Are you moving them from a Broker you dont like to a new broker or convert them from stock to cash and then move the cash into another safer investment?

If none of the above apply then your mattress is a safer place.

Sell the stock Put the cash in the bank Safe at home

?? You sell it, then buy the "safer" stock. If you mean the pieces of paper, a bank safe deposit box is a good choice - but it costs money.