Calamos Convertible and High Income Fund (CHY) 424B3Prospectus supplement

Filed pursuant to Rule 424(B)(3)
Registration No. 333-229038

Calamos Convertible and High Income Fund (the "Fund")
Supplement dated December 20, 2024 to the Fund's Prospectus dated February 24, 2022, as supplemented from time to time, and to the Fund's Statement of Information ("SAI") dated February 24, 2022, as supplemented from time to time

Recent Developments – Dividends and Distributions

On December 17, 2024, the Fund’s Board of Trustees approved an amendment to the Trust’s distribution policy approving the transition from the Trust’s managed distribution policy to a level distribution policy effective as of and from January 1, 2025.

Revised Disclosure Related to Dividends and Distributions on Common Shares

The first two paragraphs of the section titled "Dividends and Distributions on Common Shares" beginning on page 3 of the Prospectus Summary is deleted in its entirety and replaced with the following:

The Fund intends to distribute to common shareholders all or a portion of its net investment income monthly and net realized capital gains, if any, at least annually.

The Fund currently intends to make monthly distributions to common shareholders at a level rate established by the Board of Trustees. The rate may be modified by the Board of Trustees from time to time. Monthly distributions may include net investment income, net realized short-term capital gain and, if necessary to maintain a level distribution, return of capital. The Fund may at times in its discretion pay out less than the entire amount of net investment income earned in any particular period and may at times pay out such accumulated undistributed income in addition to net investment income earned in other periods in order to permit the Fund to maintain a more stable level of distributions. As a result, the distributions paid by the Fund to holders of common shares for any particular period may be more or less than the amount of net investment income earned by the Fund during such period.

The section titled "Dividends and Distributions on Common Shares" beginning on page 103 of the Prospectus is deleted in its entirety and replaced with the following:

DIVIDENDS AND DISTRIBUTIONS ON COMMON SHARES; AUTOMATIC DIVIDEND REINVESTMENT PLAN

Dividends and Distributions on Common Shares

The Fund intends to distribute to common shareholders all or a portion of its net investment income monthly and net realized capital gains, if any, at least annually.

The Fund currently intends to make monthly distributions to common shareholders at a level rate established by the Board of Trustees. The rate may be modified by the Board of Trustees from time to time. Monthly distributions may include net investment income, net realized short-term capital gain and, if necessary to maintain a level distribution, return of capital. The Fund may at times in its discretion pay out less than the entire amount of net investment income earned in any particular period and may at times pay out such accumulated undistributed income in addition to net investment income earned in other periods in order to permit the Fund to maintain a more stable level of distributions. As a result, the distributions paid by the Fund to holders of common shares for any particular period may be more or less than the amount of net investment income earned by the Fund during such period.

The Fund will seek to establish a distribution rate that roughly corresponds to the Adviser’s projections of the total return that could reasonably be expected to be generated by the Fund over an extended period of time, although the distribution rate will not be solely dependent on the amount of income earned or capital gains realized by the Fund. Calamos, in making such projections, may consider long-term historical returns and a variety of other factors. If, for any monthly distribution, net investment income and net realized capital gains were less than the amount of the distribution, the difference would be distributed from the Fund’s assets. In addition, in order to make such distributions, the Fund might have to sell a portion of its investment portfolio at a time when independent investment judgment might not dictate such action. The Fund’s final distribution for each calendar year will include any remaining net investment income undistributed during the year and may include any remaining net realized capital gains undistributed during the year. The Fund’s actual financial performance will likely vary significantly from quarter-to-quarter and from year-to-year, and there may be extended periods of up to several years when the distribution rate will exceed the Fund’s actual total returns. The Fund’s projected or actual distribution rate is not a prediction of what the Fund’s actual total returns will be over any specific future period.

As portfolio and market conditions change, the rate of distributions on the common shares and the Fund’s distribution policy could change. To the extent that the total return of the Fund exceeds the distribution rate for an extended period, the Fund may be in a position to increase the distribution rate or distribute supplemental amounts to shareholders. Conversely, if the total return of the Fund is less than the distribution rate for an extended period of time, the Fund will effectively be drawing upon its net assets to meet payments prescribed by its distribution policy. The rate may be modified by the Fund’s Board from time to time.

To the extent the Fund distributes an amount in excess of the Fund’s current and accumulated earnings and profits, such excess, if any (the “Excess”), will be treated by a shareholder for federal income tax purposes as a tax-free return of capital to the extent of the shareholder’s adjusted tax basis in their shares and thereafter as a gain from the sale or exchange of such shares. See “Certain Federal Income Tax Matters.” Any such distributions made by the Fund will reduce the shareholder’s adjusted tax basis in their shares to the extent that the distribution constitutes a return of capital during any calendar year, and thus could potentially subject the shareholder to capital gains taxation in connection with the sale of Fund shares, even if those shares are sold at a price that is lower than the shareholder’s original investment price. To the extent that the Fund’s distributions exceed the Fund’s current and accumulated earnings and profits, the distribution payout rate will exceed the yield generated from the Fund’s investments. There is no guarantee that the Fund will realize capital gain in any given year, nor that the Fund’s distribution rates will equal in any period the Fund’s net investment income. Pursuant to the requirements of the 1940 Act and other applicable laws, a notice will accompany each monthly distribution with respect to the estimated source of the distribution made. Distributions are subject to recharacterization for federal income tax purposes after the end of the fiscal year.

For U.S. federal income tax purposes, the Fund is required to distribute substantially all of its net investment income and net realized capital gains each year to both reduce its federal income tax liability and to avoid a potential excise tax. Accordingly, the Fund intends to distribute all or substantially all of its net investment income and all net realized capital gains, if any. Therefore, the Fund’s final distribution with respect to each calendar year would include any remaining net investment income and net realized capital gains, if any, undistributed during the year.

In the event the Fund distributed an Excess, such distribution would decrease the Fund’s managed assets and, therefore, have the likely effect of increasing the Fund’s expense ratio. There is a risk that the Fund would not eventually realize capital gains in an amount corresponding to a distribution of the Excess.

On November 4, 2008, the Commission granted Calamos, on behalf of itself and certain registered closed-end funds that it manages, including the Fund, or may manage in the future, an order granting an exemption from Section 19(b) of, and Rule 19b-1 under, the 1940 Act to conditionally permit the Fund to make periodic distributions of long-term capital gains with respect to the Fund’s outstanding common shares as frequently as twelve times each year, so long as it complies with the conditions of the order and maintains in effect a distribution policy with respect to its common shares calling for periodic distributions of an amount equal to a fixed amount per share, a fixed percentage of market price per share or a fixed percentage of the Fund’s net asset value per share (the “Managed Distribution Policy”). As of the date of this Prospectus, as supplemented, the Fund is not using a Managed Distribution Policy. Pursuant to and in reliance on the order granted by the Commission, under the Managed Distribution Policy, the Fund is required to:

In addition, if the Fund’s common shares were to trade at a significant premium to NAV following the implementation of the Managed Distribution Policy, and certain other circumstances were present, the Fund’s Board of Trustees would be required to determine whether to approve or disapprove the continuation, or continuation after amendment, of the Managed Distribution Policy. Finally, pursuant to the order, the Fund would not be permitted to make a public offering of common shares other than:

· a rights offering below NAV to holders of the Fund’s common shares;

· an offering in connection with a dividend reinvestment plan, merger, consolidation, acquisition, spin-off or reorganization of the Fund; or

· an offering other than those described above, unless, with respect to such other offering:

· the Fund’s average annual distribution rate for the six months ending on the last day of the month ended immediately prior to the most recent distribution record date, expressed as a percentage of NAV per share as of such date, is no more than one percentage point greater than the Fund’s average annual total return for the five-year period ending on such date; and

· the transmittal letter accompanying any registration statement filed with the Commission in connection with such offering discloses that the Fund has received an order under Section 19(b) of the 1940 Act to permit it to make periodic distributions of long-term capital gains with respect to its common stock as frequently as twelve times each year, and as frequently as distributions are specified in accordance with the terms of any outstanding preferred stock that such fund may issue.

The relief described above will expire on the effective date of any amendment to Rule 19b-1 under the 1940 Act that provides relief permitting certain closed-end investment companies to make periodic distributions of long-term capital gains with respect to their outstanding common stock as frequently as twelve times each year. Under the Managed Distribution Policy, if, for any distribution, undistributed net investment income and net realized capital gains were less than the amount of the distribution, the difference would be distributed from the Fund’s other assets. In addition, in order to make such distributions, the Fund might have to sell a portion of its investment portfolio at a time when independent investment judgment might not dictate such action.

Under the 1940 Act, the Fund is not permitted to incur indebtedness unless immediately after such incurrence the Fund has an asset coverage of at least 300% of the aggregate outstanding principal balance of indebtedness. Additionally, under the 1940 Act, the Fund generally may not declare any dividend or other distribution upon any class of its shares, or purchase any such shares, unless the aggregate indebtedness of the Fund has, at the time of the declaration of any such dividend or distribution or at the time of any such purchase, an asset coverage of at least 300% after deducting the amount of such dividend, distribution, or purchase price, as the case may be, except that dividends may be declared upon any preferred shares if such indebtedness has an asset coverage of at least 200% at the time of declaration thereof after deducting the amount of the dividend. This limitation does not apply to certain privately placed debt.

While any preferred shares are outstanding, the Fund may not declare any dividend or other distribution on its common shares, unless at the time of such declaration, (1) all accumulated preferred dividends have been paid and (2) the net asset value of the Fund’s portfolio (determined after deducting the amount of such dividend or other distribution) is at least 200% of the liquidation value of the outstanding preferred shares (expected to be equal to the original purchase price per share plus any accumulated and unpaid dividends thereon).

In addition to the limitations imposed by the 1940 Act described above, certain lenders may impose additional restrictions on the payment of dividends or distributions on common shares in the event of a default on the Fund’s borrowings. If the Fund’s ability to make distributions on its common shares is limited, such limitation could, under certain circumstances, impair the ability of the Fund to maintain its qualification for federal income taxation as a regulated investment company and to reduce or eliminate tax at the Fund level, which would have adverse tax consequences for shareholders. See “Leverage” and “Certain Federal Income Tax Matters.”

See “ — Automatic Dividend Reinvestment Plan” for information concerning the manner in which dividends and distributions to common shareholders may be automatically reinvested in common shares. Dividends and distributions are taxable to shareholders for federal income tax purposes whether they are reinvested in shares of the Fund or received in cash.

The yield on the Fund’s common shares may vary from period to period depending on factors including, but not limited to, market conditions, the timing of the Fund’s investment in portfolio securities, the securities comprising the Fund’s portfolio, changes in interest rates including changes in the relationship between short- term rates and long-term rates, the amount and timing of the use of borrowings and other leverage by the Fund, the effects of leverage on the common shares discussed above under “Leverage,” the timing of the investment of leverage proceeds in portfolio securities, the Fund’s net assets and its operating expenses. Consequently, the Fund cannot guarantee any particular yield on its common shares and the yield for any given period is not an indication or representation of future yields on the Fund’s common shares.

Please retain this supplement for future reference.