He is asking you as he's weighed up your family's wealth from observing you over the years.
It was really unwise to have allowed a sister to become professionally involved with your own academic supervisor for a lot of reasons, personal as well as professional.
Ideally I'd like to see your junior sibling removed from this academic's influence as soon as possible - any excuse, any story would do for me.
I feel though that you are leaving out a good share of the history between this academic and you. He certainly has enough information on your family to gauge your access to a significant sum of money - far more than any recent graduate could possibly have, college loans or not. And the professor wouldn't even dare raise such a proposition unless he felt that a high level of human trust existed between you all. I am wondering was la petite introduced to him while you were doing your MS or did she approach the professor after hearing a lot of "good things" (well, 'liberal' supervision and humor can attract a young career woman) about him in conversations with you.
You have allowed things to cross the line that should separate the professional and personal. It now involves a younger family member. And a request for significant investment (not a loan, mind) from your family. This should never happen.
The only way to avoid hurt to your own family - and ultimately to this professor as we all know how these 'investments' end up - is to dissociate yourself and la petite from him immediately.