   7.000    07/01/04    1,004,625
    870   Network Associates, Inc........................       *    02/13/18      522,000
    975   Network Associates, Inc., 144A--Private
          Placement (a)..................................       *    02/13/18      585,000
    350   Oak Industries, Inc............................   4.875    03/01/08      369,250
    480   Platinum Technology, Inc.......................   6.750    11/15/01      699,600
    413   Premiere Technologies, Inc.....................   5.750    07/01/04      225,085
    512   QuadraMed Corp., 144A--Private Placement (a)...   5.250    05/01/05      440,320
    400   Quantum Corp...................................   7.000    08/01/04      383,000
    350   SCI Systems, Inc., 144A--Private Placement
          (a)............................................   5.000    05/01/06      831,250
    920   STMicroelectronics NV, LYON....................       *    06/10/08      815,350
    270   Veritas Software Corp..........................   5.250    11/01/04      430,650
    250   Wind River Systems, Inc........................   5.000    08/01/02      291,250
                                                                               -----------
                                                                                20,576,948
                                                                               -----------
          UTILITIES  2.9%
   PIES   MediaOne Group, Inc., 10,800 shares
          (Convertible into 8,749 Air Touch
          Communications, Inc. common shares)............   6.250    08/15/01      713,189
    700   NTL, Inc., 144A--Private Placement (a).........   7.000    12/15/08      758,625
   DECS   Sprint Corp., 9,500 shares (Convertible into
          14,476 SBC Communications, Inc. common
          shares)........................................   8.250    03/31/00      783,611
                                                                               -----------
                                                                                 2,255,425
                                                                               -----------
TOTAL CONVERTIBLE DEBT  55.0%................................................   42,535,339
                                                                               -----------
</TABLE>
 
                                               See Notes to Financial Statements
 
                                        9
<PAGE>   11
                      PORTFOLIO OF INVESTMENTS (CONTINUED)
 
                               December 31, 1998
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                        Description                             Shares    Market Value
- --------------------------------------------------------------------------------------
<S>                                                             <C>       <C>
PREFERRED STOCK  27.9%
CONSUMER DISTRIBUTION  3.7%
AnnTaylor Finance Trust, 8.50%..............................     8,500    $   852,656
CVS Automatic Common Exchange Security Trust, 6.00%.........     8,500        851,594
Kmart Financing I Trust, 7.75%..............................     6,200        359,213
McKesson Financing Trust, 5.00%.............................     7,150        778,456
                                                                          -----------
                                                                            2,841,919
                                                                          -----------
CONSUMER DURABLES  0.7%
Fleetwood Capital Trust, 6.00%, 144A--Private Placement
  (a).......................................................    10,750        513,313
                                                                          -----------
CONSUMER NON-DURABLES  0.6%
Ralston Purina Co., 7.00%...................................     9,000        463,782
                                                                          -----------
CONSUMER SERVICES  2.2%
Chancellor Media Corp., 7.00%...............................     4,300        584,800
CSC Holdings, Inc., 8.50%...................................    12,500        942,187
Host Marriott Financial Trust, QUIPS, 6.75%, 144A--Private
  Placement (a).............................................     5,000        206,250
                                                                          -----------
                                                                            1,733,237
                                                                          -----------
ENERGY  3.9%
El Paso Energy Capital Trust I, 4.75%.......................    22,500      1,077,187
Tosco Financing Trust, 5.75%................................    10,000        487,500
Unocal Capital Trust, 6.25%.................................    30,000      1,466,250
                                                                          -----------
                                                                            3,030,937
                                                                          -----------
FINANCE  6.0%
Amerus Life Holdings, Inc., 7.00%...........................    17,400        417,600
Conseco, Inc., PRIDES, 7.00%................................    23,200        894,650
Finova Finance Trust, 5.50%.................................    10,000        743,125
General Growth Properties, Inc., 7.25%......................    17,600        453,200
Life Re Corp. Capital Trust II, QUIPS, 6.00%................     5,700        436,050
National Australia Bank, Ltd., 7.875%.......................    27,000        752,625
Philadelphia Consolidated Holdings, PRIDES, 7.00%...........    38,200        382,000
PLC Capital Trust II, 6.50%.................................     9,000        587,250
                                                                          -----------
                                                                            4,666,500
                                                                          -----------
HEALTHCARE  0.5%
Alkermes, Inc., 6.50%.......................................     9,000        408,375
                                                                          -----------
PRODUCER MANUFACTURING  1.3%
Coltec Capital Trust, 5.25%, 144A--Private Placement (a)....     8,100        352,350
Ingersoll-Rand Co., PRIDES, 6.75%...........................    28,500        676,875
                                                                          -----------
                                                                            1,029,225
                                                                          -----------
RAW MATERIALS/PROCESSING INDUSTRIES  0.7%
Monsanto Co., 6.50%, ACES (b)...............................    10,150        497,350
                                                                          -----------
</TABLE>
 
                                               See Notes to Financial Statements
 
                                       10
<PAGE>   12
                      PORTFOLIO OF INVESTMENTS (CONTINUED)
 
                               December 31, 1998
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                        Description                             Shares    Market Value
- --------------------------------------------------------------------------------------
<S>                                                             <C>       <C>
TECHNOLOGY  1.1%
Nextlink Communications, Inc., 6.50%, 144A--Private
  Placement (a).............................................    11,400    $   470,250
Tribune Co., 6.25%..........................................    15,200        370,910
                                                                          -----------
                                                                              841,160
                                                                          -----------
TRANSPORTATION  1.3%
Tower Automotive Capital Trust, 6.75%, 144A--Private
  Placement (a) (b).........................................    20,000      1,030,000
                                                                          -----------
UTILITIES  5.9%
CalEnergy Capital Trust III, 6.50%..........................    20,000        973,750
Houston Industries, Inc., ACES, 7.00%.......................     8,650        920,144
Nextel Trust, STRYPES, 7.25%................................    25,000        512,500
Omnipoint Corp., 7.00%, 144A--Private Placement (a).........    28,900        722,500
Texas Utilities Co., PRIDES, 9.25%..........................    25,000      1,409,375
                                                                          -----------
                                                                            4,538,269
                                                                          -----------
TOTAL PREFERRED STOCK  27.9%..........................................     21,594,067
                                                                          -----------
COMMON STOCKS  7.3%
ENERGY  1.1%
British Petroleum Co. PLC--ADR (United Kingdom).............     9,600        860,400
                                                                          -----------
FINANCE  0.9%
U.S. Bancorp................................................     9,200        326,600
Washington Mutual, Inc......................................     9,707        370,686
                                                                          -----------
                                                                              697,286
                                                                          -----------
TECHNOLOGY  1.9%
Motorola, Inc...............................................     5,500        335,844
Quantum Corp. (b)...........................................    20,000        425,000
Unisys Corp. (b)............................................    20,000        688,750
                                                                          -----------
                                                                            1,449,594
                                                                          -----------
TRANSPORTATION  0.6%
FDX Corp. (b)...............................................     5,000        445,000
                                                                          -----------
UTILITIES  2.8%
AT & T Corp.................................................    13,000        978,250
MCI Worldcom, Inc. (b)......................................    16,610      1,191,767
                                                                          -----------
                                                                            2,170,017
                                                                          -----------
TOTAL COMMON STOCKS...................................................      5,622,297
                                                                          -----------
TOTAL LONG-TERM INVESTMENTS  90.2%
  (cost $63,775,077)..................................................     69,751,703
                                                                          -----------
</TABLE>
 
                                               See Notes to Financial Statements
 
                                       11
<PAGE>   13
                      PORTFOLIO OF INVESTMENTS (CONTINUED)
 
                               December 31, 1998
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                             Description                                  Market Value
- --------------------------------------------------------------------------------------
<S>                                                                       <C>
SHORT-TERM INVESTMENTS  9.2%
REPURCHASE AGREEMENTS  4.1%
BA Securities ($3,175,000 par collateralized by U.S. Government
  obligations in a pooled cash account, 4.90% coupon, dated 12/31/98,
  to be sold on 01/04/99 at $3,176,729) (c)...........................    $ 3,175,000
U.S. GOVERNMENT AGENCY OBLIGATIONS  1.3%
Federal National Mortgage Association Discount Notes ($1,000,000 par,
  yielding 5.095%, 01/04/99 maturity).................................        999,581
COMMERCIAL PAPER  3.8%
General Electric Capital Corp. ($3,000,000 par, yielding 5.003%,
  01/04/99 maturity) (c)..............................................      2,998,333
                                                                          -----------
TOTAL SHORT-TERM INVESTMENTS
  (Cost $7,172,914)...................................................      7,172,914
                                                                          -----------
TOTAL INVESTMENTS  99.4%
  (Cost $70,947,991)..................................................     76,924,617
OTHER ASSETS IN EXCESS OF LIABILITIES  0.6%...........................        451,964
                                                                          -----------
NET ASSETS  100.0%....................................................    $77,376,581
                                                                          ===========
</TABLE>
 
* Zero coupon bond
 
(a) 144A Securities are those which are exempt from registration under Rule 144A
    of the Securities Act of 1993. These securities may only be resold in
    transactions exempt from registration which are normally transactions with
    qualified institutional buyers.
 
(b) Non-income producing security as this stock currently does not declare
    dividends.
 
(c) Assets segregated as collateral for open futures.
 
ACES--Automatically convertible equity securities
ADR--American depository receipts
DECS--Debt exchangeable for common stock, traded in shares
LYON--Liquid yield option note
PIES--Premium Income Exchangeable Securities, traded in shares
PRIDES--Preferred redeemable interest dividend equity security, traded in shares
QUIPS--Quarterly income preferred securities
STRYPES--Structured yield product exchangeable for stock, traded in shares
 
                                               See Notes to Financial Statements
 
                                       12
<PAGE>   14
 
                      STATEMENT OF ASSETS AND LIABILITIES
 
                               December 31, 1998
- --------------------------------------------------------------------------------
 
<TABLE>
<S>                                                           <C>
ASSETS:
Total Investments (Cost $70,947,991)........................  $76,924,617
Receivables:
  Investments Sold..........................................      584,246
  Interest..................................................      424,449
  Dividends.................................................       43,480
  Variation Margin on Futures...............................       12,750
Other.......................................................       47,845
                                                              -----------
      Total Assets..........................................   78,037,387
                                                              -----------
LIABILITIES:
Payables:
  Income Distributions......................................      369,237
  Investments Purchased.....................................      186,354
  Investment Advisory Fee...................................       31,942
  Affiliates................................................        2,974
  Custodian Bank............................................        1,090
Accrued Expenses............................................       42,772
Trustees' Deferred Compensation and Retirement Plans........       26,437
                                                              -----------
      Total Liabilities.....................................      660,806
                                                              -----------
NET ASSETS..................................................  $77,376,581
                                                              ===========
NET ASSETS CONSIST OF:
Common Shares ($1.00 par value with 12,500,000 shares
  authorized, 3,251,324 shares issued, of which 9,500 are
  held in treasury and 3,241,824 are outstanding)...........  $ 3,241,824
Paid in Surplus.............................................   68,041,601
Net Unrealized Appreciation.................................    6,226,819
Accumulated Undistributed Net Investment Income.............      258,861
Accumulated Net Realized Loss...............................     (392,524)
                                                              -----------
NET ASSETS..................................................  $77,376,581
                                                              ===========
NET ASSET VALUE PER SHARE ($77,376,581 divided by 3,241,824
  shares outstanding).......................................  $     23.87
                                                              ===========
</TABLE>
 
                                               See Notes to Financial Statements
 
                                       13
<PAGE>   15
 
                            STATEMENT OF OPERATIONS
 
                      For the Year Ended December 31, 1998
- --------------------------------------------------------------------------------
 
<TABLE>
<S>                                                           <C>
 
INVESTMENT INCOME:
Interest....................................................  $2,452,889
Dividends...................................................   1,092,330
                                                              ----------
      Total Income..........................................   3,545,219
                                                              ----------
EXPENSES:
Investment Advisory Fee.....................................     387,209
Shareholder Reports.........................................      65,489
Shareholder Services........................................      45,392
Accounting..................................................      37,371
Custody.....................................................      22,900
Trustees' Fees and Expenses.................................      13,402
Legal.......................................................       8,567
Other.......................................................      60,077
                                                              ----------
      Total Expenses........................................     640,407
                                                              ----------
NET INVESTMENT INCOME.......................................  $2,904,812
                                                              ==========
REALIZED AND UNREALIZED GAIN/LOSS:
Net Realized Gain...........................................  $  910,780
                                                              ----------
Unrealized Appreciation/Depreciation:
  Beginning of the Period...................................   5,421,338
                                                              ----------
  End of the Period:
    Investments.............................................   5,976,626
    Futures.................................................     250,193
                                                              ----------
                                                               6,226,819
                                                              ----------
Net Unrealized Appreciation During the Period...............     805,481
                                                              ----------
NET REALIZED AND UNREALIZED GAIN............................  $1,716,261
                                                              ==========
NET INCREASE IN NET ASSETS FROM OPERATIONS..................  $4,621,073
                                                              ==========
</TABLE>
 
                                               See Notes to Financial Statements
 
                                       14
<PAGE>   16
 
                       STATEMENT OF CHANGES IN NET ASSETS
 
                 For the Years Ended December 31, 1998 and 1997
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                         Year Ended           Year Ended
                                                      December 31, 1998    December 31, 1997
- --------------------------------------------------------------------------------------------
<S>                                                   <C>                  <C>
FROM INVESTMENT ACTIVITIES:
Operations:
Net Investment Income...............................    $  2,904,812         $  3,260,007
Net Realized Gain...................................         910,780           11,981,751
Net Unrealized Appreciation/Depreciation During the
  Period............................................         805,481           (2,210,905)
                                                        ------------         ------------
Change in Net Assets from Operations................       4,621,073           13,030,853
                                                        ------------         ------------
Distributions from Net Investment Income............      (2,851,284)          (3,260,007)
Distributions in Excess of Net Investment Income....             -0-             (562,429)
                                                        ------------         ------------
Distributions from and in Excess of Net Investment
  Income............................................      (2,851,284)          (3,822,436)
Distributions from Net Realized Gain................      (3,056,743)          (9,810,855)
                                                        ------------         ------------
Total Distributions.................................      (5,908,027)         (13,633,291)
                                                        ------------         ------------
NET CHANGE IN NET ASSETS FROM INVESTMENT
  ACTIVITIES........................................      (1,286,954)            (602,438)
NET ASSETS:
Beginning of the Period.............................      78,663,535           79,265,973
                                                        ------------         ------------
End of the Period (Including accumulated
  undistributed net investment income of $258,861
  and $205,333, respectively).......................    $ 77,376,581         $ 78,663,535
                                                        ============         ============
</TABLE>
 
                                               See Notes to Financial Statements
 
                                       15
<PAGE>   17
 
                              FINANCIAL HIGHLIGHTS
 
  The following schedule presents financial highlights for one common share of
             the Fund outstanding throughout the periods indicated.
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                          ---------------------------------
                                                           1998         1997         1996
- -------------------------------------------------------------------------------------------
<S>                                                       <C>          <C>          <C>
Net Asset Value, Beginning of the Period............      $24.265      $24.451      $ 24.41
                                                          -------      -------      -------
  Net Investment Income.............................         .896        1.006         .968
  Net Realized and Unrealized Gain/Loss.............         .530        3.014        1.768
                                                          -------      -------      -------
Total from Investment Operations....................        1.426        4.020        2.736
                                                          -------      -------      -------
Less:
  Distributions from and in Excess of Net Investment
    Income..........................................         .880        1.179        1.005
  Distributions from and in Excess of Net Realized
    Gain............................................         .943        3.027        1.690
                                                          -------      -------      -------
Total Distributions.................................        1.823        4.206        2.695
                                                          -------      -------      -------
Net Asset Value, End of the Period..................      $23.868      $24.265      $24.451
                                                          =======      =======      =======
Market Price Per Share at End of the Period.........      $19.875      $21.125      $21.125
Total Investment Return at Market Price (a,c).......        2.05%       19.48%       11.67%
Total Return at Net Asset Value (b,c)...............        5.90%       18.57%       11.51%
Net Assets at End of the Period (In millions).......      $  77.4      $  78.7      $  79.3
Ratio of Expenses to Average Net Assets.............         .83%         .76%         .88%
Ratio of Net Investment Income to Average Net
  Assets............................................        3.75%        3.86%        3.88%
Portfolio Turnover..................................         157%         181%         140%
</TABLE>
 
(a) Total Investment Return at Market Price reflects the change in market value
    of the shares for the period indicated with reinvestment of dividends in
    accordance with the Fund's dividend reinvestment plan.
 
(b) Total Return at Net Asset Value (NAV) reflects the change in value of the
    Fund's assets with reinvestment of dividends based upon NAV.
 
(c) This disclosure was not required in fiscal years prior to 1992.
 
                                       16
<PAGE>   18
 
- --------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
Year Ended December 31,
- ----------------------------------------------------------------------------
      1995      1994      1993      1992      1991      1990      1989
- ----------------------------------------------------------------------------
<C>            <C>       <C>       <C>       <C>       <C>       <C>     
     $ 21.62   $ 24.88   $ 23.64   $ 22.23   $ 19.41   $ 22.73    $21.94
     -------   -------   -------   -------   -------   -------   -------
        1.14      1.09      1.15     1.175      1.32      1.47      1.51
      3.5325     (2.56)     2.01     1.415      2.90   (3.2475)    1.595
     -------   -------   -------   -------   -------   -------   -------
      4.6725     (1.47)     3.16      2.59      4.22   (1.7775)    3.105
     -------   -------   -------   -------   -------   -------   -------
        1.15      1.10      1.12      1.18      1.40      1.40      1.57
       .7325       .69       .80       -0-       -0-     .1425      .745
     -------   -------   -------   -------   -------   -------   -------
      1.8825      1.79      1.92      1.18      1.40    1.5425     2.315
     -------   -------   -------   -------   -------   -------   -------
     $ 24.41   $ 21.62   $ 24.88   $ 23.64   $ 22.23   $ 19.41   $ 22.73
     =======   =======   =======   =======   =======   =======   =======
     $21.375   $18.125   $22.375   $20.375   $19.250   $16.625   $20.125
      28.88%   (11.71%)   19.43%    12.31%    24.68%   (10.39%)       --
      23.42%    (5.29%)   14.50%    12.84%    23.32%    (7.37%)       --
       $79.1     $70.1     $80.7     $76.6     $72.1     $62.9     $73.7
        .80%      .82%      .87%      .88%      .89%      .86%      .84%
       4.82%     4.70%     4.60%     5.28%     6.41%     7.01%     6.47%
        127%      111%      128%       87%      168%       95%       90%
</TABLE>
 
                                              See Notes to Financial Statements.
 
                                       17
<PAGE>   19
 
                         NOTES TO FINANCIAL STATEMENTS
 
                               December 31, 1998
- --------------------------------------------------------------------------------
 
1. SIGNIFICANT ACCOUNTING POLICIES
 
Van Kampen Convertible Securities Fund, formerly known as Van Kampen American
Capital Convertible Securities Fund (the "Fund"), is registered as a diversified
closed-end management investment company under the Investment Company Act of
1940, as amended. The Fund's investment objective is to provide current income,
capital appreciation and conservation of capital through investment in a
portfolio consisting mainly of convertible bonds and preferred stocks.
 
    The following is a summary of significant accounting policies consistently
followed by the Fund in the preparation of its financial statements. 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 and disclosure of
contingent assets and liabilities at the date of the financial statements and
the reported amounts of revenues and expenses during the reporting period.
Actual results could differ from those estimates.
 
A. SECURITY VALUATION--Fixed income investments and preferred stock are stated
at value using market quotations or indications of value obtained from an
independent pricing service. Investments in securities listed on a securities
exchange are valued at their sales price as of the close of such securities
exchange. Unlisted securities and listed securities for which the last sales
price is not available are valued at the mean of the bid and asked prices. For
those securities where quotations or prices are not available, valuations are
determined in accordance with procedures established in good faith by the Board
of Trustees. Short-term securities with remaining maturities of 60 days or less
are valued at amortized cost.
 
    Fund investments include lower rated debt securities which may be more
susceptible to adverse economic conditions than other investment grade holdings.
These securities are often subordinated to the prior claims of other senior
lenders and uncertainties exist as to an issuer's ability to meet principal and
interest payments. Debt securities rated below investment grade and comparable
unrated securities represented approximately 41% of the investment portfolio at
the end of the period.
 
B. SECURITY TRANSACTIONS--Security transactions are recorded on a trade date
basis. Realized gains and losses are determined on an identified cost basis.
 
    The Fund may invest in repurchase agreements, which are short-term
investments whereby the Fund acquires ownership of a debt security and the
seller agrees
 
                                       18
<PAGE>   20
                   NOTES TO FINANCIAL STATEMENTS (CONTINUED)
 
                               December 31, 1998
- --------------------------------------------------------------------------------
 
to repurchase the security at a future time and specified price. The Fund may
invest independently in repurchase agreements or transfer uninvested cash
balances into a pooled cash account along with other investment companies
advised by Van Kampen Asset Management Inc. (the "Adviser") or its affiliates,
the daily aggregate of which is invested in repurchase agreements. Repurchase
agreements are fully collateralized by the underlying debt security. The Fund
will make payment for such securities only upon physical delivery or evidence of
book entry transfer to the account of the custodian bank. The seller is required
to maintain the value of the underlying security at not less than the repurchase
proceeds due the Fund.
 
C. INVESTMENT INCOME--Interest income is recorded on an accrual basis and
dividend income is recorded on the ex-dividend date. Discounts are amortized
over the expected life of each applicable security. Premiums on debt securities
are not amortized.
 
D. FEDERAL INCOME TAXES--It is the Fund's policy to comply with the requirements
of the Internal Revenue Code applicable to regulated investment companies and to
distribute substantially all of its taxable income to its shareholders.
Therefore, no provision for federal income taxes is required.
 
    At December 31, 1998, for federal income tax purposes the cost of long- and
short-term investments is $70,957,145, the aggregate gross unrealized
appreciation is $9,220,750 and the aggregate gross unrealized depreciation is
$3,253,278, resulting in net unrealized appreciation on long- and short-term
investments of $5,967,472. Net realized gains or losses may differ for financial
reporting and tax purposes primarily as a result of wash sales and the mark to
market of open futures contracts at December 31, 1998.
 
E. DISTRIBUTION OF INCOME AND GAINS--The Fund declares and pays quarterly
dividends from net investment income. Net realized gains, if any, are
distributed annually. Distributions from net realized gains for book purposes
may include short-term capital gains which are included in ordinary income for
tax purposes.
 
    For federal income tax purposes, the following information is furnished with
respect to the distributions paid by the Fund during its taxable year ended
December 31, 1998. The Fund designated and paid a 20% rate gain distribution of
$3,056,079. In January 1999, the Fund provided tax information to shareholders
for 1998.
 
                                       19
<PAGE>   21
                   NOTES TO FINANCIAL STATEMENTS (CONTINUED)
 
                               December 31, 1998
- --------------------------------------------------------------------------------
 
2. INVESTMENT ADVISORY AGREEMENT AND OTHER TRANSACTIONS WITH AFFILIATES
 
Under the terms of the Fund's Investment Advisory Agreement, the Adviser will
provide investment advice and facilities to the Fund for an annual fee payable
monthly as follows:
 
<TABLE>
<CAPTION>
                   AVERAGE NET ASSETS                     % PER ANNUM
- ---------------------------------------------------------------------
<S>                                                       <C>
First $150 million.......................................  .50 of 1%
Next $100 million........................................  .45 of 1%
Next $100 million........................................  .40 of 1%
Over $350 million........................................  .35 of 1%
</TABLE>
 
    For the year ended December 31, 1998, the Fund recognized expenses of
approximately $8,600, representing legal services provided by Skadden, Arps,
Slate, Meagher & Flom (Illinois), counsel to the Fund, of which a trustee of the
Fund is an affiliated person.
 
    For the year ended December 31, 1998, the Fund recognized expenses of
approximately $37,400, representing Van Kampen Funds Inc.'s or its affiliates
(collectively "Van Kampen") cost of providing accounting services to the Fund.
 
    Certain officers and trustees of the Fund are also officers and directors of
Van Kampen. The Fund does not compensate its officers or trustees who are
officers of Van Kampen.
 
    The Fund provides deferred compensation and retirement plans for its
trustees who are not officers of Van Kampen. Under the deferred compensation
plan, trustees may elect to defer all or a portion of their compensation to a
later date. Benefits under the retirement plan are payable for a ten-year period
and are based upon each trustee's years of service to the Fund. The maximum
annual benefit per trustee under the plan is $2,500.
 
3. INVESTMENT TRANSACTIONS
 
During the period, the cost of purchases and proceeds from sales of investments,
excluding short-term investments, were $113,060,207 and $121,156,933,
respectively.
 
4. DERIVATIVE FINANCIAL INSTRUMENTS
 
A derivative financial instrument in very general terms refers to a security
whose value is "derived" from the value of an underlying asset, reference rate
or index.
 
    The Fund has a variety of reasons to use derivative instruments, such as to
attempt to protect the Fund against possible changes in the market value of its
portfolio or generate potential gain. All of the Fund's portfolio holdings,
including derivative instruments, are marked to market each day with the change
in value reflected in
 
                                       20
<PAGE>   22
                   NOTES TO FINANCIAL STATEMENTS (CONTINUED)
 
                               December 31, 1998
- --------------------------------------------------------------------------------
 
unrealized appreciation/depreciation. Upon disposition, a realized gain or loss
is recognized accordingly, except when taking delivery of a security underlying
a futures contract. In this instance, the recognition of gain or loss is
postponed until the disposal of the security underlying the futures contract.
 
    During the period, the Fund invested in futures contracts, a type of
derivative. A futures contract is an agreement involving the delivery of a
particular asset on a specified future date at an agreed upon price. The Fund
generally invests in stock index futures. These contracts are generally used to
provide the return of an index without purchasing all of the securities
underlying the index or to manage the Fund's overall exposure to the equity
markets.
 
    Upon entering into futures contracts, the Fund maintains, in a segregated
account with its custodian, securities with a value equal to its obligation
under the futures contracts. During the period the futures contract is open,
payments are received from or made to the broker based upon changes in the value
of the contract (the variation margin). The risk of loss associated with a
futures contract is in excess of the variation margin reflected on the Statement
of Assets and Liabilities.
 
    Transactions in futures contracts for the year ended December 31, 1998, were
as follows:
 
<TABLE>
<CAPTION>
                                                             CONTRACTS
- ----------------------------------------------------------------------
<S>                                                          <C>
Outstanding at December 31, 1997............................    -0-
Futures Opened..............................................     45
Futures Closed..............................................    (30)
                                                                ---
Outstanding at December 31, 1998............................     15
                                                                ===
</TABLE>
 
    The futures contracts outstanding at December 31, 1998, and the description
and unrealized appreciation are as follows:
 
<TABLE>
<CAPTION>
                                                               UNREALIZED
                                                 CONTRACTS    APPRECIATION
- --------------------------------------------------------------------------
<S>                                              <C>          <C>
Long Contracts--March 1999 S&P 500 Index Futures
  (Current Notional Value of $311,375 per
  contract).....................................    15          $250,193
                                                    ==          ========
</TABLE>
 
                                       21
<PAGE>   23
 
                       REPORT OF INDEPENDENT ACCOUNTANTS
 
To the Shareholders and Board of Trustees of
Van Kampen Convertible Securities Fund
 
    We have audited the accompanying statement of assets and liabilities,
including the portfolio of investments of Van Kampen Convertible Securities
Fund, as of December 31, 1998, and the related statement of operations for the
year then ended, the statement of changes in net assets for each of the two
years in the period then ended, and the financial highlights for each of the ten
years in the period then ended. These financial statements and financial
highlights are the responsibility of the Fund's management. Our responsibility
is to express an opinion on these financial statements and financial highlights
based on our audits.
 
    We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements and financial
highlights are free of material misstatement. An audit includes examining, on a
test basis, evidence supporting the amounts and disclosures in the financial
statements. Our procedures included confirmation of securities owned as of
December 31, 1998, by correspondence with the custodian and brokers. An audit
also includes assessing the accounting principles used and significant estimates
made by management, as well as evaluating the overall financial statement
presentation. We believe that our audits provide a reasonable basis for our
opinion.
 
    In our opinion, the financial statements and financial highlights referred
to above present fairly, in all material respects, the financial position of Van
Kampen Convertible Securities Fund at December 31, 1998, the results of its
operations for the year then ended, the changes in its net assets for each of
the two years in the period then ended, and the financial highlights for each of
the ten years in the period then ended, in conformity with generally accepted
accounting principles.
 
                                                               ERNST & YOUNG LLP
 
Houston, Texas
February 4, 1999
 
                                       22
<PAGE>   24
 
                           DIVIDEND REINVESTMENT PLAN
The Fund pays distributions in cash, but if you own more than 100 shares in your
own name, you may elect to participate in the Fund's dividend reinvestment plan
(the "Plan"). Under the Plan, shares will be issued by the Fund at net asset
value on a date determined by the Board of Trustees between the record and
payable dates on each distribution; however, if the market price, including
brokerage commissions, is less than the net asset value, the amount of the
distribution will be paid to State Street Bank and Trust Company ("State
Street"), which will buy such shares as are available at prices below the net
asset value. (If the market price is not significantly less than the net asset
value, it is possible that open market purchases of shares may increase the
market price so that such price plus brokerage commissions would equal or exceed
the net asset value of such shares.) If State Street cannot buy the necessary
shares at less than net asset value before the distribution date, the balance of
the distribution will be made in authorized but unissued shares of the Fund at
net asset value. The cost per share will be the average cost, including
brokerage commissions, of all shares purchased. Since all shares purchased from
the Fund are at net asset value, there will be no dilution, and no brokerage
commissions are charged on such shares.
    You will receive tax information annually for your personal records and to
help you prepare your federal income tax return. The automatic reinvestment of
dividends and capital gain distributions does not relieve you of any income tax
which may be payable (or required to be withheld) on dividends or distributions.
    You may begin or discontinue participation in the Plan at any time by
written notice to the address below. If you withdraw from the Plan, you may
rejoin at any time if you own the required 100 shares. Elections and
terminations will be effective for distributions declared after receipt. If you
withdraw form the Plan, a certificate for the whole shares and a check for the
fractional shares, if any, credited to your Plan account will be sent as soon as
practicable after receipt of your election to withdraw. Except for brokerage
commissions, if any, which are borne by Plan participants, all costs of the Plan
are borne by the Fund. The Fund reserves the right to amend or terminate the
Plan on 30 days' written notice prior to the record date of the distribution for
which such amendment or termination is effective.
    Record stockholders should address all notices, correspondence, questions or
other communications about the Plan to:
 
                              BOSTON EQUISERVE LP
                                 P.O. BOX 8200
                             BOSTON, MA 02266-8200
                                  800-341-2929
 
    If your shares are not held directly in your name, you should contact your
brokerage firm, bank or other nominee for more information and to see if your
nominee will participate in the Plan on your behalf. If you participate through
your broker and choose to move your account to another broker, you will need to
re-enroll in the Plan through your new broker.
 
                                       23
<PAGE>   25
 
                                VAN KAMPEN FUNDS
 
EQUITY FUNDS
 
Domestic
     Aggressive Equity
     Aggressive Growth
     American Value
     Comstock
     Emerging Growth
     Enterprise
     Equity Growth
     Equity Income
     Growth
     Growth and Income
     Harbor
     Pace
     Real Estate Securities
     Utility
     Value
Global/International
     Asian Growth
     Emerging Markets
     European Equity
     Global Equity
     Global Equity Allocation
     Global Franchise
     Global Managed Assets
     International Magnum
     Latin American
 
FIXED-INCOME FUNDS
Income
     Corporate Bond
     Global Fixed Income
     Global Government Securities
     Government Securities
     High Income Corporate Bond
     High Yield
     High Yield & Total Return
     Limited Maturity Government
     Short-Term Global Income
     Strategic Income
     U.S. Government
     U.S. Government Trust for Income
     Worldwide High Income

Tax Exempt Income
     California Insured Tax Free
     Florida Insured Tax Free Income
     High Yield Municipal
     Insured Tax Free Income
     Intermediate Term Municipal Income
     Municipal Income
     New York Tax Free Income
     Pennsylvania Tax Free Income
     Tax Free High Income
Capital Preservation
     Reserve
     Tax Free Money
Senior Loan
     Prime Rate Income Trust
     Senior Floating Rate
 
To find out more about any of these
funds, ask your financial advisor for
a prospectus, which contains more
complete information, including sales
charges, risks, and expenses. Please
read it carefully before you invest
or send money.
 
To view a current Van Kampen fund
prospectus or to receive additional
fund information, choose from one of
the following:
 
- - visit our Web site at
  WWW.VANKAMPEN.COM--to view a prospectus, select Download Prospectus
 
- - call us at 1-800-341-2911 weekdays from 7:00 a.m. to 7:00 p.m. Central time.
  Telecommunications Device for the Deaf users, call 1-800-421-2833.
 
- - e-mail us by visiting
  WWW.VANKAMPEN.COM and
  selecting Contact Us
 
                                       24
<PAGE>   26
 
                     VAN KAMPEN CONVERTIBLE SECURITIES FUND
 
BOARD OF TRUSTEES
 
DAVID C. ARCH

ROD DAMMEYER

HOWARD J KERR

DENNIS J. MCDONNELL*--Chairman

STEVEN MULLER

THEODORE A. MYERS

DON G. POWELL*

HUGO F. SONNENSCHEIN

WAYNE W. WHALEN*
 
OFFICERS
 
DON G. POWELL*
President
 
DENNIS J. MCDONNELL*
Executive Vice President
 
JOHN L. SULLIVAN*
Vice President, Treasurer and
Chief Financial Officer
 
CURTIS W. MORELL*
Vice President and Chief Accounting Officer
 
TANYA M. LODEN*
Controller
 
PETER W. HEGEL*
PAUL R. WOLKENBERG*
EDWARD C. WOOD, III*
Vice Presidents
 
                    ---------------------------------------
                          INQUIRES ABOUT AN INVESTOR'S
                       ACCOUNT SHOULD BE REFERRED TO THE
                             FUND'S TRANSFER AGENT
                                BOSTON EQUISERVE
                                 P.O. BOX 8200
                        BOSTON, MASSACHUSETTS 02266-8200
                           TELEPHONE: (800) 821-1238
                       ALASKA, CALIFORNIA AND HAWAII CALL
                            COLLECT: (713) 993-0500
                                EXTENSION: 2223
                    ---------------------------------------
INVESTMENT ADVISER
 
VAN KAMPEN
ASSET MANAGEMENT INC.
1 Parkview Plaza
P.O. Box 5555
Oakbrook Terrace, IL 60181-5555
 
CUSTODIAN
 
STATE STREET BANK AND TRUST CO.
225 Franklin Street
Boston, Massachusetts 02105
 
SHAREHOLDER SERVICING AGENT
 
BOSTON EQUISERVE LP
P.O. Box 8200
Boston, Massachusetts 02266-8200
 
LEGAL COUNSEL
 
SKADDEN, ARPS, SLATE,
MEAGHER & FLOM (ILLINOIS)
333 West Wacker Drive
Chicago, Illinois 60606
 
INDEPENDENT ACCOUNTANTS
 
ERNST & YOUNG LLP
1221 McKinney Suite 2400
Houston, Texas 77010
 
                      TAX NOTICE TO CORPORATE SHAREHOLDERS
 
 For 1998, 35.23% of the dividends taxable as ordinary income qualified for the
 70% dividends received deduction for corporations.
*  "Interested" persons of the Trust, as defined in the Investment Company Act
   of 1940.
 
(C) Van Kampen Funds Inc., 1999 All rights reserved.
 
(SM) denotes a service mark of Van Kampen Funds Inc.
 
                                       25
<PAGE>   27
 
                          RESULTS OF SHAREHOLDER VOTES
 
The Annual Meeting of Shareholders of the Fund was held on July 28, 1998, where
shareholders voted on the election of trustees, the selection of independent
public accountants and to approve the proposed changes to the Fund's fundamental
investment restrictions.
 
1) With regard to the election of the following trustees by shareholders of the
Fund:
 
<TABLE>
<CAPTION>
                                                        # OF SHARES
                                                    --------------------
                                                    IN FAVOR    WITHHELD
- ------------------------------------------------------------------------
<S>                                                 <C>         <C>
David C. Arch...................................... 2,368,960    65,945
Howard J Kerr...................................... 2,370,260    64,153
Dennis J. McDonnell................................ 2,370,260    64,645
</TABLE>
 
The other trustees of the Fund whose terms did not expire in 1998 are Rod
Dammeyer, Steven Muller, Theodore A. Myers, Don G. Powell, Hugo Sonnenschein and
Wayne W. Whalen.
 
2) With regard to the ratification of Ernst & Young LLP as independent public
accountants for the Fund, 2,401,636 shares voted in favor of the proposal, 8,749
shares voted against and 25,520 shares abstained.
 
3) With regard to the approval of the proposed changes to the Fund's fundamental
investment restrictions, the Meeting was adjourned until August 24, 1998.
 
An Adjournment Meeting of Shareholders of the Fund was held on August 24, 1998,
where shareholders voted to approve the proposed changes to the Fund's
fundamental investment restrictions. With regard to the approval of the proposed
changes, 1,631,246 shares voted in favor of the proposal, 172,949 voted against,
77,689 shares abstained and 824,469 shares represented broker non-votes.
 
                                       26
<PAGE>   28
 
                         YEAR 2000 READINESS DISCLOSURE
 
Like other mutual funds, financial and business organizations and individuals
around the world, the Fund could be adversely affected if the computer systems
used by the Fund's investment adviser and other service providers do not
properly process and calculate date-related information and data from and after
January 1, 2000. This is commonly known as the "Year 2000 Problem." The Fund's
investment adviser is taking steps that it believes are reasonably designed to
address the Year 2000 Problem with respect to computer systems that it uses and
to obtain reasonable assurances that comparable steps are being taken by the
Fund's other major service providers. At this time, there can be no assurances
that these steps will be sufficient to avoid any adverse impact to the Fund. In
addition, the Year 2000 Problem may adversely affect the markets and the issuers
of securities in which the Fund may invest that, in turn, may adversely affect
the net asset value of the Fund. Improperly functioning trading systems may
result in settlement problems and liquidity issues. In addition, corporate and
governmental data processing errors may result in production problems for
individual companies or issuers and overall economic uncertainty. Earnings of
individual issuers will be affected by remediation costs, which may be
substantial and may be reported inconsistently in U.S. and foreign financial
statements. Accordingly, the Fund's investments may be adversely affected. The
statements above are subject to the Year 2000 Information and Readiness
Disclosure Act, which may limit the legal rights regarding the use of such
statements in the case of dispute.
 
                                       27
<PAGE>   29
 
                                VAN KAMPEN FUNDS
 
YOUR NOTES:
 
                                       28

<TABLE> <S> <C>

<ARTICLE> 6
<SERIES>
   <NUMBER> 11
   <NAME> CONVERTIBLE SECS
<MULTIPLIER> 1
       
<S>                             <C>
<PERIOD-TYPE>                   12-MOS
<FISCAL-YEAR-END>                          DEC-31-1998
<PERIOD-START>                             JAN-01-1998
<PERIOD-END>                               DEC-31-1998
<INVESTMENTS-AT-COST>                       70,947,991
<INVESTMENTS-AT-VALUE>                      76,924,617
<RECEIVABLES>                                1,064,925
<ASSETS-OTHER>                                       0
<OTHER-ITEMS-ASSETS>                            47,845
<TOTAL-ASSETS>                              78,037,387
<PAYABLE-FOR-SECURITIES>                       186,354
<SENIOR-LONG-TERM-DEBT>                              0
<OTHER-ITEMS-LIABILITIES>                      474,452
<TOTAL-LIABILITIES>                            660,806
<SENIOR-EQUITY>                                      0
<PAID-IN-CAPITAL-COMMON>                    71,283,425
<SHARES-COMMON-STOCK>                        3,241,824
<SHARES-COMMON-PRIOR>                        3,241,824
<ACCUMULATED-NII-CURRENT>                      258,861
<OVERDISTRIBUTION-NII>                               0
<ACCUMULATED-NET-GAINS>                      (392,524)
<OVERDISTRIBUTION-GAINS>                             0
<ACCUM-APPREC-OR-DEPREC>                     6,226,819
<NET-ASSETS>                                77,376,581
<DIVIDEND-INCOME>                            1,092,330
<INTEREST-INCOME>                            2,452,889
<OTHER-INCOME>                                       0
<EXPENSES-NET>                               (640,407)
<NET-INVESTMENT-INCOME>                      2,904,812
<REALIZED-GAINS-CURRENT>                       910,780
<APPREC-INCREASE-CURRENT>                      805,481
<NET-CHANGE-FROM-OPS>                        4,621,073
<EQUALIZATION>                                       0
<DISTRIBUTIONS-OF-INCOME>                  (2,851,284)
<DISTRIBUTIONS-OF-GAINS>                   (3,056,743)
<DISTRIBUTIONS-OTHER>                                0
<NUMBER-OF-SHARES-SOLD>                              0
<NUMBER-OF-SHARES-REDEEMED>                          0
<SHARES-REINVESTED>                                  0
<NET-CHANGE-IN-ASSETS>                     (1,286,954)
<ACCUMULATED-NII-PRIOR>                        205,333
<ACCUMULATED-GAINS-PRIOR>                    1,753,439
<OVERDISTRIB-NII-PRIOR>                              0
<OVERDIST-NET-GAINS-PRIOR>                           0
<GROSS-ADVISORY-FEES>                          387,209
<INTEREST-EXPENSE>                                   0
<GROSS-EXPENSE>                                640,407
<AVERAGE-NET-ASSETS>                        77,459,036
<PER-SHARE-NAV-BEGIN>                           24.265
<PER-SHARE-NII>                                  0.896
<PER-SHARE-GAIN-APPREC>                          0.530
<PER-SHARE-DIVIDEND>                           (0.880)
<PER-SHARE-DISTRIBUTIONS>                      (0.943)
<RETURNS-OF-CAPITAL>                             0.000
<PER-SHARE-NAV-END>                             23.868
<EXPENSE-RATIO>                                   0.83
<AVG-DEBT-OUTSTANDING>                               0
<AVG-DEBT-PER-SHARE>                                 0
        


</TABLE>


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