Exhibit (a)(1)(iii)

THE SWISS HELVETIA FUND, INC.

7 Bryant Park

New York, New York 10018

1-800-730-2932

Offer to Purchase Up to 24,638,918 Shares of Common Stock

At a Cash Purchase Price of 98% 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 NOVEMBER 16, 2018,

UNLESS THE FUND EXTENDS THE OFFER.

October 22, 2018

To Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees:

The Swiss Helvetia Fund, Inc., a non-diversified, closed-end management investment company incorporated under the laws of the state of Delaware (the “Fund” or “we”), is proposing to purchase for cash up to 24,638,918 (approximately 65%) of its issued and outstanding shares of common stock, $0.001 par value per share, at a price per share equal to 98% 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 the seller in cash, less applicable withholding taxes and without interest, upon the terms and subject to the conditions set forth in the offer to purchase, dated October 22, 2018, and the related letter of transmittal (which together, as they may be amended and supplemented from time to time, constitute the “Offer”). Please furnish copies of the enclosed materials to those of your clients for whom you hold shares registered in your name or in the name of your nominee.

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validly tendered before the Expiration Date (as specified in Section 1 of the offer to purchase) and not properly withdrawn will be purchased by the Fund at the Purchase Price, net to the seller in cash, without interest, upon the terms and subject to the conditions of the Offer,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.

As described in the offer to purchase, if more than 24,638,918 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of shares as the Fund may elect to purchase in accordance with applicable law, are validly tendered and not properly withdrawn before the Expiration Date, then the Fund will purchase validly tendered shares tendered at the Purchase Price on a pro rata basis with appropriate rounding adjustments to avoid purchases of fractional shares, as provided in the offer to purchase.

The Offer is not conditioned on any minimum number of shares being tendered. The Offer is, however, subject to other conditions. See Section 6 of the offer to purchase.

For your information and for forwarding to your clients for whom you hold shares registered in your name or in the name of your nominee, we are enclosing the following documents:

1.    Offer to Purchase, dated October 22, 2018;

2.    Form of Letter to Clients, which you may send to your clients for whom you hold shares registered in your name or in the name of your nominee, with an accompanying Instruction Form provided for obtaining such clients’ instructions with regard to the Offer;

3.    Form of Letter of Transmittal, for your use and for the information of your clients, together with accompanying instructions, IRS Form W-9 and the instructions included therewith;

4.    Letter to Stockholders of the Fund from Mark A. Hemenetz, President of the Fund, dated October 22, 2018; and

5.    Return envelope addressed to American Stock Transfer & Trust Company, LLC, the depositary for the Offer (the “Depositary”).

WE URGE YOU TO CONTACT YOUR CLIENTS AS PROMPTLY AS POSSIBLE. THE OFFER, PRORATION PERIOD AND WITHDRAWAL RIGHTS WILL EXPIRE AT 5:00 P.M., NEW YORK CITY TIME, ON NOVEMBER 16, 2018, UNLESS THE FUND EXTENDS THE OFFER.

No fees or commissions will be payable to brokers, dealers, commercial banks, trust companies or any person for soliciting tenders of shares under the Offer other than fees paid to AST Fund Solutions, LLC, the information agent for the Offer (the “Information Agent”), as described in the offer to purchase. We will, however, upon request, reimburse brokers, dealers, commercial banks and trust companies for reasonable and necessary costs and expenses incurred by them in forwarding the enclosed materials to their customers who are beneficial owners of shares held by them as a nominee or in a fiduciary capacity. We will pay or cause to be paid any stock transfer taxes applicable to our purchase of shares pursuant to the Offer, except as otherwise provided in the offer to purchase and letter of transmittal (see Instruction 7 of the letter of transmittal). No broker, dealer, bank, trust company or fiduciary shall be deemed to be an agent of the Fund, the Information Agent or the Depositary or any affiliate of the foregoing for purposes of the Offer.

For shares to be validly tendered pursuant to the Offer, the Depositary must timely receive the share certificates or confirmation of receipt of such shares under the procedure for book-entry transfer, together with a properly completed and duly executed letter of transmittal, including any required signature guarantees or an “agent’s message” (as defined in the offer to purchase and the letter of transmittal) and any other documents required pursuant to the Offer, all in accordance with the instructions set forth in the offer to purchase and letter of transmittal.

None of the Fund, its Board of Directors, Schroder Investment Management North America Inc., the Fund’s investment adviser, Schroder Investment Management North America Ltd., the Fund’s sub-investment adviser, or its 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 Offer is not being made to, nor will the Fund accept tenders from, stockholders in any jurisdiction in which the Offer or the acceptance thereof would not be in compliance with the laws of such jurisdiction.

Please address any inquiries you may have with respect to the Information Agent at its address set forth on the back cover page of the offer to purchase and telephone number set forth below.

You may obtain additional copies of the enclosed material from the Information Agent by calling them at: (888) 540-8736.

Capitalized terms used but not defined herein have the meanings assigned to them in the offer to purchase and the letter of transmittal.

Very truly yours,

The Swiss Helvetia

Fund, Inc.

Enclosures

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL CONSTITUTE YOU OR ANY OTHER PERSON AN AGENT OF THE FUND, THE INFORMATION AGENT OR THE DEPOSITARY OR ANY AFFILIATE OF THE FOREGOING, OR AUTHORIZE YOU OR ANY OTHER PERSON TO USE ANY DOCUMENT OR MAKE ANY STATEMENT ON BEHALF OF ANY OF THEM IN CONNECTION WITH THE OFFER OTHER THAN THE DOCUMENTS ENCLOSED HEREWITH AND THE STATEMENTS CONTAINED THEREIN.