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Calamos Convertible and High Income Fund

Prospectus supplement dated December 9, 2016 to Prospectus dated April 15, 2016, as supplemented

Effective December 9, 2016, the section titled “Use of Leverage by the Fund” beginning on page 5 of the Prospectus is deleted in its entirety and replaced with the following:

Use of Leverage by the Fund

The Fund currently uses, and may in the future use, financial leverage. The Fund, with the approval of its Board of Trustees, including its independent Trustees, has entered into a financing package that includes a Committed Facility Agreement (the “BNP Agreement”) with BNP Paribas Prime Brokerage International Ltd. (“BNP”) that allows the Fund to borrow up to $240 million, and a securities lending agreement (“Lending Agreement”). In addition, the financing package also includes a Credit Agreement (the “SSB Agreement”) with State Street Bank and Trust Company (“SSB”) that allows the Fund to borrow up to $240 million, and a related securities lending and securities repurchase agreement authorization agreement (“Authorized Agreement”) that is used to offset some of the interest rate payments that would otherwise be due in respect of the borrowings under the SSB Agreement. As of January 31, 2016, the Fund had $181 million in borrowings outstanding under the BNP Agreement, representing 15.9% of managed assets as of that date. As of January 31, 2016, the Fund had $181 million in borrowings outstanding under the SSB Agreement, representing 15.9% of managed assets as of that date. Combined borrowings under both agreements as of January 31, 2016 represented $362 million, or 31.8% of managed assets. The Fund will pay, and common shareholders will effectively bear, any costs and expenses relating to any borrowings by the Fund, including the financial leverage described above, as well as any additional financial leverage secured as a result of this offering. Such costs and expenses include the higher management fee resulting from the use of any such leverage, offering and/or issuance costs, and interest and/or dividend expense and ongoing maintenance. Effective December 9, 2016, the Fund may borrow up to $360 million under the amended and restated SSB Agreement. See “Leverage” and “Risk Factors — Leverage.”

The Fund may make further use of financial leverage through the issuance of preferred shares or may borrow money or issue additional debt securities to the extent permitted under the 1940 Act. As a non-fundamental policy, the Fund may not issue debt securities, borrow money or issue preferred shares in an aggregate amount exceeding 38% of the Fund’s managed assets measured at the time of issuance of the new securities. However, the Board of Trustees reserves the right to issue preferred shares or debt securities or borrow to the extent permitted by the 1940 Act. See “Leverage.” The holders of preferred shares or debt, if any, on the one hand, and the holders of the common shares, on the other, may have interests that conflict with each other in certain situations. See “Description of Securities — Preferred Shares” and “Certain Provisions of the Agreement and Declaration of Trust and By-Laws, Including Antitakeover Provisions.”

Because Calamos’ investment management fee is a percentage of the Fund’s managed assets, Calamos’ fee will be higher if the Fund is leveraged and Calamos will have an incentive to be more aggressive and leverage the Fund. Consequently, the Fund and Calamos may have differing interests in determining whether to leverage the Fund’s assets. Any additional use of leverage by the Fund effected through new, additional or increased credit facilities or the issuance of preferred shares would require approval by the Board of Trustees of the Fund. In considering whether to approve the use of additional leverage through those means, the Board would be presented with all relevant information necessary to make a determination whether or not additional leverage would be in the best interests of the Fund, including information regarding any potential conflicts of interest. For further information about the Fund’s financial leverage, see “Use of Leverage by the Fund.”

For further information about the effects of the Fund’s financial leverage and an illustration of the hypothetical effect on the return to a holder of the Fund’s common shares of the leverage obtained by borrowing under the Fund’s financing package, see “Effects of Leverage.” For further information about leveraging, see “Risk Factors — Additional Risks to Common Shareholders — Leverage Risk.”

Effective December 9, 2016, the section titled “Description of Securities” beginning on page 58 of the Prospectus is deleted in its entirety and replaced with the following:

DESCRIPTION OF SECURITIES

The Fund is authorized to issue an unlimited number of common shares, without par value. The Fund is also authorized to issue preferred shares. The Board of Trustees is authorized to classify and reclassify any unissued shares into one or more additional classes or series of shares. As of January 31, 2016, the Fund had 72,537,011 common shares outstanding. The Board of Trustees may establish such series or class from time to time by setting or changing in any one or more respects the designations, preferences, conversion or other rights, voting powers, restrictions, limitations as to dividends, qualifications or terms or conditions of redemption of such shares and pursuant to such classification or reclassification to increase or decrease the number of authorized shares of any existing class or series. The Board of Trustees, without shareholder approval, is authorized to amend the Agreement and Declaration of Trust and Bylaws to reflect the terms of any such class or series. The Fund is also authorized to issue other securities, including debt securities.

As of January 31, 2016, the Fund had total leverage of approximately $362 million representing approximately 31.8% of the Fund’s managed assets as of that date. The Fund will pay, and common shareholders will effectively bear, any costs and expenses relating to any borrowings by the Fund, including the financial leverage described above, as well as any additional leverage incurred as a result of this offering. Such costs and expenses include the higher management fee resulting from the use of any such leverage, offering and/or issuance costs, and interest and/or dividend expense and ongoing maintenance. Borrowings under the BNP Agreement and the SSB Agreement are secured by assets of the Fund that are held with

the Fund’s custodian in a separate account. Interest under the BNP Agreement is charged at the three month LIBOR plus .65% on the amount borrowed and .55% on the undrawn balance. Interest on the SSB Agreement is charged on the drawn amount at the rate of Overnight LIBOR plus .80%, payable monthly in arrears. Interest on overdue amounts or interest on the drawn 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 0.1%, payable quarterly in arrears. As of October 31, 2015, the interest rates charged under the BNP Agreement and the SSB Agreement were 0.98% and 0.92%, respectively. The combined interest rate charged under the BNP Agreement and the SSB Agreement as of October 31, 2015 was 0.95%. The SSB Agreement and Authorized Agreement were together amended and restated into a single Liquidity Agreement (the “SSB Liquidity Agreement”) effective December 9, 2016 such that interest on the SSB Liquidity Agreement is charged on the drawn amount at the rate of Overnight LIBOR plus .80%, payable monthly in arrears. Interest on overdue amounts or interest on the drawn amount paid during an event of default will be charged at Overnight LIBOR plus 2.8%. The SSB Liquidity Agreement has a commitment fee of 0.1%, on undrawn amounts under the facility, payable quarterly in arrears.

The Lending Agreement is a separate side-agreement between the Fund and BNP pursuant to which BNP may borrow a portion of the pledged collateral in an amount not to exceed the outstanding borrowings owed by the Fund to BNP under the BNP Agreement. The Lending Agreement is intended to permit the Fund to significantly reduce the cost of its borrowings under the BNP Agreement. BNP may re-register the Lent Securities in its own name or in another name other than the Fund, and may pledge, re-pledge, sell, lend or otherwise transfer or use the Lent Securities with all attendant rights of ownership. The Fund may designate any security within the pledged collateral as ineligible to be a Lent Security, provided there are eligible securities within the pledged collateral in an amount equal to the outstanding borrowing owed by the Fund. During the period in which the Lent Securities are outstanding, BNP must remit payment to the Fund equal to the amount of all dividends, interest or other distributions earned or made by the Lent Securities. BNP will pay to the Fund a fee for borrowing the securities that is calculated as a percentage of the difference between a fair market rate and a reference rate, with a guaranteed minimum annualized rate.

Under the terms of the Lending Agreement, the Lent Securities are marked to market daily, and if the value of the Lent Securities exceeds the value of the then-outstanding borrowings owed by the Fund to BNP under the BNP Agreement (the “Current Borrowings”), BNP must, on that day, either (1) return Lent Securities to the Fund’s custodian in an amount sufficient to cause the value of the outstanding Lent Securities to equal the Current Borrowings; or (2) post cash collateral with the Fund’s custodian equal to the difference between the value of the Lent Securities and the value of the Current Borrowings. If BNP fails to perform either of these actions as required, the Fund will recall securities, as discussed below, in an amount sufficient to cause the value of the outstanding Lent Securities to equal the Current Borrowings. The Fund can recall any of the Lent Securities and BNP shall, to the extent commercially possible, return such security or equivalent security to the Fund’s custodian no later than three business days after such request. If the Fund recalls a Lent Security pursuant to the Lending Agreement, and

BNP fails to return the Lent Securities or equivalent securities in a timely fashion, BNP shall remain liable to the Fund’s custodian for the ultimate delivery of such Lent Securities, or equivalent securities, and for any buy-in costs that the executing broker for the sales transaction may impose with respect to the failure to deliver. The Fund also has the right to apply and set-off an amount equal to one hundred percent (100%) of the then-current fair market value of such Lent Securities against the Current Borrowings. In addition, the Fund is a beneficiary of an irrevocable guaranty issued by BNP’s parent, BNP Paribas, a French banking institution that meets the definition of “eligible foreign custodian” under rule 17f-5 of the 1940 Act. Under the terms of the guaranty, BNP Paribas has agreed to guarantee the obligation of BNP to pay to the Fund any cash or securities owed under the terms of the Lending Agreement. The guaranty does not create any rights or grant any remedies to any person other than the Fund and other persons who are defined as beneficiaries under the guaranty. The Fund will exercise its set-off rights, or will exercise its rights under the guaranty, when in accordance with Calamos’ business discretion, Calamos believes that doing so is in the best interests of the Fund and its shareholders.

Under the terms of the Authorized Agreement with SSB, all securities lent or subject to repurchase transactions through SSB must 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. Cash collateral held by SSB on behalf of the Fund may be credited against the amounts borrowed under the SSB Agreement, with the effect of reducing interest expense payable by the Fund. Any amounts credited against the SSB Agreement would count against the Fund’s leverage limitations under the 1940 Act, unless otherwise covered in accordance with SEC Release IC-10666. Under the terms of the Authorized Agreement with SSB, SSB will return the value of the collateral to the borrower upon the return of the lent securities, which will eliminate the credit against the SSB Agreement and will increase the balance on which the Fund will pay interest. Under the terms of the Authorized Agreement with SSB, the Fund will make a variable “net income” payment related to any collateral credited against the SSB Agreement which will be paid to the securities borrower, less any payments due to the Fund or SSB under the terms of the Authorized Agreement. This arrangement continues under the Liquidity Agreement. As of January 31, 2016, the Fund did not have any cash collateral to offset against borrowings under the SSB Agreement. The Fund’s Board of Trustees, including its independent Trustees, has determined that the financing package is in the best interest of the Fund. The Fund reserves the right to utilize sources of borrowings in addition to, or in lieu of, the BNP Agreement and the Lending Agreement and the SSB Liquidity Agreement. See “Prospectus Summary — Use of Coverage by the Fund.”

While unsecured and unsubordinated indebtedness may rank equally with the borrowings under the BNP Agreement and the SSB Liquidity Agreement in right of payment, the lenders under the agreements, together with the holders of other outstanding secured indebtedness, may, to the exclusion of unsecured creditors, seek recourse against the collateral as security for the borrowings and such other secured indebtedness until amounts owed under the BNP Agreement and the SSB Liquidity Agreement and the other secured indebtedness are satisfied in full. All borrowings under the BNP Agreement and the SSB Liquidity Agreement and the

securities lending agreements rank senior to the Fund’s common and preferred shares as to the payment of interest and distribution of assets upon liquidation.

Please retain this supplement for future reference.

CHYSPT2 12/16