ONE GROUP
N-30D, 1996-09-10
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<PAGE>
            THE ONE GROUP-REGISTERED TRADEMARK-
                   FAMILY OF MUTUAL FUNDS
 
 -------------------------------------------------------------------------------
                         INSTITUTIONAL MONEY MARKET FUNDS ANNUAL REPORT
 
                         FOR THE YEAR ENDED JUNE 30, 1996
 
                                                 TREASURY ONLY MONEY MARKET FUND
 
                                                 GOVERNMENT MONEY MARKET FUND
<PAGE>
 
<TABLE>
<S>        <C>        <C>
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
[NO FDIC]
               -      ARE SUBJECT TO INVESTMENT RISKS, INCLUDING POSSIBLE
                      LOSS OF THE PRINCIPAL AMOUNT INVESTED
</TABLE>
<PAGE>
- --------------------------------------------------------------------------------
Table of Contents
- -------------------------------------------------------------
 
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1996
 
<TABLE>
<S>                                                                                     <C>
Report From Your Investment Advisor...................................................          2
Portfolio Performance Review..........................................................          5
Schedules of Portfolio Investments....................................................          7
Statements of Assets and Liabilities..................................................          9
Statements of Operations..............................................................         10
Statements of Changes in Net Assets...................................................         11
Notes to Financial Statements.........................................................         12
Financial Highlights..................................................................         16
Report of Independent Accountants.....................................................         18
</TABLE>
 
                                                                            ----
                                                                               1
<PAGE>
- --------------------------------------------------------------------------------
Report From Your Investment Advisor
- -------------------------------------------------------------
 
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1996
 
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 JUNE 30, 1995, TO JUNE
30, 1996.
 
DEAR VALUED SHAREHOLDERS:
I would like to extend to you my personal thanks for investing in The One  Group
Family of Mutual Funds. The past year was one of exceptional growth and progress
at The One Group, thanks, in large part, to you--the shareholders.
 
By  continuing to show your  confidence, you helped The  One Group funds achieve
significant growth during  the past  12 months. Assets  under management  soared
from  $9.7 billion on June 30, 1995, to  $13.6 billion on June 30, 1996, placing
The One Group among the largest bank-advised mutual fund companies.
 
In addition, The One Group shareholder  base nearly tripled during this  period,
as  the number  of shareholder accounts  grew from  33,000 on June  30, 1995, to
95,000 on  June 30,  1996. Fourteen  thousand of  these new  accounts (and  $1.4
billion  in assets) resulted from The One Group merger with the Paragon Funds, a
family of mutual funds formerly advised by Premier Bank in Louisiana. I want  to
extend  a warm welcome  to the former Paragon  investors as well  as ALL the new
shareholders.
 
We believe that such strong growth is a reflection of The One Group's commitment
to meeting  your  investment needs  through  quality products,  good  investment
performance and top-notch service.
 
The  diversity within The One  Group mutual fund family  is designed to help you
meet all of  your portfolio needs.  It also  is a reflection  of our  investment
philosophy, which stresses:
 
- - ASSET  ALLOCATION.  When your assets are allocated to different security types
  and investment styles according to your goals, time frame and risk  tolerance,
  you have an effective, well-rounded portfolio.
 
- - DIVERSIFICATION.   By diversifying  your investments within  each asset class,
  you can help reduce the overall risk level in your portfolio.
 
- - MAINTAINING  A  LONG-TERM  PERSPECTIVE.    Short-term  market  volatility   is
  unavoidable but usually smooths out over the long term. It's time, not timing,
  that  allows investments  to realize their  full potential.  It's important to
  stay focused  on  your long-term  goals,  whether they  include  planning  for
  retirement, saving for college expenses or trying to reduce your tax burden.
 
These  are proven  investment strategies that  we encourage  all shareholders to
embrace--whether it's by  assembling a  portfolio of  assorted individual  funds
from The One Group or by investing in a new "fund of funds" alternative, The One
Group Investor Funds.
 
The  One Group Investor Funds*, which will  be introduced in early 1997, provide
you with a heightened level of diversification. The One Group Investor Funds are
mutual funds targeted  toward specific  investment objectives,  such as  growth,
income  or a combination of the two.  To achieve their objectives, The One Group
Investor Funds invest in various funds from The One Group family. The One  Group
Investor  Funds offer a  simple and convenient way  to enjoy diversification and
asset allocation from ONE investment.
 
Of course, we believe that there is  more to meeting your investment needs  than
providing  you with a broad selection of mutual funds. In order to make informed
investment decisions, you  need information  about your investments  as well  as
access  to your accounts. As such, The One Group introduced several new features
this year  that make  accessing your  fund and  account information  simple  and
convenient. Some of the highlights include:
 
- - THE  ONE GROUP WEB SITE.  From  The One Group home page (www.onegroup.com) you
  can  access  a   variety  of  fund-related   information,  including   prices,
  performance  updates,  fund manager  biographies  and assorted  literature. In
  addition, you will find an interactive asset allocation tool that can help you
  determine your investor  profile and  select an  appropriate model  portfolio.
  Future  plans  call  for  on-line  prospectuses,  annual  reports  and account
  transactions as well as an interactive retirement calculator.
 
- ----
  2
<PAGE>
- --------------------------------------------------------------------------------
Report From Your Investment Advisor, continued
- --------------------------------------------------------------------------------
 
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1996
 
- - THE ONE  GROUP  PHONE LINK.    The  new 24-hour  automated  telephone  service
  (1-800-480-4111)  lets  you  obtain  fund and  account  information  and place
  transactions when it is most convenient for you.
 
- - IN-HOUSE SHAREHOLDER SERVICING.  In order to provide the utmost in service, we
  have moved the shareholder services unit to an in-house facility. This affords
  us better insight and a heightened ability to respond to your needs.
 
You can be assured that the  commitment to high-quality service is ongoing.  The
One  Group will  continue to  look for ways  to improve  and enhance shareholder
services so that you always have the ability to access and obtain information in
a timely and accurate manner.
 
Again, thank you for placing your trust  with The One Group and for helping  The
One  Group achieve  stellar growth  over the past  year. All  of us  at Banc One
Investment Advisors and The One Group appreciate your support as we work  toward
our  most  important investment  objective--helping  you achieve  your financial
goals.
 
Sincerely,
                [SIG]
David J. Kundert
PRESIDENT & CEO,
BANC ONE INVESTMENT ADVISORS CORPORATION, INVESTMENT ADVISOR TO THE ONE GROUP
 
                            [DAVID J. KUNDERT PHOTO]
 
- ---------
 
* A REGISTRATION STATEMENT RELATING TO THESE SECURITIES HAS BEEN FILED WITH  THE
  SECURITIES  AND EXCHANGE  COMMISSION BUT HAS  NOT YET  BECOME EFFECTIVE. THESE
  SECURITIES MAY NOT BE SOLD NOR MAY OFFER TO BUY BE ACCEPTED PRIOR TO THE  TIME
  THE REGISTRATION STATEMENT BECOMES EFFECTIVE. THIS LETTER SHALL NOT CONSTITUTE
  AN  OFFER TO SELL  OR SOLICITATION OF AN  OFFER TO BUY NOR  SHALL THERE BE ANY
  SALE OF THESE  SECURITIES IN ANY  STATE IN WHICH  SUCH OFFER, SOLICITATION  OR
  SALE  WOULD  BE  UNLAWFUL PRIOR  TO  REGISTRATION OR  QUALIFICATION  UNDER THE
  SECURITIES LAW OF ANY SUCH STATE.
 
                                                                            ----
                                                                               3
<PAGE>
- --------------------------------------------------------------------------------
Report From Your Investment Advisor, continued
- --------------------------------------------------------------------------------
 
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1996
 
ECONOMIC REVIEW
The economy grew  at an  average rate  of 2.1% from  the third  quarter of  1995
through the first quarter of 1996. While the actual numbers weren't available at
the  time of  this writing, it  is expected  that the pace  of economic activity
gained additional  momentum  during the  second  quarter of  1996.  (Preliminary
readings  on  the actual  growth  pace of  economic  activity during  the second
quarter is not released until August.)
 
Given this fundamental  backdrop, short-term  interest rates  controlled by  the
Federal  Reserve (the federal  funds rate) declined from  5.6% during the second
quarter of 1995 to approximately 5.25% at the end of the second quarter of 1996.
On the inflation front,  the change in overall  prices remained quite stable  as
consumer prices rose by 3.0% (on a year-over-year basis) through the end of June
1995 compared to a similar figure of approximately 2.9% at the end of May 1996.
 
Over the last 12 months, financial market sentiment fluctuated from expecting an
immediate  recession at the beginning of 1996 to the belief that the economy was
caught in the midst of an overheated expansion requiring much higher  short-term
rates  in order to slow it down to non-inflationary growth levels. This swing in
market  sentiment  clearly  was  observed  in  the  bond  market  as  heightened
inflationary concerns caused the yield on the 30-year Treasury bond to rise from
a level of 5.95% at the beginning of the year to 6.87% on June 30, 1996. (In the
bond  market, as yields  increase, prices decline.)  In contrast, equity markets
performed quite favorably as measured by the Dow Jones Industrial Average, which
rose by 24.11% during the 12 months  ended June 1996, and the Standard &  Poor's
500 Index, which rose by 26.05%.
 
One  popular daily inflationary indicator  monitored closely by financial market
participants is the Commodity Research Bureau's (CRB) Future Price Index,  which
rose  from 244.25 at  the beginning of this  fiscal year to a  peak of 261.81 on
April 25, 1996. This was the highest  level recorded for the CRB since it  stood
at  263.26 on July 7, 1988. While  financial market participants tend to closely
monitor the daily fluctuations  in the CRB, our  own analysis suggests that  the
movements in the CRB are a poor leading indicator of actual inflationary trends.
Nonetheless,  in  light  of the  recent  declines  in this  overall  index, some
speculate that the  prospects for much  lower bond yields  could be  forthcoming
over the next 12 months.
 
However,  at the close of the second quarter of 1996, financial markets began to
expect that the U.S. central bank  would soon begin raising short-term rates  to
quell  the growing inflationary pressures that had begun to surface in the labor
market. Although the Fed kept  short-term rates steady, the growing  speculation
focused on when--rather than if--short-term rates would be increased. Given this
scenario,  investing  in  both  equity  and credit  markets  became  a  bit more
challenging as the prospects of higher  short-term rates cast a dark cloud  upon
the  financial markets.  In fact,  the robust pace  of growth  during the second
quarter of 1996, along with  the rising pace of labor  market costs, lead us  to
conclude  that short-term rates have no where else  to go but up during the next
six months.
 
Although we expect some investment challenges  to unfold over the next year,  we
believe  that pursuing  a long-term  investment approach  is likely  to continue
producing favorable results. As demonstrated by movements in both the stock  and
bond markets over the last several years, investing with only a short-term focus
has  not always been prudent. Therefore,  we encourage our investors to maintain
longer-term horizons. This type  of time frame  provides much better  insulation
against  the  short-term  fluctuations  that are  endemic  within  our financial
markets.
 
            [SIG]
Anthony Chan, Ph.D.
CHIEF ECONOMIST, BANC ONE INVESTMENT ADVISORS CORPORATION
 
- ----
  4
<PAGE>
- --------------------------------------------------------------------------------
                 The One Group Treasury Only Money Market Fund
Portfolio Performance Review
- -------------------------------------------------------------
 
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1996
 
                 THE ONE GROUP TREASURY ONLY MONEY MARKET FUND
 
In general, short-term interest rates declined over the one-year period, and the
Fund's  yield followed suit. The seven-day yield  on The One Group Treasury Only
Money Market Fund Fiduciary share  class was 5.00% on  June 30, 1996, down  from
5.61% on June 30, 1995.
 
We  invested  primarily in  Treasury bills  during  the year  due to  the narrow
spreads and  decreased  liquidity  of  investing in  Treasury  notes.  The  U.S.
Treasury  bill market primarily is driven by supply and demand, and our strategy
was to take  advantage of  Treasury bill  issues of  larger size,  such as  cash
management bills that offered better yields based on their increased supply.
 
With  the falling yields of the past 12 months, we maintained the Fund's average
weighted maturity  at the  long end  of the  45- to  55-day maturity  range.  We
accomplished  this  by employing  a barbell  strategy,  a common  technique that
involves  investing  in  both  long-   and  short-term  securities  instead   of
intermediate-term  securities. We purchased longer-term  U.S. Treasury notes and
bills along with shorter  cash management bills  that offered greater  liquidity
and higher yields.
 
Since  we focus  only on  high-quality securities, the  Fund earned  a rating of
AAA--the highest rating--by Standard & Poor's and Moody's Investors Service.  To
maintain  this rating, the  Fund's average weighted maturity  must not exceed 60
days.
Over the next year  we will try to  position the Fund to  take advantage of  the
changing  interest rate environment. This strategy  will be directly affected by
the short- and long-term economic outlooks  and how the market translates  these
outlooks into expectations for short-term interest rates.
 
                  [SIG]
Andrew T. Linton
FUND MANAGER
 
            [SIG]
Gary J. Madich, CFA
SENIOR MANAGING DIRECTOR OF FIXED-INCOME SECURITIES
 
<TABLE>
<CAPTION>
                                   Average Annual
                                    Total Return
   7 Day Yield         1 year       5 years      Since inception
<S>                 <C>           <C>           <C>
      5.00%            5.38%           NA             4.50%
</TABLE>
 
                                                                            ----
                                                                               5
<PAGE>
- --------------------------------------------------------------------------------
                   The One Group Government Money Market Fund
Portfolio Performance Review
- -------------------------------------------------------------
 
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1996
 
                   THE ONE GROUP GOVERNMENT MONEY MARKET FUND
 
In general, short-term interest rates declined over the one-year period, and the
Fund's  yield followed  suit. The  seven-day yield  on The  One Group Government
Money Market Fund Fiduciary share  class was 5.29% on  June 30, 1996, down  from
5.81% on June 30, 1995.
 
We  invested primarily in  Treasury bills, Treasury  notes and agency securities
during the year.  With a  flat yield curve,  spreads (or  differences in  yield)
between  Treasury and agency securities were very tight, which forced many money
market investors to extend their portfolios to capture extra yield.
 
Because of the falling  yield environment of the  past 12 months, we  maintained
the Fund's average weighted maturity in the 60- to 70-day range. We accomplished
this  by practicing a barbell maturity strategy,  whereby we focused on both the
short and long ends of the money market maturity spectrum. We invested in select
long-term (one-year) securities and  short, highly liquid repurchase  agreements
to  keep the Fund's  average maturity within  this range. On  June 30, 1996, the
Fund's average maturity was 71 days, equal to what it was on June 30, 1995.
 
Looking forward,  the aggressiveness  of  the Federal  Reserve  as well  as  the
performance  of the economy will be the  major factors contributing to the level
and shape  of the  yield  curve. We  believe that  the  Fund currently  is  well
positioned  to  take  advantage  of  opportunities  that  arise  as  changes  in
short-term yield occur.
 
                  [SIG]
Andrew T. Linton
FUND MANAGER
 
            [SIG]
Gary J. Madich, CFA
SENIOR MANAGING DIRECTOR OF FIXED-INCOME SECURITIES
 
<TABLE>
<CAPTION>
                                   Average Annual
                                    Total Return
   7 Day Yield         1 year       5 years      Since inception
<S>                 <C>           <C>           <C>
      5.29%            5.61%           NA             4.78%
</TABLE>
 
- ----
  6
<PAGE>
- --------------------------------------------------------------------------------
 
The One Group Family of Mutual Funds
 
TREASURY ONLY MONEY MARKET FUND
- --------------------------------------------------------------------------------
SCHEDULE OF PORTFOLIO INVESTMENTS                                  JUNE 30, 1996
(Amounts in Thousands)
<TABLE>
<CAPTION>
 PRINCIPAL                    SECURITY                    AMORTIZED
  AMOUNT                    DESCRIPTION                     COST
- -----------  ------------------------------------------  -----------
<C>          <S>                                         <C>
                          U.S. TREASURY BILLS (66.6%):
 $ 160,688   7/5/96(b).................................   $ 160,602
     5,000   8/22/96...................................       4,960
    17,005   9/12/96...................................      16,828
    85,844   9/19/96...................................      84,872
     3,150   9/26/96...................................       3,112
     1,883   2/6/97....................................       1,828
     5,000   4/3/97....................................       4,803
                                                         -----------
                             Total U.S. Treasury Bills      277,005
                                                         -----------
 
<CAPTION>
 PRINCIPAL                    SECURITY                    AMORTIZED
  AMOUNT                    DESCRIPTION                     COST
- -----------  ------------------------------------------  -----------
<C>          <S>                                         <C>
                          U.S. TREASURY NOTES (32.9%):
 $  26,430   7.88%, 7/15/96(b).........................   $  26,457
    25,000   7.88%, 7/31/96............................      25,056
    15,082   6.13%, 7/31/96............................      15,095
    25,000   6.25%, 8/31/96............................      25,030
     5,000   6.50%, 9/30/95............................       5,008
    10,000   7.25%, 11/30/96...........................      10,070
    20,000   8.00%, 1/15/97............................      20,262
    10,000   6.50%, 4/30/97............................      10,074
                                                         -----------
                             Total U.S. Treasury Notes      137,052
                                                         -----------
                 Total Investments (Cost--$414,057)(a)    $ 414,057
                                                         -----------
                                                         -----------
</TABLE>
 
- ------------
 
Percentages indicated are based on net assets of $415,961.
 
<TABLE>
<C>        <S>
      (a)  Cost for federal income tax and financial reporting purposes is the same.
</TABLE>
 
<TABLE>
<C>        <S>
      (b)  A portion of this security was loaned as of June 30, 1996.
</TABLE>
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
                                                                            ----
                                                                               7
<PAGE>
- --------------------------------------------------------------------------------
 
The One Group Family of Mutual Funds
 
GOVERNMENT MONEY MARKET FUND
- --------------------------------------------------------------------------------
SCHEDULE OF PORTFOLIO INVESTMENTS                                  JUNE 30, 1996
(Amounts in Thousands)
<TABLE>
<CAPTION>
 PRINCIPAL                                               AMORTIZED
  AMOUNT               SECURITY DESCRIPTION                COST
- -----------  -----------------------------------------  -----------
<C>          <S>                                        <C>
                    U.S. GOVERNMENT AGENCIES (67.0%):
                            Federal Farm Credit Bank:
 $  10,000   5.53%, 10/1/96...........................   $   9,993
    10,000   5.40%, 4/1/97............................       9,987
    25,000   5.84%, 6/18/97...........................      24,961
                              Federal Home Loan Bank:
    20,000   5.18%, 8/14/96...........................      19,873
    10,000   5.10%, 9/6/96............................       9,905
    16,550   4.94%, 3/4/97............................      16,529
    18,500   5.04%, 3/6/97............................      18,475
    20,000   5.33%, 3/18/97...........................      19,972
                    Federal Home Loan Mortgage Corp.:
    25,000   5.21%, 7/30/96...........................      24,895
    10,000   5.26%, 9/3/96............................       9,907
    10,000   5.30%, 11/27/96..........................       9,781
    25,000   5.73%, 6/6/97............................      24,957
                    Federal National Mortgage Assoc.:
    20,000   5.29%, 7/8/96............................      19,980
     7,230   8.00%, 7/10/96(b)........................       7,234
    10,000   5.23%, 8/6/96............................       9,948
    25,000   5.23%, 8/8/96............................      24,861
    20,000   5.58%, 8/9/96............................      19,879
    25,000   5.25%, 9/12/96...........................      24,734
    20,000   5.64%, 10/2/96...........................      19,992
    20,000   5.60%, 11/1/96...........................      19,990
    10,055   5.02%, 11/20/96..........................       9,856
     8,320   7.70%, 12/10/96..........................       8,397
     4,000   5.45%, 6/2/99*...........................       4,000
    20,000   5.45%, 7/26/99*..........................      20,000
    10,000   5.45%, 9/22/99*..........................      10,000
 
<CAPTION>
 PRINCIPAL                                               AMORTIZED
  AMOUNT               SECURITY DESCRIPTION                COST
- -----------  -----------------------------------------  -----------
</TABLE>
 
U.S. GOVERNMENT AGENCIES, CONTINUED:
<TABLE>
<C>          <S>                                        <C>
                       Student Loan Marketing Assoc.:
 $  30,000   5.41%, 10/14/97*.........................   $  29,987
    40,000   5.41%, 11/24/97*.........................      40,000
    25,000   5.44%, 9/28/98*..........................      25,000
    25,000   5.43%, 11/10/98*.........................      25,000
    10,000   5.45%, 1/13/99*..........................       9,999
    10,000   5.45%, 2/8/99*...........................      10,000
    25,000   5.44%, 2/22/99*..........................      25,000
    10,000   5.46%, 8/2/99*...........................       9,995
                                                        -----------
                       Total U.S. Government Agencies      573,087
                                                        -----------
                          U.S. TREASURY BILLS (4.0%):
    25,000   2/6/97(b)................................      24,260
    10,000   3/6/97...................................       9,657
                                                        -----------
                            Total U.S. Treasury Bills       33,917
                                                        -----------
                       Investments, at amortized cost      607,004
                                                        -----------
                       REPURCHASE AGREEMENTS (29.0%):
    75,000   Hong Kong Shanghai Banc Corp., 5.50%,
               dated 6/28/96, due 7/1/96
               (collateralized by $77,370 various U.S.
               Government Securities, 0.00% - 8.45%,
               8/1/96 - 2/14/06, Market Value
               $76,501)...............................      75,000
   173,417   Prudential Securities, 5.53%, dated
               6/28/96, due 7/1/96, (collateralized by
               $225,311 various U.S. Government
               Securities, 0.00% - 9.50%, 7/1/96 -
               8/15/22, market value $175,345)........     173,417
                                                        -----------
                          Total Repurchase Agreements      248,417
                                                        -----------
                            Total (Cost--$855,421)(a)    $ 855,421
                                                        -----------
                                                        -----------
</TABLE>
 
- ------------
 
Percentages indicated are based on net assets of $855,613.
 
<TABLE>
<C>        <S>
      (a)  Cost for federal income tax and financial reporting purposes is the same.
</TABLE>
 
<TABLE>
<C>        <S>
      (b)  A portion of this security was loaned as of June 30, 1996.
</TABLE>
 
<TABLE>
<C>        <S>
        *  Variable rate securities that have interest rates that change weekly based on the three month treasury bill bond
           equivalent yield. The final maturity date for valuation purposes is the next reset date. The rate shown on the Schedule
           of Portfolio Investments is the reset rate in effect on June 30, 1996.
</TABLE>
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
- ----
 8
<PAGE>
- --------------------------------------------------------------------------------
 
The One Group Family of Mutual Funds
- -------------------------------------------------------------
 
STATEMENTS OF ASSETS AND LIABILITIES                               JUNE 30, 1996
 
<TABLE>
<CAPTION>
                                                                           (Amounts in Thousands
                                                                         except per share amounts)
 
                                                                        TREASURY ONLY   GOVERNMENT
                                                                        MONEY MARKET   MONEY MARKET
                                                                            FUND           FUND
                                                                        -------------  -------------
<S>                                                                     <C>            <C>
ASSETS:
Investments, at amortized cost........................................    $ 414,057      $ 607,004
Repurchase agreements, at cost........................................           --        248,417
                                                                        -------------  -------------
Total.................................................................      414,057        855,421
Cash..................................................................            1              1
Interest receivable...................................................        3,688          4,330
Deferred organization costs...........................................            7             42
                                                                        -------------  -------------
TOTAL ASSETS..........................................................      417,753        859,794
                                                                        -------------  -------------
LIABILITIES:
Dividends payable.....................................................        1,652          3,698
Accrued expenses and other payables:
    Investment advisory fees..........................................           26             56
    Administration fees...............................................           16             35
    Other.............................................................           98            392
                                                                        -------------  -------------
TOTAL LIABILITIES.....................................................        1,792          4,181
                                                                        -------------  -------------
NET ASSETS:
Capital...............................................................      416,037        855,679
Accumulated undistributed net realized losses from investment
 transactions.........................................................          (76)           (66)
                                                                        -------------  -------------
NET ASSETS............................................................    $ 415,961      $ 855,613
                                                                        -------------  -------------
                                                                        -------------  -------------
Outstanding shares of beneficial interest.............................      416,037        855,679
                                                                        -------------  -------------
                                                                        -------------  -------------
Net asset value--offering and redemption price per share..............    $    1.00      $    1.00
                                                                              -----          -----
                                                                              -----          -----
</TABLE>
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
                                                                            ----
                                                                               9
<PAGE>
- --------------------------------------------------------------------------------
 
The One Group Family of Mutual Funds
- -------------------------------------------------------------
 
STATEMENTS OF OPERATIONS                        FOR THE YEAR ENDED JUNE 30, 1996
 
<TABLE>
<CAPTION>
                                                                     (Amounts in Thousands)
 
                                                                  TREASURY ONLY   GOVERNMENT
                                                                  MONEY MARKET   MONEY MARKET
                                                                      FUND           FUND
                                                                  -------------  -------------
<S>                                                               <C>            <C>
INVESTMENT INCOME:
Interest income.................................................    $  19,404      $  43,537
                                                                  -------------  -------------
Total Income....................................................       19,404         43,537
                                                                  -------------  -------------
EXPENSES:
Investment advisory fees........................................          288            618
Administration fees.............................................          180            386
Custodian and accounting fees...................................           18             68
Legal and audit fees............................................           41            157
Organization costs..............................................            4             21
Trustees' fees and expenses.....................................            5             20
Transfer agent fees.............................................           14             22
Registration and filing fees....................................           32             39
Printing costs..................................................           18             65
Other...........................................................            7             11
                                                                  -------------  -------------
Total expenses before waivers/reimbursements....................          607          1,407
Less waivers/reimbursements.....................................           --             (5)
                                                                  -------------  -------------
NET EXPENSES....................................................          607          1,402
                                                                  -------------  -------------
Net Investment Income...........................................       18,797         42,135
                                                                  -------------  -------------
REALIZED GAINS (LOSSES) FROM INVESTMENT TRANSACTIONS:
Net realized gains (losses) from investment transactions........          (76)             8
                                                                  -------------  -------------
Net increase in net assets resulting from operations............    $  18,721      $  42,143
                                                                  -------------  -------------
                                                                  -------------  -------------
</TABLE>
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
- ----
 10
<PAGE>
- --------------------------------------------------------------------------------
 
The One Group Family of Mutual Funds
- -------------------------------------------------------------
 
STATEMENTS OF CHANGES IN NET ASSETS
 
<TABLE>
<CAPTION>
                                                                         (Amounts in Thousands)
 
                                                             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,
                                                              1996         1995         1996         1995
                                                           -----------  -----------  -----------  -----------
<S>                                                        <C>          <C>          <C>          <C>
FROM INVESTMENT ACTIVITIES:
OPERATIONS:
    Net investment income................................  $    18,797   $  12,746   $    42,135  $    38,264
    Net realized gains (losses) from investment
      transactions.......................................          (76)         29             8          (66)
                                                           -----------  -----------  -----------  -----------
Change in net assets resulting from operations...........       18,721      12,775        42,143       38,198
                                                           -----------  -----------  -----------  -----------
DISTRIBUTIONS TO SHAREHOLDERS:
    From net investment income...........................      (18,797)    (12,746)      (42,135)     (38,264)
    In excess of net realized gains from investment
      transactions.......................................          (21)         --            --           --
                                                           -----------  -----------  -----------  -----------
Change in net assets from shareholder distributions......      (18,818)    (12,746)      (42,135)     (38,264)
                                                           -----------  -----------  -----------  -----------
CAPITAL TRANSACTIONS:
    Proceeds from shares issued..........................    1,135,597     894,833     2,638,822    2,818,461
    Dividends reinvested.................................        2,487       1,574        10,663       12,982
    Cost of shares redeemed..............................   (1,010,723)   (825,464)   (2,514,579)  (2,802,931)
                                                           -----------  -----------  -----------  -----------
Change in net assets from share transactions.............      127,361      70,943       134,906       28,512
                                                           -----------  -----------  -----------  -----------
Change in Net Assets.....................................      127,264      70,972       134,914       28,446
NET ASSETS:
    Beginning of period..................................      288,697     217,725       720,699      692,253
                                                           -----------  -----------  -----------  -----------
    End of period........................................  $   415,961   $ 288,697   $   855,613  $   720,699
                                                           -----------  -----------  -----------  -----------
                                                           -----------  -----------  -----------  -----------
SHARE TRANSACTIONS:
    Issued...............................................    1,135,597     894,833     2,638,822    2,818,461
    Reinvested...........................................        2,487       1,574        10,663       12,982
    Redeemed.............................................   (1,010,723)   (825,464)   (2,514,579)  (2,802,931)
                                                           -----------  -----------  -----------  -----------
Change in shares.........................................      127,361      70,943       134,906       28,512
                                                           -----------  -----------  -----------  -----------
                                                           -----------  -----------  -----------  -----------
</TABLE>
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
                                                                            ----
                                                                              11
<PAGE>
- --------------------------------------------------------------------------------
 
The One Group Family of Mutual Funds
- -------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS                                      JUNE 30, 1996
 
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  Trust is registered to
    offer four classes of shares: Fiduciary, Class A, Class B, and Service.  The
    Trust  currently  consists  of  twenty-six  active  funds.  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  Funds may invest  in repurchase agreements  with institutions that the
     Fund's investment adviser has determined are creditworthy. Each  repurchase
     agreement  is  recorded  at cost.  The  Fund requires  that  the securities
     purchased in a repurchase 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.
 
     SECURITY TRANSACTIONS AND RELATED INCOME:
 
     Security transactions are accounted for on a trade date basis. Net realized
     gains or  losses on  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.
 
CONTINUED
 
- ----
 12
<PAGE>
- --------------------------------------------------------------------------------
 
The One Group Family of Mutual Funds
- -------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS, CONTINUED                           JUNE 30, 1996
 
     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. 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  Adviser to be of good
     standing and  creditworthy under  guidelines established  by the  Board  of
     Trustees  and when, in the judgment of the Adviser, 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,  1996,  the following  Funds  had securities  with  the following
     amortized cost on loan (amounts in thousands):
 
<TABLE>
<CAPTION>
                                                                      MARKET VALUE
                                                                        OF LOANED
                                                                       SECURITIES
                                                                      -------------
<S>                                                                   <C>
Treasury Only Money Market Fund.....................................    $  90,881
Government Money Market Fund........................................       31,663
</TABLE>
 
     The loaned securities were fully collateralized by cash and U.S. Government
     securities as of June 30, 1996.
 
          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 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,   which   affect   shareholder
          distributions, have been reclassified to additional paid-in capital.
 
          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, have been allocated among  the
          Funds  of the Trust 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.
 
CONTINUED
 
                                                                            ----
                                                                              13
<PAGE>
- --------------------------------------------------------------------------------
 
The One Group Family of Mutual Funds
- -------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS, CONTINUED                           JUNE 30, 1996
 
          FEDERAL INCOME TAXES:
 
          Each Fund intends  to continue  to qualify as  a regulated  investment
          company   by  complying  with  the  provisions  available  to  certain
          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. Currently,  shares
         of the Trust are registered to be offered through thirty-two series and
         four  classes: Fiduciary, Class  A, Class B,  and Service. 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 Banc One Investment Advisors Corporation (the  "Adviser")
         are parties to an investment advisory agreement under which the Adviser
         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  payable monthly at  an
         annual  rate  of 0.05%  of each  Fund's average  daily net  assets. The
         Adviser also serves  as Sub-Administrator  to each fund  of the  Trust,
         pursuant  to an  agreement between  the Administrator  and the Adviser.
         Pursuant  to  this  agreement,  the   Adviser  performs  many  of   the
         Administrator's  duties, for which  the Adviser receives  a fee paid by
         the Administrator. Prior to November 30, 1995, The Shareholder Services
         Group d/b/a 440 Financial  served as administrator  of each Fund  under
         essentially the same terms as the current administrative agreement.
 
         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.
 
         The  Adviser  and  Administrator  have voluntarily  agreed  to  waive a
         portion of their fees and to reimburse the Funds for certain  expenses.
         For  the year ended June  30, 1996, fees in  the following amounts were
         waived or reimbursed to the Funds (amounts in thousands):
 
<TABLE>
<CAPTION>
                                                                     INVESTMENT ADVISORY
                                                                        FEES WAIVED/
                                                                         REIMBURSED
                                                                     -------------------
<S>                                                                  <C>
Government Money Market Fund.......................................       $       5
</TABLE>
 
CONTINUED
 
- ----
 14
<PAGE>
- --------------------------------------------------------------------------------
 
The One Group Family of Mutual Funds
- -------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS, CONTINUED                           JUNE 30, 1996
 
5.  FEDERAL TAX INFORMATION (UNAUDITED):
 
    At June 30, 1996 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 Fund................................   $      18         2004
Government Money Market Fund...................................           8         2002
Government Money Market Fund...................................          26         2003
Government Money Market Fund...................................          32         2004
</TABLE>
 
   Under  current  tax law,  capital  losses realized  after  October 31  may be
   deferred and treated as  occurring on the first  day of the following  fiscal
   year.  The Treasury Only  Money Market Fund  will treat approximately $58,000
   deferred losses as arising on the first day of the year ended June 30, 1997.
 
                                                                            ----
                                                                              15
<PAGE>
- --------------------------------------------------------------------------------
 
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,
                                                                                  1996       1995       1994      1993 (A)
                                                                                ---------  ---------  ---------  -----------
<S>                                                                             <C>        <C>        <C>        <C>
NET ASSET VALUE,
  BEGINNING OF PERIOD.........................................................  $   1.000  $   1.000  $   1.000   $   1.000
                                                                                ---------  ---------  ---------  -----------
Investment Activities
  Net investment income.......................................................      0.052      0.051      0.032       0.006
                                                                                ---------  ---------  ---------  -----------
Distributions
  Net investment income.......................................................     (0.052)    (0.051)    (0.032)     (0.006)
                                                                                ---------  ---------  ---------  -----------
NET ASSET VALUE,
  END OF PERIOD...............................................................  $   1.000  $   1.000  $   1.000   $   1.000
                                                                                ---------  ---------  ---------  -----------
                                                                                ---------  ---------  ---------  -----------
Total Return..................................................................       5.38%      5.22%      3.23%       2.96%(b)
RATIOS/SUPPLEMENTARY DATA:
  Net Assets at end of period (000)...........................................  $ 415,961  $ 288,697  $ 217,725   $  60,330
  Ratio of expenses to average net assets.....................................       0.17%      0.20%      0.15%       0.07%(b)
  Ratio of net investment income to average net assets........................       5.23%      5.14%      3.23%       2.95%(b)
  Ratio of expenses to average net assets*....................................       0.17%      0.21%      0.22%       0.33%(b)
  Ratio of net investment income to average net assets*.......................       5.23%      5.13%      3.16%       2.69%(b)
</TABLE>
 
- ----------
 
<TABLE>
<C>        <S>
        *  During the period, certain fees were voluntarily reduced. If such voluntary fee reductions had not
           occurred, the ratios would have been as indicated.
</TABLE>
 
<TABLE>
<C>        <S>
      (a)  Period from commencement of operations.
</TABLE>
 
<TABLE>
<C>        <S>
      (b)  Annualized.
</TABLE>
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
- ----
 16
<PAGE>
- --------------------------------------------------------------------------------
 
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,
                                                                                  1996       1995       1994     1993 (A)
                                                                                ---------  ---------  ---------  ---------
<S>                                                                             <C>        <C>        <C>        <C>
NET ASSET VALUE,
  BEGINNING OF PERIOD.........................................................  $   1.000  $   1.000  $   1.000  $   1.000
                                                                                ---------  ---------  ---------  ---------
Investment Activities
  Net investment income.......................................................      0.055      0.053      0.033      0.001
                                                                                ---------  ---------  ---------  ---------
Distributions
  Net investment income.......................................................     (0.055)    (0.053)    (0.033)    (0.001)
                                                                                ---------  ---------  ---------  ---------
NET ASSET VALUE,
  END OF PERIOD...............................................................  $   1.000  $   1.000  $   1.000  $   1.000
                                                                                ---------  ---------  ---------  ---------
                                                                                ---------  ---------  ---------  ---------
Total Return..................................................................       5.61%      5.41%      3.40%      3.28%(b)
RATIOS/SUPPLEMENTARY DATA:
  Net Assets at end of period (000)...........................................  $ 855,613  $ 720,699  $ 692,253  $ 244,991
  Ratio of expenses to average net assets.....................................       0.18%      0.21%      0.11%      0.07%(b)
  Ratio of net investment income to average net assets........................       5.46%      5.28%      3.41%      3.13%(b)
  Ratio of expenses to average net assets*....................................       0.18%      0.22%      0.20%      0.33%(b)
  Ratio of net investment income to average net assets*.......................       5.46%      5.27%      3.32%      2.87%(b)
</TABLE>
 
- ----------
 
<TABLE>
<C>        <S>
        *  During the period, certain fees were voluntarily reduced. If such voluntary fee reductions had not
           occurred, the ratios would have been as indicated.
</TABLE>
 
<TABLE>
<C>        <S>
      (a)  Period from commencement of operations.
</TABLE>
 
<TABLE>
<C>        <S>
      (b)  Annualized.
</TABLE>
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
                                                                            ----
                                                                              17
<PAGE>
- --------------------------------------------------------------------------------
Report of Independent Accountants
- -------------------------------------------------------------
 
THE ONE GROUP FAMILY OF MUTUAL FUNDS                               JUNE 30, 1996
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,  1996, and  the related  statements of operations,
statements of changes in net assets and the financial highlights for each period
presented.  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  and financial
highlights are free of material misstatement. An audit includes examining, on  a
test  basis, evidence  supporting the amounts  and disclosures  in the financial
statements. Our procedures included confirmation of securities owned as of  June
30,  1996  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 Money Market Fund as of  June
30,  1996, the results of their operations,  the changes in their net assets and
the financial highlights for each period presented, in conformity with generally
accepted accounting principles.
 
Columbus, Ohio                                          Coopers & Lybrand L.L.P.
August 19, 1996
 
- ----
 18
<PAGE>
                 (This page has been left blank intentionally)
<PAGE>
                 (This page has been left blank intentionally)
<PAGE>
IMPORTANT CUSTOMER INFORMATION. PLEASE READ:
 
SHARES OF THE ONE GROUP:
 
- -  ARE  NOT DEPOSITS OR OBLIGATIONS OF, OR GUARANTEED BY BANC ONE CORPORATION OR
   ANY OF 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.
 
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 BY CALLING 1-800-480-4111. READ THE PROSPECTUS CAREFULLY BEFORE
INVESTING.
 
THE COMPOSITION OF EACH FUND'S HOLDINGS IS SUBJECT TO CHANGE.
 
THIS MATERIAL MUST BE ACCOMPANIED OR PRECEDED BY A PROSPECTUS.
 
THE PERFORMANCE DATA QUOTED REPRESENTS PAST PERFORMANCE AND IS NOT AN INDICATION
OF  FUTURE RESULTS. AN INVESTMENT  IN THE MONEY MARKET  FUNDS IS NEITHER INSURED
NOR GUARANTEED BY THE U.S. GOVERNMENT. YIELDS WILL FLUCTUATE AND THERE CAN BE NO
ASSURANCE THAT THE  FUNDS WILL BE  ABLE TO MAINTAIN  A STABLE NAV  OF $1.00  PER
SHARE.
 
FOR MORE DETAIL ON THE ONE GROUP, VISIT OUR WEB SITE AT HTTP://WWW.ONEGROUP.COM.
 
TOG-F-033-AN (8-96)                 [LOGO]

<TABLE> <S> <C>

<PAGE>
<ARTICLE> 6
<CIK> 0000763852
<NAME> THE ONE GROUP FAMILY OF MUTUAL FUNDS
<SERIES>
   <NUMBER> 150
   <NAME> THE ONE GROUP TREASURY ONLY MONEY MARKET FUND
<MULTIPLIER> 1,000
       
<S>                             <C>
<PERIOD-TYPE>                   YEAR
<FISCAL-YEAR-END>                          JUN-30-1996
<PERIOD-START>                             JUL-01-1995
<PERIOD-END>                               JUN-30-1996
<INVESTMENTS-AT-COST>                           414057
<INVESTMENTS-AT-VALUE>                          414057
<RECEIVABLES>                                     3688
<ASSETS-OTHER>                                       8
<OTHER-ITEMS-ASSETS>                                 0
<TOTAL-ASSETS>                                  417753
<PAYABLE-FOR-SECURITIES>                             0
<SENIOR-LONG-TERM-DEBT>                              0
<OTHER-ITEMS-LIABILITIES>                         1792
<TOTAL-LIABILITIES>                               1792
<SENIOR-EQUITY>                                      0
<PAID-IN-CAPITAL-COMMON>                        416037
<SHARES-COMMON-STOCK>                           416037
<SHARES-COMMON-PRIOR>                           288676
<ACCUMULATED-NII-CURRENT>                            0
<OVERDISTRIBUTION-NII>                               0
<ACCUMULATED-NET-GAINS>                              0
<OVERDISTRIBUTION-GAINS>                            76
<ACCUM-APPREC-OR-DEPREC>                             0
<NET-ASSETS>                                    415961
<DIVIDEND-INCOME>                                    0
<INTEREST-INCOME>                                19404
<OTHER-INCOME>                                       0
<EXPENSES-NET>                                     607
<NET-INVESTMENT-INCOME>                          18797
<REALIZED-GAINS-CURRENT>                          (76)
<APPREC-INCREASE-CURRENT>                            0
<NET-CHANGE-FROM-OPS>                            18721
<EQUALIZATION>                                       0
<DISTRIBUTIONS-OF-INCOME>                        18797
<DISTRIBUTIONS-OF-GAINS>                             0
<DISTRIBUTIONS-OTHER>                               21
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<TABLE> <S> <C>

<PAGE>
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<NAME> THE ONE GROUP FAMILY OF MUTUAL FUNDS
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   <NAME> THE ONE GROUP GOVERNMENT MONEY MARKET FUND
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