Securities that have a market value of zero. Worthless securities can include stocks or bonds that are either publicly traded or privately held. These securities result in a capital loss for the owner and can be claimed as such when filing taxes. The problem with declaring worthless securities as a loss for tax purposes is that you must sell securities before making this claim. Unfortunately, worthless securities are unsellable. Another difficulty comes from investors who own securities that they are not sure are totally worthless in a given year. If they go ahead and declare them as such and then they are deemed to have value the next year, taxpayers can file an amended return for the previous year and redeclare the loss the following year.