An offer issued by a corporation to shareholders to purchase more shares of the corporation's stock (usually at a discount). Renounceable rights have a value and can be traded. Taobiz explains Renounceable Right Stockholders that have received renounceable rights have three choices of what to do with the rights. They can act on the rights and buy more shares as per the particulars of the rights issue; they can sell them on the market; or they can pass on taking advantage of their rights.