Buying a house for the parents

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As a first time home buyer, I want to buy a house for my parents before I purchase my own. The idea would be to pay 20% down and parents would pay the mortgage. I could then close on an FHA mortgage paying 3.5% down. Would I benefit from having the first house in my name in order to close the second deal? In other words, from a lender's perspective is it better to have the collateral or would lenders see it as too risky if my income could not cover 2 homes if something were to happen?