Oversubscription rights are an optional choice to buy extra shares from the subscription that have not been exercised by other shareholders. In a lot of subscription offerings, shares remain unsold (mostly retail, investors that don't do the paperwork, forget about it, or don't understand it). Those unexercised shares often get offered to shareholders that are willing to exercise them - that way, the company makes sure, that they get the funds they want from the rights offering.
The interesting thing about an over subscription right is that it does not matter how many shares you own, it does only matter, how many shares and you are willing to subscribe to. So you can be feet to buy many shares via ovesubsciption right, even if you only own one share, and might get a lot of shares, if a lot of shareholders chose not to buy their allotment of shares.
Malone has used this in the past to increase his share of ownership by buying oversubscription shares. |