<PAGE>   1
 
                             THE ARCH FUND(R), INC.
 
                        THE ARCH EQUITY INCOME PORTFOLIO
                   THE ARCH NATIONAL MUNICIPAL BOND PORTFOLIO
              THE ARCH SHORT-INTERMEDIATE CORPORATE BOND PORTFOLIO
 
                      SUPPLEMENT DATED JANUARY 21, 1997 TO
                         PROSPECTUS DATED MAY 13, 1996
                         (AS REVISED OCTOBER 25, 1996)
 
     Effective January 21, 1997, the name of the Short-Intermediate Corporate
Bond Portfolio (the "Portfolio") is changed to the Intermediate Corporate Bond
Portfolio. The Portfolio's average weighted maturity will be between three and
ten years and will vary in light of current market and economic conditions, the
comparative yields on instruments with different maturities, and other factors.



© 2022 IncJournal is not affiliated with or endorsed by the U.S. Securities and Exchange Commission