CALAMOS^® CONVERTIBLE AND HIGH INCOME FUND

(THE “FUND”)

Supplement dated November 1, 2018 to the

Statement of Additional Information dated March 1, 2018,

as supplemented on March 2, 2018 and July 23, 2018

Effectively immediately, the second paragraph in the section titled “Fund Accountant” is replaced in its entirety with the following paragraphs:

On October 12, 2018, the Board of Trustees approved terminating the financial accounting services agreement between the Calamos Funds and Calamos effective November 1, 2018. For the period November 1, 2017 through October 31, 2018, Calamos provided the following financial accounting services to the Calamos Funds: management of expenses and expense payment processing; monitoring of the calculation of expense accrual amounts for any fund and making of any necessary modifications; coordination of any expense reimbursement calculations and payment; calculation of yields on the funds in accordance with the SEC’s rules and regulations; calculation of net investment income dividends and capital gains distributions; calculation, tracking and reporting of tax adjustments on all assets of each fund, including but not limited to contingent debt and preferred trust obligations; preparation of excise tax and fiscal year distributions schedules; preparation of tax information required for financial statement footnotes; preparation of state and federal income tax returns; preparation of specialized calculations of amortization on convertible securities; preparation of year-end dividend disclosure information; monitoring of trustee deferred compensation plan accruals and valuations; and preparation of Form 1099 information statements for board members and service providers. For such services, Calamos received a fee payable monthly at the annual rate of 0.0175% on the first $1 billion of Combined Assets, 0.0150% on the next $1 billion, and 0.0110% on Combined Assets above $2 billion (“financial accounting service fee”). Each fund of the Calamos Funds paid its pro-rata share of the financial accounting service fee payable to Calamos based on relative managed assets of each fund.

Effective November 1, 2018, the Fund entered into an agreement with Ernst & Young LLP (“EY”) located at 155 N. Wacker Drive, Chicago, IL 60606 to provide certain tax services to the Funds. The tax services include the following: calculating, tracking and reporting tax adjustments on all assets of the Fund, including but not limited to contingent debt and preferred trust obligations; preparing excise tax and fiscal year distribution schedules; preparing tax information required for financial statement footnotes; preparing state and federal income tax returns; preparing specialized calculations of amortization on convertible securities; preparing year-end dividend disclosure information proving treaty-based foreign withholding tax reclaim services; providing certain global compliance and reporting services; providing a match service and analysis of the “passive foreign investment company status of foreign corporate entities; and providing services related to corporate actions that may or may not have a tax impact on the Fund’s holdings.

Effective November 1, 2018, the Fund entered into an agreement with State Street located at One Iron Street, Boston, MA 02111 pursuant to which State Street provides certain administration treasury services to the Fund. These services include: monitoring the calculation of expense accrual amounts for the Fund and making any necessary modifications; managing the Fund’s expenses and expense payment processing; coordinating any expense reimbursement calculations and payment; calculating net investment income dividends and capital gain distributions; coordinating the audits for the Fund; preparing financial reporting statements for the Fund; preparing certain regulatory filings; and calculating asset coverage tests for certain Calamos Funds.

Please retain this supplement for future reference