Statement 1 is incorrect. A borrower who prepays a mortgage is in effect exercising a call option, similar to a corporate bond issuer who calls a bond and prepays the principal. Therefore the pool of mortgages and the securities created from it behave as if they had an embedded call feature.

Statement 2 is also incorrect. Sequential tranches issued as a collateralized mortgage obligation do not have proportionate claims on the cash flows from the pool. Instead they have sequential claims. The shortest-term tranche receives principal and interest payments until it is paid off. The cash flows then go to the second tranche until it is paid off, and so on. This structure allows securities with different timing and risk profiles to be issued from the same pool of certificates.