CALAMOS^® CONVERTIBLE AND HIGH INCOME FUND

Supplement dated January 28, 2013 to the Prospectus and Statement of Additional

Information each dated February 29, 2012, as supplemented July 2, 2012, and

August 31, 2012

The following supplements the “Prospectus Summary—Use of Leverage” section beginning on page 6 of the Base Prospectus, the “Leverage” section beginning on page 25 of the Base Prospectus, and supplements the “Description of Securities” section beginning on page 54 of the Base Prospectus:

On January 22, 2013 the Fund diversified the source of its financial leverage by entering into a new credit agreement (the “SSB Agreement”) with State Street Bank & Trust Company (“SSB”), and revising its existing credit agreement with BNP Paribas Prime Brokerage Inc. (the “BNP Agreement”). Under the terms of the SSB Agreement, the Fund may borrow up to an initial limit of $200,000,000. Interest is charged on the drawn amount at the rate of Overnight LIBOR (London Inter-bank Offered Rate) plus .80%, payable monthly in arrears. Interest on overdue amounts or interest on the draw amount paid during an event of default will be charged at Overnight Libor plus 2.8%. The SSB Agreement has a commitment fee of .2% of any undrawn amount if the undrawn amount is more than 75% of the borrowing limit, otherwise the commitment fee on the undrawn amount is .1%, payable quarterly in arrears. Under the terms of the revised BNP Agreement, BNP Paribas Prime Brokerage International, Ltd. (“BNP”) has replaced BNP Paribas Prime Brokerage Inc. as the lender. Under the terms of the revised BNP Agreement, the Fund may borrow up to $200,000,000. All other terms of the original BNP Agreement, including interest rates, remain unchanged. The Lending Agreement between BNP Paribas Prime Broker Inc. and the Fund has also been amended to substitute BNP, but otherwise remains unchanged.

The purpose of borrowings made under the SSB Agreement will be to reduce borrowings under the BNP Agreement or for investment purposes. Borrowings under the SSB Agreement and the BNP Agreement are secured by assets of the Fund that are held with the Fund’s custodian in a separate account (the “pledged collateral”). BNP and SSB share an equal claim on the pledged collateral, subject to any adjustment that may be agreed upon between the lenders.

The section on Page 24 of the Base Prospectus captioned “Lending of Portfolio Securities is amended to read as follows:

Lending of Portfolio Securities. In addition to the Lending Agreement with BNP, the Fund may lend portfolio securities through SSB as securities lending agent, or through another securities lending agent, to registered broker-dealers or other institutional investors deemed by Calamos to be of good standing under agreements which require that the loans be secured continuously by collateral received in cash, cash equivalents, or U.S. Treasury bills and maintained on a current basis at an amount at least equal to the market value of the securities loaned. The Fund does not use affiliated agents in

managing its lending program. The Fund continues to receive the equivalent of the interest or dividends paid by the issuer on the securities loaned as well as the benefit of an increase and the detriment of any decrease in the market value of the securities loaned and would also receive compensation based on investment of the collateral. The Fund would not, however, have the right to vote any securities having voting rights during the existence of the loan, but could call the loan in advance of an important vote to be taken among holders of the securities or of the giving or withholding of consent on a material matter affecting the investment.

As with other extensions of credit, there are risks of delay in recovery or even loss of rights in the collateral should the borrower of the securities fail financially. At no time would the value of the securities loaned exceed 33 ¹/₃% of the value of the Fund’s managed assets. See “Description of Securities” for more information on lending of portfolio securities

The section on page S-9 of the Fund’s Statement of Additional Information captioned “Lending of Portfolio Securities is amended to read as follows:

Lending of Portfolio Securities

In addition to the Lending Agreement with BNP, the Fund may lend portfolio securities through SSB as securities lending agent, or through another securities lending agent, to broker-dealers and banks. Any such loan must be continuously secured by collateral received in cash or cash equivalents maintained on a current basis in an amount at least equal to the market value of the securities loaned by the Fund. The Fund would continue to receive the equivalent of the interest or dividends paid by the issuer on the securities loaned, and would also receive an additional return that may be in the form of a fixed fee or a percentage of the collateral. The Fund may pay reasonable fees to persons unaffiliated with the Fund for services in arranging these loans. The Fund would have the right to call the loan and obtain the securities loaned at any time on notice of not more than five business days. The Fund would not have the right to vote the securities during the existence of the loan but would call the loan to permit voting of the securities, if, in Calamos’ judgment, a material event requiring a shareholder vote would otherwise occur before the loan was repaid. In the event of bankruptcy or other default of the borrower, the Fund could experience both delays in liquidating the loan collateral or recovering the loaned securities and losses, including (a) possible decline in the value of the collateral or in the value of the securities loaned during the period while the Fund seeks to enforce its rights thereto, (b) possible subnormal levels of income and lack of access to income during this period, and (c) expenses of enforcing its rights.

Please retain this supplement for future reference.

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