Answer
It is as safe as you want to make it. normally all transactional and personal details are encrypted and banks would wish to have a mass panic because their online banking site is unsafe.but if you want to start giving out passwords etc over any unsafe (ie not https) sites, are easily conned by fraudulent websites and like sending passwords by unsecured mails, then i guess it is not for you and the tin box under the bed option suddenly seems attractive.be sensible it is fine
