ONE GROUP
N-30D, 1997-08-29
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<PAGE>   1

                                                             Institutional Money
                                                                    Market Funds
                                                                   Annual Report
                                                For the year ended June 30, 1997



                                                 Treasury Only Money Market Fund


                                                    Government Money Market Fund








                                     [THE ONE GROUP FAMILY OF MUTUAL FUNDS LOGO]
<PAGE>   2
           ----------------------------------------------------------

              Important Customer Information. Investment Products:

              * are not deposits or obligations of or guaranteed by,
                BANC ONE CORPORATION or any of its affiliates,
               
              * are not insured by the FDIC, and
                                                                         ----
              * are subject to investment risks, including possible      FDIC
                loss of the principal amount invested.                   LOGO
                                                                         ----
           -----------------------------------------------------------
<PAGE>   3
 
- --------------------------------------------------------------------------------
Table of Contents
- --------------------------------------------------------------------------------
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1997
 
Report From Your Investment Advisor........................................    2
Portfolio Performance Review...............................................    4
Schedules of Portfolio Investments.........................................    6
Statements of Assets and Liabilities.......................................    8
Statements of Operations...................................................    9
Statements of Changes in Net Assets........................................   10
Notes to Financial Statements..............................................   11
Financial Highlights.......................................................   14
Report of Independent Accountants..........................................   16
 
                                                                               1
<PAGE>   4
 
- --------------------------------------------------------------------------------
Report From Your Investment Advisor
- --------------------------------------------------------------------------------
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1997
 
We are pleased to present this annual report for The One Group Family of Mutual
Funds. On the following pages you will find an overview of the financial markets
and your fund's performance for the period from July 1, 1996, to June 30, 1997.
 
DEAR VALUED SHAREHOLDERS:
Thank you for continuing to place your confidence in The One Group Family of
Mutual Funds. In the funds' semiannual report, we advised you to stay focused on
your financial goals and not to let short-term volatility interfere with your
long-term investment strategy. At that time, stock returns were abnormally
strong, and bond returns were unusually weak.
 
Since then, the bond market has recovered nicely, and the stock market continues
to soar--even after falling nearly 10% between March 12 and April 14. In fact,
by early May, the stock market had regained what it had lost and was well on its
way to new heights. Looking forward, investors should be prepared for continued
volatility as the market reacts to earnings reports, moves by the Federal
Reserve, and the continuous stream of economic data coming from Washington.
 
REINFORCING OUR PHILOSOPHY
Once again, I want to reiterate our philosophy that it's time, not timing, that
best serves investors. By maintaining a long-term perspective and riding out the
inevitable volatility in the markets, your investments may realize their full
potential. For those who stay on track with their investment plans, short-term
performance fluctuations may not matter in the long run.
 
The financial media will be filled with opinions about the expected short-term
course of the markets, and these opinions will swing between euphoria and gloom.
But the fundamentals supporting the financial markets--a growing economy, rising
corporate profits, low inflation--remain favorable, and long-term investors
should be rewarded by staying the course.
 
INVESTING MADE EASY
Along with maintaining a long-term perspective, we believe that investment
success is dependent on two other strategies:
 
- - ASSET ALLOCATION, or spreading your money among stocks, bonds and money market
  investments according to your goals, time frame and risk tolerance in order
  create a well-rounded investment plan.
 
- - DIVERSIFICATION, or investing in a variety of securities within each asset
  class to enhance your return potential and limit your overall risk profile.
 
Over the past year, The One Group made it easier for you to take advantage of
these strategies by introducing THE ONE GROUP INVESTOR FUNDS. These funds make
it simple and convenient for you to enjoy asset allocation and diversification
from one investment (versus structuring an asset allocation portfolio by
purchasing multiple funds). Each Investor fund seeks a particular investment
goal and, accordingly, invests in an assortment of funds from The One Group
family. You simply choose the Investor Fund suited to your goals.
 
INFORMATION ON DEMAND
Along with making investing easy, we want to make it simple for you to obtain
the information you need when you want it. Now, in addition to offering fund
prices, fund performance information and fund manager biographies, The One Group
web site (WWW.ONEGROUP.COM) provides on-line fund prospectuses.
 
In addition, the site offers an interactive portfolio-building tool that you can
use to design a customized portfolio. Future plans for the site include
interactive retirement and college planning calculators as well as account
access, which will enable you to obtain information on your account and place
orders to buy or exchange shares between funds.
 
LOOK FOR GUIDANCE
Perhaps one of the simplest ways to make investing easy is to seek guidance from
an experienced investment advisor. Achieving long-term investment success
depends on your investment plan and how your investment strategies are put to
work. It's the full-time responsibility of a professional investment advisor to
monitor the investment markets and evaluate the assortment of investment
opportunities in today's marketplace. Your investment advisor will help you
develop an effective investment plan and then implement and monitor that plan
for you.
 
   2
<PAGE>   5
 
- --------------------------------------------------------------------------------
Report From Your Investment Advisor, continued
- --------------------------------------------------------------------------------
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1997
 
Once again, I appreciate the trust and confidence that you have placed in The
One Group Family of Mutual Funds. All of the professionals at The One Group
value your ongoing support and strive to help you achieve your financial goals
with investment solutions that are designed to meet your individual needs.
 
Sincerely,
LOGO
David J. Kundert
President and CEO,
Banc One Investment Advisors Corporation,
Investment Advisor to The One Group
 
David J. Kundert photo
 
For a prospectus with more complete information on The One Group Investor Funds,
including management fees and expenses, please contact The One Group at
1-800-480-4111. Please read the prospectus carefully before investing.
 
                                                                               3
<PAGE>   6
 
                 The One Group Treasury Only Money Market Fund
Portfolio Performance Review
- --------------------------------------------------------------------------------
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1997
 
PERFORMANCE
The seven-day yield on The One Group Treasury Only Money Market Fund was 5.12%
on June 30, 1997, up from 5.00% on June 30, 1996.
 
The Fund's yield reflects the slight increase in interest rates brought on by
the Federal Reserve's only monetary policy adjustment during the fiscal year--a
0.25% federal funds rate hike on March 25, 1997. Interim rate movements were
fairly moderate, and they reflected market participants' changing views on
economic strength and whether that strength would lead to inflationary pressures
requiring Federal Reserve action.
 
STRATEGIES AND TACTICS
The portfolio continued to benefit from a "barbell" maturity structure, a common
technique that involves investing in securities at the long and short ends of a
particular maturity range instead of those with intermediate maturities.
 
This strategy led to an average maturity of 49 days on June 30, 1997, enabling
the Fund to maintain its "AAA" average quality rating--the best possible--from
Standard & Poor's and Moody's Investors Service. This rating indicates that the
Fund's securities are of the highest quality and offer the lowest risk. In order
to receive this rating, a fund must have an average maturity no greater than 60
days.
OUTLOOK
Economic activity and how it influences the Federal Reserve's policies will have
a direct effect on the Fund over the next year. Over the near term, the Federal
Reserve may make another move to slow down the economy and take a proactive
stance against inflation. As investors factor this potential rate hike into the
market, the yield curve should steepen, meaning securities with longer
maturities would offer higher yields. If this happens, we would extend the
Fund's average weighted maturity to take advantage of a steeper yield curve.
 
Andrew T. Linton Signature
Andrew T. Linton
Fund Manager
 
Gary J. Madich Signature
Gary J. Madich, CFA
Senior Managing Director of Fixed-Income Securities
 
<TABLE>
<CAPTION>
                            AVERAGE ANNUAL
7 DAY YIELD     1 YEAR       TOTAL RETURN 5 YEARS SINCE INCEPTION
<S>             <C>        <C>         <C>             <C>
    5.12         5.24         NA             4.67
</TABLE>
 
Please refer to the prospectus and the accompanying financial statements for
further information about your Fund.
 
   4
<PAGE>   7
 
                   The One Group Government Money Market Fund
Portfolio Performance Review
- --------------------------------------------------------------------------------
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1997
 
PERFORMANCE
The seven-day yield on The One Group Government Money Market Fund was 5.30% on
June 30, 1997, up slightly from 5.29% on June 30, 1996.
 
The Fund's yield reflects the slight increase in interest rates brought on by
the Federal Reserve's only monetary policy adjustment during the fiscal year--a
0.25% federal funds rate hike on March 25, 1997. Interim rate movements were
fairly moderate, and they reflected market participants' changing views on
economic strength and whether that strength would lead to inflationary pressures
requiring Federal Reserve action.
 
STRATEGIES AND TACTICS
The Fund was invested primarily in agency securities because they offered a
yield advantage of 10 to 15 basis points over Treasuries (one basis point equals
1/100th of a percent). The Fund also held between 15% and 20% of its assets in
floating-rate securities, which offered yields that changed on a weekly basis.
This position helped the Fund quickly take advantage of rising interest rates.
 
The portfolio continued to benefit from a "barbell" maturity structure, a common
strategy that involves favoring securities at the long and short ends of a
particular maturity range over those with intermediate maturities. At the "long"
end, we purchased securities with maturities of six months to one year, and at
the "short" end, we held overnight repurchase agreements. The longer securities
allowed the Fund to benefit from the steep yield curve (which occurs when
securities with longer maturities offer relatively higher yields), while the
overnight securities helped the Fund maintain a high degree of liquidity.
 
The Fund's barbell structure contributed to an average maturity of 72 days on
June 30, 1997, compared to 71 days on June 30, 1996.
 
OUTLOOK
Economic activity and how it influences the Federal Reserve's policies will have
a direct effect on the Fund over the next year. Over the near term, the Federal
Reserve may make another move to slow down the economy and take a proactive
stance against inflation. This outlook warrants the continued use of a barbell
maturity structure, which should allow us to quickly take advantage of higher
rates should the Federal Reserve take action. If there is a rate hike and it
appears that it may be the last one for a while, we will reduce the Fund's
position in repurchase agreements and reinvest in securities with longer-term
maturities.
 
Andrew T. Linton Signature
Andrew T. Linton
Fund Manager
 
Gary J. Madich Signature
Gary J. Madich, CFA
Senior Managing Director of Fixed-Income Securities
 
<TABLE>
<CAPTION>
                            AVERAGE ANNUAL
7 DAY YIELD     1 YEAR       TOTAL RETURN 5 YEARS SINCE INCEPTION
<S>             <C>        <C>         <C>             <C>
    5.30         5.43         NA             4.94
</TABLE>
 
Please refer to the prospectus and the accompanying financial statements for
further information about your Fund.
 
                                                                               5
<PAGE>   8
 
- --------------------------------------------------------------------------------
The One Group Family of Mutual Funds
Treasury Only Money Market Fund
- --------------------------------------------------------------------------------
SCHEDULE OF PORTFOLIO INVESTMENTS                                  JUNE 30, 1997
(Amounts in Thousands)
<TABLE>
<CAPTION>
PRINCIPAL                                          AMORTIZED
 AMOUNT             SECURITY DESCRIPTION             COST
- ---------    -----------------------------------   ---------
<C>          <S>                                   <C>
U.S. TREASURY OBLIGATIONS (98.5%):
U.S. Treasury Bills (16.4%):
$ 14,807     7/24/97............................   $ 14,757
  13,783     8/7/97 (b).........................     13,709
   5,178     8/14/97............................      5,146
   5,864     8/21/97............................      5,822
   9,830     8/28/97............................      9,753
   2,593     9/4/97.............................      2,569
  12,225     9/11/97............................     12,102
   6,186     9/18/97............................      6,117
   3,942     11/13/97...........................      3,864
   5,000     3/5/98.............................      4,816
                                                   --------
                                                     78,655
                                                   --------
 
PRINCIPAL                                          AMORTIZED
 AMOUNT             SECURITY DESCRIPTION             COST
- ---------    -----------------------------------   --------
U.S. TREASURY OBLIGATIONS, CONTINUED:
U.S. Treasury Notes (82.1%):
$  8,418     8.50%, 7/15/97.....................   $  8,428
 196,434     5.88%, 7/31/97 (b).................    196,555
  20,000     5.50%, 7/31/97.....................     20,001
  20,000     8.63%, 8/15/97 (b).................     20,076
  50,000     6.50%, 8/15/97 (b).................     50,071
  50,000     6.00%, 8/31/97.....................     50,014
  50,000     5.75%, 9/30/97.....................     50,052
                                                   --------
                                                    395,197
                                                   --------
  Total U.S. Treasury Obligations                   473,852
                                                   --------
Total (Amortized Cost--$473,852) (a)               $473,852
                                                   ========
</TABLE>
 
- ------------
 
Percentages indicated are based on net assets of $480,860.
 
(a) Represents cost for financial reporting purposes and differs from cost for
    federal income tax by $8.
 
(b) A portion of this security was loaned as of June 30, 1997.
 
See notes to financial statements.
 
   6
<PAGE>   9
 
- --------------------------------------------------------------------------------
The One Group Family of Mutual Funds
Government Money Market Fund
- --------------------------------------------------------------------------------
SCHEDULE OF PORTFOLIO INVESTMENTS                                  JUNE 30, 1997
(Amounts in Thousands)
<TABLE>
<CAPTION>
PRINCIPAL                                          AMORTIZED
 AMOUNT             SECURITY DESCRIPTION              COST
- ---------    -----------------------------------   ----------
<C>          <S>                                   <C>
U.S. GOVERNMENT AGENCY SECURITIES (76.7%):
Federal Farm Credit Bank (3.2%):
$ 10,000     5.61%, 11/13/97....................   $   9,790
  25,000     5.45%, 3/3/98......................      24,952
                                                   ---------
                                                      34,742
                                                   ---------
Federal Home Loan Bank (4.8%):
  10,000     5.80%, 8/12/97.....................       9,998
   7,000     5.83%, 12/19/97....................       7,009
   9,750     5.99%, 2/9/98......................       9,765
  25,000     6.12%, 4/17/98.....................      24,996
                                                   ---------
                                                      51,768
                                                   ---------
Federal Home Loan Mortgage Corp. (6.9%):
  50,000     5.50%, 7/2/97......................      49,993
  25,000     5.95%, 6/19/98.....................      24,988
                                                   ---------
                                                      74,981
                                                   ---------
Federal National Mortgage Assoc. (47.0%):
  88,790     5.36%, 7/10/97.....................      88,670
  65,000     5.50%, 7/18/97.....................      64,831
  19,750     5.64%, 9/3/97......................      19,735
  30,000     5.26%, 9/3/97*.....................      29,997
  23,000     5.26%, 9/9/97*.....................      23,001
  39,785     5.56%, 9/24/97.....................      39,263
  25,000     5.59%, 10/14/97....................      24,592
  25,000     5.65%, 11/3/97.....................      24,510
  17,955     5.45%, 11/6/97.....................      17,934
  20,000     5.40%, 12/5/97.....................      19,988
  25,000     5.52%, 12/18/97....................      24,348
  25,000     5.48%, 1/2/98......................      24,978
  25,000     6.02%, 4/15/98.....................      24,981
  48,420     5.89%, 5/21/98.....................      48,382
   4,000     5.25%, 6/2/99*.....................       4,000
  20,000     5.25%, 7/26/99*....................      20,000
  10,000     5.25%, 9/22/99*....................      10,000
                                                   ---------
                                                     509,210
                                                   ---------
 
PRINCIPAL                                          AMORTIZED
 AMOUNT             SECURITY DESCRIPTION              COST
- ---------    -----------------------------------   ---------
U.S. GOVERNMENT AGENCY SECURITIES, CONTINUED
Student Loan Marketing Assoc. (14.8%):
$ 25,000     5.32%, 8/4/97*.....................   $  25,001
  25,000     5.26%, 8/21/97*....................      25,001
  40,000     5.24%, 11/24/97*...................      40,001
  25,000     5.26%, 9/28/98*....................      25,000
  25,000     5.26%, 11/10/98*...................      25,000
  10,000     5.28%, 1/13/99*....................       9,999
  10,000     5.29%, 8/2/99*.....................       9,997
                                                   ---------
                                                     159,999
                                                   ---------
Total U.S. Government Agency Securities              830,700
                                                   ---------
REPURCHASE AGREEMENTS (23.4%):
  73,289     Aubrey G. Lanston & Co., 5.40%,
               7/1/97 (collateralized by $56,614
               various U.S. Treasury Bonds,
               8.75% - 9.88%,
               11/15/15 - 5/15/17, market value
               $75,446).........................      73,289
  45,000     HSBC Securities, 5.90%, 7/1/97
               (collateralized by $46,015
               various U.S. Government
               Securities, 5.01% -  9.25%,
               6/8/98 - 6/27/07, market value
               $45,901).........................      45,000
  35,000     Lehman Brothers, 6.13%, 7/1/97
               (collateralized by $32,742
               various U.S. Government
               Securities, 0.00% -  9.05%,
               6/10/98 - 8/12/19, market value
               $35,691).........................      35,000
 100,000     Prudential Securities, 6.10%,
               7/1/97 (collateralized by
               $139,882 various U.S. Government
               Securities, 0.00% -  7.89%,
               7/22/97 - 2/1/25, market value
               $102,738)                             100,000
                                                   ---------
Total Repurchase Agreements                          253,289
                                                   ---------
Total (Amortized Cost--$1,083,989) (a)            $1,083,989
                                                   =========
</TABLE>
 
- ------------
 
Percentages indicated are based on net assets of $1,083,438.
 
(a) Cost and value for federal income tax and financial reporting purposes are
    the same.
 
 * Variable rate securities having liquidity agreements. The interest rate,
   which will change periodically, is based upon an index of market rates. The
   rate reflected on the Schedule of Portfolio Investments is the rate in effect
   at June 30, 1997.
 
See notes to financial statements.
 
                                                                               7
<PAGE>   10
 
- --------------------------------------------------------------------------------
The One Group Family of Mutual Funds
- --------------------------------------------------------------------------------
STATEMENTS OF ASSETS AND LIABILITIES                               JUNE 30, 1997
 
<TABLE>
<CAPTION>
                                                                              (Amounts in Thousands,
                                                                            except per share amounts)
<S>                                                                       <C>              <C>
                                                                          TREASURY ONLY     GOVERNMENT
                                                                          MONEY MARKET     MONEY MARKET
                                                                              FUND             FUND
                                                                          -------------    ------------ 
ASSETS:
Investments, at amortized cost.........................................     $ 473,852       $   830,700
Repurchase agreements, at cost.........................................            --           253,289
                                                                          -----------      ------------ 
Total..................................................................       473,852         1,083,989
Cash...................................................................            66                 1
Interest receivable....................................................         9,211             4,723
Deferred organization costs............................................             3                20
Prepaid expenses and other assets......................................             8               122
                                                                          -----------      ------------ 
TOTAL ASSETS...........................................................       483,140         1,088,855
                                                                          -----------      ------------ 
LIABILITIES:
Dividends payable......................................................         2,179             5,090
Accrued expenses and other payables:
     Investment advisory fees..........................................            34                77
     Administration fees...............................................            21                48
     Accounting and transfer agent fees................................             2                 2
     Other.............................................................            44               200
                                                                          -----------      ------------  
TOTAL LIABILITIES......................................................         2,280             5,417
                                                                          -----------      ------------  
NET ASSETS:
Capital................................................................       480,952         1,083,623
Accumulated undistributed net realized losses from investment
  transactions.........................................................           (92)             (185)
                                                                          -----------      ------------ 
NET ASSETS.............................................................     $ 480,860       $ 1,083,438
                                                                          ===========      ============
Outstanding shares of beneficial interest..............................       480,950         1,083,623
                                                                          ===========      ============
Net Asset Value:
  Offering and redemption price per share..............................         $1.00             $1.00
                                                                              =======            ======
</TABLE>                                                   
 
See notes to financial statements.
 
   8
<PAGE>   11
 
- --------------------------------------------------------------------------------
The One Group Family of Mutual Funds
- --------------------------------------------------------------------------------
STATEMENTS OF OPERATIONS                        FOR THE YEAR ENDED JUNE 30, 1997
 
<TABLE>
<CAPTION>
                                                                              (Amounts in Thousands)
<S>                                                                       <C>              <C>
                                                                          TREASURY ONLY     GOVERNMENT
                                                                          MONEY MARKET     MONEY MARKET
                                                                              FUND             FUND
                                                                          -------------    -------------
INVESTMENT INCOME:
Interest income........................................................      $25,226          $57,712
Income from securities lending.........................................          145               13
                                                                          ----------       ----------
TOTAL INCOME...........................................................       25,371           57,725
                                                                          ----------       ----------
EXPENSES:
Investment advisory fees...............................................          385              849
Administration fees....................................................          241              530
Custodian and accounting fees..........................................           23                2
Legal and audit fees...................................................           11               19
Organization costs.....................................................            4               21
Trustees' fees and expenses............................................            3                5
Transfer agent fees....................................................            7                1
Registration and filing fees...........................................           58                1
Printing costs.........................................................            8                2
Other..................................................................            2                7
                                                                          ----------       ----------
TOTAL EXPENSES.........................................................          742            1,437
                                                                          ----------       ----------
Net Investment Income..................................................       24,629           56,288
                                                                          ----------       ----------
REALIZED LOSSES FROM INVESTMENT TRANSACTIONS:
Net realized losses from investment transactions.......................          (16)            (119)
                                                                          ----------       ----------
Net increase in net assets resulting from operations...................      $24,613          $56,169
                                                                          ==========       ==========
</TABLE>                                                               
 
See notes to financial statements.
 
                                                                               9
<PAGE>   12
 
- --------------------------------------------------------------------------------
The One Group Family of Mutual Funds
- --------------------------------------------------------------------------------
STATEMENTS OF CHANGES IN NET ASSETS
<TABLE>
<CAPTION>
                                                                      (Amounts in Thousands)
<S>                                                  <C>            <C>            <C>            <C>
                                                        TREASURY ONLY MONEY             GOVERNMENT MONEY
                                                            MARKET FUND                   MARKET FUND
                                                     --------------------------    --------------------------
                                                     YEAR ENDED     YEAR ENDED     YEAR ENDED     YEAR ENDED
                                                      JUNE 30,       JUNE 30,       JUNE 30,       JUNE 30,
                                                        1997           1996           1997           1996
                                                     -----------    -----------    -----------    -----------
FROM INVESTMENT ACTIVITIES:
OPERATIONS:
     Net investment income........................   $    24,629    $    18,797    $    56,288    $    42,135
     Net realized gains (losses) from investment
       transactions...............................           (16)           (76)          (119)             8
                                                     -----------    -----------    -----------    -----------
Change in net assets resulting from operations....        24,613         18,721         56,169         42,143
                                                     -----------    -----------    -----------    -----------
DISTRIBUTIONS TO SHAREHOLDERS:
     From net investment income...................       (24,629)       (18,797)       (56,288)       (42,135)
     In excess of net realized gains from
       investment transactions....................            --            (21)            --             --
                                                     -----------    -----------    -----------    -----------
Change in net assets from shareholder
  distributions...................................       (24,629)       (18,818)       (56,288)       (42,135)
                                                     -----------    -----------    -----------    -----------
CAPITAL TRANSACTIONS:
     Proceeds from shares issued..................     1,603,666      1,135,597      4,075,935      2,638,822
     Dividends reinvested.........................         3,409          2,487         11,375         10,663
     Cost of shares redeemed......................    (1,542,160)    (1,010,723)    (3,859,366)    (2,514,579)
                                                     -----------    -----------    -----------    -----------
Change in net assets from share transactions......        64,915        127,361        227,944        134,906
                                                     -----------    -----------    -----------    -----------
Change in Net Assets..............................        64,899        127,264        227,825        134,914
NET ASSETS:
     Beginning of period..........................       415,961        288,697        855,613        720,699
                                                     -----------    -----------    -----------    -----------
     End of period................................   $   480,860    $   415,961    $ 1,083,438    $   855,613
                                                     ===========    ===========    ===========    ===========
SHARE TRANSACTIONS:
     Issued.......................................     1,603,664      1,135,597      4,075,935      2,638,822
     Reinvested...................................         3,409          2,487         11,375         10,663
     Redeemed.....................................    (1,542,160)    (1,010,723)    (3,859,366)    (2,514,579)
                                                     -----------    -----------    -----------    -----------
Change in shares..................................        64,913        127,361        227,944        134,906
                                                     ===========    ===========    ===========    ===========
</TABLE>
 
See notes to financial statements.
 
  10
<PAGE>   13
 
- --------------------------------------------------------------------------------
The One Group Family of Mutual Funds
- --------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS                                      JUNE 30, 1997
 
1. ORGANIZATION:
 
   The One Group (the "Trust") is registered under the Investment Company Act of
   1940, as amended (the "1940 Act"), as an open-end investment company
   established as a Massachusetts business trust. The accompanying financial
   statements and financial highlights are those of the Treasury Only Money
   Market Fund and the Government Money Market Fund (individually a "Fund",
   collectively the "Funds") only. The Funds are diversified mutual funds and
   are not offered in multiple classes.
 
   The Funds' investment objectives are as follows:
 
<TABLE>
<CAPTION>
                    FUND                                           OBJECTIVE
      --------------------------------     ---------------------------------------------------------
      <S>                                  <C>
      Treasury Only Money Market Fund      High current income with liquidity and stability of
                                            principal with the added assurance of a fund that does
                                            not purchase securities that are subject to repurchase
                                            agreements.
 
      Government Money Market Fund         High current income with liquidity and stability of
                                            principal.
</TABLE>
 
2. SIGNIFICANT ACCOUNTING POLICIES:
 
   The following is a summary of significant accounting policies followed by the
   Trust in the preparation of its financial statements. The policies are in
   conformity with generally accepted accounting principles. The preparation of
   financial statements requires management to make estimates and assumptions
   that affect the reported amounts of assets and liabilities at the date of the
   financial statements and the reported amounts of income and expenses for the
   period. Actual results could differ from those estimates.
 
       SECURITY VALUATION
 
       Securities are valued utilizing the amortized cost method permitted in
       accordance with Rule 2a-7 under the 1940 Act. Under the amortized cost
       method, discount or premium is amortized on a constant basis to the
       maturity of the security. In addition, the Funds may not (a) purchase any
       instrument with a remaining maturity greater than thirteen months unless
       such instrument is subject to a demand feature, or (b) maintain a
       dollar-weighted average maturity which exceeds 90 days.
 
       REPURCHASE AGREEMENTS
 
       The Government Money Market Fund may invest in repurchase agreements with
       institutions that Banc One Investment Advisors (the "Advisor") has
       determined are creditworthy. Each repurchase agreement is recorded at
       cost. The Fund requires that the securities purchased in a repurchase
       agreement transaction be transferred to the custodian in a manner
       sufficient to enable the Fund to obtain those securities in the event of
       a counterparty default. The seller, under the repurchase agreement, is
       required to maintain the value of the securities held at not less than
       the repurchase price, including accrued interest. Repurchase agreements
       are considered to be loans by a fund under the 1940 Act.
 
       SECURITY TRANSACTIONS AND RELATED INCOME
 
       Security transactions are accounted for on a trade date basis. Net
       realized gains or losses from sales of securities are determined on the
       specific identification cost method. Interest income and expenses are
       recognized on the accrual basis. Interest income, including any discount
       or premium, is accrued as earned using the effective interest method.
 
       SECURITIES LENDING
 
       To generate additional income, the Funds may lend up to 33% of securities
       in which they are invested pursuant to agreements requiring that the loan
       be continuously secured by cash, U.S. Government or U.S.
Continued
 
                                                                              11
<PAGE>   14
 
- --------------------------------------------------------------------------------
The One Group Family of Mutual Funds
- --------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS, CONTINUED                           JUNE 30, 1997
 
       Government Agency securities, shares of an investment trust or mutual
       fund, or any combination of cash and such securities as collateral equal
       at all times to at least 100% of the market value plus accrued interest
       on the securities lent. The Funds continue to earn interest on securities
       lent while simultaneously seeking to earn interest on the investment of
       collateral. Collateral is marked to market daily to provide a level of
       collateral at least equal to the market value of securities lent. There
       may be risks of delay in recovery of the securities or even loss of
       rights in the collateral should the borrower of the securities fail
       financially. However, loans will be made only to borrowers deemed by the
       Advisor to be of good standing and creditworthy under guidelines
       established by the Board of Trustees and when, in the judgement of the
       Advisor, the consideration which can be earned currently from such
       securities loans justifies the attendant risk. Loans are subject to
       termination by the Funds or the borrower at any time, and are, therefore,
       not considered to be illiquid investments. As of June 30, 1997, the
       following Fund had securities with the following amortized cost on loan
       (amount in thousands):
 
<TABLE>
<CAPTION>
                                                                            AMORTIZED COST
                                                                               OF LOANED
                                                                              SECURITIES
                                                                            ---------------
            <S>                                                             <C>
            Treasury Only Money Market Fund..............................      $116,076
</TABLE>
 
       The loaned securities were fully collateralized by cash and U.S.
       Government securities as of June 30, 1997.
 
       EXPENSES
 
       Expenses directly attributable to a Fund are charged directly to that
       Fund, while the expenses which are attributable to more than one fund of
       the Trust are allocated among the respective Funds.
 
       DIVIDENDS AND DISTRIBUTIONS TO SHAREHOLDERS
 
       Dividends from net investment income are declared daily and paid monthly.
       Net investment income for this purpose consists of interest accrued and
       discount earned (including both original issue discount and market
       discount) less amortization of any market premium and accrued expenses.
       Net realized capital gains, if any, are distributed at least annually.
 
       Distributions from net investment income and from net capital gains are
       determined in accordance with income tax regulations which may differ
       from generally accepted accounting principles. These differences are
       primarily due to differing treatments for expiring capital loss
       carryforwards and deferrals of certain losses. Permanent book and tax
       basis differences, if any, have been reclassified among the components of
       net assets.
 
       ORGANIZATION COSTS
 
       Costs incurred by the Trust in connection with its organization,
       including the fees and expenses of registering and qualifying its shares
       for distribution have been deferred and are being amortized using the
       straight-line method over a period of five years beginning with the
       commencement of each Fund's operations. All such costs, which are
       attributable to more than one fund of the Trust, have been allocated
       among the respective funds pro-rata, based on the relative net assets of
       each Fund. In the event that any of the initial shares are redeemed
       during such period by any holder thereof, the related Fund will be
       reimbursed by such holder for any unamortized organization costs in the
       proportion as the number of initial shares being redeemed bears to the
       number of initial shares outstanding at the time of redemption.
 
       FEDERAL INCOME TAXES
 
       The Trust treats each Fund as a separate entity for Federal income tax
       purposes. Each Fund intends to continue to qualify as a regulated
       investment company by complying with the provisions available to certain
Continued
 
  12
<PAGE>   15
 
- --------------------------------------------------------------------------------
The One Group Family of Mutual Funds
- --------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS, CONTINUED                           JUNE 30, 1997
 
       investment companies as defined in applicable sections of the Internal
       Revenue Code, and to make distributions of net investment income and net
       realized capital gains sufficient to relieve it from all, or
       substantially all, Federal income taxes.
 
3. SHARES OF BENEFICIAL INTEREST:
 
   The Trust has an unlimited number of shares of beneficial interest, with no
   par value, which may, without shareholder approval, be divided into an
   unlimited number of series of such shares and any series may be classified or
   reclassified into one or more classes. The Trust is registered to offer forty
   series and five classes of shares: Fiduciary, Class A, Class B, Class C and
   Service Class. Currently, the Trust consists of thirty three active Funds
   and, not all Funds can offer all classes of shares. As of June 30, 1997,
   there were no shareholders in the Class C or Service Class of the Funds.
   Shareholders are entitled to one vote for each full share held and will vote
   in the aggregate and not by class or series, except as otherwise expressly
   required by law or when the Board of Trustees has determined that the matter
   to be voted on affects only the interest of shareholders of a particular
   class or series.
 
4. INVESTMENT ADVISORY, ADMINISTRATIVE AND DISTRIBUTION AGREEMENTS:
 
   The Trust and Advisor are parties to an investment advisory agreement under
   which the Advisor is entitled to receive a fee, computed daily and paid
   monthly, equal to 0.08% of the average daily net assets of each Fund.
 
   The Trust and The One Group Services Company (the "Administrator"), a
   wholly-owned subsidiary of The BISYS Group, Inc., are parties to an
   administrative agreement under which the Administrator provides services for
   a fee that is computed daily and paid monthly at an annual rate of 0.05% of
   each Fund's average daily net assets. The Advisor also serves as
   Sub-Administrator to each fund of the Trust, pursuant to an agreement between
   the Administrator and the Advisor. Pursuant to this agreement, the Advisor
   performs many of the Administrator's duties, for which the Advisor receives a
   fee paid by the Administrator.
 
   The One Group Services Company (the "Distributor") and the Trust are parties
   to a distribution agreement under which shares of the Funds are sold on a
   continuous basis. No compensation is paid to the Distributor for distribution
   services for the Funds.
 
   Certain officers of the Trust are affiliated with the Administrator. Such
   officers receive no compensation from the Funds for serving in their
   respective roles.
 
5. FEDERAL TAX INFORMATION (UNAUDITED):
 
   At June 30, 1997 the following Funds have capital loss carryforwards which
   are available to offset future capital gains, if any (amounts in thousands):
 
<TABLE>
<CAPTION>
            FUND                                                        AMOUNT     EXPIRES
            ---------------------------------------------------------   ------     --------
            <S>                                                         <C>        <C>
            Treasury Only Money Market...............................    $ 18        2004
            Treasury Only Money Market...............................      58        2005
            Government Money Market..................................       8        2002
            Government Money Market..................................      26        2003
            Government Money Market..................................      32        2004
            Government Money Market..................................     119        2005
</TABLE>
 
  Capital losses incurred after October 31 within the Fund's fiscal year may be
  deferred and treated as occurring on the first day of the following fiscal
  year. The following deferred losses will be treated as arising on the first
  day of the fiscal year ending June 30, 1998 (amounts in thousands):
 
<TABLE>
<CAPTION>
            FUND                                                                 AMOUNT
            ------------------------------------------------------------------   ------
            <S>                                                                  <C>
            Treasury Only Money Market........................................     $8
</TABLE>
 
                                                                              13
<PAGE>   16
 
- --------------------------------------------------------------------------------
The One Group Family of Mutual Funds
- --------------------------------------------------------------------------------
FINANCIAL HIGHLIGHTS
 
<TABLE>
<CAPTION>
                                                                          TREASURY ONLY MONEY MARKET FUND
                                                              --------------------------------------------------------
                                                                                                               APRIL
                                                                                                                16,
                                                                          YEARS ENDED JUNE 30,                1993 TO
                                                              --------------------------------------------    JUNE 30,
                                                                1997        1996        1995        1994      1993(a)
                                                              --------    --------    --------    --------    --------
<S>                                                           <C>         <C>         <C>         <C>         <C>
NET ASSET VALUE,
  BEGINNING OF PERIOD......................................   $  1.000    $  1.000    $  1.000    $  1.000    $ 1.000
                                                              --------    --------    --------    --------    ------- 
Investment Activities:
  Net investment income....................................      0.051       0.052       0.051       0.032      0.006
                                                              --------    --------    --------    --------    ------- 
Distributions:
  Net investment income....................................     (0.051)     (0.052)     (0.051)     (0.032)    (0.006) 
                                                              --------    --------    --------    --------    ------- 
NET ASSET VALUE,
  END OF PERIOD............................................   $  1.000    $  1.000    $  1.000    $  1.000    $ 1.000
                                                              ========    ========    ========    ========    ======= 
Total Return...............................................       5.24%       5.38%       5.22%       3.23%      2.96% (b)
 
RATIOS/SUPPLEMENTARY DATA:
  Net Assets at end of period (000)........................   $480,860    $415,961    $288,697    $217,725    $60,330
  Ratio of expenses to average net assets..................       0.15%       0.17%       0.20%       0.15%      0.07% (b)
  Ratio of net investment income to average net assets.....       5.12%       5.23%       5.14%       3.23%      2.95% (b)
  Ratio of expenses to average net assets*.................       0.15%       0.17%       0.21%       0.22%      0.33% (b)
  Ratio of net investment income to average net assets*....       5.12%       5.23%       5.13%       3.16%      2.69% (b)
</TABLE>
 
- ------------
 
 *  During the period certain fees were voluntarily reduced. If such voluntary
    fee reductions had not occurred, the ratios would have been as indicated.
(a) Period from commencement of operations.
(b) Annualized.
 
See notes to financial statements.
 
  14
<PAGE>   17
 
- --------------------------------------------------------------------------------
The One Group Family of Mutual Funds
- --------------------------------------------------------------------------------
FINANCIAL HIGHLIGHTS
 
<TABLE>
<CAPTION>
                                                                            GOVERNMENT MONEY MARKET FUND
                                                             ----------------------------------------------------------
                                                                                                               JUNE 14,
                                                                          YEARS ENDED JUNE 30,                 1993 TO
                                                             ----------------------------------------------    JUNE 30,
                                                                1997         1996        1995        1994      1993(a)
                                                             ----------    --------    --------    --------    --------
<S>                                                          <C>           <C>         <C>         <C>         <C>
NET ASSET VALUE,
  BEGINNING OF PERIOD.....................................   $    1.000    $  1.000    $  1.000    $  1.000    $  1.000
                                                             ----------    --------    --------    --------    --------
Investment Activities:
  Net investment income...................................        0.053       0.055       0.053       0.033       0.001
                                                             ----------    --------    --------    --------    --------
Distributions:
  Net investment income...................................       (0.053)     (0.055)     (0.053)     (0.033)     (0.001)
                                                             ----------    --------    --------    --------    --------
NET ASSET VALUE,
  END OF PERIOD...........................................   $    1.000    $  1.000    $  1.000    $  1.000    $  1.000
                                                             ==========    ========    ========    ========    ======== 
Total Return..............................................         5.43%       5.61%       5.41%       3.40%       3.28%(b)
 
RATIOS/SUPPLEMENTARY DATA:
  Net Assets at end of period (000).......................   $1,083,438    $855,613    $720,699    $692,253    $244,991
  Ratio of expenses to average net assets.................         0.14%       0.18%       0.21%       0.11%       0.07%(b)
  Ratio of net investment income to average net assets....         5.31%       5.46%       5.28%       3.41%       3.13%(b)
  Ratio of expenses to average net assets*................         0.14%       0.18%       0.22%       0.20%       0.33%(b)
  Ratio of net investment income to average net assets*...         5.31%       5.46%       5.27%       3.32%       2.87%(b)
</TABLE>
 
- ------------
 
 *  During the period certain fees were voluntarily reduced. If such voluntary
    fee reductions had not occurred, the ratios would have been as indicated.
(a) Period from commencement of operations.
(b) Annualized.
 
See notes to financial statements.
 
                                                                              15
<PAGE>   18
 
- --------------------------------------------------------------------------------
Report of Independent Accountants
- --------------------------------------------------------------------------------
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1997
 
To the Shareholders and Board of Trustees of
  The One Group Family of Mutual Funds:
 
We have audited the accompanying statements of assets and liabilities of the
Treasury Only Money Market Fund and the Government Money Market Fund (two series
of The One Group Family of Mutual Funds), including the schedules of portfolio
investments, as of June 30, 1997, and the related statements of operations for
the year then ended, statements of changes in net assets for the two years in
the period then ended, and the financial highlights for each of the periods
indicated herein. These financial statements and financial highlights are the
responsibility of The One Group Family of Mutual Funds' management. Our
responsibility is to express an opinion on these financial statements and the
financial highlights based on our audits.
 
We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements are free of material
misstatement. An audit includes examining on a test basis, evidence supporting
the amounts and disclosures in the financial statements. Our procedures included
confirmation of securities owned as of June 30, 1997 by correspondence with the
custodian and brokers. An audit also includes assessing the accounting
principles used and significant estimates made by management, as well as
evaluating the overall financial statement presentation. We believe that our
audits provide a reasonable basis for our opinion.
 
In our opinion, the financial statements and financial highlights referred to
above present fairly, in all material respects, the financial position of the
Treasury Only Money Market Fund and the Government Only Money Market Fund as of
June 30, 1997, the results of their operations, the changes in their net assets
and the financial highlights for the periods indicated herein, in conformity
with generally accepted accounting principles.
 
Columbus, Ohio                                          Coopers & Lybrand L.L.P.
August 22, 1997
 
  16
<PAGE>   19
Important Customer Information.
Please Read:

Shares of The One Group:
* are not deposits or obligations
  of, or guaranteed by, BANC ONE
  CORPORATION or its affiliates
* are not insured or guaranteed by the 
  FDIC or by any other governmental 
  agency or government-sponsored
  agency of the federal government 
  or any state
* are subject to investment risks,
  including possible loss of the
  principal amount invested.

Banc One Investment Advisors
Corporation, a registered investment 
advisor and an indirect subsidiary of 
BANC ONE CORPORATION, serves 
as an investment advisor to The One
Group, for which it receives advisory 
fees. The One Group is distributed by 
The One Group Services Company, 
3435 Stelzer Road, Columbus,
Ohio 43219, which is not affiliated
with BANC ONE CORPORATION and 
is not a bank. Contact us at our web
site address: www.onegroup.com or
e-mail us at [email protected].

For more complete information on
any of The One Group Funds, including
management fees and expenses,
you may obtain a prospectus from 
The One Group Services Company.
Read the prospectus carefully                                
before investing.                                            

BANC ONE 
INVESTMENT                                                       [LOGO]
ADVISORS
CORPORATION
                                                            TOG-F-033-AN(8/97)


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