What is the average life of a pool of $30-$year fixed$-$rate mortgages? What is the average life of a pool of $30-$year adjustable rate mortgages? What happens to the $$average life$$ of a pool of mortgages when prepayment speed increases? Why does prepayment speed increase when interest rates decrease $?$ Discuss the negative convexity exhibited by mortgage$-$backed $$passthrough$$ certificates in the context of duration and pre$-$payment speed.