ROPES & GRAY LLP 1211 AVENUE OF THE AMERICAS NEW YORK, NY 10036-8704 WWW.ROPESGRAY.COM

January 7, 2016	Crystal T. Travanti
	T +1 212 596 9128
	F +1 646 728 1622
	crystal.travanti@ropesgray.com

VIA EDGAR

Division of Investment Management

Securities and Exchange Commission

100 F Street NE

Washington, DC 20549

Attention: Jay Williamson

Re: Calamos Convertible and High Income Fund (the “Registrant” or the “Fund”) Registration Statement on Form N-2 Filed on July 13, 2015, File No. 333-205640

Dear Mr. Williamson:

This letter is in response to the comments we received from you on August 11, 2015, regarding the Registrant’s registration statement on Form N-2 filed on July 13, 2015. The registration statement relates to the registration and offering of common shares, preferred shares, and debt securities pursuant to Rule 415 under the Securities Act of 1933, as amended (the “Securities Act”).

The comments, together with the Registrant’s responses, are set forth below.

Calculation of Registration Fee Under the Securities Act of 1933

1. Comment: The Fee Table indicates that you are registering preferred shares. Please advise whether you intend to offer preferred within 12 months of effectiveness of the registration statement. If so, please include disclosure of the consequences to common shareholders of the issuance of preferred, e.g., subordination, diminished voting power, increased expense ratio; and provide appropriate fee table disclosure.

Response: The Registrant does not anticipate offering preferred shares within 12 months of the effective date of the registration statement.

Prospectus Cover Page

2. Comment: Please confirm that you will include the table required by Item 1.4 of Form N-2 in any prospectus supplement you use.

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Response: The Registrant does not anticipate providing an overallotment option to any underwriter in connection with the proposed offering. If it nonetheless grants an overallotment option, the Registrant would expect to include the referenced table.

3. Comment: We note you disclose your share price on the cover page. Please disclose your NAV as of the same date.

Response: The Registrant will make the requested change in its next pre-effective amendment.

Prospectus Summary, page 1

4. Comment: The Summary you provide is approximately 14 pages long and contains information that is substantially repeated elsewhere, too detailed for a summary, or of questionable relevance. For example, much of the discussion under “Fund Risks” on page seven could be truncated as the disclosure is repeated elsewhere, and the disclosure about your Managed Dividend Policy does not appear relevant enough for a summary, if you have no intention of adopting such a policy. Please revise your Summary to more concisely focus on the material aspects of your business and offering. See Rule 421 under the Securities Act and the General Instructions to Form N-2.

Response: The Registrant will revise the Summary with the intent of describing more concisely the material aspects of the offering.

5. Comment: On page four you state that “[u]nder normal circumstances, the Fund invests at least 80% of its managed assets in a diversified portfolio of convertible securities and below investment grade (high yield/high risk) non-convertible debt securities.” Please replace the reference to “managed assets” with “net assets, plus borrowings for investment purposes” or advise why your statement is appropriate.

Response: The Registrant believes its statement of policy is appropriate. The Registrant defines “managed assets” to mean the total assets of the Fund (including any assets attributable to any leverage that may be outstanding) minus the sum of liabilities (other than debt representing financial leverage), which is the substantial equivalent of “net assets, plus borrowings for investment purposes.”

6. Comment: We note the disclosure on page 12 and elsewhere discussing “Recent Market Events.” The focus of this disclosure appears to be on events currently taking place within the European Union; however, based on your website, approximately 90% of your exposure is in the United States and you have a 10% sector weighting in Energy. Please update your “Recent Market Events” discussion to address how recent events impact or may impact your portfolio. For example, your revised disclosure might address trends in oil and natural gas

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prices and how they relate to the credit quality of the energy sector bonds included in your portfolio.

Response: The Registrant has reviewed the disclosure and will make a number of disclosure enhancements to address the Staff’s comment in its next pre-effective amendment.

7. Comment: Please add summary risk disclosure under “Additional Risks to Common Shareholders” to address the risks associated with the potential issuance of preferred shares. Please provide more detailed disclosures in your Risk Factors.

Response: The Registrant refers the Staff to summary risk disclosure in the section titled “Leverage Risk” beginning on page 9 of the prospectus, which addresses the risks associated with the potential issuance of preferred shares to holders of common shares. Additionally, the Registrant refers the Staff to the Risk Factor titled “Leverage Risk” beginning on page 32 of the prospectus, which also addresses the risks associated with the potential issuance of preferred shares to holders of common shares.

8. Comment: To the extent material and appropriate, please revise the discussion under Investment Policies and Fund Risks to address whether you predominately borrow and/or invest at fixed or floating interest rates.

Response: The Registrant respectfully refers the Staff to the section entitled “Leverage – Effects of Leverage” where the Registrant provides the formulas that determine the interest rate payable on the Fund’s credit facilities, which are each based on a London Inter-bank Offered Rate (LIBOR). Registrant intends to enhance its disclosure in its next pre-effective amendment to state expressly that those rates represent floating rates of interest that may change over time.

Financial Highlights, page 16

9. Comment: Please advise whether you will present the Senior Securities table required by Item 4.3 of Form N-2. If not, please explain why.

Response: The Registrant will present the referenced table in its next pre-effective amendment.

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Leverage, page 25

10. Comment: On page 25 you state that you “generally will not issue preferred shares or debt securities …” unless you expect to achieve greater returns as a result of such leverage. Your registration statement suggests that you may issue preferred at any time. Please revise the disclosure throughout the filing to reflect the issuance of preferred shares at this time.

Response: The Registrant respectfully submits that the statements are not inconsistent, but Registrant intends to make a number of clarifying disclosure changes in its next pre-effective amendment.

Dividends and Distributions on Common Shares; Automatic Dividend Reinvestment Plan, page 52

11. Comment: We note the disclosure on page 53 that you make regularly monthly distributions to shareholders and “[t]he sources of these distributions may include net investment income, capital gain, and return of capital.” In places where you refer to a return of capital, please clarify that: (a) distributions representing a return of capital are not dividends, but rather are a return of the money that an investor originally invested; and (b) while returns of capital may not be immediately taxable, they reduce basis, which may result in an investor having to pay higher taxes in the future when shares are sold, even if the investor sells the shares at a loss from the original investment.

Response: The Registrant refers the Staff to disclosure in the section titled “Certain Federal Income Tax Matters – Federal Income Taxation of Common and Preferred Shares – Federal Income Tax Treatment of Common Share Distributions,” beginning on page 45 of the prospectus, which explains that a “distribution of an amount in excess of the Fund’s current and accumulated earnings and profits, if any, will be treated by a shareholder as a tax-free return of capital, which is applied against and reduces the shareholder’s basis in his, her or its shares.” That section further states that “to the extent that the amount of any such distribution exceeds a shareholder’s basis in his, her or its shares, the excess will be treated by the shareholder as a gain from the sale or exchange of shares, and thus, could potentially subject the shareholder to capital gains taxation in connection with the later sale of Fund shares, even if those shares are sold at a price that is lower than the shareholder’s original investment price.” However, the Registrant will enhance the disclosure in the registration statement to clarify that distributions representing a return of capital are not dividends, where appropriate, in its next pre-effective amendment

Description of Securities, page 57

12. Comment: In your response letter, please describe the types of debt that the Fund contemplates offering through this registration statement. Additionally, undertake to advise

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us in advance of any proposed debt offering pursuant to this registration statement and to provide for staff review the preliminary prospectus supplement relating to any debt offering by the Fund. Further undertake to clear all staff comments prior to the commencement of any such debt offering whenever the preliminary prospectus supplement materially differs from the form of prospectus supplement included in this registration statement at the time of effectiveness.

In this regard, please note that the prospectus supplement should, as applicable:

• Disclose that currently none of the Fund’s indebtedness is subordinated to the debt securities. It should also disclose whether there is a current intention to issue indebtedness that expressly provides that it is subordinated to the debt securities.

• Disclose that the debt securities are “structurally subordinated” and are “effectively subordinated” to all existing and future indebtedness of the Fund and other obligations of its subsidiaries, financing vehicles and similar facilities. The significance of the debt securities being structural subordinated and effectively subordinated should be explained in plain English, specifically highlighting how such subordination affects the rights and priorities of the holders of the debt securities. Also, disclose the approximate total dollar amount of all liabilities and obligations to which the debt securities being offered are structurally subordinated and effectively subordinated.

• Refrain from using the word “senior” in the title of any debt securities issued by the Fund, or when describing/identifying their ranking, if the debt securities are not contractually senior in right of repayment to all of the other outstanding obligations of the Fund. Even where the Fund’s debt securities are contractually senior in right of repayment to all of the other outstanding obligations of the Fund, refrain from referring to the debt securities as “senior” when they are also are structurally subordinated to the obligations of the Fund’s subsidiaries, financing vehicles and similar facilities.

• Disclose that the debt securities will not be subject to any sinking fund and explain the significance thereof; for example, state that no amounts will be set aside for the express purpose of repayment of principal and any unpaid interest on the debt securities, and that repayment of the debt securities will depend upon the financial condition of the Fund and its subsidiaries as they exist as of the maturity date of the debt securities.

Response: The Registrant does not anticipate offering debt securities within 12 months of the effective date of this registration statement. The Registrant undertakes to advise the Staff of any debt offering pursuant to this registration statement and intends to provide the preliminary prospectus to the Staff, as requested.

Preferred Shares, page 59

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13. Comment: Consistent with our comments above, please move forward and prominently disclose the following statements about your preferred shares:

• “[T]he holders of preferred shares will be entitled to receive a preferential liquidating distribution, which is expected to equal the original purchase price per preferred share plus accumulated and unpaid dividends, whether or not declared, before any distribution of assets is made to holders of common shares.”

• “The 1940 Act requires that the holders of any preferred shares, voting separately as a single class, have the right to elect at least two Trustees at all times. The remaining Trustees will be elected by holders of common shares and preferred shares, voting together as a single class.”

• “[T]he holders of any preferred shares have the right to elect a majority of the Trustees at any time two years’ accumulated dividends on any preferred shares are unpaid.”

Response: The Registrant intends to revise the disclosure consistent with the requested changes in its next pre-effective amendment.

Plan of Distribution, page 65

14. Comment: Please confirm to the staff in your response letter that the Fund will submit any underwritten offering to FINRA for its prior approval of the underwriting terms.

Response: The Registrant confirms that it or the relevant underwriters subject to FINRA regulation intend to submit the terms of any underwriting of the Registrant’s securities to FINRA for review as required by applicable law.

15. Comment: In your response letter, undertake to include in any prospectus supplement, as applicable, under a section captioned “Additional Underwriter Compensation” a description of the terms of any agreement that the Fund will have entered into with the underwriters or their affiliates in connection with any offering, and specify the nature of the services that the underwriters or their affiliates have provided or will provide thereunder. Further undertake to disclose whether any such fee payable thereunder is a one-time fee or whether it is payable annually. Also undertake to file all such agreements as exhibits in a post-effective amendment to the registration statement.

Response: The Registrant undertakes to disclose the material facts known to it regarding any of the referenced obligations into which it may enter and to comply with the applicable requirements of Form N-2, including with respect to the inclusion of exhibits.

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Statement of Additional Information

Investment Restrictions, page S-19

16. Comment: We note the statement that the Fund may not concentrate its investments in securities of companies in any particular industry as defined in the 1940 Act. Please note that Item 17 of Form N-2 refers to concentration of investments in a particular industry or groups of industries. Please revise if possible.

Response: The Registrant respectfully submits that the referenced disclosure correctly reflects its fundamental policy that cannot be changed without approval of shareholders. The Registrant does not have a policy to maintain an investment concentration in any group of industries.

Part C

Exhibits

17. Comment: We note you are registering debt securities and propose to include a “form of” note and an indenture. Please also file a Statement of Eligibility of Trustee on Form T-1 or advise why none is required. For guidance, please consider Trust Indenture Act Interpretation No. 201.04 and 206.01 available at http://www.sec.gov/divisions/corpfin/guidance/tiainterp.htm.

Response: As noted in response to comment 12 above, the Registrant does not anticipate offering debt securities within 12 months of the effective date of this registration statement, and as such, pursuant to Section 305(b)(2) of the Trust Indenture Act of 1939, as amended, intends to designate a trustee on a delayed basis and file a State of Eligibility of Trustee on Form T-1 separately prior to any future offering of debt securities.

18. Comment: We note that you will file several exhibits, including your legality opinion, in a subsequent amendment. Please note that we review and comment upon the exhibits. Please allow for sufficient time for us to do so.

Response: The Registrant notes the Staff’s comment and intends to file the referenced exhibits in one or more additional pre-effective amendments for the Staff’s review.

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Accounting Comments

Prospectus

19. Comment: Fee table and other financial information are currently incomplete. We may have more comments once the information is included.

Response: The Registrant intends to complete the fee table and provide other financial information in one or more additional pre-effective amendments.

Website

20. Comment: The expense ratio listed on the website and fund fact sheet is calculated using managed assets:

Expense Ratio (based upon managed assets) 1.09%

The expense ratio from the 4/30/15 financial highlights was 1.52%. Please update the website to include the expense ratio calculated using net assets. The website expense ratios should tie to the financial statements and the fee table. This comment applies to all funds with leverage.

Response: The Registrant intends to revise the disclosure consistent with the Staff’s comment.

Financial Statements filed on Form N-CSR

21. Comment: The Report of Independent Registered Public Accounting Firm should include the city and state where the auditor practices. See paragraph .40 of AU-C, Forming an Opinion and Reporting on Financial Statements, section 700.

Response: The Registrant notes the Staff’s comment and has passed the comment on to its independent auditors.

* * * * *

On behalf of the Registrant, we hereby state the following:

1. The Registrant acknowledges that should the Securities and Exchange Commission (“Commission”) or the Staff, acting pursuant to delegated authority, declare the filing effective, it does not foreclose the Commission from taking any action with respect to the filing;

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2. The Registrant acknowledges that the action of the Commission or of the Staff, acting pursuant to delegated authority, in declaring the filing effective, does not relieve the Registrant from its full responsibility for the adequacy and accuracy of the disclosure in the filing; and

3. The Registrant acknowledges that it may not assert Staff comments and the declaration of effectiveness as a defense in any proceeding initiated by the Commission or any person under the federal securities laws of the United States.

* * * * *

We believe that this submission fully responds to your comments. Please feel free to call me at (212) 596-9128 if you have any questions regarding the foregoing.

Very truly yours,

/s/ Crystal T. Travanti

Crystal T. Travanti

cc: John P. Calamos, Sr., Calamos Advisors LLC

Christopher Russell, Calamos Investments LLC

Jeremy C. Smith, Ropes & Gray LLP