Worthless Securities have a market value of zero and, along with any securities that an investor has abandoned, result in a capital loss for the owner. They can be claimed as such when filing taxes.Abandoned securities are those which an investor has given up all hope of recovering any value from. This is different from selling the security at a loss, as there is no intention to ever recover the investment. Worthless securities are those where there is literally no market for them – they cannot be sold under any circumstances. As such, they have a value of zero and simply represent a wasted investment.Investors can claim both worthless securities and abandoned securities as capital losses on their taxes. This provides some measure of relief, though it will not make up for the entire loss suffered on the investment.