HIGH INCOME ADVANTAGE TRUST III
N-30D, 1996-03-27
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<PAGE>   1
 
HIGH INCOME ADVANTAGE TRUST III Two World Trade Center, New York, New York 10048
LETTER TO THE SHAREHOLDERS January 31, 1996
 
DEAR SHAREHOLDER:

The fixed-income markets rebounded sharply during 1995,
as economic growth slowed and inflation fears subsided.
The high-yield market recorded a strong year,
benefiting from the rally in the U.S. Treasury market,
as well as from the continued strength in corporate
earnings. However, as is typical in a decelerating
economic environment, the high-yield bond market lagged
the U.S. Treasuries rally, as concerns over the
severity of the economic slowdown offset some of the
benefit of lower interest rates.

For the twelve-month period ended January 31, 1996,
High Income Advantage Trust III produced a total return
of 15.31 percent, based on its closing market price on
the New York Stock Exchange (NYSE) of $6.75 per share.
Based on its net asset value (NAV) of $6.39 per share
on January 31, 1996, the Trust's total return for the
twelve-month period was 15.94 percent. As of January
31, 1996, the Trust had net assets in excess of $82
million. Over the past twelve months, the Trust
continued to distribute regular income dividends at a
rate of $.06 per share per month. For the full fiscal
year, income dividends totaled $.72 per share.

INVESTMENT STRATEGY

The Trust's investment strategy throughout 1995 was to
capitalize on the opportunity created by the 1994
market correction by positioning the Trust for an
eventual rebound in the market. Despite the fact that
corporate credit quality remained strong, the 1994
market correction pushed yields on many B-rated issues
300-400 basis points higher (to the 13-14 percent
range) and caused bond prices in some cases to decline
by as much as 15-20 percent. In light of this
correction, the Trust increased its emphasis on
discounted issues during the second half of 1994, which
helped to provide more capital appreciation potential
for the Trust. While the Trust's portfolio is still
positioned for further upside in the high yield market,
it continues to maintain a sizable position in various
defensive securities, in order to provide the
flexibility needed to take advantage of any interim
opportunities that may arise.
<PAGE>   2
 
HIGH INCOME ADVANTAGE TRUST III
 
LETTER TO THE SHAREHOLDERS January 31, 1996, continued
 
 MARKET OUTLOOK
 
 Given our outlook for continued, albeit slower economic growth, we find that
 many of today's B-rated issues -- still yielding more than 600 basis points (6
 percent) above U.S. Treasury securities and trading at significant
 discounts -- offer excellent long-term return potential. Over the near term, we
 expect continued volatility in the financial markets as investors assess the
 economy's strength, possible Federal Reserve Board actions and ongoing budget
 negotiations in Washington. However, despite any potential short-term weakness,
 we consider today's high-yield market to be an attractive long-term opportunity
 for investors. Many current high-yield issues provide an exceptionally
 attractive yield advantage over U.S. Treasury securities, with the opportunity
 for substantial capital appreciation if the high-yield market continues its
 recovery.
 
 We would like to remind you that the Trustees have approved a procedure whereby
 the Trust, when appropriate, may purchase shares in the open market or in
 privately negotiated transactions at a price not above market value or net
 asset value, whichever is lower at the time of purchase.
 
 We appreciate your support of High Income Advantage Trust III and look forward
 to continuing to serve your investment needs.
 
 Very truly yours,
 
 /s/  CHARLES A. FIUMEFREDDO

 CHARLES A. FIUMEFREDDO
 Chairman of the Board
<PAGE>   3
 
HIGH INCOME ADVANTAGE III
 
PORTFOLIO OF INVESTMENTS January 31, 1996
 
<TABLE>
<CAPTION>
PRINCIPAL
AMOUNT IN                                              COUPON       MATURITY
THOUSANDS                                               RATE          DATE         VALUE
- -------------------------------------------------------------------------------------------
<C>          <S>                                       <C>          <C>         <C>
             CORPORATE BONDS (93.1%)
             Aerospace (2.9%)
 $ 2,500     Sabreliner Corp. (Series B)...........    12.50  %     04/15/03    $ 2,368,750
                                                                                 ----------
             Airlines (4.4%)
   3,850     GPA Delaware, Inc. ...................     8.75        12/15/98      3,667,125
                                                                                  ---------
             Automotive (3.6%)
     400     APS, Inc. - 144A*.....................    11.875       01/15/06        414,500
   3,250     Envirotest Systems, Inc. .............     9.625       04/01/03      2,567,500
                                                                                 ----------
                                                                                  2,982,000
                                                                                 ----------
             Cable & Telecommunications (9.7%)
   2,048     Adelphia Communications Corp. (Series B)   9.50+       02/15/04      1,689,980
   2,000     AT&T Capital Corp. ...................    15.00        05/05/97      2,230,400
   6,500     In-Flight Phone Corp. (Series B)......    14.00++      05/15/02      2,015,000
   1,000     Paxson Communications - 144A*.........    11.625       10/01/02      1,050,000
   1,000     Rifkin Acquisition Partners
              L.P. - 144A*.........................    11.125       01/15/06      1,017,500
                                                                                 ----------
                                                                                  8,002,880
                                                                                 ----------
             Computer Equipment (8.0%)
   3,000     IBM Credit Corp. .....................    15.00        06/13/96      3,098,880
   3,400     Unisys Corp. .........................    13.50        07/01/97      3,502,000
                                                                                 ----------
                                                                                  6,600,880
                                                                                 ----------
             Consumer Products (1.2%)
   1,000     J.B. Williams Holdings, Inc. .........    12.00        03/01/04      1,007,500
                                                                                 ----------
             Containers (2.0%)
   2,750     Ivex Holdings Corp. (Series B)........    13.25++      03/15/05      1,677,500
                                                                                 ----------
             Electrical & Alarm Systems (2.2%)
   2,250     Mosler, Inc. .........................    11.00        04/15/03      1,777,500
                                                                                 ----------
             Entertainment/Gaming & Lodging (5.3%)
   2,000     Motels of America, Inc. (Series B)....    12.00        04/15/04      1,990,000
     750     Plitt Theaters, Inc. .................    10.875       06/15/04        697,500
   6,722     Spectravision, Inc. (c)...............    11.65        12/01/02        658,741
   1,000     Trump Taj Mahal (Series A)............    11.35+       11/15/99        995,000
                                                                                  ---------
                                                                                  4,341,241
                                                                                 ----------
             Foods & Beverages (14.8%)
   4,200     Envirodyne Industries, Inc. ..........    10.25        12/01/01      3,297,000
   3,000     PepsiCo Inc. .........................    15.00        06/14/96      3,101,310
   1,000     SC International Services, Inc. ......    13.00        10/01/05      1,072,500
   2,000     Seven Up/RC Bottling Co. Southern
              California, Inc. (d).................    11.50        08/01/99      1,242,500
   7,000     Specialty Foods Acquisition Corp.
              (Series B)...........................    13.00++      08/15/05      3,430,000
                                                                                 ----------
                                                                                 12,143,310
                                                                                 ----------
</TABLE>
 
                       SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   4
 
HIGH INCOME ADVANTAGE III
 
PORTFOLIO OF INVESTMENTS January 31, 1996, continued
 
<TABLE>
<CAPTION>
PRINCIPAL
AMOUNT IN                                              COUPON       MATURITY
THOUSANDS                                               RATE          DATE         VALUE
- -------------------------------------------------------------------------------------------
<C>          <S>                                       <C>          <C>         <C>
             Manufacturing (6.4%)
 $ 1,700     Alpine Group, Inc. ...................    12.25  %     07/15/03    $ 1,666,000
   1,000     Berry Plastics Corp. .................    12.25        04/15/04      1,085,000
   1,000     Cabot Safety Corp. ...................    12.50        07/15/05      1,085,000
     500     International Wire Group..............    11.75        06/01/05        488,750
   1,000     Uniroyal Technology Corp. ............    11.75        06/01/03        960,000
                                                                                  ---------
                                                                                  5,284,750
                                                                                  ---------
             Manufacturing - Diversified (7.8%)
   1,500     Foamex L.P. ..........................    11.875       10/01/04      1,447,500
   1,750     Interlake Corp. ......................    12.125       03/01/02      1,680,000
   1,000     J.B. Poindexter & Co., Inc. ..........    12.50        05/15/04        850,000
   1,000     Jordan Industries, Inc. ..............    10.375       08/01/03        903,750
   2,400     Jordan Industries, Inc. ..............    11.75++      08/01/05      1,524,000
                                                                                  ---------
                                                                                  6,405,250
                                                                                  ---------
             Oil & Gas (3.3%)
   1,000     Deeptech International, Inc. .........    12.00        12/15/00        910,000
   2,000     Empire Gas Corp. .....................     7.00        07/15/04      1,800,000
                                                                                  ---------
                                                                                  2,710,000
                                                                                  ---------
             Publishing (6.1%)
   4,000     Affiliated Newspapers Investments,
              Inc. ................................    13.25++      07/01/06      2,580,000
   1,000     Garden State Newspapers, Inc. ........    12.00        07/01/04      1,035,000
   1,875     United States Banknote Corp. .........    10.375       06/01/02      1,368,750
                                                                                  ---------
                                                                                  4,983,750
                                                                                  ---------
             Restaurants (7.9%)
   4,750     American Restaurant Group Holdings,
              Inc. ................................    14.00++      12/15/05      2,196,875
   1,000     Carrols Corp. ........................    11.50        08/15/03      1,030,000
   4,700     Flagstar Corp. .......................    11.25        11/01/04      3,290,000
                                                                                  ---------
                                                                                  6,516,875
                                                                                  ---------
             Retail (3.0%)
     800     Cort Furniture Rental Corp. ..........    12.00        09/01/00        856,000
   1,000     County Seat Stores Co. ...............    12.00        10/01/02        725,000
     900     Thrifty Payless Holdings, Inc. .......    11.625+      04/15/06        882,000
                                                                                  ---------
                                                                                  2,463,000
                                                                                  ---------
             Retail - Food Chains (0.6%)
     500     Ralphs Grocery Co. ...................    11.00        06/15/05        475,000
                                                                                  ---------
</TABLE>
 
                       SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   5
 
HIGH INCOME ADVANTAGE III
 
PORTFOLIO OF INVESTMENTS January 31, 1996, continued
<TABLE>
<CAPTION>
PRINCIPAL
AMOUNT IN                                              COUPON       MATURITY
THOUSANDS                                               RATE          DATE         VALUE
- -------------------------------------------------------------------------------------------
<C>          <S>                                       <C>          <C>         <C>
             Textiles - Apparel Manufacturers
              (3.9%)
 $    57     Farley, Inc. (Conv.)..................     0.00  %     01/01/12    $     5,552
   3,048     JPS Textile Group, Inc. ..............    10.85        06/01/99      2,468,880
   1,000     U.S. Leather, Inc. ...................    10.25        07/31/03        700,000
                                                                                 ----------
                                                                                  3,174,432
                                                                                 ----------
             TOTAL CORPORATE BONDS
             (Identified Cost $83,856,301)..................................     76,581,743
                                                                                 ----------
</TABLE>
<TABLE>
<CAPTION>
NUMBER OF
 SHARES                                                                            VALUE
- -------------------------------------------------------------------------------------------
<C>          <S>                                                                <C>
             COMMON STOCKS (a) (1.1%)
             Computer Equipment (0.1%)
  95,553     Memorex Telex NV (ADR) (Netherlands) (b).......................        113,469
                                                                                  ---------
             Entertainment/Gaming & Lodging (0.2%)
   2,000     Motels of America, Inc. - 144A*................................        170,000
                                                                                  ---------
             Foods & Beverages (0.4%)
  90,000     Specialty Foods Acquisition Corp. (Restricted) - 144A*.........        247,500
                                                                                  ---------
             Publishing (0.1%)
   4,000     Affiliated Newspapers Investments, Inc. (Class B)..............        120,000
                                                                                  ---------
             Restaurants (0.1%)
   4,750     American Restaurant Group Holdings, Inc. - 144A*...............         71,250
                                                                                  ---------
             Retail (0.2%)
  38,000     Thrifty Payless Holdings, Inc. (Class C).......................        190,000
                                                                                  ---------
             TOTAL COMMON STOCKS
             (Identified Cost $2,981,994)...................................        912,219
                                                                                  ---------
             PREFERRED STOCKS (2.5%)
             Entertainment/Gaming & Lodging (2.5%)
  80,000     Fitzgeralds Gaming Corp. (Units)+++ $3.75......................      2,020,000
                                                                                  ---------
             Utilities - Electric (0.0%)
 327,500     TGX Corp. Series A (a) (b).....................................         40,938
                                                                                  ---------
             TOTAL PREFERRED STOCKS
             (Identified Cost $4,718,250)...................................      2,060,938
                                                                                  ---------
</TABLE>
 
                       SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   6
 
HIGH INCOME ADVANTAGE III
 
PORTFOLIO OF INVESTMENTS January 31, 1996, continued
<TABLE>
<CAPTION>
NUMBER OF                                                           EXPIRATION
WARRANTS                                                              DATE         VALUE
- -------------------------------------------------------------------------------------------
<C>          <S>                                                    <C>         <C>
             WARRANTS (a) (0.7%)
             Aerospace (0.0%)
   2,500     Sabreliner Corp. (Restricted) - 144A*............      04/15/03    $    25,000
                                                                                  ---------
             Cable & Telecommunications (0.1%)
   5,500     In-Flight Phone Corp. - 144A*....................      08/31/02         55,000
                                                                                  ---------
             Containers (0.1%)
   2,000     Crown Packaging Holdings, Ltd.
              (Canada) - 144A*................................      11/01/03        110,000
                                                                                  ---------
             Entertainment/Gaming & Lodging (0.0%)
   3,263     Casino America, Inc. ............................      11/15/96        --
   4,500     Fitzgeralds Gaming Corp. - 144A*.................      03/15/99         31,500
                                                                                  ---------
                                                                                     31,500
                                                                                  ---------
             Manufacturing (0.0%)
   2,000     BPC Holdings Corp. ..............................      04/15/04         25,000
  10,000     Uniroyal Technology Corp. .......................      06/01/03         20,000
                                                                                  ---------
                                                                                     45,000
                                                                                  ---------
             Oil & Gas (0.0%)
   2,760     Empire Gas Corp. ................................      07/15/04         27,600
                                                                                  ---------
             Retail (0.5%)
   2,000     County Seat Holdings Co. ........................      10/15/98         40,000
  66,000     New Cort Holdings Corp. .........................      09/01/98        297,000
                                                                                  ---------
                                                                                    337,000
                                                                                  ---------
             Retail - Food Chains (0.0%)
   8,608     Grand Union Co. (Series 1) (b)...................      06/16/00        --
  17,216     Grand Union Co. (Series 2) (b)...................      06/16/00        --
                                                                                  ---------
                                                                                    --
                                                                                  ---------
             TOTAL WARRANTS
             (Identified Cost $619,608).......................                      631,100
                                                                                  ---------
</TABLE>
 
                       SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   7
 
HIGH INCOME ADVANTAGE III
 
PORTFOLIO OF INVESTMENTS January 31, 1996, continued
<TABLE>
<CAPTION>
PRINCIPAL
AMOUNT IN                                              COUPON       MATURITY
THOUSANDS                                               RATE          DATE         VALUE
- -------------------------------------------------------------------------------------------
<C>          <S>                                       <C>          <C>         <C>
             SHORT-TERM INVESTMENT (0.2%)
             REPURCHASE AGREEMENT
 $   144     The Bank of New York (dated 01/31/96;
              proceeds $144,062; collateralized by
              $152,753 U.S. Treasury Bill 4.84% due
              11/14/96 valued at $146,920)
              (Identified Cost $144,039)...........     5.75%       02/01/96    $   144,039
                                                                                -----------

             TOTAL INVESTMENTS
             (Identified Cost $92,320,192) (e)......................    97.6%    80,330,039
             OTHER ASSETS IN EXCESS OF LIABILITIES....................   2.4      1,946,860
                                                                       -----    -----------
             NET ASSETS.............................................   100.0%   $82,276,899
                                                                       =====    ===========
</TABLE>
 
                ----------------------------------------------
 
<TABLE>
<CAPTION>
ADR    American Depository Receipt.
<C>    <S>
 *     Resale is restricted to qualified institutional investors.
 +++   Consists of one or more class of securities traded together as a unit;
       generally stocks with attached warrants.
 +     Payment-in-kind security.
 ++    Currently a zero coupon bond and will pay interest at the rate shown at a
       future specified date.
(a)    Non-income producing securities.
(b)    Acquired through exchange offer.
(c)    Non-income producing security, issuer in bankruptcy.
(d)    Non-income producing security, bond in default.
(e)    The aggregate cost for federal income tax purposes approximates identified
       cost.
</TABLE>
 
                       SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   8
 
HIGH INCOME ADVANTAGE TRUST III
 
FINANCIAL STATEMENTS
 
<TABLE>
<CAPTION>
STATEMENT OF ASSETS AND LIABILITIES
<S>                                          <C>
January 31, 1996
ASSETS:
Investments in securities, at value
 (identified cost $92,320,192)...........    $ 80,330,039
Receivable for:
    Interest.............................       1,557,520
    Investments sold.....................       1,318,125
Prepaid expenses and other assets........           4,340
                                               ----------
    TOTAL ASSETS.........................      83,210,024
                                               ----------
LIABILITIES:
Payable for:
    Investments purchased................         816,250
    Investment management fee............          55,465
Accrued expenses and other payables......          61,410
                                               ----------
    TOTAL LIABILITIES....................         933,125
                                               ----------
NET ASSETS:
Paid-in-capital..........................     121,076,287
Net unrealized depreciation..............     (11,990,153)
Accumulated undistributed net investment
 income..................................       1,017,548
Accumulated net realized loss............     (27,826,783)
                                               ----------
    NET ASSETS...........................    $ 82,276,899
                                               ==========
NET ASSET VALUE PER SHARE,
 12,876,779 shares outstanding (unlimited
 shares authorized of $.01 par value)....           $6.39
                                                     ====
STATEMENT OF OPERATIONS
For the year ended January 31, 1996

NET INVESTMENT INCOME:
INTEREST INCOME..........................     $10,430,133
                                               ----------
EXPENSES
Investment management fee................         612,604
Professional fees........................          56,003
Transfer agent fees and expenses.........          52,608
Shareholder reports and notices..........          26,113
Registration fees........................          24,847
Custodian fees...........................          21,223
Trustees' fees and expenses..............          17,589
Other....................................           5,689
                                               ----------
    TOTAL EXPENSES.......................         816,676
                                               ----------
    NET INVESTMENT INCOME................       9,613,457
                                               ----------
NET REALIZED AND UNREALIZED GAIN (LOSS):
Net realized loss........................      (2,246,851)
Net change in unrealized depreciation....       5,416,939
                                               ----------
    NET GAIN.............................       3,170,088
                                               ----------
NET INCREASE.............................     $12,783,545
                                               ==========
</TABLE>
 
                       SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   9
 
HIGH INCOME ADVANTAGE TRUST III
 
FINANCIAL STATEMENTS, continued
 
<TABLE>
<CAPTION>
STATEMENT OF CHANGES IN NET ASSETS
<S>                                                  <C>                    <C>
                                                       FOR THE YEAR           FOR THE YEAR
                                                          ENDED                  ENDED
                                                     JANUARY 31, 1996       JANUARY 31, 1995
- --------------------------------------------------------------------------------------------
INCREASE (DECREASE) IN NET ASSETS:
OPERATIONS:
Net investment income...........................       $  9,613,457           $  9,615,361
Net realized loss...............................         (2,246,851)           (12,646,621)
Net change in unrealized depreciation...........          5,416,939             (5,793,370)
                                                        -----------           ------------
    NET INCREASE (DECREASE).....................         12,783,545             (8,824,630)
Dividends from net investment income............         (9,271,281)            (9,876,489)
                                                        -----------           ------------
    TOTAL INCREASE (DECREASE)...................          3,512,264            (18,701,119)
NET ASSETS:
Beginning of period.............................         78,764,635             97,465,754
                                                        -----------           ------------
    END OF PERIOD
    (Including undistributed net investment
    income of $1,017,548 and $675,372,
    respectively)...............................       $ 82,276,899           $ 78,764,635
                                                        ===========           ============


</TABLE>
 
                       SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   10
 
HIGH INCOME ADVANTAGE TRUST III
 
NOTES TO FINANCIAL STATEMENTS January 31, 1996
 
 1. ORGANIZATION AND ACCOUNTING POLICIES
 
 High Income Advantage Trust III (the "Trust") is registered under the
 Investment Company Act of 1940, as amended, as a diversified, closed-end
 management investment company. The Trust's primary investment objective is to
 earn a high level of current income and, as a secondary objective, capital
 appreciation, but only when consistent with its primary objective. The Trust
 seeks to achieve its objective by investing primarily in lower-rated fixed
 income securities. The Trust was organized as a Massachusetts business trust on
 November 23, 1988 and commenced operations on February 28, 1989.
 
 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. The following is a summary of significant accounting
 policies:
 
 A. VALUATION OF INVESTMENTS -- (1) an equity security listed or traded on the
 New York or American Stock Exchange is valued at its latest sale price on that
 exchange prior to the time when assets are valued; if there were no sales that
 day, the security is valued at the latest bid price; (2) all other portfolio
 securities for which over-the-counter market quotations are readily available
 are valued at the latest available bid price prior to the time of valuation;
 (3) when market quotations are not readily available, portfolio securities are
 valued at their fair value as determined in good faith under procedures
 established by and under the general supervision of the Trustees; (4) certain
 of the Trust's portfolio securities may be valued by an outside pricing service
 approved by the Trustees. The pricing service utilizes a matrix system
 incorporating security quality, maturity and coupon as the evaluation model
 parameters, and/or research and evaluations by its staff, including review of
 broker-dealer market price quotations, if available, in determining what it
 believes is the fair valuation of the portfolio securities valued by such
 pricing service; and (5) short-term debt securities having a maturity date of
 more than sixty days at time of purchase are valued on a mark-to-market basis
 until sixty days prior to maturity and thereafter at amortized cost based on
 their value on the 61st day. Short-term debt securities having a maturity date
 of sixty days or less at the time of purchase are valued at amortized cost.
 
 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 over the life of the respective securities. Interest
 income is accrued daily except where collection is not expected.
<PAGE>   11
 
HIGH INCOME ADVANTAGE TRUST III
 
NOTES TO FINANCIAL STATEMENTS January 31, 1996, continued
 
 C. FEDERAL INCOME TAX STATUS -- It is the Trust's policy to comply with the
 requirements of the Internal Revenue Code applicable to regulated investment
 companies and to distribute all of its taxable income to its shareholders.
 Accordingly, no federal income tax provision is required.
 
 D. DIVIDENDS AND DISTRIBUTIONS TO SHAREHOLDERS -- The Trust records dividends
 and distributions to its shareholders on the record date. The amount of
 dividends and distributions from net investment income and net realized capital
 gains are determined in accordance with federal income tax regulations which
 may differ from generally accepted accounting principles. These "book/tax"
 differences are either considered temporary or permanent in nature. To the
 extent these differences are permanent in nature, such amounts are reclassified
 within the capital accounts based on their federal tax-basis treatment;
 temporary differences do not require reclassification. Dividends and
 distributions which exceed net investment income and net realized capital gains
 for financial reporting purposes but not for tax purposes are reported as
 dividends in excess of net investment income or distributions in excess of net
 realized capital gains. To the extent they exceed net investment income and net
 realized capital gains for tax purposes, they are reported as distributions of
 paid-in-capital.
 
 2. INVESTMENT MANAGEMENT AGREEMENT
 
 Pursuant to an Investment Management Agreement with Dean Witter InterCapital
 Inc. (the "Investment Manager"), the Trust pays a management fee, calculated
 weekly and payable monthly, by applying the following annual rates to the
 Trust's weekly net assets: 0.75% to the portion of weekly net assets not
 exceeding $250 million; 0.60% to the portion of weekly net assets exceeding
 $250 million but not exceeding $500 million; 0.50% to the portion of weekly net
 assets exceeding $500 million but not exceeding $750 million; 0.40% to the
 portion of weekly net assets exceeding $750 million but not exceeding $1
 billion; and 0.30% to the portion of weekly net assets exceeding $1 billion.
 
 Under the terms of the Agreement, in addition to managing the Trust's
 investments, the Investment Manager maintains certain of the Trust's books and
 records and furnishes, at its own expense, office space, facilities, equipment,
 clerical, bookkeeping and certain legal services and pays the salaries of all
 personnel, including officers of the Trust who are employees of the Investment
 Manager. The Investment Manager also bears the cost of telephone services,
 heat, light, power and other utilities provided to the Trust.
<PAGE>   12
 
HIGH INCOME ADVANTAGE TRUST III
 
NOTES TO FINANCIAL STATEMENTS January 31, 1996, continued
 
 3. SECURITY TRANSACTIONS AND TRANSACTIONS WITH AFFILIATES
 
 The cost of purchases and proceeds from sales of portfolio securities,
 excluding short-term investments, for the year ended January 31, 1996
 aggregated $62,972,241 and $59,936,162, respectively.
 
 Dean Witter Trust Company, an affiliate of the Investment Manager, is the
 Trust's transfer agent. At January 31, 1996, the Trust had transfer agent fees
 and expenses payable of approximately $5,000.
 
 4. SHARES OF BENEFICIAL INTEREST
 
<TABLE>
<CAPTION>
                                                                                                                     CAPITAL PAID
                                                                                                    PAR VALUE OF     IN EXCESS OF
                                                                                       SHARES          SHARES         PAR VALUE
                                                                                     ----------     ------------     ------------
  <S>                                                                                <C>            <C>              <C>
  Balance, January 31, 1995 and 1996.............................................    12,876,779       $128,768       $120,947,519
                                                                                       ========      =========         ==========
</TABLE>
 
 5. DIVIDENDS
 
 The Trust has declared the following dividends from net investment income:
 
<TABLE>
<CAPTION>
                          AMOUNT             RECORD               PAYABLE
   DECLARATION DATE      PER SHARE            DATE                  DATE
  -------------------    ---------     ------------------    ------------------
  <S>                    <C>           <S>                   <S>
   January 30, 1996        $0.06        February 9, 1996     February 23, 1996
   February 27, 1996       $0.06         March 8, 1996         March 22, 1996
</TABLE>
 
 6. FEDERAL INCOME TAX STATUS
 
 At January 31, 1995, the Trust had an approximate net capital loss carryover
 which may be used to offset future capital gains to the extent provided by
 regulations as follows:
 
<TABLE>
<CAPTION>
                            AVAILABLE THROUGH JANUARY 31
- ------------------------------------------------------------------------------------
   2000              2002              2003               2004              TOTAL
- ----------        ----------        -----------        ----------        -----------
<S>               <C>               <C>                <C>               <C>
$9,648,000        $3,256,000        $10,665,000        $4,232,000        $27,801,000
==========        ==========        ===========        ==========        ===========
</TABLE>
<PAGE>   13
 
HIGH INCOME ADVANTAGE TRUST III
 
NOTES TO FINANCIAL STATEMENTS January 31, 1996, continued
 
 7. SELECTED QUARTERLY FINANCIAL DATA (UNAUDITED)
<TABLE>
<CAPTION>
                                                                              QUARTERS ENDED
                                          ---------------------------------------------------------------------------------------
                                               1/31/96                10/31/95               7/31/95                4/30/95
                                          ------------------     ------------------     ------------------     ------------------
                                                       PER                    PER                    PER                    PER
                                          TOTAL*      SHARE      TOTAL*      SHARE      TOTAL*      SHARE      TOTAL*      SHARE
                                          -------     ------     -------     ------     -------     ------     -------     ------
  <S>                                     <C>         <C>        <C>         <C>        <C>         <C>        <C>         <C>
  Total investment income.............    $ 2,703     $ 0.21     $ 2,521     $ 0.20     $ 2,736     $ 0.21     $ 2,470     $ 0.19
  Net investment income...............      2,521       0.20       2,303       0.18       2,515       0.19       2,274       0.18
  Net realized and unrealized gain
   (loss).............................        193       0.01      (1,731)     (0.13)      2,205       0.17       2,503       0.19
 
<CAPTION>
                                                                              QUARTERS ENDED
                                          ---------------------------------------------------------------------------------------
                                               1/31/95                10/31/94               7/31/94                4/30/94
                                          ------------------     ------------------     ------------------     ------------------
                                                       PER                    PER                    PER                    PER
                                          TOTAL*      SHARE      TOTAL*      SHARE      TOTAL*      SHARE      TOTAL*      SHARE
                                          -------     ------     -------     ------     -------     ------     -------     ------
  <S>                                     <C>         <C>        <C>         <C>        <C>         <C>        <C>         <C>
  Total investment income.............    $ 2,522     $ 0.20     $ 2,698     $ 0.21     $ 2,675     $ 0.21     $ 2,609     $ 0.20
  Net investment income...............      2,299       0.18       2,492       0.19       2,451       0.19       2,373       0.19
  Net realized and unrealized loss....     (2,635)     (0.20)     (4,587)     (0.36)     (6,559)     (0.51)     (4,659)     (0.36)
</TABLE>
 
- ---------------------
 * Amounts in thousands.
<PAGE>   14
 
HIGH INCOME ADVANTAGE TRUST III
 
FINANCIAL HIGHLIGHTS
 
Selected ratios and per share data for a share of beneficial interest
outstanding throughout each period:
 
<TABLE>
<CAPTION>
                                                                          -------------------------------------------------------
                                                                                       FOR THE YEAR ENDED JANUARY 31
                                                                           1996        1995        1994        1993        1992
- ---------------------------------------------------------------------------------------------------------------------------------
<S>                                                                       <C>         <C>         <C>         <C>         <C>
PER SHARE OPERATING PERFORMANCE:
Net asset value, beginning of period..................................     $ 6.12      $ 7.57      $ 6.70      $ 6.83      $ 5.18
                                                                            -----       -----       -----       -----       -----
Net investment income.................................................       0.75        0.75        0.81        0.91        0.84
Net realized and unrealized gain (loss)...............................       0.24       (1.43)       0.91       (0.13)       1.58
                                                                            -----       -----       -----       -----       -----
Total from investment operations......................................       0.99       (0.68)       1.72        0.78        2.42
Dividends from net investment income..................................      (0.72)      (0.77)      (0.85)      (0.91)      (0.77)
                                                                            -----       -----       -----       -----       -----
Net asset value, end of period........................................     $ 6.39      $ 6.12      $ 7.57      $ 6.70      $ 6.83
                                                                            =====       =====       =====       =====       =====
Market value, end of period...........................................     $ 6.75      $ 6.50      $ 7.75      $6.875      $ 6.50
                                                                            =====       =====       =====       =====       =====
TOTAL INVESTMENT RETURN+..............................................     15.31%      (6.30%)     26.21%      20.77%      60.31%
RATIOS TO AVERAGE NET ASSETS:
Expenses..............................................................      1.00%       1.02%       0.99%       1.06%       1.17%
Net investment income.................................................     11.80%      11.04%      11.40%      13.22%      13.53%
SUPPLEMENTAL DATA:
Net assets, end of period, in thousands...............................    $82,277     $78,765     $97,466     $86,305     $89,084
Portfolio turnover rate...............................................        78%         82%        231%        118%        137%
</TABLE>
 
- ---------------------
+ Total investment return is based upon the current market value on the last day
  of each period reported. Dividends are assumed to be reinvested at the prices
  obtained under the Trust's dividend reinvestment plan. Total investment return
  does not reflect brokerage commissions.
 
                       SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   15
 
HIGH INCOME ADVANTAGE TRUST III
 
REPORT OF INDEPENDENT ACCOUNTANTS
 
 TO THE SHAREHOLDERS AND TRUSTEES
 OF HIGH INCOME ADVANTAGE TRUST III
 
 In our opinion, the accompanying statement of assets and liabilities, including
 the portfolio of investments, and the related statements of operations and of
 changes in net assets and the financial highlights present fairly, in all
 material respects, the financial position of High Income Advantage Trust III
 (the "Trust") at January 31, 1996, 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 five years in
 the period then ended, in conformity with generally accepted accounting
 principles. These financial statements and financial highlights (hereafter
 referred to as "financial statements") are the responsibility of the Trust'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 January 31, 1996 by correspondence with the
 custodian, provide a reasonable basis for the opinion expressed above.
 
 PRICE WATERHOUSE LLP
 1177 Avenue of the Americas
 New York, New York 10036
 March 13, 1996
<PAGE>   16


<TABLE>
<S>                                                      <C>
TRUSTEES
- ----------------------------------------------
Michael Bozic
Charles A. Fiumefreddo
Edwin J. Garn
John R. Haire
Dr. Manuel H. Johnson                                    HIGH
Paul Kolton                                              INCOME
Michael E. Nugent                                        ADVANTAGE
Philip J. Purcell                                        TRUST III
John L. Schroeder


OFFICERS
- ----------------------------------------------
Charles A. Fiumefreddo
Chairman and Chief Executive Officer

Sheldon Curtis
Vice President, Secretary and General Counsel

Peter M. Avelar
Vice President

Thomas F. Caloia
Treasurer


TRANSFER AGENT
- ----------------------------------------------
Dean Witter Trust Company
Harborside Financial Center--Plaza Two
Jersey City, New Jersey  07311


INDEPENDENT ACCOUNTANTS
- ----------------------------------------------
Price Waterhouse LLP
1177 Avenue of the Americas
New York, New York  10036


INVESTMENT MANAGER
- ----------------------------------------------
Dean Witter InterCapital Inc.
Two World Trade Center
New York, New York  10048


                                                         ANNUAL REPORT
                                                         JANUARY 31, 1996
</TABLE>




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