THE SWISS HELVETIA FUND, INC.

1270 AVENUE OF THE AMERICAS, SUITE 400

NEW YORK, NEW YORK 10020

1-888-SWISS-00 (1-888-794-7700)

Offer to Purchase Up to 4,579,480 Shares of Common Stock

At a Cash Purchase Price of 95% of Net Asset Value Per Share

THE OFFER, PRORATION PERIOD AND WITHDRAWAL RIGHTS WILL EXPIRE AT

5:00 P.M., NEW YORK CITY TIME, ON FEBRUARY 11, 2014,

UNLESS THE FUND EXTENDS THE OFFER.

January 13, 2014

To Our Clients:

Enclosed for your consideration are the offer to purchase, dated January 13, 2014, and the related letter of transmittal (which together, as they may be amended and supplemented from time to time, constitute the “Offer”), in connection with the offer by The Swiss Helvetia Fund, Inc., a non-diversified, closed-end management investment company incorporated under the laws of the state of Delaware (the “Fund”), to purchase for cash up to 4,579,480 (approximately 15%) of its issued and outstanding shares of common stock, $0.001 par value per share, at a price per share equal to 95% of its net asset value (“NAV”) per share determined as of the close of the regular trading session of the New York Stock Exchange, the principal market on which the shares are traded, on the business day immediately following the day the offer expires (the “Pricing Date,” and such price, expressed as a percentage of NAV per share, the “Purchase Price”), net to you in cash, less applicable withholding taxes and without interest, upon the terms and subject to the conditions of the Offer.

All shares validly tendered before the Expiration Date (as specified in Section 1 of the offer to purchase) and not properly withdrawn will be purchased by the Fund at the Purchase Price, net to the seller in cash, without interest, upon the terms and subject to the conditions of the Offer, including the proration provisions thereof. All shares that the Fund does not accept for purchase because of proration will be returned at the Fund’s expense to the stockholders that tendered such shares promptly after the Expiration Date.

We are the owner of record of shares held for your account. As such, we are the only ones who can tender your shares, and then only pursuant to your instructions. We are sending you the letter of transmittal for your information only. You cannot use the letter of transmittal to tender shares we hold for your account. The letter of transmittal must be completed and executed by us, according to your instructions.

Please instruct us as to whether you wish us to tender, on the terms and subject to the conditions of the Offer, any or all of the shares we hold for your account, by completing and signing the Instruction Form enclosed herein.

Please note carefully the following:

1. You should consult with your broker and/or tax advisor as to whether (and if so, in what manner) you should designate the priority in which you want your tendered shares to be purchased in the event of proration.

2. The Offer is not conditioned upon any minimum number of shares being tendered. The Offer is, however, subject to other conditions set forth in Section 6 of the offer to purchase, which you should read carefully.

3. The Offer, the proration period and the withdrawal rights will expire at 5:00 p.m., New York City time, on February 11, 2014, unless the Fund extends the Offer.

4. The Offer is for up to 4,579,480 shares, constituting approximately 15% of the Fund’s issued and outstanding shares of common stock as of January 10, 2014.

5. No fees or commissions will be payable to the Fund in connection with the Offer. However, brokers and other nominees who tender their shares of common stock pursuant to your instructions may charge you a fee for doing so. Any stock transfer taxes applicable to the sale of shares of common stock to the Fund pursuant to the Offer will be paid by the Fund except as otherwise provided in the offer to purchase.

6. The Board of Directors of the Fund (the “Board”) has approved the Offer. However, none of the Fund, its Board, its investment adviser or AST Fund Solutions, LLC, the information agent for the Offer (the “Information Agent”), makes any recommendation to any stockholder as to whether to tender or refrain from tendering any shares. Stockholders should carefully evaluate all information in the Offer, should consult their own investment and tax advisors, and should make their own decisions about whether to tender shares, and, if so, how many shares to tender. The Fund has been advised that none of its directors or executive officers intends to tender any shares in the Offer.

The current NAV per share of the Fund will be calculated daily and may be obtained by calling the Information Agent at (866) 207-3649 (toll-free) between the hours of 9:00 a.m. and 5:00 p.m. New York City time, Monday through Friday (except holidays).

If you wish to have us tender any or all of your shares, please instruct us to that effect by completing, executing and returning to us the enclosed Instruction Form. If you authorize us to tender your shares, we will tender all of the shares that we hold beneficially for your account unless you specify otherwise on the enclosed Instruction Form.

Please forward your completed Instruction Form to us in a timely manner to give us ample time to permit us to submit the tender on your behalf before the Expiration Date of the Offer. The Offer, proration period and withdrawal rights will expire at 5:00 p.m., New York City time, on February 11, 2014, unless the Fund extends the Offer.

As described in the offer to purchase, if more than 4,579,480 shares, or such greater number of shares as the Fund may elect to purchase in accordance with applicable law, are validly tendered and not properly withdrawn before the Expiration Date, then the Fund will purchase validly tendered shares on a pro rata basis with appropriate rounding adjustments to avoid purchases of fractional shares, as provided in the offer to purchase.

-2-

The Offer is being made solely under the offer to purchase and the letter of transmittal and is being made to all record holders of shares as of the close of business on January 10, 2014. The Offer is not being made to, nor will tenders be accepted from or on behalf of, holders of shares residing in any jurisdiction in which the making of the Offer or acceptance thereof would not be in compliance with the securities, blue sky or other laws of such jurisdiction.

Payment for shares purchased pursuant to the Offer will in all cases be made only after timely receipt by The Colbent Corporation, the depositary for the Offer (the “Depositary”), of: (a) timely confirmation of the book-entry transfer of such shares into the account maintained by the Depositary at The Depository Trust Company (the “Book-Entry Transfer Facility”) pursuant to the procedures set forth in Section 3 of the offer to purchase; (b) an agent’s message (as defined in the offer to purchase), in connection with a book-entry delivery, or the letter of transmittal, properly completed and duly executed, with any required signature guarantees; and (c) any other documents required by the letter of transmittal. Accordingly, payment may not be made to all tendering stockholders at the same time depending upon when confirmation of book-entry transfer of such shares into the Depositary’s account at the Book-Entry Transfer Facility are actually received by the Depositary.

YOUR PROMPT ACTION IS REQUESTED. PLEASE FORWARD YOUR COMPLETED INSTRUCTION FORM TO US IN AMPLE TIME TO PERMIT US TO SUBMIT THE TENDER ON YOUR BEHALF BEFORE THE EXPIRATION OF THE OFFER.

-3-

INSTRUCTION FORM

With Respect to the Offer by

THE SWISS HELVETIA FUND, INC.

to Purchase up to 4,579,480 Shares of Common Stock

At a Cash Purchase Price of 95% of Net Asset Value Per Share

The undersigned acknowledge(s) receipt of your letter in connection with the offer by The Swiss Helvetia Fund, Inc., a non-diversified, closed-end management investment company incorporated under the laws of the state of Delaware (the “Fund”), to purchase for cash up to 4,579,480 (approximately 15%) of its issued and outstanding shares of common stock, $0.001 par value per share, at a price per share equal to 95% of its net asset value (“NAV”) per share determined as of the close of the regular trading session of the New York Stock Exchange, the principal market on which the shares are traded, on the business day immediately following the day the offer expires (the “Pricing Date,” and such price, expressed as a percentage of NAV, the “Purchase Price”), net to the seller in cash, without interest, upon the terms and subject to the conditions set forth in the offer to purchase, dated January 13, 2014, and the related letter of transmittal (which, together with any supplements or amendments thereto, collectively constitute the “Offer”).

All shares validly tendered before the Expiration Date (as specified in Section 1 of the offer to purchase) and not properly withdrawn will be purchased by the Fund at the Purchase Price, net to the seller in cash, without interest, upon the terms and subject to the conditions of the Offer, including the proration provisions thereof. See Section 1 of the offer to purchase. All shares that the Fund does not accept for purchase because of proration will be returned at the Fund’s expense to the stockholders that tendered such shares promptly after the Expiration Date.

The undersigned hereby instruct(s) you to tender to the Fund the number of shares indicated below or, if no number is indicated, all shares you hold for the account of the undersigned, in accordance with the terms and subject to the conditions of the Offer.

NUMBER OF SHARES TO BE TENDERED BY YOU FOR

THE ACCOUNT OF THE UNDERSIGNED:

SHARES*

THE METHOD OF DELIVERY OF THIS DOCUMENT IS AT THE OPTION AND RISK OF

THE TENDERING STOCKHOLDER. IF DELIVERY IS BY MAIL, WE RECOMMEND

REGISTERED MAIL WITH RETURN RECEIPT REQUESTED, PROPERLY INSURED. IN

ALL CASES, PLEASE ALLOW SUFFICIENT TIME TO ASSURE DELIVERY.

—PLEASE SIGN ON THE NEXT PAGE—

* | Unless you indicate otherwise, we will assume that you are instructing us to tender all of the shares that we hold for your account.

Signature(s): |  |  |  |
Name(s): |  |  |  |
|  | Please Print |  |
Address(es): |  |  |  |
|  | (Please Include Zip Code) |  |
Telephone Number(s), including Area Code(s): |  |  |  |
Taxpayer ID or Social Security No.: |  |  |  |
Dated: |  |  |  |

-2-