No, there is no formula for this; formula functions like ISCHANGED and PRIORVALUE only work in the context when a field value is transitioning from one value to another (i.e. during a DML update). Old values are not stored in the database (other than field history, which can't be used in a formula anyways).
The best you could do is create a text field called something like "Field Previous Value," then set a Process Builder/Workflow Rule that copies the prior value of the field to this second text field when the field changes. As a workflow example: "Evaluate when the following formula is true:
ISCHANGED(FieldName)" with a workflow field update "Previous Field Value set to formula