COHEN & STEERS SPECIAL EQUITY FUND
N-30D, 1999-02-22
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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
 
February 5, 1999
 
To Our Shareholders:
 
     We are pleased to submit to you the annual report for Cohen & Steers
Special Equity Fund, Inc. for the quarter and year ended December 31, 1998. The
net asset value per share at that date was $20.88. In addition, a semi-annual
dividend of $0.24 per share was declared for shareholders of record December 22,
1998 and paid on December 23, 1998. The Fund did not make capital gains
distributions in 1998.
 
1998 REVIEW
 
     1998 was a difficult year for REITs in general and for the Fund in
particular. The NAREIT Equity REIT Index total return in 1998 was  - 17.5%, the
worst year on record since 1974 and the worst year ever relative to stocks. For
the full year the Fund's total return was  - 33.8%. The poor performance by
REITs is difficult to reconcile in an environment of strong economic growth, low
inflation and interest rates, strong financial asset returns and
higher-than-expected REIT earnings growth. The Fund performed below our
expectations due to positions in companies with high growth rates or higher-risk
business plans, both of which under-performed REITs with high dividend yields
and conservative business plans. In the second half of the year we made changes
to our portfolio strategy which have begun to show results: the Fund's total
return was  - 3.0% in the fourth quarter of 1998, which was in line with the
NAREIT Equity REIT Index total return of  - 2.9%.
 
     The correction in REIT share prices was precipitated by a scenario whereby
valuations were high, psychology was positive, and perceived risk was low -- yet
capital market and economic factors impacting real estate were about to
transition more quickly than anyone could have foreseen. These macro-factors had
a greater impact on performance than did underlying property level and REIT
fundamentals, which performed ahead of expectations in terms of demand, rent
growth and earnings.
 
     Real estate capital flows accelerated dramatically in the first half of
1998, driving real estate prices higher and setting the stage for a significant
ramp up in new development. This capital influx proved to be ill timed
considering that all property sectors had transitioned from recovery to
equilibrium throughout 1997-98 and, therefore, risk levels had actually
escalated. In an abrupt turnabout, public market real estate capital flows froze
during the third quarter. First, equity capital became prohibitively expensive
and unavailable to REITs. Then the dislocations in the credit markets, which
threatened the stability of the entire financial system and the U.S. economy,
nearly shut down all activity in the public real estate debt markets.
Fortunately, just when it appeared that real estate markets were headed for an
oversupply situation the public markets shut down capital flows.
 
     The corrective mechanism of the real estate capital markets had both
positive and negative implications for REITs. The negatives: a) property prices
declined 10-20%, and b) REITs were shut off from equity capital, causing a
decline in earnings estimates and growth rates. Ironically, despite the
self-correcting response of the public markets, confidence in REITs slipped as
investors seemed to dwell on the notion that real estate industry was again
experiencing a capital driven boom-bust cycle. On the positive side, the
development backlog quickly reversed, eliminating the threat of over-building.
In addition, the capital vacuum improved the investment environment for
companies with capital, due to higher property yields and less competition. In a
move related to the credit market disruptions, the Federal Reserve reduced
interest rates three times in the fourth quarter, improving the outlook for the
economy and for real estate demand. Despite the improved fundamental outlook for
REITs, performance was a disappointment in the fourth quarter: REITs returned
 - 2.9%, far below the S&P 500 and Russell 2000 Indexes
 
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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
which soared 21.3% and 16.5%, respectively -- causing investors to re-evaluate
the factors driving REIT performance.
 
     Investors have likely become concerned about persistent deflationary
pressures and the long-term impact on rents and property values. It is no
coincidence, in our opinion, that in addition to REITs, 1998's worst performing
investments included other potential victims of deflation such as most
commodities, precious and non-precious metals, and just about anything
energy-related. In a low inflation (or deflationary) and low interest rate
environment, investors often pay the highest price for longer-term investments,
such as safe long-term bonds or high growth stocks such as technology,
communications or Internet companies, for example. If deflation is expected to
persist for a long period, investors demand a higher current return in order to
offset the risk of a potential long-term decline in asset values. The net
result: Equity REIT dividend yields rose from 5.5% at the beginning of the year
to a five-year high of 7.5% by year end.
 
INVESTMENT OUTLOOK
 
     In contrast to last year, 1999 began with low expectations for REIT
performance -- the sector is out of favor, and little is expected in terms of
positive fundamental surprises. For example, analysts have assumed that REITs
will not have access to equity capital and, therefore, will not produce
incremental growth through acquisitions. By contrast, growth expectations last
year were very high. Managements then believed that high valuations were awarded
to those companies with the greatest growth; they crafted business plans and
staffed their organizations to deliver growth, and many reached for acquisitions
that did not earn their cost of capital. Now that growth expectations are lower,
the risk inherent in most business plans is lower. In addition, capital invested
in 1999 will earn a greater return than the capital invested last year. In our
view, the low expectations for REIT performance have set the stage for positive
surprises.
 
     In addition to lower risk in REIT business plans, the risk in real estate
prices is also lower. During the fourth quarter of last year the 'speculative'
capital driving real estate prices and development was sidelined. As a result,
real estate prices are now 10-20% lower and capital flows are disciplined.
Volume in the commercial mortgage-backed securities ('CMBS') market, the public
debt market analog to REIT equities, should decline to an annualized pace of $55
billion in 1999, 30% below last year's pace.
 
     Economic prospects should be less volatile than last year. In 1998 REIT
valuations were hurt by the threat of a credit crunch and recession, which was
precipitated by the Asian contagion and Russian debt crisis. The U.S. economy
withstood those challenges. The economy entered 1999 with strong momentum and
favorable readings on interest rates, inflation, employment, consumer spending
and fiscal issues. In addition, the economy has imbedded support from the
monetary stimulus provided by the Federal Reserve and central banks around the
world. While REIT share prices discounted the prospect for recession last fall,
they did not rally in response to the Fed's easings (and improved economic
prospects) as did the broader equity markets.
 
     While the risks in REIT fundamentals appear to be lower than last year,
valuations are much lower. REITs traded at a 20-25% premium to the underlying
value of their real estate at the beginning of 1998, but entered 1999 trading at
a 5-10% discount. This devaluation reflects lower growth expectations, as well
as an assessment that it is more difficult to add value in the equilibrium phase
of the cycle. Importantly, the potential for REIT fundamentals to drive share
prices is greater today than last year when, with perfect hindsight, the risk
was high
 
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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
that fundamentals would fall short of expectations. As was the case for most of
last year, REITs continue to have record low share price valuations relative to
stocks and bonds.
 
     Summarizing our outlook, the transition that occurred in the real estate
and REIT markets last year has created a situation where risk, expectations, and
valuations have been reduced. Yet at the same time, fundamentals are still
attractive. Therefore, the investment profile of REITs -- dividend yields of
7.5% and high single-digit earnings growth -- should become more highly valued
in the capital markets. It will likely take some time for REITs to regain
credibility and for investor psychology to mend. This process should gradually
unfold throughout 1999 as the profile of risk-adjusted fundamentals for REITs
becomes apparent.
 
     We do not believe, however, that a new bull market in REIT shares is about
to begin. Rather, we expect most real estate markets to remain in equilibrium,
whereby the supply and demand for space are about equal. Based upon the
experience of last year, the near instantaneous reaction of the financial
markets to any actual or perceived imbalances will likely serve to maintain this
equilibrium condition. The swiftness with which the real estate markets have
moved is primarily the result of the domination of public securities markets for
debt and equity financing of real estate.
 
     While a persistent equilibrium condition is a consequence of public market
discipline and is generally very positive for the industry, it does pose a
number of challenges. These conditions represent a vast increase in the
efficiency of the market and thereby a reduction of profit opportunities, both
in the direct property markets as well as in REIT investing. Thus, it is our
belief that future returns from REITs will be consistent with this less
cyclical, steady fundamental environment. Equilibrium should foster the
continued consolidation of the real estate industry, resulting in the creation
of ever-larger companies. These companies may begin to produce 'index-like'
returns due to the increasing size and scope of their property holdings.
 
INVESTMENT STRATEGY
 
     Regarding the Fund's strategy, we are committed to holding approximately
twenty companies that possess the best return potential in the real estate
sector. In the third quarter of 1998 we shifted to a portfolio strategy whereby
a foundation is built from the best of the 'Realty Majors' -- a name we have
given to those 25-35 companies that, by virtue of value-added management,
financial strength and protected markets, will generate sustainable growth in
equilibrium conditions. The balance of the Fund's assets will be allocated to
strategies where the return potential exceeds that of high-quality REITs. At
year end 53% of the Fund's assets were invested in REITs and 43% were invested
in C-corporations that operate a variety of real estate related businesses.
 
     The challenge for the Fund is to find opportunities that will produce
returns exceeding those that REITs can provide, taking an acceptable level of
risk. We have allocated approximately 50% of the Fund's assets to three sectors
that, we believe, offer unique return potential: Office, Health Care, and
Hotel/Gaming. All three sectors under-performed by a wide margin in 1998, appear
to be undervalued, and should show better-than-expected fundamentals. Another
theme is companies operating in urban or protected markets -- these companies
are best positioned to deal with the competitive threats that equilibrium poses.
The Fund has over 40% of its assets in these types of companies, principally
those that operate in the New York metropolitan area. Primarily due to the
difficulty of adding value in equilibrium, the Fund has little or no exposure to
the Apartment, Industrial, Self-storage, Retail, and Manufactured Home sectors.
Longer term, the process by which the public market awards
 
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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
capital to the winners, and neglects the losers, should create a broader
divergence in valuations, thereby creating value opportunities.
 
     One segment of the Health Care sector that we are excited about as a
contrarian opportunity is long-term care. The stocks of these owners and
operators of nursing homes, which have good long-term fundamentals due to the
aging of America and the restrictions on development, have under-performed the
market for several years due to pending changes in the Medicare reimbursement
system. This regulatory change is causing significant dislocations, which should
create attractive market share, profit, and consolidation opportunities for
companies that are quality, efficient operators with strong balance sheets.
Reflecting uncertainty, the sector is trading at a P/E ratio that is half the
intrinsic growth rate of the sector.
 
     In summary, 1998 was a year of transition and volatility, which negatively
impacted share prices of all real estate securities -- particularly those with
higher risk and growth-oriented business plans. In hindsight, we should have
adopted a more defensive strategy for what proved to be a difficult investing
climate, despite good underlying fundamentals. Looking to 1999 we believe that
the Fund is well positioned for what should be a more stable environment.
Accordingly, the Fund has a good mix of high quality REITs that will excel in
equilibrium as well as several contrarian holdings where share prices do not
adequately reflect fundamentals.
 
Sincerely,
 
<TABLE>
<S>                                               <C>
             MARTIN COHEN                         ROBERT H. STEERS
             MARTIN COHEN                         ROBERT H. STEERS
             President                                      Chairman

                               JOSEPH M. HARVEY
                               JOSEPH M. HARVEY
                               Director of Research
                               Cohen & Steers Capital Management, Inc.
</TABLE>
 
Cohen & Steers is now online at WWW.COHENANDSTEERS.COM. Visit our website for
daily NAVs, portfolio information, performance information, recent news
articles, literature and insights on the REIT market.
 
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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
 
PERFORMANCE REVIEW
 
     The investment objective of Cohen & Steers Special Equity Fund, Inc. is
maximum capital appreciation over the long-term through investment in real
estate companies. The Fund pursues its investment objective by seeking
investments in a limited number of companies which are engaged in the real
estate industry or related industries, or in companies which own significant
real estate assets and are believed by the investment advisor to have
unrecognized intrinsic value. Investments are selected for long-term capital
appreciation; current income is incidental to the Fund's investment objective.
 
     In 1998 the Fund's investment performance was below the total returns of
the benchmark indexes. In the Adviser's opinion, real estate securities
under-performed common stocks in general due to concerns about the maturation of
the real estate cycle, the decline in capital flows to the real estate sector,
and uncertainty regarding the economy. The Fund under-performed its real estate
benchmark indexes due to holdings in REITs and C-corporations with high growth
(and higher risk) business plans and low dividend yields. In 1998, the share
prices of REITs with low valuations, high dividend yields, and conservative
business plans generally out-performed the share prices of real estate companies
with aggressive, growth-oriented business plans, in our opinion. In light of the
share price declines in 1998 and the decline in capital to fund new real estate
development, we believe that the factors impacting real estates securities
performance are adequately reflected in share valuations.
 

<TABLE>
<CAPTION>
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                                         AVERAGE ANNUAL TOTAL RETURNS
                                       FOR PERIODS ENDED DEC. 31, 1998
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                                     1 YEAR      SINCE INCEPTION (5/8/97)
- -------------------------------------------------------------------------
<S>                                <C>                  <C>
  Fund                                -33.83%              -3.85%
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  NAREIT All**                        -18.32%              -0.91%
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  Wilshire                            -17.43%               0.23%
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  S&P                                  28.58%              30.32%
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</TABLE>


                                      [GRAPH]

                            Growth of a $10,000 Investment
                                   Since Inception
<TABLE>
<CAPTION>
                   Cohen &                           Wilshire 
                   Steers            NAREIT          Real Estate
                   Special          All REIT         Securities
                 Equity Fund         Index              Index             S&P 500
                 -----------        --------         -----------          -------
<S>                <C>              <C>              <C>                  <C>
 5/8/97*           $10,000           $10,000            $10,000           $10,000
 6/30/97           $10,917           $10,815            $10,809           $10,885
 9/30/97           $13,627           $12,005            $12,174           $11,700
12/31/97           $14,511           $12,131            $12,156           $12,036
 3/31/98           $14,074           $12,065            $12,065           $13,715
 6/30/98           $13,145           $11,507            $11,511           $14,168
 9/30/98           $ 9,900           $10,251            $10,134           $12,758
12/31/98           $ 9,608           $ 9,847            $10,038           $15,475

</TABLE>

Past performance is not predictive of future performance. Your investment return
and principal value will fluctuate. When shares are redeemed, they may be worth
more or less than the original cost.
 
 *  Commencement of operations.
 
'D' The comparative indices are not adjusted to reflect expenses or other fees
    that the SEC requires to be reflected in the Fund's performance. The Fund's
    performance assumes the reinvestment of all dividends and distributions. The
    NAREIT Index of All REITs is comprised of 210 real estate investment trusts.
    The Wilshire Real Estate Securities Index is comprised of 119 companies
    operating in the real estate industry and includes REITs. This index does
    not include REITs with investments in health care facilities. The Fund
    invests in REITs with investments in health care facilities. The S&P 500
    Index is an unmanaged list of common stocks that is frequently used as a
    general measure of stock market performance. For more information, including
    charges and expenses, please read the prospectus carefully before you
    invest.
 
 ** The NAREIT All REIT Index (prior to January 4, 1999) and the Wilshire Real
    Estate Securities Index are published monthly. Total returns and cumulative
    values of a $10,000 investment are calculated from April 30, 1997, the date
    nearest the Fund's inception for which comparable performance data exist.
 
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                                       5

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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
                            SCHEDULE OF INVESTMENTS
                               DECEMBER 31, 1998
 
<TABLE>
<CAPTION>
                                                                                                         % OF
                                                                              NUMBER         VALUE       NET
                                                                             OF SHARES     (NOTE 1)     ASSETS
                                                                            -----------   -----------   ------
<S>                                                                         <C>           <C>           <C>
EQUITIES
      LNR Property Corp. .............................................          386,600   $ 7,707,838    13.97%
      *Alexander's....................................................           62,200     4,863,262     8.82
      Starwood Hotels & Resorts Worldwide.............................          205,400     4,660,013     8.45
      Vornado Realty Trust............................................          114,600     3,867,750     7.01
      SL Green Realty Corp. ..........................................          149,800     3,239,425     5.87
      Mack-Cali Realty Corp. .........................................           92,400     2,852,850     5.17
      *American Retirement Corp. .....................................          176,500     2,768,844     5.02
      *Omega Worldwide................................................          626,100     2,739,188     4.97
      Arden Realty Group..............................................          115,500     2,678,156     4.86
      Crescent Real Estate Equities Co. ..............................          105,500     2,426,500     4.40
      *HCR Manor Care.................................................           82,300     2,417,562     4.38
      *Vencor.........................................................          519,100     2,335,950     4.23
      *Station Casinos................................................          285,000     2,333,438     4.23
      *Crescent Operating.............................................          454,700     2,159,825     3.92
      Forest City Enterprises -- Class A .............................           80,900     2,123,625     3.85
      Apartment Investment & Management Co. -- Class A................           54,600     2,030,437     3.68
      **Brookfield Properties Corp. ..................................          151,800     1,857,969     3.37
      Prime Group Realty Trust........................................          120,200     1,818,025     3.30
      Ventas..........................................................          128,000     1,560,000     2.83
      *Assisted Living Concepts.......................................           11,500       150,937     0.27
                                                                                          -----------   ------
            TOTAL EQUITIES (Identified cost -- $71,877,186)...........                     56,591,594   102.60
                                                                                          -----------   ------

<CAPTION>
                                                                           PRINCIPAL
                                                                             AMOUNT
                                                                           ----------
<S>                                                                        <C>          <C>            <C>
COMMERCIAL PAPER
      Preferred Finance Corp., 4.80%, 1/4/99 (Identified Cost --
         $1,530,400).................................................      $1,531,000      1,530,400     2.77
                                                                                        ------------   ------
TOTAL INVESTMENTS (Identified cost -- $73,407,586)...................                     58,121,994   105.37
LIABILITIES IN EXCESS OF OTHER ASSETS................................                     (2,962,792)   (5.37)
                                                                                        ------------   ------
NET ASSETS (Equivalent to $20.88 per share based on 2,642,310 shares
   of capital stock outstanding).....................................                   $ 55,159,202   100.00%
                                                                                        ------------   ------
                                                                                        ------------   ------
</TABLE>
 
- ------------------------
 
 * Non-income producing security.
 
** Brookfield Properties Corp. is a Canadian company listed on the Toronto Stock
   Exchange. Its market value in Canadian dollars on December 31, 1998 was
   $2,853,840. The Canadian dollar exchange rate on December 31, 1998 was 0.651
   to 1 U.S. dollar.
 
                See accompanying notes to financial statements.
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                                       6



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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
                      STATEMENT OF ASSETS AND LIABILITIES
                               DECEMBER 31, 1998
 
<TABLE>
<S>                                                                                                  <C>
ASSETS:
      Investments in securities, at value (Identified cost -- $73,407,586) (Note 1)................  $ 58,121,994
      Cash.........................................................................................           270
      Receivable for investment securities sold....................................................       977,528
      Dividends receivable.........................................................................       219,079
      Receivable for fund shares sold..............................................................       134,471
      Other assets.................................................................................        80,226
                                                                                                     ------------
            Total Assets...........................................................................    59,533,568
                                                                                                     ------------
LIABILITIES:
      Payable for outstanding borrowings (Note 6)..................................................     4,010,960
      Payable for fund shares redeemed.............................................................       255,609
      Payable to investment adviser................................................................        38,267
      Payable to administrator.....................................................................        12,837
      Other liabilities............................................................................        56,693
                                                                                                     ------------
            Total Liabilities......................................................................     4,374,366
                                                                                                     ------------
NET ASSETS applicable to 2,642,310 shares of $0.001 par value common stock
      outstanding (Note 4).........................................................................  $ 55,159,202
                                                                                                     ------------
                                                                                                     ------------
NET ASSET VALUE PER SHARE:
      ($55,159,202[div]2,642,310 shares outstanding)...............................................  $      20.88
                                                                                                     ------------
                                                                                                     ------------
NET ASSETS consist of:
      Paid-in capital (Notes 1 and 4)..............................................................  $ 91,703,400
      Accumulated net realized loss on investments sold............................................   (21,258,606)
      Net unrealized depreciation on investments...................................................   (15,285,592)
                                                                                                     ------------
                                                                                                     $ 55,159,202
                                                                                                     ------------
                                                                                                     ------------
</TABLE>
 
                See accompanying notes to financial statements.
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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
                            STATEMENT OF OPERATIONS
                      FOR THE YEAR ENDED DECEMBER 31, 1998
 
<TABLE>
<S>                                                                                                  <C>
Investment Income (Note 1):
      Dividend income (net of $1,852 of foreign withholding tax)...................................  $  3,096,879
      Interest income..............................................................................       335,127
                                                                                                     ------------
            Total Income...........................................................................     3,432,006
                                                                                                     ------------
Expenses:
      Investment advisory fees (Note 2)............................................................     1,035,302
      Administration and transfer agent fees (Note 2)..............................................       190,335
      Professional fees............................................................................        80,973
      Reports to shareholders......................................................................        64,778
      Directors' fees and expenses (Note 2)........................................................        32,000
      Interest expense (Note 6)....................................................................        30,643
      Registration and filing fees.................................................................        30,206
      Amortization of organization expenses (Note 1)...............................................        21,219
      Custodian fees and expenses..................................................................         5,703
      Miscellaneous................................................................................        11,313
                                                                                                     ------------
            Total Expenses.........................................................................     1,502,472
                                                                                                     ------------
      Reduction of expenses (Note 5)...............................................................       (35,057)
                                                                                                     ------------
            Net Expenses...........................................................................     1,467,415
                                                                                                     ------------
Net Investment Income..............................................................................     1,964,591
                                                                                                     ------------
Net Realized and Unrealized Loss on Investments:
      Net realized loss on investments.............................................................   (22,083,208)
      Net change in unrealized appreciation/(depreciation) on investments..........................   (29,250,377)
                                                                                                     ------------
            Net realized and unrealized loss on investments........................................   (51,333,585)
                                                                                                     ------------
Net Decrease in Net Assets Resulting from Operations...............................................  $(49,368,994)
                                                                                                     ------------
                                                                                                     ------------
</TABLE>
 
                See accompanying notes to financial statements.
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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
                       STATEMENT OF CHANGES IN NET ASSETS
 
<TABLE>
<CAPTION>
                                                                         FOR THE             FOR THE PERIOD
                                                                       YEAR ENDED        MAY 8, 1997'D' THROUGH
                                                                    DECEMBER 31, 1998       DECEMBER 31, 1997
                                                                    -----------------  ---------------------------
 
<S>                                                                 <C>                <C>
Change in Net Assets:
      From Operations:
            Net investment income.................................    $   1,964,591           $     933,105
            Net realized gain/(loss) on investments...............      (22,083,208)              9,814,004
            Net change in unrealized appreciation/
               (depreciation) on investments......................      (29,250,377)             13,964,785
                                                                    -----------------       ---------------
                  Net increase/(decrease) in net assets resulting
                     from operations..............................      (49,368,994)             24,711,894
                                                                    -----------------       ---------------
      Dividends and Distributions to Shareholders from (Note 1):
            Net investment income.................................       (1,288,005)               (734,589)
            Net realized gain on investments......................               --              (9,864,504)
            Tax return of capital.................................         (618,421)               (429,791)
                                                                    -----------------       ---------------
                  Total dividends and distributions to
                     shareholders.................................       (1,906,426)            (11,028,884)
                                                                    -----------------       ---------------
      Capital Stock Transactions (Note 4):
            Increase/(decrease) in net assets from Fund share
               transactions.......................................      (29,499,782)            122,151,394
                                                                    -----------------       ---------------
                  Total increase/(decrease) in net assets.........      (80,775,202)            135,834,404
      Net Assets:
            Beginning of period...................................      135,934,404                 100,000
                                                                    -----------------       ---------------
            End of period.........................................    $  55,159,202           $ 135,934,404
                                                                    -----------------       ---------------
                                                                    -----------------       ---------------
</TABLE>
 
- ------------------------
 
'D' Commencement of operations.
 
                See accompanying notes to financial statements.
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                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
                              FINANCIAL HIGHLIGHTS
 
     The following table includes selected data for a share outstanding
throughout each period and other performance information derived from the
Financial Statements. It should be read in conjunction with the Financial
Statements and notes thereto.
 
<TABLE>
<CAPTION>
                                                                                           FOR THE PERIOD
                                                                        FOR THE            MAY 8, 1997'D'
                                                                      YEAR ENDED              THROUGH
PER SHARE OPERATING PERFORMANCE:                                   DECEMBER 31, 1998     DECEMBER 31, 1997
- ------------------------------------------------------------------ -----------------    --------------------
<S>                                                                <C>                  <C>
Net asset value, beginning of period..............................      $ 32.25               $  25.00
                                                                        -------             ----------
Income from investment operations
     Net investment income........................................         0.53                   0.31
     Net realized and unrealized gain/(loss) on investments.......       (11.39)                  9.92
                                                                        -------             ----------
           Total from investment operations.......................       (10.86)                 10.23
                                                                        -------             ----------
Less dividends and distributions to shareholders from:
     Net investment income........................................        (0.34)                 (0.27)
     Net realized gain on investments.............................           --                  (2.59)
     Tax return of capital........................................        (0.17)                 (0.12)
                                                                        -------             ----------
           Total dividends and distributions to shareholders......        (0.51)                 (2.98)
                                                                        -------             ----------
     Net asset value, end of period...............................      $ 20.88               $  32.25
                                                                        -------             ----------
                                                                        -------             ----------
- ------------------------------------------------------------------------------------------------------------
Total investment return...........................................      - 33.83%                 41.68%(1)
                                                                        -------             ----------
                                                                        -------             ----------
- ------------------------------------------------------------------------------------------------------------
RATIOS/SUPPLEMENTAL DATA:
     Net assets, end of period (in millions)......................      $55.159               $135.934
                                                                        -------             ----------
                                                                        -------             ----------
     Ratios of expenses to average daily net assets (before
        expense reduction)........................................         1.31%                  1.35%(2)
                                                                        -------             ----------
                                                                        -------             ----------
     Ratios of expenses to average daily net assets (net of
        expense reduction)........................................         1.28%                  1.35%(2)
                                                                        -------             ----------
                                                                        -------             ----------
     Ratio of net investment income to average daily net assets
        (before expense reduction)................................         1.68%                  1.73%(2)
                                                                        -------             ----------
                                                                        -------             ----------
     Ratio of net investment income to average daily net assets
        (net of expense reduction)................................         1.71%                  1.73%(2)
                                                                        -------             ----------
                                                                        -------             ----------
     Portfolio turnover rate......................................       112.32%                 96.68%
                                                                        -------             ----------
                                                                        -------             ----------
</TABLE>
 
- ------------------------
'D' Commencement of operations.
(1) Not annualized.
(2) Annualized.
 
                See accompanying notes to financial statements.
- --------------------------------------------------------------------------------
                                       10



<PAGE>

<PAGE>

- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
                         NOTES TO FINANCIAL STATEMENTS
 
NOTE 1. SIGNIFICANT ACCOUNTING POLICIES
 
     Cohen & Steers Special Equity Fund, Inc. (the 'Fund') was incorporated
under the laws of the State of Maryland on February 14, 1997 and is registered
under the Investment Company Act of 1940, as amended, as an open-end,
non-diversified management investment company. The following is a summary of
significant accounting policies followed by the Fund in the preparation of its
financial statements. The policies are in conformity with generally accepted
accounting principles. The preparation of the financial statements in accordance
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 reported period. Actual results could differ from
those estimates.
 
     Portfolio Valuation: Investments in securities that are listed on the New
York Stock Exchange are valued, except as indicated below, at the last sale
price reflected at the close of the New York Stock Exchange on the business day
as of which such value is being determined. If there has been no sale on such
day, the securities are valued at the mean of the closing bid and asked prices
for the day.
 
     Securities not listed on the New York Stock Exchange but listed on other
domestic or foreign securities exchanges or admitted to trading on the National
Association of Securities Dealers Automated Quotations, Inc. ('NASDAQ') National
Market System are valued in a similar manner. Securities traded on more than one
securities exchange are valued at the last sale price on the business day as of
which such value is being determined as reflected on the tape at the close of
the exchange representing the principal market for such securities.
 
     Readily marketable securities traded in the over-the-counter market,
including listed securities whose primary market is believed by the Adviser to
be over-the-counter, but excluding securities admitted to trading on the NASDAQ
National List, are valued at the mean of the current bid and asked prices as
reported by NASDAQ, the National Quotation Bureau or such other comparable
sources as the Board of Directors deems appropriate to reflect their fair market
value. Where securities are traded on more than one exchange and also
over-the-counter, the securities will generally be valued using the quotations
the Board of Directors believes reflect most closely the value of such
securities.
 
     Short-term debt securities, which have a maturity value of 60 days or less,
are valued at amortized cost which approximates value.
 
     Security Transactions and Investment Income: Security transactions are
recorded on trade date. Realized gains and losses on investments sold are
recorded on the basis of identified cost for accounting and tax purposes.
Interest income is recorded on the accrual basis. Dividend income is recorded on
the ex-dividend date.
 
     Dividends and Distributions to Shareholders: Dividends from net investment
income are declared and paid semi-annually. A portion of the Fund's dividend may
consist of amounts in excess of net investment income
 
- --------------------------------------------------------------------------------
                                       11
 


<PAGE>

<PAGE>

- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
derived from non-taxable components of the dividends from the Fund's portfolio
investments. As a result, the Fund had a return of capital of $618,421 ($0.17
per share) for the period ended December 31, 1998, which has been deducted from
paid-in capital. Net realized capital gains, unless offset by any available
capital loss carryforward, are distributed to shareholders annually.
Distributions to shareholders are recorded on the ex-dividend date.
 
     Dividends will automatically be reinvested in full and fractional shares of
the Fund based on the net asset value per share at the close of business on the
ex-dividend date unless the shareholder has elected to have them paid in cash.
 
     Dividends from net investment income and capital gain distributions are
determined in accordance with U.S. Federal income tax regulations which may
differ from generally accepted accounting principles. During the year ended
December 31, 1998, the Fund decreased undistributed net investment income and
accumulated net realized loss on investments sold by $676,586. These differences
are primarily due to return of capital and capital gain distributions received
by the Fund on portfolio securities.
 
     Federal Income Taxes: It is the policy of the Fund to qualify as a
regulated investment company, if such qualification is in the best interest of
the shareholders, by complying with the requirements of Subchapter M of the
Internal Revenue Code applicable to regulated investment companies, and by
distributing substantially all of its taxable earnings to its shareholders.
Accordingly, no provision for federal income or excise tax is necessary.
 
     Organization Costs: All costs incurred in connection with organizing and
establishing the Fund are being amortized on the straight-line basis over a
period of five years from the date on which the Fund commenced operations. For
the year ended December 31, 1998, the Fund amortized $21,219 in organization
expenses.
 
NOTE 2. INVESTMENT ADVISORY AND ADMINISTRATION FEES AND OTHER TRANSACTIONS WITH
AFFILIATES
 
     Investment Advisory Fees: Cohen & Steers Capital Management, Inc. (the
'Adviser') serves as the Fund's investment adviser pursuant to an investment
advisory agreement (the 'Advisory Agreement'). Under the terms of the Advisory
Agreement, the Adviser provides the Fund with the day-to-day investment
decisions and generally manages the Fund's investments in accordance with the
stated policies of the Fund, subject to the supervision of the Fund's Board of
Directors. For the services provided to the Fund, the Adviser receives a monthly
fee in an amount equal to 1/12th of 0.90% of the average daily net assets of the
Fund. For the year ended December 31, 1998, the Fund incurred $1,035,302 in
advisory fees.
 
     The Investment Adviser has voluntarily agreed to limit the total expenses
of the Fund (excluding interest, taxes, brokerage, and extraordinary expenses)
to an annual rate of 1.35% of the Fund's average net assets until December 31,
1998. As long as this expense cap continues, it may lower the Fund's expenses
and increase its total return. After December 31, 1998, the expense limitation
may be terminated or revised at any time, at which time the Fund's expenses may
increase and its total return may be reduced depending on the total assets of
the Fund.
 
- --------------------------------------------------------------------------------
                                       12



 

<PAGE>

<PAGE>

- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
For the year ended December 31, 1998, the Fund's actual expense ratio did not
exceed 1.35% and the expense limitation was not needed.
 
     Administration Fees: The Fund has entered into an administrative agreement
with the Adviser under which the Adviser performs certain administrative
functions for the Fund and receives a fee of 0.02% of the Fund's average daily
net assets. For the year ended December 31, 1998, the Fund paid the Adviser
$23,033 in fees under this administrative agreement.
 
     In addition, the Fund has entered into a fund accounting and
sub-administration agreement with the Chase Manhattan Bank ('Chase') for
performing administration functions for the Fund. Chase receives a monthly sub-
administration fee at the annual rate of 0.08% on the first $500 million of the
Fund's average daily net assets and at lower rates on the Fund's average daily
net assets in excess of that amount.
 
     Directors' Fees: Certain directors and officers of the Fund are also
directors, officers and/or employees of the Adviser. None of the directors and
officers so affiliated received compensation for their services as directors of
the Fund. For the year ended December 31, 1998, fees and related expenses
accrued for non-affiliated directors totaled $32,000.
 
NOTE 3. PURCHASES AND SALES OF SECURITIES
 
     Purchases and sales of securities, excluding short-term investments, for
the year ended December 31, 1998 totaled $121,487,267 and $139,357,545,
respectively.
 
     At December 31, 1998, the cost and unrealized appreciation or depreciation
in value of the investments owned by the Fund, as computed on a federal income
tax basis, are as follows:
 
<TABLE>
<S>                                                                          <C>
Aggregate cost.............................................................  $ 73,687,572
                                                                             ------------
Gross unrealized appreciation..............................................  $  1,001,485
Gross unrealized depreciation..............................................  $(16,567,063)
                                                                             ------------
Net unrealized depreciation................................................  $(15,565,578)
                                                                             ------------
                                                                             ------------
</TABLE>
 
- --------------------------------------------------------------------------------
                                       13
 


<PAGE>

<PAGE>

- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
 
NOTE 4. CAPITAL STOCK
 
     The Fund is authorized to issue 50 million shares of capital stock, par
value $0.001 per share. The Board of Directors of the Fund may increase or
decrease the aggregate number of shares of common stock that the Fund has
authority to issue. Transactions in Fund shares were as follows:
 
<TABLE>
<CAPTION>
                                                                                        FOR THE PERIOD MAY 8,
                                                                                               1997'D'
                                                              FOR THE YEAR ENDED               THROUGH
                                                               DECEMBER 31, 1998          DECEMBER 31, 1997
                                                           -------------------------   ------------------------
                                                             SHARES        AMOUNT       SHARES        AMOUNT
                                                           ----------   ------------   ---------   ------------
<S>                                                        <C>          <C>            <C>         <C>
Sold.....................................................   1,527,210   $ 44,026,634   4,119,793   $119,603,412
Issued as reinvestment of dividends......................      62,196      1,534,584     346,987     10,609,778
Redeemed.................................................  (3,162,004)   (75,061,000)   (255,872)    (8,061,796)
                                                           ----------   ------------   ---------   ------------
Net increase/(decrease)..................................  (1,572,598)  $(29,499,782)  4,210,908   $122,151,394
                                                           ----------   ------------   ---------   ------------
                                                           ----------   ------------   ---------   ------------
</TABLE>
 
- ------------------------
'D' Commencement of operations.
 
NOTE 5. DIRECTED BROKERAGE ARRANGEMENTS
 
     The Adviser has directed certain portfolio trades to brokers who paid a
portion of the Fund's expenses. For the year ended December 31, 1998, the Fund's
expenses were reduced by $35,057 under this arrangement.
 
NOTE 6. BORROWINGS
 
     The Fund, in conjunction with Cohen & Steers Realty Shares, Inc. and Cohen
& Steers Equity Income Fund, Inc., has entered into a Line of Credit Agreement
with Chase Manhattan Bank for $250,000,000. At December 31, 1998, the Fund had
loans outstanding totaling $4,000,000. For the period November 16, 1998 through
December 31, 1998, the average daily balance of loans outstanding was $4,000,000
at a weighted average interest rate of 6.00%. The maximum amount of loans
outstanding at any time during the year ended was $4,000,000. The loan is
collaterized by the Fund's portfolio.
 
NOTE 7. FEDERAL INCOME TAX-CAPITAL LOSS CARRYFORWARD
     At December 31, 1998, the Fund had a capital loss carryforward of
$20,978,620 expiring in 2006.
 
- --------------------------------------------------------------------------------
                                       14



<PAGE>
 

<PAGE>

- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC.
                       REPORT OF INDEPENDENT ACCOUNTANTS
 
To the Shareholders and Board of Directors of
Cohen & Steers Special Equity Fund, Inc.:
 
     In our opinion, the accompanying statement of assets and liabilities,
including the portfolio of investments, and the related statement of operations,
statements of changes in net assets and the financial highlights present fairly,
in all material respects, the financial position of Cohen & Steers Special
Equity Fund, Inc. (the 'Fund') at December 31, 1998, the results of its
operations for the year then ended and the changes in its net assets and
financial highlights for the year then ended and for the period from May 8, 1997
(commencements of operations) to December 31, 1997, in conformity with generally
accepted accounting principles. These financial statements and financial
highlights (hereafter referred to as 'financial statements') are the
responsibility of the Fund's management; our responsibility is to express an
opinion on these financial statements based on our audits. We conducted our
audits of these financial statements in accordance with generally accepted
auditing standards which require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements are free of material
misstatement. An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements, assessing the
accounting principles used and significant estimates made by management, and
evaluating the overall financial statement presentation. We believe that our
audits, which included confirmation of securities at December 31, 1998 by
correspondence with the custodian and brokers, provide a reasonable basis for
the opinion expressed above.

                                                      PricewaterhouseCoopers LLP
 
New York, New York
February 5, 1999
 
- --------------------------------------------------------------------------------
                                       15



<PAGE>

<PAGE>

- --------------------------------------------------------------------------------
                    COHEN & STEERS SPECIAL EQUITY FUND, INC. 
<TABLE>
<S>                                                        <C>
OFFICERS AND DIRECTORS                                     KEY INFORMATION
 
 Robert H. Steers                                          INVESTMENT ADVISER
 Director and Chairman                                     Cohen & Steers Capital Management, Inc.
                                                           757 Third Avenue
 Martin Cohen                                              New York, NY 10017
 Director and President                                    (212) 832-3232

 Gregory C. Clark                                          FUND ADMINISTRATOR AND TRANSFER AGENT
 Director                                                  Chase Global Funds Services Co.
                                                           73 Tremont Street
 George Grossman                                           Boston, MA 02108
 Director                                                  (800) 437-9912

 Jeffrey H. Lynford                                        CUSTODIAN
 Director                                                  The Chase Manhattan Bank, N.A.
                                                           One Chase Manhattan Plaza
 Willard H. Smith, Jr.                                     New York, NY 10081
 Director                                                  
                                                           LEGAL COUNSEL
 Elizabeth O. Reagan                                       Dechert Price & Rhoads
 Vice President                                            1775 Eye Street, NW
                                                           Washington, DC 20006
 Adam Derechin                                             
 Vice President and                                        NASDAQ Symbol: CSSPX
 Assistant Treasurer                                       Website: www.cohenandsteers.com
                                                           
                                                           Net asset value (NAV) can be found in the daily mutual
                                                           fund listings in the financial section of most major
                                                           newspapers under Cohen & Steers.

                                                           This report is authorized for delivery only to
                                                           shareholders of Cohen & Steers Special Equity Fund, Inc.
                                                           unless accompanied or preceded by the delivery of a
                                                           currently effective prospectus setting forth details of
                                                           the Fund.
</TABLE>
 
- --------------------------------------------------------------------------------
                                       16
 


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                      [THIS PAGE INTENTIONALLY LEFT BLANK]


<PAGE>

<PAGE>


                                 COHEN & STEERS
                               SPECIAL EQUITY FUND
                               -------------------
                                  ANNUAL REPORT
                                DECEMBER 31, 1998


COHEN & STEERS
SPECIAL EQUITY FUND
757 THIRD AVENUE
NEW YORK, NY 10017

First Class Mail
  U.S. Postage 
     PAID
  Boston, MA
Permit No. 56712


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

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





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