Bank asks for personal details by phone - security risk?

Didn't realise this was an option. Any idea where to navigate on android to select this option?

Does it confirm to the caller the reason their call has been rejected?
 
Didn't realise this was an option. Any idea where to navigate on android to select this option?

Does it confirm to the caller the reason their call has been rejected?

I've a Samsung Galaxy.

Call Settings >> Call rejection >> Auto reject list

I was playing with it and temporarily blocked my own landline as a test. When I then rang from the landline, it went straight to voice-mail. Although the phone didn't ring, it did appear as a missed call.
 
I use a free app called Blacklist Plus. It does not show blocked calls as missed calls.
 
Thanks to you both - will give those a try.
I have one solitary contact that calls me from a skype number - which shows up as "private number". Asking the obvious I'd imagine but presumably, there's no way of allowing this one and blocking all other private numbers?