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                                                                  EXHIBIT (a)(4)
                               [ALEX. BROWN LOGO]
 
                                                                    MAY 30, 1997
 
Special Committee of the Board
 of Directors of Acordia, Inc.
120 Monument Circle
Indianapolis, IN 46204
 
Dear Members of the Special Committee:
 
     We understand that Acordia, Inc. ("Acordia"), Anthem Inc. ("Anthem") and
AIC Acquisition Corp. ("Purchaser"), a Delaware corporation and wholly-owned
subsidiary of Anthem, intend to enter into an Agreement and Plan of Merger
("Agreement"). Pursuant to the Agreement, Purchaser will commence a tender offer
for all outstanding shares of common stock of Acordia, par value $1.00 per share
(the "Common Stock"), other than shares of Common Stock owned by Anthem, at a
price of $40.00 per share net to the selling stockholders in cash (the "Tender
Offer"). Anthem currently owns approximately 66.8% of the outstanding shares of
Common Stock. Following the consummation of the Tender Offer, Purchaser will be
merged into Acordia (the "Merger") and in the Merger each outstanding share of
Common Stock (other than shares held in treasury or shares owned by Anthem, its
affiliates or stockholders who have perfected dissenters' rights) will be
converted into the right to receive $40.00 in cash. You have requested our
opinion as to whether the consideration to be received in the Tender Offer and
the Merger by Acordia stockholders other than Anthem is fair, from a financial
point of view, to such stockholders.
 
     Alex. Brown & Sons Incorporated ("Alex. Brown"), as a customary part of its
investment banking business, is engaged in the valuation of businesses and their
securities in connection with mergers and acquisitions, negotiated
underwritings, private placements and valuations for estate, corporate and other
purposes. We have acted as financial advisor to the Special Committee of the
Board of Directors of Acordia in connection with the transaction described above
and will receive a fee for our services, a substantial portion of which is
payable upon delivery of the opinion. We have in the past acted as a co-manager
on a public offering of securities for Acordia. Alex. Brown regularly publishes
research reports regarding the insurance and insurance brokerage industries and
the businesses and securities of Acordia and other publicly traded companies in
the insurance and insurance brokerage industries. In the ordinary course of
business, Alex. Brown may actively trade the securities of Acordia for our own
account and the account of our customers and, accordingly, may at any time hold
a long or short position in such securities. We have also in the past acted as
financial advisor to Anthem in connection with certain other transactions.
 
     In connection with this opinion, we have reviewed certain publicly
available financial information and other information concerning Acordia and
Anthem and certain internal analyses and other information with respect to the
business, operations and prospects of Acordia and Anthem furnished to us by
Acordia and Anthem. We have also held discussions with the members of the senior
managements of Acordia and Anthem regarding the businesses and prospects of
their respective companies and the joint prospects of a combined company. In
addition, we have (i) reviewed the reported prices and trading activity for the
common stock of Acordia, (ii) compared certain financial and stock market
information for Acordia with similar information for certain companies whose
securities are publicly traded, (iii) reviewed the financial terms of certain
recent business combinations which we deemed relevant in whole or in part, (iv)
held discussions with Anthem, Anthem's financial advisor and the management of
Acordia regarding the sale process for Acordia's unaffiliated, independent
insurance brokerage operations, (v) reviewed the terms of the May 29, 1997 draft
of the Agreement and certain related documents, and (vi) performed such other
studies and analyses and considered such other factors as we deemed appropriate
for the purpose of rendering our opinion.
 
     We have not independently verified the information described above and for
purposes of this opinion have assumed the accuracy, completeness and fairness
thereof. With respect to the information relating to the prospects of Acordia
and Anthem, we have assumed that such information provided to us was reasonably
prepared on bases reflecting the best currently available judgments and
estimates of the managements of Acordia and Anthem, respectively, as to the
likely future financial performances of their respective companies
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                               [ALEX. BROWN LOGO]
 
Special Committee of the Board
 of Directors of Acordia, Inc.
May 30, 1997
Page 2
 
and of the combined entity. In addition, we did not conduct physical inspections
of the properties and facilities of Acordia and Anthem, and we did not make or
obtain, or assume any responsibility for making or obtaining an independent
evaluation or appraisal of the assets or liabilities of Acordia or Anthem, nor
have we been furnished with any such evaluations or appraisals. Our opinion is
based on market, economic and other conditions as they exist and can be
evaluated as of the date of this letter.
 
     In arriving at our opinion, we were not authorized to solicit, and did not
solicit, interest from any party with respect to the acquisition of Acordia or
any of its assets.
 
     Our advisory services were rendered to, and the opinion expressed herein
was prepared for the use of, the Special Committee of the Board of Directors of
Acordia and may not be used for any other purpose or reproduced, disseminated,
quoted or referred to at any time, in any manner for any purpose, without the
written consent of Alex. Brown.
 
     Based upon and subject to the foregoing, it is our opinion that, as of the
date of this letter, the consideration to be received in the Tender Offer and
Merger by Acordia stockholders other than Anthem is fair, from a financial point
of view, to such stockholders.
 
                                          Very truly yours,
 
                                          ALEX. BROWN & SONS INCORPORATED
 
                                          By: /s/ Peter F. de Vos
 
                                            ------------------------------------
                                            Peter F. de Vos
                                            Managing Director