GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND INC
N-30D, 1995-03-29
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LETTER TO SHAREHOLDERS
Dear Shareholder:
    Yields on short-term Government securities have continued to rise for the
past year, due to a combination of factors: the Federal Reserve Board's
campaign to curb inflation, and the pressures of a robustly expanding
economy.
    The return to investors in the General Government Securities Money Market
Fund, Inc. reflects these developments.
    For the fiscal year ended January 31, 1995, the yield of the Fund's
shares was 3.83%. The effective yield, after compounding, was 3.90%.*
    The actions of the Federal Reserve in raising interest rates seven times
during the past twelve months were instrumental in shaping the yield curve.
However, the role of the expanding U.S. economy cannot be underestimated. For
most of the year, there has been steady expansion in such critical
measurements as Gross Domestic Product, utilization of factory capacity,
creation of new jobs, production of automobiles, new housing and heavy
construction.
    All this has been accomplished, so far, with very modest increases in
consumer and producer prices.
    Lately, there have been some signs of slowing in the rate of expansion,
along with an indication that the costs of raw materials and semi-finished
goods may be starting to rise.
    At the time of this writing, it is too early to tell whether the economy
is in fact starting to slow down. If that is the case, it might not be
necessary for the Federal Reserve Board to raise interest rates in late May.
The economy itself could conceivably act as a brake on inflation.
    However, if the indications of a so-called "soft landing" for the U.S.
economy are misleading, then the cost increases that have been noted in the
early stages of the production pipeline may soon work through to the consumer
level. In that case, increases in producer prices and in the consumer price
level could likely persuade the Federal Reserve Board to take further
measures to increase the Federal Funds rate, or the discount rate, or both.
    With such important questions still unresolved, we are currently
following cautious policies in handling the portfolio of your Fund. Our
preference is to keep average maturities shorter than we would under more
stable market conditions. This places the Fund in a good position to lengthen
maturities if we detect signs that interest rates are stabilizing, or even
turning around.
    We will be watching economic developments closely and will make portfolio
adjustments as we deem appropriate.
    As announced by The Dreyfus Corporation, Joseph S. DiMartino resigned as
President of the Dreyfus Corporation in December of 1994, and as President of
the General Government Securities Money Market Fund, Inc. in August of 1994.
Mr. DiMartino assumed the duties of Chairman of the Board of Directors of the
General Government Securities Money Market Fund Inc. in January of 1995. I
have worked closely with Mr. DiMartino for the past eight years and presently
manage other Dreyfus money market funds.
    We are committed to continuing the investment service this Fund has
provided to you in the past, and look forward to serving your investment
needs in the future.
                              Sincerely,
                             (Robert P. Fort, Jr.)
                              Robert P. Fort, Jr.
                              Portfolio Manager
February 23, 1995
New York, N.Y.
  *    Effective yield is based upon dividends declared daily and reinvested
monthly.
<TABLE>
<CAPTION>

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                                                                  JANUARY 31, 1995
                                                                             ANNUALIZED
                                                                              YIELD ON
                                                                              DATE OF              PRINCIPAL
U.S. TREASURY BILLS--4.8%                                                     PURCHASE               AMOUNT           VALUE
                                                                           ------------          --------------   ------------
    <S>                                                                     <C>                   <C>             <C>
    6/1/95
      (cost $24,522,917)........................................            5.90%                 $  25,000,000   $24,522,917
                                                                                                                  ===========
U.S. GOVERNMENT AGENCIES--80.9%
Federal Farm Credit Banks, Discount Notes
    2/13/95.....................................................            6.05%                 $  13,700,000   $13,672,691
Federal Farm Credit Banks, Floating Rate Notes
    11/29/95....................................................            5.94(a)                  25,000,000    24,991,754
    9/3/96......................................................            5.88(a)                  50,000,000    50,000,000
Federal Home Loan Banks, Discount Notes
    3/27/95.....................................................            6.09                     20,000,000    19,819,700
    4/19/95.....................................................            6.12                     40,000,000    39,484,100
    5/18/95.....................................................            6.20                     23,990,000    23,560,526
Federal Home Loan Banks, Floating Rate Notes
    5/6/96......................................................            5.82(a)                  20,000,000    19,989,430
Federal National Mortgage Association, Discount Notes
    2/13/95.....................................................            5.18                     20,000,000    19,966,333
    3/3/95......................................................            5.73                     26,490,000    26,365,854
    5/4/95......................................................            6.06                     30,000,000    29,543,833
    5/17/95.....................................................            6.20                     29,010,000    28,495,556
    6/12/95.....................................................            6.49                     10,000,000     9,770,022
    6/16/95.....................................................            6.27                     20,000,000    19,541,750
Federal National Mortgage Association, Floating Rate Notes
    10/4/96.....................................................            5.95(a)                  25,000,000    25,000,000
Student Loan Marketing Association, Floating Rate Notes
    4/24/95.....................................................            6.39(b)                  25,000,000    25,000,000
    6/2/95......................................................            6.17(b)                   2,500,000     2,500,000
    3/20/96.....................................................            6.22(b)                  17,500,000    17,500,000
    12/20/96....................................................            6.09(b)                  20,000,000    20,000,000
                                                                                                                  ------------
TOTAL U.S. GOVERNMENT AGENCIES (cost $415,201,549)..............                                                 $415,201,549
                                                                                                                  ============


GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                        JANUARY 31, 1995
                                                                             ANNUALIZED
                                                                              YIELD ON
                                                                              DATE OF              PRINCIPAL
REPURCHASE AGREEMENTS--12.8%                                                  PURCHASE               AMOUNT          VALUE
                                                                           ------------          --------------    -----------

First Interstate Bank of California
    dated 1/31/95, due 2/1/95 in the amount of
    $3,624,529 (fully collateralized by
    $3,530,000 U.S. Treasury Notes 11.25%,
    due 5/15/95, valued $3,665,209).............................            5.25%                 $   3,624,000    $3,624,000
Lehman Government Securities, Inc.
    dated 1/31/95, due 2/1/95 in the amount of
    $16,002,578 (fully collateralized by
    $16,135,000 U.S. Treasury Notes 4.625%,
    due 8/15/95, valued $16,318,382)............................            5.80                     16,000,000    16,000,000
Yamaichi International America, Inc.
    dated 1/31/95, due 2/1/95 in the amount of
    $46,007,411 (fully collateralized by
    $46,445,000 U.S. Treasury Notes 3.875%,
    due 8/31/95, valued $46,528,476)............................            5.80                     46,000,000    46,000,000
                                                                                                                  ------------
TOTAL REPURCHASE AGREEMENTS (cost $65,624,000)..................                                                 $ 65,624,000
                                                                                                                 ============
TOTAL INVESTMENTS (cost  $505,348,466).................                    98.5%                                 $505,348,466
                                                                         =======                                 ============
CASH AND RECEIVABLES (NET).............................                     1.5%                                  $ 7,997,008
                                                                         =======                                 ============
NET ASSETS.............................................                   100.0%                                 $513,345,474
                                                                         =======                                 ============
</TABLE>
NOTES TO STATEMENT OF INVESTMENTS:
    (a)  The interest rate, which will change periodically, is based on the
         bank's prime rate.
    (b)  Variable interest rate_subject to change approximately every 7 to 30
         days.



See notes to financial statements.
<TABLE>
<CAPTION>

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                                                                           JANUARY 31, 1995
<S>                                                                                               <C>             <C>
ASSETS:
    Investments in securities, at value
      (including repurchase agreements of $65,624,000)--Note 1(a,b).........                                      $505,348,466
    Cash....................................................................                                         7,495,416
    Interest receivable.....................................................                                         1,387,451
    Prepaid expenses........................................................                                            82,298
                                                                                                                --------------
                                                                                                                   514,313,631
LIABILITIES:
    Due to The Dreyfus Corporation..........................................                      $  292,994
    Payable for Common Stock redeemed.......................................                         498,688
    Accrued expenses........................................................                         176,475           968,157
                                                                                                ------------    --------------
NET ASSETS  ................................................................                                      $513,345,474
                                                                                                                ==============
REPRESENTED BY:
    Paid-in capital.........................................................                                      $513,350,168
    Accumulated net realized (loss) on investments..........................                                            (4,694)
                                                                                                                --------------
NET ASSETS at value applicable to 513,350,168 shares outstanding
    (15 billion shares of $.01 par value Common Stock authorized)...........                                      $513,345,474
                                                                                                                ==============
NET ASSET VALUE, offering and redemption price per share
    ($513,345,474 / 513,350,168 shares).....................................                                             $1.00
                                                                                                                         =====

STATEMENT OF OPERATIONS                                                                       YEAR ENDED JANUARY 31, 1995
INVESTMENT INCOME:
    INVESTMENT INCOME.......................................................                                      $ 24,418,169
    EXPENSES:
      Management fee_Note 2(a)..............................................                      $2,624,643
      Shareholder servicing costs_Note 2(b,c)...............................                       1,426,053
      Custodian fees........................................................                         160,174
      Registration fees.....................................................                         53,093
      Professional fees.....................................................                         35,902
      Directors' fees and expenses_Note 2(d)................................                         25,217
      Prospectus and shareholders' reports..................................                         10,669
      Miscellaneous.........................................................                         14,390
                                                                                                ------------
          TOTAL EXPENSES....................................................                                         4,350,141
                                                                                                                --------------
INVESTMENT INCOME--NET......................................................                                        20,068,028
NET REALIZED (LOSS) ON INVESTMENTS--Note 1(b)...............................                                            (4,571)
                                                                                                                --------------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                     $  20,063,457
                                                                                                                ==============
</TABLE>

See notes to financial statements.

<TABLE>
<CAPTION>

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS


                                                                                            YEAR ENDED JANUARY 31,

                                                                                      -------------------------------
                                                                                            1994              1995
                                                                                      ----------------     ----------
<S>                                                                                  <C>               <C>
OPERATIONS:
    Investment income--net..................................................         $  16,844,770     $ 20,068,028
    Net realized gain (loss) on investments.................................                20,284           (4,571)
                                                                                  ----------------  ---------------
      NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS..................            16,865,054       20,063,457
                                                                                  ----------------  ---------------
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income--net..................................................           (16,844,770)     (20,068,028)
                                                                                  ----------------  ---------------
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold...........................................         4,909,502,664    4,356,251,849
    Dividends reinvested....................................................            15,932,788       19,433,620
    Cost of shares redeemed.................................................        (5,113,990,985)  (4,399,218,939)
                                                                                  ----------------  ---------------
      (DECREASE) IN NET ASSETS FROM CAPITAL STOCK TRANSACTIONS..............          (188,555,533)     (23,533,470)
                                                                                  ----------------  ---------------
          TOTAL (DECREASE) IN NET ASSETS....................................          (188,535,249)     (23,538,041)
NET ASSETS:
    Beginning of year.......................................................           725,418,764      536,883,515
                                                                                  ----------------  ---------------
    End of year.............................................................       $   536,883,515   $  513,345,474
                                                                                   ===============  ===============
</TABLE>


See notes to financial statements.

<TABLE>
<CAPTION>

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
FINANCIAL HIGHLIGHTS
    Contained below is per share operating performance data for a share of
Common Stock outstanding, total investment return, ratios to average net
assets and other supplemental data for each year indicated. This information
has been derived from the Fund's financial statements.

                                                                                YEAR ENDED JANUARY 31,
                                                           --------------------------------------------------------
PER SHARE DATA:                                              1991         1992       1993          1994        1995
                                                           --------     --------   --------      -------- ---------
    <S>                                                     <C>          <C>        <C>           <C>       <C>
    Net asset value, beginning of year...........           $1.0000      $ .9999    $ .9999       $1.0000   $1.0000
                                                           --------     --------   --------      -------- ---------
    INVESTMENT OPERATIONS:
    Investment income--net.......................             .0718        .0532      .0330         .0266     .0383
    Net realized gain (loss) on investments......            (.0001)       --         .0001         --        --
                                                           --------     --------   --------      -------- ---------
      TOTAL FROM INVESTMENT OPERATIONS...........             .0717        .0532      .0331         .0266     .0383
                                                           --------     --------   --------      -------- ---------
    DISTRIBUTIONS:
    Dividends from investment income--net........            (.0718)      (.0532)    (.0330)       (.0266)   (.0383)
    Dividends from net realized gain on investments           --           --         --            --        --
                                                           --------     --------   --------      -------- ---------
      TOTAL DISTRIBUTIONS........................            (.0718)      (.0532)    (.0330)       (.0266)   (.0383)
                                                           --------     --------   --------      -------- ---------
    Net asset value, end of year.................           $ .9999      $ .9999    $1.0000       $1.0000   $1.0000
                                                           ========     ========   ========      ======== =========
TOTAL INVESTMENT RETURN                                      7.42%        5.46%      3.36%         2.69%     3.90%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets......             .86%         .82%       .82%          .81%      .83%
    Ratio of net investment income to average net assets     7.14%        5.27%      3.28%         2.66%     3.82%
    Net Assets, end of year (000's Omitted)......           $408,817     $609,015   $725,419      $536,884  $513,345
</TABLE>


See notes to financial statements.
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS
NOTE 1--SIGNIFICANT ACCOUNTING POLICIES:
    The Fund is registered under the Investment Company Act of 1940 ("Act")
as a diversified open-end management investment company. Dreyfus Service
Corporation, until August 24, 1994, acted as the distributor of the Fund's
shares, which are sold to the public without a sales load. Dreyfus Service
Corporation is a wholly-owned subsidiary of The Dreyfus Corporation
("Manager"). Effective August 24, 1994, the Manager became a direct
subsidiary of Mellon Bank, N.A.
    On August 24, 1994, Premier Mutual Fund Services, Inc. (the
"Distributor") was engaged as the Fund's distributor. The Distributor,
located at One Exchange Place, Boston, Massachusetts 02109, is a wholly-owned
subsidiary of Institutional Administration Services, Inc., a provider of
mutual fund administration services, the parent company of which is Boston
Institutional Group, Inc.
    It is the Fund's policy to maintain a continuous net asset value per
share of $1.00; the Fund has adopted certain investment, portfolio valuation
and dividend and distribution policies to enable it to do so. There is no
assurance, however, that the Fund will be able to maintain a stable net asset
value of $1.00.
    (A) PORTFOLIO VALUATION: Investments are valued at amortized cost, which
has been determined by the Fund's Board of Directors to represent the fair
value of the Fund's investments.
    (B) SECURITIES TRANSACTIONS AND INVESTMENT INCOME: Securities
transactions are recorded on a trade date basis. Realized gain and loss from
securities transactions are recorded on the identified cost basis. Interest
income is recognized on the accrual basis. Cost of investments represents
amortized cost.
    The Fund may enter into repurchase agreements with financial
institutions, deemed to be creditworthy by the Manager, subject to the
seller's agreement to repurchase and the Fund's agreement to resell such
securities at a mutually agreed upon price. Securities purchased subject to
repurchase agreements are deposited with the Fund's custodians and, pursuant
to the terms of the repurchase agreement, must have an aggregate market value
greater than or equal to the repurchase price plus accrued interest at all
times. If the value of the underlying securities falls below the value of the
repurchase price plus accrued interest, the Fund will require the seller to
deposit additional collateral by the next business day. If the request for
additional collateral is not met, or the seller defaults on its repurchase
obligation, the Fund maintains the right to sell the underlying securities at
market value and may claim any resulting loss against the seller.
    (C) DIVIDENDS TO SHAREHOLDERS: It is the policy of the Fund to declare
dividends from investment income--net on each business day. Such dividends
are paid monthly. Dividends from net realized capital gain are normally
declared and paid annually, but the Fund may make distributions on a more
frequent basis to comply with the distribution requirements of the Internal
Revenue Code. To the extent that net realized capital gain can be offset by
capital loss carryovers, if any, it is the policy of the Fund not to
distribute such gain.
    (D) FEDERAL INCOME TAXES: It is the policy of the Fund to continue to
qualify as a regulated investment company, if such qualification is in the
best interests of its shareholders, by complying with the applicable
provisions of the Internal Revenue Code, and to make distributions of taxable
income sufficient to relieve it from substantially all Federal income and
excise taxes.

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
    At January 31, 1995, the cost of investments for Federal income tax
purposes was substantially the same as the cost for financial reporting
purposes (see the Statement of Investments).
NOTE 2--MANAGEMENT FEE AND OTHER TRANSACTIONS WITH AFFILIATES:
    (A) Pursuant to a management agreement ("Agreement") with the Manager,
the management fee is computed at the annual rate of .50 of 1% of the average
daily value of the Fund's net assets and is payable monthly.
    The Agreement provides for an expense reimbursement from the Manager
should the Fund's aggregate expenses, exclusive of taxes, brokerage, interest
on borrowings and extraordinary expenses, exceed 1-1/2% of the average value
of the Fund's net assets for any full fiscal year. There was no expense
reimbursement for the year ended January 31, 1995.
    (B) On August 3, 1994, Fund shareholders approved a revised Service Plan
(the "Plan") pursuant to Rule 12b-1 under the Act. Pursuant to the Plan,
effective August 24, 1994, the Fund (a) reimburses the Distributor for
payments to third parties for distributing the Fund's shares and servicing
shareholder accounts and (b) pays the Manager, Dreyfus Service Corporation or
any affiliate (collectively "Dreyfus") for advertising and marketing relating
to the Fund and servicing Shareholders accounts, at an aggregate annual rate
of .20 of 1% of the value of the Fund's average daily net assets. Each of the
Distributor and Dreyfus may pay Service Agents (a securities dealer,
financial institution or other industry professional) a fee in respect of the
Fund's shares owned by shareholders with whom the Service Agent has a
servicing relationship or for whom the Service Agent is the dealer or holders
of record. Each of the Distributor and Dreyfus determine the amounts to be
paid to Service Agents to which it will make payments and the basis on which
such payments are made.
    Prior to August 24, 1994, the Fund's Service Plan ("prior Service Plan")
provided that the Fund pay Dreyfus Service Corporation at an annual rate of
.20 of 1% of the value of the Fund's average daily net assets, for costs and
expenses in connection with advertising, marketing and distributing the
Fund's shares and for servicing shareholder accounts. Dreyfus Service
Corporation made payments to one or more Service Agents based on the value of
the Fund's shares owned by clients of the Service Agent.
    During the year ended January 31, 1995, $460,344 was charged to the Fund
pursuant to the Plan and 589,513 was charged pursuant to the prior Service
Plan.
    (C) Pursuant to the Fund's Shareholder Services Plan, the Fund reimburses
Dreyfus Service Corporation an amount not to exceed an annual rate of .25 of
1% of the value of the Fund's average daily net assets for servicing
shareholder accounts. The services provided may include personal services
relating to shareholder accounts, such as answering shareholder inquiries
regarding the Fund and providing reports and other information, and services
related to the maintenance of shareholder accounts. During the year ended
January 31, 1995, $181,926 was charged to the Fund pursuant to the
Shareholder Services Plan.
    (D) Prior to August 24, 1994, certain officers and directors of the Fund
were "affiliated persons," as defined in the Act, of the Manager and/or
Dreyfus Service Corporation. Each director who is not an "affiliated person"
receives an annual fee of $2,500 and an attendance fee of $500 per meeting.

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS
SHAREHOLDERS AND BOARD OF DIRECTORS
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
    We have audited the accompanying statement of assets and liabilities of
General Government Securities Money Market Fund, Inc., including the
statement of investments, as of January 31, 1995, 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 financial highlights
for each of the years indicated therein. 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 January 31, 1995 by correspondence with the custodians
and others. 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 General Government Securities Money Market Fund, Inc. at January
31, 1995, 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 indicated years, in conformity with
generally accepted accounting principles.

                              (Ernst & Young LLP Signature Logo)
New York, New York
March 6, 1995
GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND, INC.
IMPORTANT TAX INFORMATION (UNAUDITED)
    For State individual income tax purposes, the Fund hereby designates
53.63% of the ordinary income dividends paid during its fiscal year ended
January 31, 1995 as attributable to interest income from direct obligations
of the United States. Such dividends are currently exempt from taxation for
individual income tax purposes in most states, including New York, California
and the District of Columbia.

GENERAL GOVERNMENT SECURITIES
MONEY MARKET FUND, INC.
200 Park Avenue
New York, NY 10166
Manager
THE DREYFUS CORPORATION
200 Park Avenue
New York, NY 10166
Custodian
THE BANK OF NEW YORK
90 Washington Street
New York, NY 10286
Transfer Agent &
Dividend Disbursing Agent
The Shareholder Services Group, Inc.
P.O. Box 9671
Providence, RI 02940




Further information is contained
in the Prospectus, which must
precede or accompany this report.




Printed in U.S.A.                              975AR951


GENERAL
GOVERNMENT
SECURITIES
MONEY MARKET
FUND, INC.


(General Government Logo)



ANNUAL REPORT
January 31, 1995
















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