UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  FORM N-CSRS

                   CERTIFIED SHAREHOLDER REPORT OF REGISTERED
                         MANAGEMENT INVESTMENT COMPANIES

Investment Company Act file number: 811-03159

Active Assets Money Trust
               (Exact name of registrant as specified in charter)

1221 Avenue of the Americas, New York, New York 10020
               (Address of principal executive offices)             (Zip code)

Ronald E. Robison
1221 Avenue of the Americas, New York, New York 10020
                     (Name and address of agent for service)

Registrant's telephone number, including area code: 212-762-4000

Date of fiscal year end: June 30, 2004

Date of reporting period: December 31, 2003

Item 1 - Report to Shareholders


Welcome, Shareholder:

In this report, you'll learn about how your investment in Active Assets Money
Trust performed during the semiannual period. We will provide an overview of the
market conditions, and discuss some of the factors that affected performance
during the reporting period. In addition, this report includes the Fund's
financial statements and a list of Fund investments.

This material must be preceded or accompanied by a prospectus for the fund being
offered. Market forecasts provided in this report may not necessarily come to
pass. There is no assurance that the Fund will achieve its investment objective.
The Fund is subject to market risk, which is the possibility that market values
of securities owned by the Fund will decline and, therefore, the value of the
Fund's shares may be less than what you paid for them. Accordingly, you can lose
money investing in this Fund.


FUND REPORT

For the six-month period ended December 31, 2003

MARKET CONDITIONS

The Federal Open Market Committee (the "Fed") lowered its target rate for
federal funds to 1.00 percent, a 45-year low, on June 25, 2003. It maintained
that target throughout the second half of the year to encourage a faster pace of
economic activity. By the second half of 2003 the combination of this highly
accommodative monetary posture and stimulative fiscal policies in the form of
tax cuts appeared to begin to have an effect, with many companies reporting
improved second-half earnings and the third-quarter GDP increasing to 8.2
percent. The Fed's sustained emphasis on low interest rates had a marked impact
on money market fund yields, which reached record low levels during the period.

PERFORMANCE ANALYSIS

As of December 31, 2003, Active Assets Money Trust had net assets of more than
$21.2 billion and the average maturity of the Fund's portfolio was 63 days. For
the six-month period ended December 31, 2003, the Fund returned 0.34 percent.
For the seven-day period ended December 31, 2003, the Fund provided an effective
annualized yield of 0.69 and a current yield of 0.68 percent, while its 30-day
moving average yield for December was 0.68 percent. Past performance is no
guarantee of future results.

Our strategy in managing the Fund remained consistent with our long-term focus
on maintaining preservation of capital and very high liquidity.* As we have in
the past, we adhered to a conservative approach that avoided the use of
derivatives or structured notes that might fluctuate excessively with changing
interest rates. On December 31, 2003, approximately 55 percent of the Fund's
portfolio was invested in high-quality commercial paper, 28 percent in U.S.
Treasury and federal agency obligations and the remaining 17 percent in
certificates of deposit and short-term bank notes issued by financially strong
commercial banks. At the end of the fiscal period, approximately 89 percent of
the Fund's holdings were due to mature in less than four months.
- ----------------------------------------------------
*  An investment in the Fund is not insured or guaranteed by the Federal Deposit
   Insurance Corporation or any other government agency. Although the Fund seeks
   to preserve the value of your investment at $1.00 per share, it is possible
   to lose money by investing in the Fund.

2


<Table>
<Caption>
   PORTFOLIO COMPOSITION
                                                
   Commercial Paper                                    55.0%
   U.S. Government & Agency Obligations                27.9
   Certificates of Deposit                             12.4
   Bank Notes                                           4.7
</Table>

<Table>
<Caption>
   MATURITY SCHEDULE
                                                
     1 - 30 Days                                       29.1%
    31 - 60 Days                                       27.8
    61 - 90 Days                                       18.5
    91 - 120 Days                                      14.5
   121+ Days                                           10.1
</Table>

Subject to change daily. All percentages are as a percentage of total
investments. Provided for informational purposes only and should not be deemed
as a recommendation to buy or sell the securities mentioned. Morgan Stanley is a
full-service securities firm engaged in securities trading and brokerage
activities, investment banking, research and analysis, financing and financial
advisory services.

INVESTMENT STRATEGY

1) THE FUND INVESTS IN HIGH QUALITY, SHORT-TERM DEBT OBLIGATIONS.

2) IN SELECTING INVESTMENTS, THE FUND'S "INVESTMENT MANAGER," MORGAN STANLEY
   INVESTMENT ADVISORS INC., SEEKS TO MAINTAIN THE FUND'S SHARE PRICE AT $1.00.
   THE SHARE PRICE REMAINING STABLE AT $1.00 MEANS THAT THE FUND WOULD PRESERVE
   THE PRINCIPAL VALUE OF YOUR INVESTMENT.

                                                                               3


Active Assets Money Trust
PORTFOLIO OF INVESTMENTS - DECEMBER 31, 2003 (UNAUDITED)

<Table>
<Caption>
                                                                           ANNUALIZED
PRINCIPAL                            DESCRIPTION                              YIELD
AMOUNT IN                                AND                               ON DATE OF
THOUSANDS                           MATURITY DATES                          PURCHASE          VALUE
- ---------------------------------------------------------------------------------------------------------
                                                                                
             Commercial Paper (55.0%)
             Banking (1.8%)
$  376,000   Citicorp
               01/05/04 - 03/10/04.......................................  1.07 - 1.08%  $   375,642,501
                                                                                         ---------------
             Finance - Automotive (4.4%)
    92,000   DaimlerChrysler Revolving Auto Conduit
               01/16/04..................................................     1.10            91,957,833
   845,000   New Center Asset Trust
               01/09/04 - 02/18/04.......................................  1.08 - 1.09       844,252,471
                                                                                         ---------------
                                                                                             936,210,304
                                                                                         ---------------
             Finance - Corporate (0.2%)
    50,000   CIESCO, LLC
               01/15/04..................................................     1.08            49,979,000
                                                                                         ---------------

             Financial Conglomerates (8.0%)
 1,072,075   General Electric Capital Corp.
               01/05/04 - 06/04/04.......................................  1.09 - 1.19     1,068,996,449
   639,075   Mortgage Interest Networking Trust
               01/14/04 - 02/25/04.......................................  1.08 - 1.10       638,432,570
                                                                                         ---------------
                                                                                           1,707,429,019
                                                                                         ---------------
             Integrated Oil (0.9%)
   200,000   Shell Finance (U.K.) PLC
               01/30/04..................................................     1.11           199,821,167
                                                                                         ---------------

             International Banks (39.1%)
   400,650   ANZ (DE) Inc.
               02/10/04 - 03/02/04.......................................     1.08           400,016,390
    75,000   BNP Paribas Finance Inc.
               01/22/04..................................................     1.08            74,952,750
   350,000   Barclays U.S. Funding Corp.
               01/08/04 - 02/27/04.......................................  1.06 - 1.08       349,571,194
    33,650   CBA (Delaware) Finance Inc.
               03/12/04..................................................     1.08            33,578,657
   450,000   Canadian Imperial Holdings Inc.
               02/24/04 - 03/30/04.......................................  1.07 - 1.09       449,062,194
 1,064,550   Dexia Delaware LLC
               01/21/04 - 03/30/04.......................................  1.06 - 1.09     1,062,581,645
</Table>

4
                       See Notes to Financial Statements


Active Assets Money Trust
PORTFOLIO OF INVESTMENTS - DECEMBER 31, 2003 (UNAUDITED) continued

<Table>
<Caption>
                                                                           ANNUALIZED
PRINCIPAL                            DESCRIPTION                              YIELD
AMOUNT IN                                AND                               ON DATE OF
THOUSANDS                           MATURITY DATES                          PURCHASE          VALUE
- ---------------------------------------------------------------------------------------------------------
                                                                                
$1,042,250   ING (U.S.) Funding LLC
               01/06/04 - 03/17/04.......................................  1.07 - 1.09%  $ 1,041,612,892
   300,000   Rabobank USA Financial Corp.
               02/19/04 - 05/06/04.......................................  1.07 - 1.16       299,049,361
 1,050,000   Royal Bank of Canada
               02/26/04 - 04/30/04.......................................  1.07 - 1.13     1,047,494,042
 1,100,000   Royal Bank of Scotland PLC
               01/02/04 - 02/17/04.......................................  1.08 - 1.09     1,099,484,792
 1,018,075   Societe Generale N.A. Inc.
               02/02/04 - 04/29/04.......................................  1.07 - 1.08     1,015,993,787
 1,045,375   Toronto - Dominion Holdings (U.S.A.), Inc.
               01/07/04 - 02/25/04.......................................  1.08 - 1.09     1,044,654,425
   400,000   UBS Finance (Delaware) LLC
               04/30/04 - 07/30/04.......................................  1.16 - 1.27       397,228,834
                                                                                         ---------------
                                                                                           8,315,280,963
                                                                                         ---------------
             Investment Banks/Brokers (0.6%)
   125,000   Goldman Sachs Group, Inc. (The)
               03/01/04..................................................     1.11           124,768,750
                                                                                         ---------------
             Total Commercial Paper (Cost $11,709,131,704)............................    11,709,131,704
                                                                                         ---------------
             U.S. Government & Agency Obligations (27.9%)
 1,289,439   Federal Home Loan Banks
               01/14/04 - 06/09/04.......................................  1.03 - 1.09     1,288,128,805
   915,136   Federal National Mortgage Assoc.
               01/14/04 - 04/30/04.......................................  1.05 - 1.15       913,159,353
 2,812,825   Freddie Mac
               02/26/04 - 05/24/04.......................................  1.06 - 1.12     2,803,840,372
   929,300   U.S. Treasury Bills
               01/29/04 - 04/22/04.......................................  0.97 - 1.04       926,960,604
                                                                                         ---------------
             Total U.S. Government & Agency Obligations (Cost $5,932,089,134).........     5,932,089,134
                                                                                         ---------------
</Table>

                                                                               5
                       See Notes to Financial Statements


Active Assets Money Trust
PORTFOLIO OF INVESTMENTS - DECEMBER 31, 2003 (UNAUDITED) continued

<Table>
<Caption>
                                                                           ANNUALIZED
PRINCIPAL                            DESCRIPTION                              YIELD
AMOUNT IN                                AND                               ON DATE OF
THOUSANDS                           MATURITY DATES                          PURCHASE          VALUE
- ---------------------------------------------------------------------------------------------------------
                                                                                
             Certificates of Deposit (12.4%)
$  700,000   Bank of America, N.A.
               03/18/04..................................................    1.10%       $   700,000,000
   350,000   Citibank, N.A.
               02/06/04 - 02/23/04.......................................     1.09           350,000,000
   580,250   State Street Bank & Trust Co.
               02/09/04 - 03/09/04.......................................  1.04 - 1.08       580,250,000
 1,000,000   Wells Fargo Bank, N.A.
               01/15/04 - 03/19/04.......................................  1.04 - 1.07     1,000,000,000
                                                                                         ---------------
             Total Certificates of Deposit (Cost $2,630,250,000)......................     2,630,250,000
                                                                                         ---------------
             Short-Term Bank Notes (4.7%)
   350,000   Bank of America, N.A.
               05/07/04 - 05/13/04.......................................     1.13           350,000,000
   250,000   LaSalle Bank, N.A.
               01/22/04 - 02/05/04.......................................     1.08           250,000,000
   400,000   Standard Federal Bank, N.A.
               01/15/04 - 03/24/04.......................................  1.07 - 1.08       400,000,000
                                                                                         ---------------
             Total Short-Term Bank Notes (Cost $1,000,000,000)........................     1,000,000,000
                                                                                         ---------------
</Table>

<Table>
                                                                                
             Total Investments (Cost $21,271,470,838) (a).................    100.0%      21,271,470,838

             Liabilities in Excess of Other Assets........................     (0.0)          (3,928,313)
                                                                              -----      ---------------
             Net Assets...................................................    100.0%     $21,267,542,525
                                                                              =====      ===============
</Table>

- ---------------------
(a) Cost is the same for federal income tax purposes.

6
                       See Notes to Financial Statements


Active Assets Money Trust
FINANCIAL STATEMENTS

Statement of Assets and Liabilities
December 31, 2003 (unaudited)

<Table>
                                                           
Assets:
Investments in securities, at value
  (cost $21,271,470,838)....................................  $21,271,470,838
Cash........................................................           24,365
Interest receivable.........................................        3,570,304
Prepaid expenses and other assets...........................          237,090
                                                              ---------------
    Total Assets............................................   21,275,302,597
                                                              ---------------
Liabilities:
Payable for:
    Investment management fee...............................        5,336,883
    Distribution fee........................................        2,021,994
Accrued expenses and other payables.........................          401,195
                                                              ---------------
    Total Liabilities.......................................        7,760,072
                                                              ---------------
    Net Assets..............................................  $21,267,542,525
                                                              ===============
Composition of Net Assets:
Paid-in-capital.............................................  $21,267,485,831
Accumulated undistributed net investment income.............           56,694
                                                              ---------------
    Net Assets..............................................  $21,267,542,525
                                                              ===============
Net Asset Value Per Share,
21,267,527,630 shares outstanding (unlimited shares
authorized of $.01 par value)...............................            $1.00
                                                              ===============
</Table>

                                                                               7
                       See Notes to Financial Statements


Active Assets Money Trust
FINANCIAL STATEMENTS continued

Statement of Operations
For the six months ended December 31, 2003 (unaudited)

<Table>
                                                           
Net Investment Income:
Interest Income.............................................  $124,669,789
                                                              ------------
Expenses
Investment management fee...................................    30,516,278
Distribution fee............................................    11,580,246
Transfer agent fees and expenses............................     4,300,199
Custodian fees..............................................       449,225
Shareholder reports and notices.............................       353,434
Trustees' fees and expenses.................................       124,170
Registration fees...........................................        88,268
Professional fees...........................................        38,874
Other.......................................................       228,977
                                                              ------------
    Total Expenses..........................................    47,679,671
                                                              ------------
    Net Investment Income...................................    76,990,118

    Net Realized Gain.......................................        11,534
                                                              ------------
Net Increase................................................  $ 77,001,652
                                                              ============
</Table>

8
                       See Notes to Financial Statements


Active Assets Money Trust
FINANCIAL STATEMENTS continued

Statement of Changes in Net Assets

<Table>
<Caption>
                                                                 FOR THE SIX       FOR THE YEAR
                                                                MONTHS ENDED           ENDED
                                                              DECEMBER 31, 2003    JUNE 30, 2003
                                                              -----------------   ---------------
                                                                 (unaudited)
                                                                            
Increase (Decrease) in Net Assets:
Operations:
Net investment income.......................................   $    76,990,118    $   273,810,931
Net realized gain...........................................            11,534              1,905
                                                               ---------------    ---------------
    Net Increase............................................        77,001,652        273,812,836
                                                               ---------------    ---------------
Dividends and Distributions to Shareholders from:
Net investment income.......................................       (76,998,519)      (273,802,951)
Net realized gain...........................................           (11,534)            (1,905)
                                                               ---------------    ---------------
    Total Dividends and Distributions.......................       (77,010,053)      (273,804,856)
                                                               ---------------    ---------------

Net decrease from transactions in shares of beneficial
  interest..................................................    (2,010,108,839)    (1,760,025,590)
                                                               ---------------    ---------------
    Net Decrease............................................    (2,010,117,240)    (1,760,017,610)
Net Assets:
Beginning of period.........................................    23,277,659,765     25,037,677,375
                                                               ---------------    ---------------
End of Period
(Including accumulated undistributed net investment income
of $56,694 and $65,095, respectively).......................   $21,267,542,525    $23,277,659,765
                                                               ===============    ===============
</Table>

                                                                               9
                       See Notes to Financial Statements


Active Assets Money Trust
NOTES TO FINANCIAL STATEMENTS - DECEMBER 31, 2003 (UNAUDITED)

1. Organization and Accounting Policies

Active Assets Money Trust (the "Fund") is registered under the Investment
Company Act of 1940, as amended (the "Act"), as a diversified, open-end
management investment company. The Fund's investment objective is high current
income, preservation of capital and liquidity. The Fund was organized as a
Massachusetts business trust on March 30, 1981 and commenced operations on July
7, 1981.

The following is a summary of significant accounting policies:

A. Valuation of Investments -- Portfolio securities are valued at amortized
cost, which approximates market value.

B. Accounting for Investments -- Security transactions are accounted for on the
trade date (date the order to buy or sell is executed). Realized gains and
losses on security transactions are determined by the identified cost method.
Discounts are accreted and premiums are amortized over the life of the
respective securities. Interest income is accrued daily.

C. Repurchase Agreements -- The Fund may invest directly with institutions in
repurchase agreements. The Fund's custodian receives the collateral, which is
marked-to-market daily to determine that the value of the collateral does not
decrease below the repurchase price plus accrued interest.

D. Federal Income Tax Policy -- It is the Fund's policy to comply with the
requirements of the Internal Revenue Code applicable to regulated investment
companies and to distribute substantially all of its taxable income to its
shareholders. Accordingly, no federal income tax provision is required.

E. Dividends and Distributions to Shareholders -- The Fund records dividends and
distributions to shareholders as of the close of each business day.

F. Use of Estimates -- The preparation of financial statements in accordance
with generally accepted accounting principles requires management to make
estimates and assumptions that affect the reported amounts and disclosures.
Actual results could differ from those estimates.

2. Investment Management Agreement

Pursuant to an Investment Management Agreement with Morgan Stanley Investment
Advisors Inc. (the "Investment Manager"), the Fund pays the Investment Manager a
management fee, accrued daily and payable monthly, by applying the following
annual rates to the net assets of the Fund determined as of the close of each
business day: 0.50% to the portion of the daily net assets not exceeding $500
million; 0.425% to the portion of the daily net assets exceeding $500 million
but not

10


Active Assets Money Trust
NOTES TO FINANCIAL STATEMENTS - DECEMBER 31, 2003 (UNAUDITED) continued

exceeding $750 million; 0.375% to the portion of the daily net assets exceeding
$750 million but not exceeding $1 billion; 0.35% to the portion of the daily net
assets exceeding $1 billion but not exceeding $1.5 billion; 0.325% to the
portion of the daily net assets exceeding $1.5 billion but not exceeding $2
billion; 0.30% to the portion of the daily net assets exceeding $2 billion but
not exceeding $2.5 billion; 0.275% to the portion of the daily net assets
exceeding $2.5 billion but not exceeding $3 billion; 0.25% to the portion of the
daily net assets exceeding $3 billion but not exceeding $15 billion; 0.249% to
the portion of the daily net assets exceeding $15 billion but not exceeding
$17.5 billion; 0.248% to the portion of the daily net assets exceeding $17.5
billion but not exceeding $25 billion; 0.247% to the portion of daily net assets
exceeding $25 billion but not exceeding $30 billion; and 0.246% to the portion
of the daily net assets exceeding $30 billion.

3. Plan of Distribution

Morgan Stanley Distributors Inc. (the "Distributor"), an affiliate of the
Investment Manager, is the distributor of the Fund's shares and in accordance
with a Plan of Distribution (the "Plan") pursuant to Rule 12b-1 under the Act,
finances certain expenses in connection with the promotion of sales of Fund
shares.

Reimbursements for these expenses are made in monthly payments by the Fund to
the Distributor, which will in no event exceed an amount equal to a payment at
the annual rate of 0.15% of the Fund's average daily net assets during the
month. Expenses incurred by the Distributor pursuant to the Plan in any fiscal
year will not be reimbursed by the Fund through payments accrued in any
subsequent fiscal year. For the six months ended December 31, 2003, the
distribution fee was accrued at the annual rate of 0.10%.

4. Security Transactions and Transactions with Affiliates

The cost of purchases and proceeds from sales/maturities of portfolio securities
for the six months ended December 31, 2003, aggregated $55,657,528,013 and
$57,779,539,463, respectively.

Morgan Stanley Trust, an affiliate of the Investment Manager and Distributor, is
the Fund's transfer agent. At December 31, 2003, the Fund had transfer agent
fees and expenses payable of approximately $59,400.

The Fund has an unfunded noncontributory defined benefit pension plan covering
certain independent Trustees of the Fund who will have served as independent
Trustees for at least five years at the time of retirement. Benefits under this
plan are based on factors which include years of service and compensation.
Aggregate pension costs for the year ended December 31, 2003, included in
Trustees' fees and expenses in the Statement of Operations amounted to $3,674.
At

                                                                              11


Active Assets Money Trust
NOTES TO FINANCIAL STATEMENTS - DECEMBER 31, 2003 (UNAUDITED) continued

December 31, 2003, the Fund had an accrued pension liability of $60,293 which is
included in accrued expenses in the Statement of Assets and Liabilities.

On December 2, 2003, the Trustees voted to close the plan to new participants,
eliminate the future benefits growth due to increases to compensation after July
31, 2003 and effective April 1, 2004, establish an unfunded deferred
compensation plan which allows each independent Trustee to defer payment of all
or a portion of the fees he receives for serving on the Board of Trustees
throughout the year.

5. Shares of Beneficial Interest

Transactions in shares of beneficial interest, at $1.00 per share, were as
follows:

<Table>
<Caption>
                                                                 FOR THE SIX       FOR THE YEAR
                                                                MONTHS ENDED           ENDED
                                                              DECEMBER 31, 2003    JUNE 30, 2003
                                                              -----------------   ---------------
                                                                 (unaudited)
                                                                            

Shares sold.................................................    36,182,616,458     70,079,943,853
Shares issued in reinvestment of dividends and
  distributions.............................................        76,816,576        273,033,113
                                                               ---------------    ---------------
                                                                36,259,433,034     70,352,976,966
Shares redeemed.............................................   (38,269,541,873)   (72,113,002,556)
                                                               ---------------    ---------------
Net decrease in shares outstanding..........................    (2,010,108,839)    (1,760,025,590)
                                                               ===============    ===============
</Table>

6. Legal Matters

The Investment Manager, certain affiliates of the Investment Manager and certain
investment companies advised by the Investment Manager or its affiliates,
including the Fund, are named as defendants in a number of recently filed,
similar class action complaints. These complaints generally allege that
defendants, including the Fund, violated their statutory disclosure obligations
and fiduciary duties by failing properly to disclose (i) that the Investment
Manager and certain affiliates of the Investment Manager allegedly offered
economic incentives to brokers and others to steer investors to the funds
advised by the Investment Manager or its affiliates rather than funds managed by
other companies, and (ii) that the funds advised by the Investment Manager or
its affiliates, including the Fund, allegedly paid excessive commissions to
brokers in return for their alleged efforts to steer investors to these funds.
The complaints seek, among other things, unspecified compensatory damages,
rescissionary damages, fees and costs. The defendants intend to move to dismiss
these actions and otherwise vigorously to defend them. While the Fund believes
that it has meritorious defenses, the ultimate outcome of these matters is not
presently determinable at this early stage of the litigation, and no provision
has been made in the Fund's financial statements for the effect, if any, of
these matters.

12


Active Assets Money Trust
FINANCIAL HIGHLIGHTS

Selected ratios and per share data for a share of beneficial interest
outstanding throughout each period:

<Table>
<Caption>
                                                 FOR THE SIX                  FOR THE YEAR ENDED JUNE 30,
                                                MONTHS ENDED      ----------------------------------------------------
                                              DECEMBER 31, 2003     2003       2002       2001       2000       1999
                                              -----------------   --------   --------   --------   --------   --------
                                                 (unaudited)
                                                                                            
Selected Per Share Data:

Net asset value, beginning of period........        $ 1.00         $ 1.00     $ 1.00     $ 1.00     $ 1.00    $  1.00
                                                    ------         ------     ------     ------     ------    -------

Net income from investment operations.......         0.003          0.011      0.023      0.056      0.054      0.048

Less dividends from net investment income...        (0.003)+       (0.011)+   (0.023)+   (0.056)+   (0.054)    (0.048)
                                                    ------         ------     ------     ------     ------    -------

Net asset value, end of period..............        $ 1.00         $ 1.00     $ 1.00     $ 1.00     $ 1.00    $  1.00
                                                    ======         ======     ======     ======     ======    =======

Total Return................................          0.34%(1)       1.13%      2.33%      5.76%      5.50%      4.92%

Ratios to Average Net Assets:
Expenses....................................          0.41%(2)       0.41%      0.40%      0.41%      0.42%      0.43%

Net investment income.......................          0.66%(2)       1.12%      2.32%      5.58%      5.38%      4.78%

Supplemental Data:
Net assets, end of period, in millions......       $21,268        $23,278    $25,038    $26,212    $20,972    $15,989
</Table>

- ---------------------

<Table>
  
(1)  Not annualized.
(2)  Annualized.
 +   Includes capital gain distribution of less than $0.001.
</Table>

                                                                              13
                       See Notes to Financial Statements


                      (This Page Intentionally Left Blank)


                      (This Page Intentionally Left Blank)


TRUSTEES

Michael Bozic
Charles A. Fiumefreddo
Edwin J. Garn
Wayne E. Hedien
James F. Higgins
Dr. Manuel H. Johnson
Joseph J. Kearns
Michael E. Nugent
Philip J. Purcell
Fergus Reid

OFFICERS

Charles A. Fiumefreddo
Chairman of the Board

Mitchell M. Merin
President

Ronald E. Robison
Executive Vice President and Principal Executive Officer

Barry Fink
Vice President and General Counsel

Joseph J. McAlinden
Vice President

Stefanie V. Chang
Vice President

Francis J. Smith
Treasurer and Chief Financial Officer

Thomas F. Caloia
Vice President

Mary E. Mullin
Secretary

TRANSFER AGENT

Morgan Stanley Trust
Harborside Financial Center, Plaza Two
Jersey City, New Jersey 07311

INDEPENDENT AUDITORS

Deloitte & Touche LLP
Two World Financial Center
New York, New York 10281

INVESTMENT ADVISOR

Morgan Stanley Investment Advisors Inc.
1221 Avenue of the Americas
New York, New York 10020

The financial statements included herein have been taken from the records of the
Fund without examination by the independent auditors and accordingly they do not
express an opinion thereon.

This report is submitted for the general information of shareholders of the
Fund. Fore more detailed information about the Fund, its fees and expenses and
other pertinent information, please read its Prospectus. The Fund's Statement of
Additional Information contains additional information about the Fund, including
its trustees. It is available, without charge, by calling (800) 869-NEWS.

This report is not authorized for distribution to prospective investors in the
Fund unless preceded or accompanied by an effective Prospectus. Read the
Prospectus carefully before investing.

Investments and services offered through Morgan Stanley DW Inc., member SIPC.
Morgan Stanley Distributors Inc., member NASD.

(c) 2003 Morgan Stanley

[MORGAN STANLEY LOGO]

MORGAN STANLEY FUNDS

Active Assets
Money Trust

Semiannual Report
December 31, 2003

[MORGAN STANLEY LOGO]

13679B04-AP-2/04


Item 2. Code of Ethics.

Not applicable for semiannual reports.

Item 3. Audit Committee Financial Expert.

Not applicable for semiannual reports.

Item 4. Principal Accountant Fees and Services

Not applicable for semiannual reports.

Item 5. Audit Committee of Listed Registrants.

Not applicable for semiannual reports.

Item 6. [Reserved.]

Item 7. Disclosure of Proxy Voting Policies and Procedures for Closed-End
Management Investment Companies.

Not applicable for semiannual reports.

Item 8. [Reserved.]

Item 9 - Controls and Procedures

(a) The Fund's principal executive officer and principal financial officer have
concluded that the Fund's disclosure controls and procedures are sufficient to
ensure that information required to be disclosed by the Fund in this Form N-CSR
was recorded, processed, summarized and reported within the time periods
specified in the Securities and Exchange Commission's rules and forms, based
upon such officers' evaluation of these controls and procedures as of a date
within 90 days of the filing date of the report.

There were no significant changes or corrective actions with regard to
significant deficiencies or material weaknesses in the Fund's internal controls
or in other factors that could significantly affect the Fund's internal controls
subsequent to the date of their evaluation.



(b) There were no changes in the registrant's internal control over financial
reporting that occurred during the registrant's most recent fiscal half-year
(the registrant's second fiscal half-year in the case of an annual report) that
has materially affected, or is reasonably likely to materially affect, the
registrant's internal control over financial reporting.

Item 10 Exhibits

(a) Code of Ethics - Not applicable for semiannual reports.

(b) A separate certification for each principal executive officer and principal
financial officer of the registrant are attached hereto as part of EX-99.CERT.

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                                   SIGNATURES

         Pursuant to the requirements of the Securities Exchange Act of 1934 and
the Investment Company Act of 1940, the registrant has duly caused this report
to be signed on its behalf by the undersigned, thereunto duly authorized.

Active Assets Money Trust

/s/ Ronald E. Robison
Ronald E. Robison
Principal Executive Officer
February 18, 2004

         Pursuant to the requirements of the Securities Exchange Act of 1934 and
the Investment Company Act of 1940, this report has been signed by the following
persons on behalf of the registrant and in the capacities and on the dates
indicated.

/s/ Ronald E. Robison
Ronald E. Robison
Principal Executive Officer
February 18, 2004

/s/ Francis Smith
Francis Smith
Principal Financial Officer
February 18, 2004

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