424B3

Calamos Convertible and High Income Fund (the "Fund")
Supplement dated September 30, 2022 to the Fund's Prospectus dated February 24, 2022, and as
supplemented from time to time and to the Fund's Statement of Information ("SAI") dated
February 24, 2022, and as supplemented from time to time

I. Recent Developments — Mandatory Redeemable Preferred Shares

On September 6, 2022, the Fund redeemed 100% (1,460,000) of the outstanding Series A mandatory redeemable preferred shares ("MRP Shares") with an aggregate liquidation preference totaling $36,500,000.

Additional updated information regarding the Fund's MRP Shares is included in the restated disclosures set forth below.

Revised Disclosure Related to MRP Shares

In accordance with the above, the Fund's Prospectus, SAI and Prospectus Supplement are hereby amended as follows:

The section titled "Capitalization" beginning on page SUP-2 of the Prospectus Supplement is deleted in its entirety and replaced with the following:

CAPITALIZATION

The Fund may offer and sell up to 5,170,926 of our common shares, no par value per share, from time to time through the Sub-Placement Agent as sub-placement agent under this prospectus supplement and the accompanying prospectus. There is no guarantee that there will be any sales of our common shares pursuant to this prospectus supplement and the accompanying prospectus. The table below assumes that we will sell 5,170,926 common shares (the number of common shares remaining to be sold under the current sales agreement as of September 6, 2022) at a price of $12.22 per share (the last reported sale price per share of our common shares on NASDAQ on September 6, 2022).

The table below shows our historical capitalization as of April 30, 2022 and the estimated capitalization of the Fund assuming the sale of all 5,170,926 common shares that are subject to the sales agreement at a price of $12.22 per share, the last reported sales price per share of our common shares on a pro forma, as adjusted basis as of September 6, 2022. Actual sales, if any, of the Fund's common shares under this prospectus supplement and accompanying prospectus may be different than as set forth in the table below. In addition, the price per share of any such sale may be greater or less than $12.22 per share, depending on the market price of the Fund's common shares at the time of any such sale and/or the Fund's net asset value ("NAV") for purposes of calculating the Minimum Price. The Fund and the Distributor will determine whether any sales of the Fund's common shares will be authorized on a particular day; the Fund and the Distributor, however, will not authorize sales of the Fund's common shares if the per share price of the shares is less than the Minimum Price. The Fund and the Distributor may elect not to authorize sales of the Fund's common shares on a particular day even if the per share price of the shares is equal to or greater than the Minimum Price, or may only authorize a fixed number of shares to be sold on any particular day. The Fund and the Distributor will have full discretion regarding whether sales of Fund common shares will be authorized on a particular day and, if so, in what amounts.

The following table sets forth our capitalization:

•  on an actual basis as of April 30, 2022; and

•  on a pro forma as adjusted basis to reflect (1) the assumed sale of 5,170,926 common shares at $12.22 per share (the last reported sale price of the Fund's common shares on NASDAQ on September 6, 2022), in an offering under this prospectus supplement and the accompanying prospectus and the issuance of 5,170,926 of our common shares through the Fund's dividend reinvestment plan, (2) the investment of net proceeds assumed from such offering in accordance with the Fund's investment objective and policies, after deducting the assumed aggregate commission of $631,887 (representing an estimated commission of 1% of the gross sales price in connection with sale of common shares), and (3) the redemption of $36,500,000 of Series A MRP Shares on September 6, 2022.

	Actual		As Adjusted
Loans(1)	$	240,000,000	$	240,000,000
Preferred Shares		145,000,000		145,000,000
Common shares, no par value per share, unlimited shares authorized, 8,982,260 outstanding (actual) and 80,724,440 shares outstanding (as further adjusted)		881,164,197		960,740,965
Accumulated distributable earnings (loss)		61,006,149		61,006,149
Net assets applicable to common shareholders		942,170,346		1,021,747,114
Total Capitalization	$	1,327,170,346	$	1,373,747,114

⁽¹⁾ Figures do not reflect additional structural leverage related to certain securities lending programs, which were $196 million and $158 million as of April 30, 2022 and September 6, 2022, respectively.

The section titled "Summary of Fund Expenses" beginning on page SUP-3 of the Prospectus Supplement is deleted in its entirety and replaced with the following:

SUMMARY OF FUND EXPENSES

The following table and example contain information about the costs and expenses that common shareholders will bear directly or indirectly. In accordance with Commission requirements, the table below shows our expenses, including interest payments on borrowed funds, as a percentage of our average net assets as of September 6, 2022, and not as a percentage of gross assets or managed assets.

By showing expenses as a percentage of average net assets, expenses are not expressed as a percentage of all of the assets we invest. The table and example are based on our capital structure as of September 6, 2022. As of September 6, 2022, we had $207 million in borrowings outstanding, $145 million in outstanding preferred shares and additional structural leverage of $158 million, collectively representing 37.3% of managed assets as of that date.

Shareholder Transaction Expenses
Sales Load (as a percentage of offering price)		1.00	%(1)
Offering Expenses Borne by the Fund (as a percentage of offering price)		—	%(2)
Dividend Reinvestment Plan Fees (per sales transaction fee)(3)	$	15.00

Annual Expenses	Percentage of Average Net Assets Attributable to Common Shareholders
Management Fee(4)		1.25	%
Interest Payments on Borrowed Funds(5)		0.36	%
Preferred Stock Dividend Payments(6)		0.58	%
Other Expenses(7)		0.08	%
Total Annual Expenses		2.27	%

Example:

The following example illustrates the expenses that common shareholders would pay on a $1,000 investment in common shares, assuming (1) net annual expenses of 2.27% of net assets attributable to common shareholders; (2) a 5% annual gross return; and (3) all distributions are reinvested at net asset value:

	1 Year		3 Years		5 Years		10 Years
Total Expenses Paid by Common Shareholders(8)	$	33	$	80	$	130	$	268

The example should not be considered a representation of future expenses. Actual expenses may be greater or less than those assumed. Moreover, our actual rate of return may be greater or less than the hypothetical 5% return shown in the example.

(1)  Represents the estimated commission with respect to the Fund's common shares being sold in this offering. There is no guarantee that there will be any sales of the Fund's common shares pursuant to this prospectus supplement and the accompanying prospectus. Actual sales of the Fund's common shares under this prospectus supplement and the accompanying prospectus, if any, may be less than as set forth under "Capitalization" above. In addition, the price per share of any such sale may be greater or less than the price set forth under "Capitalization" above, depending on the market price of the Fund's common shares at the time of any such sale.

(2)  Calamos will pay the expenses of the offering (other than the applicable commissions). However, Calamos may recapture from the Fund previously paid offering expenses in an amount up to $200,000 per each 12-month period of the three-year duration of the offering beginning March 1, 2019, provided that the Fund has made sales resulting in net proceeds of $5 million from the offering during that 12-month period. In the event that the Fund does not achieve sales resulting in net proceeds of $5 million from the offering in that 12-month period, the $200,000 recapture amount will carry forward and be added to the total amount that Calamos can recapture from the Fund in the next 12-month period. The maximum amount that Calamos can recapture from the Fund during the duration of the offering is $600,000. The arrangement is hereinafter referred to as the "recapture provision." As of the date of this prospectus supplement and the accompanying prospectus, Calamos will pay all of the expenses associated with the offering (other than the applicable commissions). If the recapture provision is triggered in the future, such expenses that will be borne by Fund shareholders will be set forth in the "Shareholder Transaction Expenses" table above.

(3)  Shareholders will pay a $15.00 transaction fee plus a $0.02 per share brokerage charge if they direct Computershare Shareowner Services LLC (the "Plan Agent") to sell common shares held in an account of the Fund's Automatic Dividend Reinvestment Plan (the "Plan"). In addition, each participant will pay a pro rata share of brokerage commissions incurred with respect to the Plan Agent's open-market purchases in connection with the reinvestment of dividends or distributions. If a participant elects to have the Plan Agent sell part or all of his or her common shares and remit the proceeds, such participant will be charged his or her pro rata share of brokerage commissions on the shares sold. See "Dividends and Distributions on Common Shares; Automatic Dividend Reinvestment Plan" on page 103 of the accompanying prospectus.

(4)  The Fund pays Calamos an annual management fee, payable monthly in arrears, for its investment management services in an amount equal to 0.80% of the Fund's average weekly managed assets. In accordance with the requirements of the Commission, the table above shows the Fund's management fee as a percentage of average net assets attributable to common shareholders. By showing the management fee as a percentage of net assets, the management fee is not expressed as a percentage of all of the assets the Fund intends to invest. For purposes of the table, the management fee has been converted to 1.25% of the Fund's average weekly net assets as of September 6, 2022 by dividing the total dollar amount of the management fee by the Fund's average weekly net assets (managed assets less outstanding leverage).

(5)  Reflects interest expense paid on $165 million in average borrowings under the Fund's Amended and Restated Liquidity Agreement with State Street Bank and Trust Company, plus $158 million in additional average structural leverage related to certain securities lending programs, as described in the accompanying prospectus under "Leverage."

(6)  Reflects estimated dividend expense on $145 million aggregate liquidation preference of mandatory redeemable preferred shares ("MRP Shares" or "MRPS") outstanding. See "Prospectus Summary — Use of Leverage by the Fund" and "Leverage" in the accompanying prospectus for additional information.

(7)  "Other Expenses" are based on estimated amounts for the Fund's current fiscal year.

(8)  The example includes sales load and estimated offering costs.

The third, fourth and fifth sentences of the first paragraph of the section titled "Prospectus Summary — The Fund" beginning on page 1 of the Prospectus are deleted in their entirety and replaced with the following:

As of September 6, 2022, we had $1.4 billion of total managed assets, including $145 million of outstanding mandatory redeemable preferred shares ("MRP Shares" or "MRPS"). As of September 6, 2022 the Fund had utilized $365 million of the $480 million available under the Amended and Restated Liquidity Agreement (the "SSB Agreement") with State Street Bank and Trust Company ("SSB" or "State Street") ($207 million in borrowings outstanding, and $158 million in structural leverage consisting of collateral received from SSB in connection with securities on loan), representing 26.7% of the Fund's managed assets as of that date, and had $145 million of MRP Shares outstanding, representing 10.6% of the Fund's managed assets. Combined, the borrowings under the SSB Agreement and the outstanding MRP Shares represented 37.3% of the Fund's managed assets.

The first two paragraphs of the section titled "Use of Leverage by the Fund" beginning on page 8 of the Prospectus are deleted in their 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 has obtained financial leverage (i) under the SSB Agreement that allows the Fund to borrow up to $480 million and (ii) through the issuance of four series of MRP Shares with an aggregate liquidation preference of $145 million, as described in greater detail below. The SSB Agreement provides for securities lending and securities repurchase transactions that may offset some of the interest rate payments that would otherwise be due in respect of the borrowings under the SSB Agreement. The Fund's outstanding MRP Shares include 1,460,000 Series B MRP Shares, with an aggregate liquidation preference of $36,500,000 and a mandatory redemption date of September 6, 2024; 1,480,000 Series C MRP Shares, with an aggregate liquidation preference of $37,000,000 and a mandatory redemption date of September 6, 2027; 1,400,000 Series D MRP Shares, with an aggregate liquidation preference of $35,000,000 and a mandatory redemption date of August 24, 2026; and 1,460,000 Series E MRP Shares, with an aggregate liquidation preference of $36,500,000 and a mandatory redemption date of May 24, 2027. The Series B, Series C, Series D and Series E MRP Shares are to pay monthly cash dividends initially at rates of 4.00%, 4.24%, 2.45% and 2.68%, respectively, subject to adjustment under certain circumstances. Additional details regarding the SSB Agreement and the MRP Shares are included under "Leverage.”

As of September 6, 2022, the Fund had utilized $365 million of the $480 million available under the SSB Agreement ($207 million in borrowings outstanding, and $158 million in structural leverage consisting of collateral received from SSB in connection with securities on loan), representing 26.7% of the Fund's managed assets as of that date, and had $145 million of MRP Shares outstanding, representing 10.6% of the Fund's managed assets. Combined, the borrowings under the SSB Agreement and the outstanding MRP Shares represented 37.3% of the Fund's managed assets.

The third and fourth paragraphs of the section titled "The Fund" beginning on page 36 of the Prospectus is deleted in its entirety and replaced with the following:

As of September 6, 2022, the Fund had utilized $365 million of the $480 million available under the SSB Agreement ($207 million in borrowings outstanding, and $158 million in structural leverage consisting of collateral received from SSB in connection with securities on loan), representing 26.7% of the Fund's managed assets as of that date, and had $145 million of MRP Shares outstanding, representing 10.6% of the Fund's managed assets. Combined, the borrowings under the SSB Agreement and the outstanding MRP Shares represented 37.3% of the Fund's managed assets. Structural leverage refers to borrowings under the SSB Agreement in respect of which the Fund’s interest payments are reduced or eliminated by the Fund’s securities lending activities. See “Leverage.” The Fund’s common shares are listed on Nasdaq under the symbol “CHY.” The Fund’s principal office is located at 2020 Calamos Court, Naperville, Illinois 60563, and its telephone number is 800-582-6959.

The following table provides information about our outstanding securities as of September 6, 2022:

Title of Class	Amount Authorized		Amount Held by the Fund for its Account		Amount Outstanding
Common Shares		Unlimited		75,553,514		80,724,440
MRPS-Series B		1,460,000		0		1,460,000
MRPS-Series C		1,480,000		0		1,480,000
MRPS-Series D		1,400,000		0		1,400,000
MRPS-Series E		1,460,000		0		1,460,000

The first paragraph in the section titled "Leverage" beginning on page 49 of the Prospectus is deleted in its entirety and replaced with the following:

The Fund may issue preferred shares or debt securities or borrow to increase its assets available for investment. As of September 6, 2022, the Fund had $365 million in borrowings outstanding under the SSB Agreement, MRP Shares outstanding with an aggregate liquidation preference of $145 million and used approximately $158 million of collateral obtained through securities lending arrangements as an offset against borrowings under the SSB Agreement, for a total of $510 million of leverage representing 37.3% of managed assets as of that date. The SSB Agreement provides for additional credit availability for the Fund, such that it may borrow up to $480 million. Additional information regarding the Fund's preferred shares is included below under "Mandatory Redeemable Preferred Shares."

The section titled "Mandatory Redeemable Preferred Shares" beginning on page 53 of the Prospectus is deleted in its entirety and replaced with the following:

Mandatory Redeemable Preferred Shares

On September 6, 2017, the Fund completed a private placement of 1,460,000 Series B MRP Shares and 1,480,000 Series C MRP Shares. On August 24, 2021, the Fund completed a private placement of 1,400,000 Series D MRP Shares and 1,460,000 Series E MRP Shares. Each MRP Share has a liquidation preference of $25.00, resulting in an aggregate liquidation preference of $145 million for all MRP Shares.

The holders of MRP Shares for the Fund ("MRP Shareholders") are entitled to receive monthly cash dividends, payable on the first business day (a "Dividend Payment Date") of each month following issuance.

Subject to adjustment as described below under "MRP Shares Dividends," the dividend rate per annum (the "Applicable Rate") for each class of MRP Shares is as follows:

MRP Shares	Applicable Rate
Series B MRP Shares		4.00	%
Series C MRP Shares		4.24	%
Series D MRP Shares		2.45	%
Series E MRP Shares		2.68	%

The MRP Shares have a term redemption date of September 6, 2024 for the Series B MRP Shares, September 6, 2027 for the Series C MRP Shares, August 24, 2026 for the Series D MRP Shares and May 24, 2027 for the Series E MRP Shares.

Previously, the Series B MRP Shares and the Series C MRP Shares had been assigned a rating of "AA" by Fitch Ratings, Inc. ("Fitch"). As of December 17, 2020, Kroll Bond Rating Agency LLC ("KBRA") replaced Fitch as the rating agency for the Series B MRP Shares and the Series C MRP Shares and each of the Series B MRP Shares and the Series C MRP Shares have been assigned a rating of 'AA-' by KBRA. As of August 24, 2021, the Series D MRP Shares and Series E MRP Shares have each been assigned a rating of ‘AA-’ by KBRA. If the ratings of the MRP Shares are downgraded, the Fund's dividend expense may increase, as described below.

Liquidation Preference. In the event of any voluntary or involuntary liquidation, dissolution or winding up of the Fund, the MRP Shareholders will be entitled to receive a preferential liquidating distribution equal to $25.00 per MRP Share plus accrued and unpaid dividends, after satisfaction of claims of creditors of the Fund, but before any distribution of assets is made to common shareholders.

MRP Shares Dividends. If, on the first day of the monthly dividend period immediately preceding a Dividend Payment Date (each such period a "Dividend Period"), Series B MRP Shares or Series C MRP Shares is rated no less than "A" by Fitch (and no less than the equivalent of such rating by some other NRSRO, if any, other than Fitch, such as KBRA, providing a rating for the MRP Shares pursuant to the request of the Fund) or with respect to Series D MRP Shares or Series E MRP Shares, by KBRA (or lower than the equivalent of such rating by any Other Rating Agency), then the dividend rate for such period (the "Dividend Rate") will be equal to the Applicable Rate for such series.

If, on the first day of a Dividend Period, the credit rating assigned on any date to Series B MRP Shares or Series C MRP Shares by Fitch (or some other NRSRO then rating any series of the outstanding MRP Shares pursuant to the request of the Fund, such as KBRA) is lower than a rating of "A" (or lower than the equivalent of such rating by such other rating agency), or with respect to Series D MRP Shares or Series E MRP Shares, are rated lower than the equivalent of "A" by KBRA (or lower than the equivalent of such rating by any Other Rating Agency) the Dividend Rate applicable to such series of outstanding MRP Shares for such Dividend Period shall be the Applicable Rate plus the enhanced dividend amount (which shall not be cumulative) set opposite the lowest of such ratings in the table below:

Fitch Rating or KBRA Rating (Or Equivalent by an Other Rating Agency)	Enhanced Dividend Amount
“A-”		0.5	%
“BBB+” to “BBB-”		2.0	%
“BB+” or below		4.0	%

A 4.0% premium in addition to the Applicable Rate may apply when the Fund fails to maintain a current credit rating, and a 5.0% premium may apply when the Fund fails to make timely payments with regard to the MRP Shares (subject to cure periods in each case).

Limitation on Common Share Distributions. With regard to the Series B MRP Shares or Series C MRP Shares, so long as any MRP Shares are outstanding, the Fund will not declare, pay or set apart for payment any dividend or other distribution (other than non-cash distributions) with respect to Fund shares ranking junior to or on parity with the MRP Shares, unless (1) the Fund has satisfied the MRP Shares Overcollateralization Test (as defined below) on at least one "valuation date" in the preceding 65 calendar days, (2) immediately after such transaction the Fund would satisfy the MRP Shares Asset Coverage Test (as defined below), (3) full cumulative dividends on the MRP Shares due on or prior to the date of the transaction have been declared and paid to the holders of MRP Shares and (4) the Fund has redeemed the full number of MRP Shares required to be redeemed by any provision for mandatory redemption or deposited sufficient monies with the Fund's paying agent for that purpose, subject to certain grace periods and exceptions.

MRP Shares Asset Coverage Test: Asset coverage with respect to all outstanding senior securities and preferred shares, including the MRP Shares, determined in accordance with Section 18(h) of the 1940 Act, on the basis of values calculated as of a time within 48 hours (not including Sundays or holidays) next preceding the time of determination, must be greater than or equal to 225%.

MRP Shares Overcollateralization Test: So long as Fitch or any other NRSRO, such as KBRA, is then rating any class of the outstanding MRP Shares pursuant to the request of the Fund, satisfaction of only those overcollateralization ratios applicable to closed-end fund issuers with the same rating(s) as the Fund's MRP Shares' then-current rating(s) issued by Fitch or such other NRSRO, such as KBRA, by application of the applicable rating agency guidelines.

With regard to Series D MRP Shares or Series E MRP Shares, for so long as any MRP Shares are Outstanding, the Fund will not declare, pay or set apart for payment any dividend or other distribution (other than a dividend or distribution paid in shares of, or options, warrants or rights to subscribe for or purchase, Common Shares or other shares of beneficial interest, if any, ranking junior to the MRP Shares as to dividends or upon liquidation (collectively "non-cash distributions")) with respect to Common Shares or any other shares of the Series or Fund ranking junior to or on a parity with the MRP Shares as to dividends or upon liquidation, or call for redemption, redeem, purchase or otherwise acquire for consideration any Common Shares or any other such junior shares (except by conversion into or exchange for shares of the Fund ranking junior to the MRP Shares as to dividends and upon liquidation) or any such parity shares (except by conversion into or exchange for shares of the Fund ranking junior to or on a parity with the MRP Shares as to dividends and upon liquidation), unless (1) immediately after such transaction the Fund would satisfy the MRP Shares Asset Coverage Test, (2) full cumulative dividends on the MRP Shares due on or prior to the date of the transaction have been declared and paid to the holders of MRP Shares, and (3) the Fund has redeemed the full number of MRP Shares required to be redeemed by any provision for mandatory redemption contained in Section 3(a) or deposited sufficient monies with the Paying Agent for that purpose (without regard to the provisions of the Special Proviso); provided that the Fund may make any distributions reasonably necessary for the Fund to continue to qualify as a "regulated investment company" under Subchapter M of the Internal Revenue Code and to avoid excise tax under Section 4982 of the Internal Revenue Code ("Tax Required Payments"). For the avoidance of doubt, any such Tax Required Payments would only be paid to holders of Common Shares after full cumulative dividends due on or prior to the date of the applicable distribution and any mandatory redemptions occurring on or prior to the date of the applicable distribution have been paid to the holders of Preferred Shares.

The terms of the MRP Shares and rights and preferences of the holders of the MRP Shares are set forth in the Statement of Preferences of Series B Mandatory Redeemable Preferred Shares, Series C Mandatory Redeemable Preferred Shares, Series D Mandatory Redeemable Preferred Shares, and Series E Mandatory Redeemable Preferred Shares of the Fund.

Redemption. The terms of the MRP Shares provide that: (i) the Fund may redeem the MRP Shares at its option at the liquidation preference plus accrued and unpaid dividends and plus a make-whole premium, subject to notice and other requirements; (ii) the Fund is required to redeem the MRP Shares upon failure to satisfy the MRP Shares Asset Coverage Test (tested monthly) or MRP Shares Overcollateralization Test (tested weekly), subject to cure periods; and (iii) the Fund is required to redeem the MRP Shares on the term redemption date of September 6, 2024 for the Series B MRP Shares, September 6, 2027 for the Series C MRP Shares, August 24, 2026 for the Series D MRP Shares, and May 24, 2027 for the Series E MRP Shares.

Voting Rights. Except as otherwise required in the prospectus, the governing documents of the Fund, or as otherwise required by applicable law, the Fund's preferred shareholders, including the MRP Shares, have one vote per share and vote together with the Fund's common shareholders as a single class. The 1940 Act grants the holders of preferred stock the right to elect at least two Trustees at all times (the "Preferred Share Trustees") and the remaining Trustees will be elected by the holders of common stock and preferred stock voting as a single class. Except during any time when the Fund has failed to make a dividend or redemption payment in respect of MRP Shares outstanding, the holders of MRP Shares have agreed to vote in accordance with the recommendation of the Board of Trustees on any matter submitted to them for their vote or to the vote of shareholders of the Fund generally.

With respect to the MRP Shares, William R. Rybak and Virginia G. Breen were designated by the Board of Trustees as the Preferred Share Trustees of the Fund. As of September 6, 2022, there were five other Trustees of the Fund, Ms. Stuckey and Messrs. Calamos, Neal, Toub and Wennlund. See "Management of the Fund" in the Fund's statement of additional information. The Fund's preferred shareholders, including the MRP Shareholders, are entitled to elect a majority of the Trustees of the Fund during any period when (i) at least two years' accumulated dividends on the preferred stock are due and unpaid or (ii) the preferred shares are otherwise entitled under the 1940 Act to elect a majority of the Trustees of the Fund. The MRP Shareholders have certain additional customary voting rights pursuant to the MRP Shares governing documents and the 1940 Act.

The summary information regarding the MRP Shares contained herein is qualified in its entirety by reference to the Statement of Preferences and other documents related to the terms and conditions and the offering of the MRP Shares.

The section titled "Effects of Leverage" beginning on page 57 of the Prospectus is deleted in its entirety and replaced with the following:

The SSB Agreement provides for credit availability for the Fund, such that it may borrow up to $480 million. As of September 6, 2022, the Fund had utilized $365 million of the $480 million available under the SSB Agreement ($207 million in borrowings outstanding, and $158 million in structural leverage consisting of collateral received from SSB in connection with securities on loan), representing 26.7% of the Fund's managed assets as of that date, and had $145 million of MRP Shares outstanding, representing 10.6% of the Fund's managed assets. Combined, the borrowings under the SSB Agreement and the outstanding MRP Shares represented 37.3% of the Fund's managed assets. Interest on the SSB Agreement is charged on the drawn amount at the rate of the Overnight Bank Financing Rate (“OBFR”) plus 0.80%, payable monthly in arrears. Interest on overdue amounts or interest on the drawn amount paid during an event of default will be charged at OBFR plus 2.80%. These rates represent floating rates of interest that may change over time. The SSB Agreement has a commitment fee of 0.10% of any undrawn amount. As of September 6, 2022, the interest rate charged under the SSB Agreement was 3.12%. "Net income" payments related to cash collateral in connection with securities lending were 1.56% of the borrowed amount on an annualized basis as of that date, although this amount can vary based on changes in underlying interest rates.

The Fund's MRP Shareholders are entitled to receive monthly cash dividends, at a currently effective dividend rate per annum for each series of MRP Shares as follows (subject to adjustment as described above in "Mandatory Redeemable Preferred Shares"): 4.00% for Series B MRP Shares, 4.24% for Series C MRP Shares, 2.45% for Series D MRP Shares, and 2.68% for Series E MRP Shares.

To cover the interest expense on the borrowings under the SSB Agreement (including "net income" payments made with respect to borrowings offset by collateral for securities on loan) and the dividend payments associated with the MRP Shares, based on rates in effect on September 6, 2022, the Fund's portfolio would need to experience an annual return of 2.27% (before giving effect to expenses associated with senior securities).

Leverage is a speculative technique that could adversely affect the returns to common shareholders. Leverage can cause the Fund to lose money and can magnify the effect of any losses. To the extent the income or capital appreciation derived from securities purchased with funds received from leverage exceeds the cost of leverage, the Fund's return will be greater than if leverage had not been used. Conversely, if the income or capital appreciation from the securities purchased with such funds is not sufficient to cover the cost of leverage or if the Fund incurs capital losses, the return of the Fund will be less than if leverage had not been used, and therefore the amount available for distribution to common shareholders as dividends and other distributions will be reduced or potentially eliminated.

The Fund will pay, and common shareholders will effectively bear, any costs and expenses relating to any borrowings and to the issuance and ongoing maintenance of preferred shares, including the MRP Shares, or debt securities. 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.

Certain types of borrowings may result in the Fund being subject to covenants in credit agreements, including those relating to asset coverage, borrowing base and portfolio composition requirements and additional covenants that may affect the Fund's ability to pay dividends and distributions on common shares in certain instances. The Fund may also be required to pledge its assets to the lenders in connection with certain types of borrowings. The Fund may be subject to certain restrictions on investments imposed by guidelines of and covenants with rating agencies for the preferred shares or short-term debt instruments issued by the Fund. These guidelines and covenants may impose asset coverage or portfolio composition requirements that are more stringent than those imposed by the 1940 Act.

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.

The following table illustrates the hypothetical effect on the return to a holder of the Fund's common shares of the leverage obtained by us (and utilized on September 6, 2022). The purpose of this table is to assist you in understanding the effects of leverage. As the table shows, leverage generally increases the return to common shareholders when portfolio return is positive and greater than the cost of leverage and decreases the return when the portfolio return is negative or less than the cost of leverage. The figures appearing in the table are hypothetical and actual returns may be greater or less than those appearing in the table.

Assumed Portfolio Return (Net of Expenses)	(10.00	)%	(5.00	)%	0.00	%	5.00	%	10.00	%
Corresponding Common Share Return(1)	(18.57	)%	(10.62	)%	(2.67	)%	5.28	%	13.23	%

(1) Includes interest expense on the borrowings under the SSB Agreement, accrued at interest rates in effect on September 6, 2022 of 3.12%, and dividend expense on the MRP Shares.

For further information about leveraging, see "Risk Factors — Fund Risks — Leverage Risk."

The second and third paragraphs under the section titled "Description of Securities" beginning on page 109 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 and debt securities. As of September 6, 2022, the Fund had 75,553,514 common shares outstanding and MRP Shares outstanding in the following amounts: 1,460,000 Series B MRP Shares, 1,480,000 Series C MRP Shares, 1,400,000 Series D MRP Shares, and 1,460,000 Series E MRP Shares. As of such date, the Fund had not issued any debt securities. Subject to the restrictions under the 1940 Act, the Board of Trustees may, from time to time, establish additional series or classes of Fund shares and set forth 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 but the Board may not change any outstanding shares in a manner materially adverse to such shareholders. The Board of Trustees, without shareholder approval but subject to the governing documents of the Fund and the MRP Shares, is authorized to amend the Agreement and Declaration of Trust and By-Laws to reflect the terms of any such class or series.

As of September 6, 2022, the Fund had total leverage of approximately $510 million representing approximately 37.3% 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 SSB Agreement are secured by assets of the Fund that are held with the Fund's custodian in a separate account. Interest on the SSB Agreement is charged on the drawn amount at the rate of OBFR plus 0.80%, payable monthly in arrears. Interest on overdue amounts or interest on the drawn amount paid during an event of default will be charged at OBFR plus 2.80%. The SSB Agreement has a commitment fee of 0.10% of any undrawn amount. As of September 6, 2022, the interest rate charged under the SSB Agreement was 3.12%. Prior to January 1, 2022, the reference rate used by the SSB Agreement was Overnight LIBOR.

II. Further Revisions to Disclosure

All disclosure in the Fund's Prospectus, SAI and Prospectus Supplement not specifically referenced above is hereby amended to the extent necessary to conform to the information provided in this supplement.

Please retain this supplement for future reference.

XML

N-2

Sep. 30, 2022

USD ($)

shares

Cover [Abstract]

Entity Central Index Key

0001222719

Amendment Flag

false

Document Type

424B3

Entity Registrant Name

Calamos Convertible and High Income Fund

Fee Table [Abstract]

Shareholder Transaction Expenses [Table Text Block]

Shareholder Transaction Expenses
Sales Load (as a percentage of offering price)		1.00	%(1)
Offering Expenses Borne by the Fund (as a percentage of offering price)		—	%(2)
Dividend Reinvestment Plan Fees (per sales transaction fee)(3)	$	15.00

Sales Load [Percent]

1.00%

^[1]

Dividend Reinvestment and Cash Purchase Fees | $

$ 15

^[2]

Other Transaction Expenses [Abstract]

Other Transaction Expenses [Percent]

0.00%

^[3]

Annual Expenses [Table Text Block]

Annual Expenses	Percentage of Average Net Assets Attributable to Common Shareholders
Management Fee(4)		1.25	%
Interest Payments on Borrowed Funds(5)		0.36	%
Preferred Stock Dividend Payments(6)		0.58	%
Other Expenses(7)		0.08	%
Total Annual Expenses		2.27	%

Management Fees [Percent]

1.25%

^[4]

Interest Expenses on Borrowings [Percent]

0.36%

^[5]

Dividend Expenses on Preferred Shares [Percent]

0.58%

^[6]

Other Annual Expenses [Abstract]

Other Annual Expenses [Percent]

0.08%

^[7]

Total Annual Expenses [Percent]

2.27%

Expense Example [Table Text Block]

The following example illustrates the expenses that common shareholders would pay on a $1,000 investment in common shares, assuming (1) net annual expenses of 2.27% of net assets attributable to common shareholders; (2) a 5% annual gross return; and (3) all distributions are reinvested at net asset value:

	1 Year		3 Years		5 Years		10 Years
Total Expenses Paid by Common Shareholders(8)	$	33	$	80	$	130	$	268

The example should not be considered a representation of future expenses. Actual expenses may be greater or less than those assumed. Moreover, our actual rate of return may be greater or less than the hypothetical 5% return shown in the example.

Expense Example, Year 01 | $

$ 33

^[8]

Expense Example, Years 1 to 3 | $

80

^[8]

Expense Example, Years 1 to 5 | $

130

^[8]

Expense Example, Years 1 to 10 | $

$ 268

^[8]

Purpose of Fee Table , Note [Text Block]

The following table and example contain information about the costs and expenses that common shareholders will bear directly or indirectly. In accordance with Commission requirements, the table below shows our expenses, including interest payments on borrowed funds, as a percentage of our average net assets as of September 6, 2022, and not as a percentage of gross assets or managed assets.

By showing expenses as a percentage of average net assets, expenses are not expressed as a percentage of all of the assets we invest. The table and example are based on our capital structure as of September 6, 2022. As of September 6, 2022, we had $207 million in borrowings outstanding, $145 million in outstanding preferred shares and additional structural leverage of $158 million, collectively representing 37.3% of managed assets as of that date.

Basis of Transaction Fees, Note [Text Block]

as a percentage of offering price

Management Fee not based on Net Assets, Note [Text Block]

The Fund pays Calamos an annual management fee, payable monthly in arrears, for its investment management services in an amount equal to 0.80% of the Fund's average weekly managed assets. In accordance with the requirements of the Commission, the table above shows the Fund's management fee as a percentage of average net assets attributable to common shareholders. By showing the management fee as a percentage of net assets, the management fee is not expressed as a percentage of all of the assets the Fund intends to invest. For purposes of the table, the management fee has been converted to 1.25% of the Fund's average weekly net assets as of September 6, 2022 by dividing the total dollar amount of the management fee by the Fund's average weekly net assets (managed assets less outstanding leverage).

General Description of Registrant [Abstract]

Effects of Leverage [Text Block]

The SSB Agreement provides for credit availability for the Fund, such that it may borrow up to $480 million. As of September 6, 2022, the Fund had utilized $365 million of the $480 million available under the SSB Agreement ($207 million in borrowings outstanding, and $158 million in structural leverage consisting of collateral received from SSB in connection with securities on loan), representing 26.7% of the Fund's managed assets as of that date, and had $145 million of MRP Shares outstanding, representing 10.6% of the Fund's managed assets. Combined, the borrowings under the SSB Agreement and the outstanding MRP Shares represented 37.3% of the Fund's managed assets. Interest on the SSB Agreement is charged on the drawn amount at the rate of the Overnight Bank Financing Rate (“OBFR”) plus 0.80%, payable monthly in arrears. Interest on overdue amounts or interest on the drawn amount paid during an event of default will be charged at OBFR plus 2.80%. These rates represent floating rates of interest that may change over time. The SSB Agreement has a commitment fee of 0.10% of any undrawn amount. As of September 6, 2022, the interest rate charged under the SSB Agreement was 3.12%. "Net income" payments related to cash collateral in connection with securities lending were 1.56% of the borrowed amount on an annualized basis as of that date, although this amount can vary based on changes in underlying interest rates.

The Fund's MRP Shareholders are entitled to receive monthly cash dividends, at a currently effective dividend rate per annum for each series of MRP Shares as follows (subject to adjustment as described above in "Mandatory Redeemable Preferred Shares"): 4.00% for Series B MRP Shares, 4.24% for Series C MRP Shares, 2.45% for Series D MRP Shares, and 2.68% for Series E MRP Shares.

To cover the interest expense on the borrowings under the SSB Agreement (including "net income" payments made with respect to borrowings offset by collateral for securities on loan) and the dividend payments associated with the MRP Shares, based on rates in effect on September 6, 2022, the Fund's portfolio would need to experience an annual return of 2.27% (before giving effect to expenses associated with senior securities).

Leverage is a speculative technique that could adversely affect the returns to common shareholders. Leverage can cause the Fund to lose money and can magnify the effect of any losses. To the extent the income or capital appreciation derived from securities purchased with funds received from leverage exceeds the cost of leverage, the Fund's return will be greater than if leverage had not been used. Conversely, if the income or capital appreciation from the securities purchased with such funds is not sufficient to cover the cost of leverage or if the Fund incurs capital losses, the return of the Fund will be less than if leverage had not been used, and therefore the amount available for distribution to common shareholders as dividends and other distributions will be reduced or potentially eliminated.

The Fund will pay, and common shareholders will effectively bear, any costs and expenses relating to any borrowings and to the issuance and ongoing maintenance of preferred shares, including the MRP Shares, or debt securities. 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.

Certain types of borrowings may result in the Fund being subject to covenants in credit agreements, including those relating to asset coverage, borrowing base and portfolio composition requirements and additional covenants that may affect the Fund's ability to pay dividends and distributions on common shares in certain instances. The Fund may also be required to pledge its assets to the lenders in connection with certain types of borrowings. The Fund may be subject to certain restrictions on investments imposed by guidelines of and covenants with rating agencies for the preferred shares or short-term debt instruments issued by the Fund. These guidelines and covenants may impose asset coverage or portfolio composition requirements that are more stringent than those imposed by the 1940 Act.

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.

The following table illustrates the hypothetical effect on the return to a holder of the Fund's common shares of the leverage obtained by us (and utilized on September 6, 2022). The purpose of this table is to assist you in understanding the effects of leverage. As the table shows, leverage generally increases the return to common shareholders when portfolio return is positive and greater than the cost of leverage and decreases the return when the portfolio return is negative or less than the cost of leverage. The figures appearing in the table are hypothetical and actual returns may be greater or less than those appearing in the table.

Assumed Portfolio Return (Net of Expenses)	(10.00	)%	(5.00	)%	0.00	%	5.00	%	10.00	%
Corresponding Common Share Return(1)	(18.57	)%	(10.62	)%	(2.67	)%	5.28	%	13.23	%

(1) Includes interest expense on the borrowings under the SSB Agreement, accrued at interest rates in effect on September 6, 2022 of 3.12%, and dividend expense on the MRP Shares.

Annual Interest Rate [Percent]

3.12%

Effects of Leverage [Table Text Block]

Assumed Portfolio Return (Net of Expenses)	(10.00	)%	(5.00	)%	0.00	%	5.00	%	10.00	%
Corresponding Common Share Return(1)	(18.57	)%	(10.62	)%	(2.67	)%	5.28	%	13.23	%

Return at Minus Ten [Percent]

(18.57%)

^[9]

Return at Minus Five [Percent]

(10.62%)

^[9]

Return at Zero [Percent]

(2.67%)

^[9]

Return at Plus Five [Percent]

5.28%

^[9]

Return at Plus Ten [Percent]

13.23%

^[9]

Effects of Leverage, Purpose [Text Block]

The following table illustrates the hypothetical effect on the return to a holder of the Fund's common shares of the leverage obtained by us (and utilized on September 6, 2022). The purpose of this table is to assist you in understanding the effects of leverage. As the table shows, leverage generally increases the return to common shareholders when portfolio return is positive and greater than the cost of leverage and decreases the return when the portfolio return is negative or less than the cost of leverage. The figures appearing in the table are hypothetical and actual returns may be greater or less than those appearing in the table.

Capital Stock, Long-Term Debt, and Other Securities [Abstract]

Outstanding Securities [Table Text Block]

The following table provides information about our outstanding securities as of September 6, 2022:

Title of Class	Amount Authorized		Amount Held by the Fund for its Account		Amount Outstanding
Common Shares		Unlimited		75,553,514		80,724,440
MRPS-Series B		1,460,000		0		1,460,000
MRPS-Series C		1,480,000		0		1,480,000
MRPS-Series D		1,400,000		0		1,400,000
MRPS-Series E		1,460,000		0		1,460,000

Common Shares [Member]

Capital Stock, Long-Term Debt, and Other Securities [Abstract]

Outstanding Security, Title [Text Block]

Common Shares

Outstanding Security, Held [Shares]

75,553,514

Outstanding Security, Not Held [Shares]

80,724,440

Mandatory Redeemable Preferred Shares Series B [Member]

Capital Stock, Long-Term Debt, and Other Securities [Abstract]

Outstanding Security, Title [Text Block]

MRPS-Series B

Outstanding Security, Authorized [Shares]

1,460,000

Outstanding Security, Held [Shares]

0

Outstanding Security, Not Held [Shares]

1,460,000

Mandatory Redeemable Preferred Shares Series C [Member]

Capital Stock, Long-Term Debt, and Other Securities [Abstract]

Outstanding Security, Title [Text Block]

MRPS-Series C

Outstanding Security, Authorized [Shares]

1,480,000

Outstanding Security, Held [Shares]

0

Outstanding Security, Not Held [Shares]

1,480,000

Mandatory Redeemable Preferred Shares Series D [Member]

Capital Stock, Long-Term Debt, and Other Securities [Abstract]

Outstanding Security, Title [Text Block]

MRPS-Series D

Outstanding Security, Authorized [Shares]

1,400,000

Outstanding Security, Held [Shares]

0

Outstanding Security, Not Held [Shares]

1,400,000

Mandatory Redeemable Preferred Shares Series E [Member]

Capital Stock, Long-Term Debt, and Other Securities [Abstract]

Outstanding Security, Title [Text Block]

MRPS-Series E

Outstanding Security, Authorized [Shares]

1,460,000

Outstanding Security, Held [Shares]

0

Outstanding Security, Not Held [Shares]

1,460,000

[1] Represents the estimated commission with respect to the Fund's common shares being sold in this offering. There is no guarantee that there will be any sales of the Fund's common shares pursuant to this prospectus supplement and the accompanying prospectus. Actual sales of the Fund's common shares under this prospectus supplement and the accompanying prospectus, if any, may be less than as set forth under "Capitalization" above. In addition, the price per share of any such sale may be greater or less than the price set forth under "Capitalization" above, depending on the market price of the Fund's common shares at the time of any such sale.

[2] Shareholders will pay a $15.00 transaction fee plus a $0.02 per share brokerage charge if they direct Computershare Shareowner Services LLC (the "Plan Agent") to sell common shares held in an account of the Fund's Automatic Dividend Reinvestment Plan (the "Plan"). In addition, each participant will pay a pro rata share of brokerage commissions incurred with respect to the Plan Agent's open-market purchases in connection with the reinvestment of dividends or distributions. If a participant elects to have the Plan Agent sell part or all of his or her common shares and remit the proceeds, such participant will be charged his or her pro rata share of brokerage commissions on the shares sold. See "Dividends and Distributions on Common Shares; Automatic Dividend Reinvestment Plan" on page 103 of the accompanying prospectus.

[3] Calamos will pay the expenses of the offering (other than the applicable commissions). However, Calamos may recapture from the Fund previously paid offering expenses in an amount up to $200,000 per each 12-month period of the three-year duration of the offering beginning March 1, 2019, provided that the Fund has made sales resulting in net proceeds of $5 million from the offering during that 12-month period. In the event that the Fund does not achieve sales resulting in net proceeds of $5 million from the offering in that 12-month period, the $200,000 recapture amount will carry forward and be added to the total amount that Calamos can recapture from the Fund in the next 12-month period. The maximum amount that Calamos can recapture from the Fund during the duration of the offering is $600,000. The arrangement is hereinafter referred to as the "recapture provision." As of the date of this prospectus supplement and the accompanying prospectus, Calamos will pay all of the expenses associated with the offering (other than the applicable commissions). If the recapture provision is triggered in the future, such expenses that will be borne by Fund shareholders will be set forth in the "Shareholder Transaction Expenses" table above.

[4] The Fund pays Calamos an annual management fee, payable monthly in arrears, for its investment management services in an amount equal to 0.80% of the Fund's average weekly managed assets. In accordance with the requirements of the Commission, the table above shows the Fund's management fee as a percentage of average net assets attributable to common shareholders. By showing the management fee as a percentage of net assets, the management fee is not expressed as a percentage of all of the assets the Fund intends to invest. For purposes of the table, the management fee has been converted to 1.25% of the Fund's average weekly net assets as of September 6, 2022 by dividing the total dollar amount of the management fee by the Fund's average weekly net assets (managed assets less outstanding leverage).

[5] Reflects interest expense paid on $165 million in average borrowings under the Fund's Amended and Restated Liquidity Agreement with State Street Bank and Trust Company, plus $158 million in additional average structural leverage related to certain securities lending programs, as described in the accompanying prospectus under "Leverage."

[6] Reflects estimated dividend expense on $145 million aggregate liquidation preference of mandatory redeemable preferred shares ("MRP Shares" or "MRPS") outstanding. See "Prospectus Summary — Use of Leverage by the Fund" and "Leverage" in the accompanying prospectus for additional information.

[7] "Other Expenses" are based on estimated amounts for the Fund's current fiscal year.

[8] The example includes sales load and estimated offering costs.

[9] Includes interest expense on the borrowings under the SSB Agreement, accrued at interest rates in effect on September 6, 2022 of 3.12%, and dividend expense on the MRP Shares.