[mcnees287]

Yes. FHA and the GSEs pool mortgages from banks, stamp them with their guarantee, and then sell the loan pools as MBS to investors.

(Most) banks, especially small ones, are unwilling to sell and hold a fixed rate 30 year mortgage. There's way too much risk, price volatility (driven by rates) and uncertainty about what will happen over a 30 year time period.

Banks only do a 30 year mortgage because they know they can sell it to FHA or the GSEs.