CHY Calamos Convertible and High Income Fund

CALAMOS® CONVERTIBLE AND HIGH INCOME FUND

(THE “FUND”)

Supplement dated December 17, 2020 to the

Prospectus dated February 28, 2020,

as supplemented March 4, 2020

Effective immediately, the fourth paragraph in the section titled “Mandatory Redeemable Preferred Shares” on page 36 is hereby deleted and replaced with the following:

Effective December 17, 2020, Kroll Bond Rating Agency LLC (“Kroll”) replaced Fitch Ratings, Inc. (“Fitch”) as the rating agency for the MRP Shares. The MRP Shares have been assigned a rating of ‘AA-’ by Kroll. If the ratings of the MRP Shares are downgraded, the Fund’s dividend expense may increase, as described below.

Please retain this supplement for future reference.

CHYSUP 12/20