to lower the mortgage rates the Fed can purchase agency MBS - likely they did in QE 1 2008

to lower the mortgage rates the Fed can purchase agency MBS - likely they did in QE 1 2008 buying mortgage backed securities raises their price and provides liquidity for dealers. this directly pushes down the yields expect some MBS QE to come in the near future

Ginnie & Fannie Mae conservatorship in Sept 2008 made agency MBS default risk free essentially, the US Treasury covers all losses from GNMA and FNMA up to $200 billion each from the total $400B budget ≈$170B are still available once exhausted it will surely be increased

Fed's balance sheet expansion with agency MBS reduced risks in liquidity, market depth and optionality/convexity this is a crucial point to understand - it wasn't just the Fed buying agency MBS, but the explicit government guarantee that accompanied it thus, the yields fell

optionality/convexity premium in mortgage backed securities is interesting when market yields fall the price should rise, but since borrowers take advantage of lower mortgage rates to make early payments - the price does not raise as much, due to lowered duration

raising yields means lower incentives to re-finance mortgages which reduces the amount of pre-payments thus, the duration increases when yields are raising - so even a higher price decrease

the duration formula for MBS assumes for some pre-payments if those happen at a smaller rate - the duration increases

legally mortgage backed securities are bonds since they are tradable debt securities but they're not a plain bond, due to the option of borrower's early repayment Macaulay or modified duration used for Treasuries doesn't work - you need effective/option-adjusted duration