HIGH INCOME ADVANTAGE TRUST III
N-30D, 1998-03-23
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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, 1998
 
DEAR SHAREHOLDER:
 
Continuing the trend of recent years, high-yield bonds remained one of the
better-performing sectors of the fixed-income market for calendar 1997.
Benefiting from a healthy economy, improved credit quality and a relatively
favorable interest-rate environment, the high-yield market posted a strong
double-digit return for the year. This performance compares favorably with the
single-digit returns generated by the high-quality end of the fixed-income
market for the same period.
 
Despite some market weakness in March and April following the Federal Reserve
Board's rate hike, and again in October and November, as a result of the
emerging market crisis, the sector finished the year on a high note. Continued
strength in the economy has resulted in solid earnings improvements on the part
of many high-yield companies during the year and has provided the fuel for the
sharp equity market advance experienced in 1997. Many high-yield companies have
taken advantage of higher equity valuations to raise equity and strengthen their
own balance sheets. The resulting credit quality improvement has helped keep the
high-yield market's performance strong relative to that of many of the other
fixed-income markets.
 
PERFORMANCE AND PORTFOLIO STRATEGY
 
In this context, High Income Advantage Trust III produced a total return of
16.86 percent for the twelve-month period ended January 31, 1998, based on its
month end closing market price on the New York Stock Exchange (NYSE) of $7 3/8
per share. Based on its net asset value (NAV) of $6.18 per share, the Trust's
total return for the same period was 11.82 percent. Over the past twelve months,
the Trust continued to distribute regular income dividends at a rate of $0.06
per share per month. For the fiscal year, the Trust's distributions totaled
$0.7588 per share, including an extra income dividend of $0.0388 per share paid
on December 19, 1997. On January 31, 1998, the Trust's net assets exceeded $79.5
million.
<PAGE>   2
HIGH INCOME ADVANTAGE TRUST III
 
LETTER TO THE SHAREHOLDERS January 31, 1998, continued
 
As the economy has continued to expand over the past few years, the Trust has
tended to concentrate on B-rated issues. In a growing economy one can generally
find undervalued upgrade candidates in this sector of the market that provide
attractive yields as well as appreciation potential. Given our expectation for
continued growth in the economy this year, we continue to feel that many of
these issues are very attractive investments. However, in light of the lower
market yields available today and the potential for a modest correction in the
market, we have taken some defensive steps for the portfolio over the past year.
This includes increasing our allocation to the higher-quality end of the market
(BB-rated issues or higher). We feel that these holdings will better protect
shareholders during a potentially nervous market environment as well as provide
the liquidity and portfolio flexibility needed to take advantage of future
opportunities. In addition, the Trust has sold many of its heavily cyclical
positions and is now focused mainly on more predictable, recession-resistant and
growth sectors of the economy, such as food/beverage, health care,
telecommunications, media and cable. In some of these sectors, such as media and
telecommunications, we expect to see continued consolidation, which should bode
well for many of the Trust's individual holdings. Finally, in keeping with our
more conservative posture, we continue to limit our exposure to the foreign
emerging high-yield markets, given the potential risk associated with the
ongoing foreign emerging market crisis.
 
LOOKING AHEAD
 
The one- to two-year outlook for the high-yield market remains favorable, with
our expectations for continued economic growth. We caution, however, that during
this period the possibility exists for another round of investor nervousness in
reaction to potential Federal Reserve Board moves or another disruption in
foreign emerging markets.
 
We would like to remind you that the Trustees have approved a procedure whereby
the Trust may, when appropriate, repurchase 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 thank you for your continued 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 TRUST III
 
PORTFOLIO OF INVESTMENTS January 31, 1998
 
<TABLE>
<CAPTION>
PRINCIPAL
AMOUNT IN                                           COUPON    MATURITY
THOUSANDS                                            RATE       DATE         VALUE
- -------------------------------------------------------------------------------------
<C>         <S>                                     <C>       <C>         <C>
            CORPORATE BONDS (91.6%)
            Aerospace (1.0%)
 $   750    Sabreliner Corp. (Series B)...........  12.50%    04/15/03    $  791,250
                                                                          ----------
 
            Automotive (2.4%)
   1,800    Toyota Motor Credit Corp. ............  15.00     09/25/98     1,906,254
                                                                          ----------
 
            Broadcast Media (6.8%)
     500    Adams Outdoor Advertising L.P. .......  10.75     03/15/06       557,500
     750    Australis Holdings Ltd. (Australia)...  15.00++   11/01/02       375,000
     750    Echostar DBS Corp. ...................  12.50     07/01/02       837,187
     750    Echostar Satellite Broadcasting.......  13.125++  03/15/04       660,000
   1,000    Paxson Communications Corp. ..........  11.625    10/01/02     1,076,250
     750    Spanish Broadcasting System, Inc. ....  12.50     06/15/02       863,437
   1,500    TCI Satellite Entertainment
             Corp. - 144A*........................  12.25++   02/15/07     1,038,750
                                                                          ----------
                                                                           5,408,124
                                                                          ----------
 
            Business Services (5.4%)
   1,500    Anacomp, Inc. (Series B)..............  10.875    04/01/04     1,578,750
     750    Comforce Operating Inc. - 144A*.......  12.00     12/01/07       780,000
   1,800    Xerox Credit Corp. ...................  15.00     10/07/98     1,912,266
                                                                          ----------
                                                                           4,271,016
                                                                          ----------
 
            Cable & Telecommunications (14.9%)
     500    Adelphia Communications, Inc.
             (Series B)...........................   9.875    03/01/07       547,500
   1,500    Advanced Radio Telecommunication
             (Units)++............................  14.00     02/15/07     1,515,000
     500    American Communications Services,
             Inc..................................  13.75     07/15/07       607,500
     500    Cablevision Systems Corp. ............   9.875    04/01/23       555,000
     500    Charter Communication South East L.P.
             (Series B)...........................  11.25     03/15/06       557,500
     491    Falcon Holdings Group L.P. (Series
             B)...................................  11.00+    09/15/03       549,926
     500    FrontierVision Operating Partners,
             L.P..................................  11.00     10/15/06       560,000
     350    GST Equipment Funding, Inc. ..........  13.25     05/01/07       415,625
   1,000    Hyperion Telecommunication, Inc.
             (Series B)...........................  12.25     09/01/04     1,145,000
   8,750    In-Flight Phone Corp. (Series B)
             (a)..................................  14.00++   05/15/02     1,225,000
     500    IXC Communications, Inc. (Series B)...  12.50     10/01/05       580,000
     500    NextLink Communications, Inc. ........  12.50     04/15/06       580,000
     750    Paging Network, Inc. .................  10.125    08/01/07       783,750
   1,000    Peoples Telephone Co., Inc. ..........  12.25     07/15/02     1,075,062
     500    Rifkin Acquisition Partners L.P. .....  11.125    01/15/06       553,125
     750    Winstar Communications, Inc. .........  14.00++   10/15/05       626,250
                                                                          ----------
                                                                          11,876,238
                                                                          ----------
</TABLE>
 
        SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   4
HIGH INCOME ADVANTAGE TRUST III
 
PORTFOLIO OF INVESTMENTS January 31, 1998, continued
 
<TABLE>
<CAPTION>
PRINCIPAL
AMOUNT IN                                           COUPON    MATURITY
THOUSANDS                                            RATE       DATE         VALUE
- -------------------------------------------------------------------------------------
<C>         <S>                                     <C>       <C>         <C>
            Computer Equipment (2.0%)
 $ 1,500    IBM Credit Corp. .....................  15.00%    02/02/99    $1,639,530
                                                                          ----------
 
            Consumer Products (2.7%)
   1,000    J.B. Williams Holdings, Inc...........  12.00     03/01/04     1,035,000
   1,500    Renaissance Cosmetics, Inc. ..........  11.75     02/15/04     1,125,000
                                                                          ----------
                                                                           2,160,000
                                                                          ----------
 
            Containers (2.0%)
     750    Mail-Well Corp. ......................  10.50     02/15/04       810,000
     750    Packaging Resources, Inc. ............  11.625    05/01/03       795,000
                                                                          ----------
                                                                           1,605,000
                                                                          ----------
 
            Electrical & Alarm Systems (1.7%)
   1,750    Mosler, Inc. .........................  11.00     04/15/03     1,365,000
                                                                          ----------
 
            Entertainment/Gaming & Lodging (14.1%)
     500    AMF Group Inc. (Series B).............  10.875    03/15/06       554,375
     750    Fitzgerald Gaming Corp. - 144A*.......  12.25     12/15/04       780,000
   1,500    Lady Luck Gaming Finance Corp. .......  11.875    03/01/01     1,545,000
   2,500    Motels of America, Inc. (Series B)....  12.00     04/15/04     2,425,000
     800    Players International, Inc. ..........  10.875    04/15/05       876,000
     750    Plitt Theaters, Inc. (Canada).........  10.875    06/15/04       812,813
     800    Station Casinos, Inc. ................   9.625    06/01/03       835,000
   1,750    Stuart Entertainment, Inc. (Series
             B)...................................  12.50     11/15/04     1,417,500
   1,800    Walt Disney Co. ......................  15.00     12/14/98     1,944,864
                                                                          ----------
                                                                          11,190,552
                                                                          ----------
 
            Finance (4.4%)
   1,450    General Electric Capital Corp. .......  15.00     01/21/99     1,578,543
   1,800    Household Finance Corp. ..............  15.00     09/25/98     1,903,284
                                                                          ----------
                                                                           3,481,827
                                                                          ----------
 
            Foods & Beverages (10.6%)
   1,500    Envirodyne Industries, Inc............  10.25     12/01/01     1,492,500
   1,500    General Mills, Inc. ..................  15.00     01/29/99     1,637,985
   2,250    PepsiCo, Inc. ........................  15.00     08/06/98     2,358,000
     500    Sparkling Spring Water - 144A*
             (Canada).............................  11.50     11/15/07       520,000
   5,525    Specialty Foods Acquisition Corp.
             (Series B)...........................  13.00++   08/15/05     2,431,000
                                                                          ----------
                                                                           8,439,485
                                                                          ----------
</TABLE>
 
        SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   5
HIGH INCOME ADVANTAGE TRUST III
 
PORTFOLIO OF INVESTMENTS January 31, 1998, continued
 
<TABLE>
<CAPTION>
PRINCIPAL
AMOUNT IN                                           COUPON    MATURITY
THOUSANDS                                            RATE       DATE         VALUE
- -------------------------------------------------------------------------------------
<C>         <S>                                     <C>       <C>         <C>
            Healthcare (2.6%)
 $   750    Unilab Corp. .........................  11.00%    04/01/06    $  770,625
   1,500    Unison Healthcare Corp. - 144A*.......  12.25     11/01/06     1,290,000
                                                                          ----------
                                                                           2,060,625
                                                                          ----------
 
            Manufacturing (3.4%)
   1,000    Berry Plastics Corp. .................  12.25     04/15/04     1,100,000
     500    International Wire Group, Inc. .......  11.75     06/01/05       555,000
   1,000    Uniroyal Technology Corp. ............  11.75     06/01/03     1,042,500
                                                                          ----------
                                                                           2,697,500
                                                                          ----------
 
            Manufacturing -- Diversified (5.0%)
     800    Interlake Corp. ......................  12.125    03/01/02       827,000
     750    J.B. Poindexter & Co., Inc. ..........  12.50     05/15/04       712,500
   3,900    Jordan Industries, Inc. (Series B)....  11.75++   04/01/09     2,418,000
                                                                          ----------
                                                                           3,957,500
                                                                          ----------
 
            Oil & Gas (0.7%)
     500    Texaco Capital LLC....................  15.00     01/13/99       543,070
                                                                          ----------
 
            Publishing (0.7%)
     500    American Media Operations, Inc. ......  11.625    11/15/04       542,500
                                                                          ----------
 
            Restaurants (5.8%)
   4,570    American Restaurant Group Holdings,
             Inc..................................  14.00++   12/15/05     1,325,300
   1,500    Carrols Corp. ........................  11.50     08/15/03     1,590,000
   1,500    FRD Acquisition Corp. (Series B)......  12.50     07/15/04     1,672,500
                                                                          ----------
                                                                           4,587,800
                                                                          ----------
 
            Retail (1.3%)
   1,000    Kmart Corp. ..........................  13.50     01/01/09     1,080,000
                                                                          ----------
 
            Retail -- Food Chains (3.2%)
     750    Mrs Fields Original - 144A*...........  10.125    12/01/04       759,375
     375    Pantry Inc. - 144A*...................  10.25     10/15/07       390,000
     750    Pueblo Xtra International.............   9.50     08/01/03       712,500
     750    Pueblo Xtra International (Series
             C)...................................   9.50     08/01/03       712,500
                                                                          ----------
                                                                           2,574,375
                                                                          ----------
 
            Textiles (0.9%)
   1,505    U.S. Leather, Inc. (b)................  10.25     07/31/03       707,350
                                                                          ----------
 
            TOTAL CORPORATE BONDS
            (Identified Cost $76,847,744)..............................   72,884,996
                                                                          ----------
</TABLE>
 
        SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   6
HIGH INCOME ADVANTAGE TRUST III
 
PORTFOLIO OF INVESTMENTS January 31, 1998, continued
 
<TABLE>
<CAPTION>
NUMBER OF
 SHARES                                                                    VALUE
- ------------------------------------------------------------------------------------
<C>         <S>                                                         <C>
            COMMON STOCKS (c) (4.8%)
            Entertainment/Gaming & Lodging (0.1%)
   2,000    Motels of America, Inc. - 144A*...........................  $   100,000
                                                                        -----------
 
            Foods & Beverages (0.1%)
  90,000    Specialty Foods Acquisition Corp. - 144A*.................       90,000
                                                                        -----------
 
            Manufacturing -- Diversified (0.9%)
  21,462    Thermadyne Holdings Corp. (d).............................      724,342
                                                                        -----------
 
            Restaurants (0.0%)
   4,750    American Restaurant Group Holdings, Inc. - 144A*..........        4,750
                                                                        -----------
 
            Retail (3.7%)
 585,200    County Seat Store Corp. (d)(e)............................    2,896,740
                                                                        -----------
 
            TOTAL COMMON STOCKS
            (Identified Cost $4,238,167)..............................    3,815,832
                                                                        -----------
</TABLE>
 
<TABLE>
<CAPTION>
NUMBER OF                                                   EXPIRATION
WARRANTS                                                       DATE
- ---------                                                   ----------
<C>         <S>                                             <C>          <C>
            WARRANTS (c) (0.1%)
            Aerospace (0.0%)
   2,500    Sabreliner Corp. - 144A*......................   04/15/03         25,000
                                                                         -----------
 
            Broadcast Media (0.0%)
     750    Australis Holdings Ltd. - 144A* (Australia)...   10/30/01        --
                                                                         -----------
 
            Cable & Telecommunications (0.1%)
     800    Hyperion Telecommunication, Inc.
             (Series B) - 144A*...........................   04/01/01         72,042
                                                                         -----------
 
            Containers (0.0%)
   2,000    Crown Packaging Holdings, Ltd. - 144A*........   11/01/03        --
                                                                         -----------
 
            Entertainment/Gaming & Lodging (0.0%)
   1,250    Fitzgeralds South Inc. - 144A*................   03/15/99        --
                                                                         -----------
 
            Retail (0.0%)
   2,000    County Seat Holdings Co. (a)..................   10/15/98        --
                                                                         -----------
 
            TOTAL WARRANTS
            (Identified Cost $220,067)................................        97,042
                                                                         -----------
</TABLE>
 
        SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   7
HIGH INCOME ADVANTAGE TRUST III
 
PORTFOLIO OF INVESTMENTS January 31, 1998, continued
 
<TABLE>
<CAPTION>
PRINCIPAL
AMOUNT IN                                           COUPON    MATURITY
THOUSANDS                                            RATE       DATE         VALUE
- -------------------------------------------------------------------------------------
<C>         <S>                                     <C>       <C>         <C>
            SHORT-TERM INVESTMENTS (5.7%)
            U.S. GOVERNMENT AGENCY (f) (5.4%)
 $4,300     Federal Home Loan Mortgage Corp.
            (Amortized Cost $4,299,335)...........     5.57%  02/02/98    $ 4,299,335
                                                                          -----------
 
            REPURCHASE AGREEMENT (0.3%)
    202     The Bank of New York (dated 01/30/98;
            proceeds $202,076) (g)
            (Identified Cost $201,986)............     5.375  02/02/98        201,986
                                                                          -----------
 
            TOTAL SHORT-TERM INVESTMENTS
            (Identified Cost $4,501,321)...............................     4,501,321
                                                                          -----------
 
            TOTAL INVESTMENTS
            (Identified Cost $85,807,299) (h)....................102.2%    81,299,191
 
            LIABILITIES IN EXCESS OF OTHER ASSETS.............    (2.2)    (1,726,730)
                                                                 -----    -----------
 
            NET ASSETS.........................................  100.0%   $79,572,461
                                                                 =====    ===========
</TABLE>
 
- ---------------------
 *  Resale is restricted to qualified institutional investors.
++  Consists of one or more classes of securities traded together as a unit;
    bonds with attached stocks and warrants.
 +  Payment-in-kind security.
++  Currently a zero coupon bond that will pay interest at the rate shown at a
    future specified date.
(a) Non-income producing security; issuer in bankruptcy.
(b) Non-income producing security; bond in default.
(c) Non-income producing security.
(d) Acquired through exchange offer.
(e) Includes 209,956 shares which are due from the issuer pursuant to a
    reorganization.
(f) Security was purchased on a discount basis. The interest rate shown has
    been adjusted to reflect a money market equivalent yield.
(g) Collateralized by $200,286 U.S. Treasury Note 6.75% due 05/31/99 valued at
    $206,026.
(h) The aggregate cost for federal income tax purposes approximates identified
    cost. The aggregate gross unrealized appreciation is $3,763,330 and the
    aggregate gross unrealized depreciation is $8,271,438, resulting in net
    unrealized depreciation of $4,508,108.
 







       SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   8
 
HIGH INCOME ADVANTAGE TRUST III
 
FINANCIAL STATEMENTS
 
<TABLE>
<S>                                                           <C>
STATEMENT OF ASSETS AND LIABILITIES
January 31, 1998
ASSETS:
Investments in securities, at value
 (identified cost $85,807,299)..............................  $ 81,299,191
Receivable for:
    Interest................................................     1,956,030
    Investments sold........................................     1,909,375
Prepaid expenses and other assets...........................         2,788
                                                              ------------
 
    TOTAL ASSETS............................................    85,167,384
                                                              ------------
 
LIABILITIES:
Payable for:
    Investments purchased...................................     5,477,773
    Investment management fee...............................        58,724
Accrued expenses and other payables.........................        58,426
                                                              ------------
 
    TOTAL LIABILITIES.......................................     5,594,923
                                                              ------------
 
    NET ASSETS..............................................  $ 79,572,461
                                                              ============
 
COMPOSITION OF NET ASSETS:
Paid-in-capital.............................................  $121,076,287
Net unrealized depreciation.................................    (4,508,108)
Accumulated undistributed net investment income.............     1,011,828
Accumulated net realized loss...............................   (38,007,546)
                                                              ------------
 
    NET ASSETS..............................................  $ 79,572,461
                                                              ============
 
NET ASSET VALUE PER SHARE,
 12,876,779 shares outstanding
 (unlimited shares authorized of $.01 par value)............         $6.18
                                                                     =====
</TABLE>
 
        SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   9
 
HIGH INCOME ADVANTAGE TRUST III
 
FINANCIAL STATEMENTS, continued
 
<TABLE>
<S>                                                           <C>
STATEMENT OF OPERATIONS
For the year ended January 31, 1998

NET INVESTMENT INCOME:

INTEREST INCOME.............................................  $10,825,337
                                                              -----------
 
EXPENSES
Investment management fee...................................      596,066
Professional fees...........................................       57,717
Shareholder reports and notices.............................       36,538
Transfer agent fees and expenses............................       29,986
Trustees' fees and expenses.................................       14,322
Custodian fees..............................................       13,445
Other.......................................................       10,944
                                                              -----------
 
    TOTAL EXPENSES..........................................      759,018
                                                              -----------
 
    NET INVESTMENT INCOME...................................   10,066,319
                                                              -----------
 
NET REALIZED AND UNREALIZED GAIN (LOSS):
Net realized loss...........................................   (5,009,921)
Net change in unrealized depreciation.......................    5,579,923
                                                              -----------
 
    NET GAIN................................................      570,002
                                                              -----------
 
NET INCREASE................................................  $10,636,321
                                                              ===========
</TABLE>
 
        SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   10
 
HIGH INCOME ADVANTAGE TRUST III
 
FINANCIAL STATEMENTS, continued
 
<TABLE>
<CAPTION>
STATEMENT OF CHANGES IN NET ASSETS
                                                          FOR THE YEAR       FOR THE YEAR
                                                             ENDED              ENDED
                                                        JANUARY 31, 1998   JANUARY 31, 1997
- -------------------------------------------------------------------------------------------
<S>                                                     <C>                <C>
INCREASE (DECREASE) IN NET ASSETS:
 
OPERATIONS:
Net investment income.................................    $10,066,319        $ 9,871,376
Net realized loss.....................................     (5,009,921)        (5,170,842)
Net change in unrealized depreciation.................      5,579,923          1,902,122
                                                          -----------        -----------
 
    NET INCREASE......................................     10,636,321          6,602,656
 
Dividends from net investment income..................     (9,770,760)       (10,172,655)
                                                          -----------        -----------
 
    NET INCREASE (DECREASE)...........................        865,561         (3,569,999)

NET ASSETS:
Beginning of period...................................     78,706,900         82,276,899
                                                          -----------        -----------
 
    END OF PERIOD
    (Including undistributed net investment income of
    $1,011,828 and $716,269, respectively)............    $79,572,461        $78,706,900
                                                          ===========        ===========
</TABLE>
 
        SEE NOTES TO FINANCIAL STATEMENTS
<PAGE>   11
 
HIGH INCOME ADVANTAGE TRUST III
 
NOTES TO FINANCIAL STATEMENTS January 31, 1998
 
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, American or other domestic or foreign 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 (in
cases where securities are traded on more than one exchange; the securities are
valued on the exchange designated as the primary market pursuant to procedures
adopted by the Trustees); (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, including circumstances under which it is
determined by Dean Witter InterCapital Inc. (the "Investment Manager") that sale
or bid prices are not reflective of a security's market value, 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 may utilize 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.
<PAGE>   12
HIGH INCOME ADVANTAGE TRUST III
 
NOTES TO FINANCIAL STATEMENTS January 31, 1998, continued
 
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.
 
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 the Investment Manager, the
Trust pays the Investment Manager 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
<PAGE>   13
HIGH INCOME ADVANTAGE TRUST III
 
NOTES TO FINANCIAL STATEMENTS January 31, 1998, continued
 
Investment Manager also bears the cost of telephone services, heat, light, power
and other utilities provided to the Trust.
 
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, 1998 aggregated
$86,119,871 and $87,388,549, respectively.
 
Dean Witter Trust FSB, an affiliate of the Investment Manager, is the Trust's
transfer agent. At January 31, 1998, the Trust had transfer agent fees and
expenses payable of approximately $1,200.
 
4. SHARES OF BENEFICIAL INTEREST
 
<TABLE>
<CAPTION>
                                                                                         CAPITAL
                                                                                         PAID IN
                                                                                        EXCESS OF
                                                                SHARES     PAR VALUE    PAR VALUE
                                                              ----------   ---------   ------------
<S>                                                           <C>          <C>         <C>
Balance, January 31, 1996, 1997 and 1998....................  12,876,779   $128,768    $120,947,519
                                                              ==========   ========    ============
</TABLE>
 
5. DIVIDENDS
 
The Trust declared the following dividends from net investment income:
 
<TABLE>
<CAPTION>
   DECLARATION      AMOUNT          RECORD            PAYABLE
      DATE         PER SHARE         DATE              DATE
- -----------------  ---------   ----------------  -----------------
<S>                <C>         <C>               <C>
January 27, 1998     $0.06     February 6, 1998  February 20, 1998
February 24, 1998    $0.06      March 6, 1998     March 20, 1998
</TABLE>
 
6. FEDERAL INCOME TAX STATUS
 
At January 31, 1998, the Trust had a net capital loss carryover of approximately
$36,744,000 which may be used to offset future capital gains to the extent
provided by regulations which is available through January 31 of the following
years:
 
<TABLE>
<CAPTION>
                       AMOUNTS IN THOUSANDS
- -------------------------------------------------------------------
      2000       2002       2003       2004       2005       2006
    --------   --------   --------   --------   --------   --------
<S>            <C>        <C>        <C>        <C>        <C>
     $9,648     $3,256    $10,665     $4,258     $3,007     $5,910
     ======     ======    =======     ======     ======     ======
</TABLE>
 
Capital losses incurred after October 31 ("post-October" losses) within the
taxable year are deemed to arise on the first business day of the Trust's next
taxable year. The Trust incurred and will elect to defer net capital losses of
approximately $130,000 during fiscal 1998.
 
At January 31, 1998, the Trust had temporary book/tax differences primarily
attributable to post-October losses and capital loss deferrals on wash sales.
<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
                                                               ----------------------------------------------------
                                                                 1998       1997       1996       1995       1994
<S>                                                            <C>        <C>        <C>        <C>        <C>
- -------------------------------------------------------------------------------------------------------------------
PER SHARE OPERATING PERFORMANCE:
Net asset value, beginning of period........................   $   6.11   $   6.39   $   6.12   $   7.57   $   6.70
                                                               --------   --------   --------   --------   --------
Net investment income.......................................       0.78       0.77       0.75       0.75       0.81
Net realized and unrealized gain (loss).....................       0.05      (0.26)      0.24      (1.43)      0.91
                                                               --------   --------   --------   --------   --------
Total from investment operations............................       0.83       0.51       0.99      (0.68)      1.72
                                                               --------   --------   --------   --------   --------
Less dividends from net investment income...................      (0.76)     (0.79)     (0.72)     (0.77)     (0.85)
                                                               --------   --------   --------   --------   --------
Net asset value, end of period..............................   $   6.18   $   6.11   $   6.39   $   6.12   $   7.57
                                                               ========   ========   ========   ========   ========
Market value, end of period.................................   $  7.375   $   7.00   $   6.75   $   6.50   $   7.75
                                                               ========   ========   ========   ========   ========
TOTAL INVESTMENT RETURN+....................................      16.86%     16.03%     15.31%    (6.30)%     26.21%
 
RATIOS TO AVERAGE NET ASSETS:
Expenses....................................................       0.96%      0.98%      1.00%      1.02%      0.99%
Net investment income.......................................      12.70%     12.13%     11.80%     11.04%     11.40%
 
SUPPLEMENTAL DATA:
Net assets, end of period, in thousands.....................    $79,572    $78,707    $82,277    $78,765    $97,466
Portfolio turnover rate.....................................        113%       161%        78%        82%       231%
</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, 1998, the results of its operations for the year
then ended, the changes in its net assets for each of the two years in the
period then ended and the financial highlights for each of the 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, 1998 by correspondence with the custodian and brokers and the application of
alternative auditing procedures where confirmations from brokers were not
received, provide a reasonable basis for the opinion expressed above.
 
PRICE WATERHOUSE LLP
1177 Avenue of the Americas
New York, New York 10036
March 6, 1998
<PAGE>   16

TRUSTEES
- -------------------------------------------------
Michael Bozic
Charles A. Fiumefreddo
Edwin J. Garn
John R. Haire
Wayne E. Hedien
Dr. Manuel H. Johnson
Michael E. Nugent
Philip J. Purcell
John L. Schroeder

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

Barry Fink
Vice President, Secretary and General Counsel

Peter M. Avelar
Vice President

Thomas F. Caloia
Treasurer

TRANSFER AGENT
- -------------------------------------------------
Dean Witter Trust FSB
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




HIGH
INCOME
ADVANTAGE
TRUST III



ANNUAL REPORT
JANUARY 31, 1998



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