Absolute Minimum Down Payment - High Collateral

[Jure Miller]

Assume that I want to buy a non-owner-occupied property worth $200k.  Also assume I own a $800k property with a $300k mortgage on it (thus, it has $500k of equity).

If I was willing to pledge both the new property ($200k) and give the bank/lender a second mortgage on the owned one ($500k in equity), what would be the lowest down payment I could provide on the new ($200k) property?

I'd like the down payment to be 5-10% because obviously that improves the ROI of my project. From googling, it looks like the down payment will still need to be at least 15% but I don't understand why that is so: with all this collateral, the bank will easily recover all accreued principal, interest, and fees if I do not keep paying the mortgage.