how slower prepayments affect PV

can someone plz help me understand the following? im trying to understand how slower prepayments on mortgages affect the PV of a mortgage portfolio: here’s the explanation that i don’t understand: there are two offsetting factors to the PV: 1) The slower prepayments causes the duration to extend to we are discounting for a longer time which will cause the PV to decrease. 2) There is more interest being paid because the coupon rate is the same but the amortized notional balance has increased, and thus will cause the PV to increase. just wondering if anyone could explain the two factors in more detail. the only thing that makes sense to me is that the duration will extend when prepayments decrease. thanks a lot!

Is this from the curriculum? Intuitively from a FI perspective it sounds like #2 is saying if you’re getting paid 10% pa on your portfolio of $1MM and the notional increases to $1.1MM, your PV will increase, all else equal. Specifically, I think this has to do with IO pieces increasing in value with slowing prepayment rates. As principal gets prepaid IO cash flows decline, and vice versa. Prepayment rates slow with IR increases, so IO pieces increase in value with IR increases, having the same effect as increasing your notional and increasing PV (holding all else equal). Does that make sense or am I off in the explanation?

  1. Because pre-payments are not being received now, instead these cashflows will be received sometime in the future, therefore PV deceases 2) I think thats self explanatory, if the balance is not being reduced by the prepayments, then the balance will be bigger, so interest based on that balance will be higher

thanks guys! so im still a little confused on #2. so it makes sense that if prepayments are going to slow down, then in the future the principal balance after prepayments will be higher. and i guess since the coupon rate is a % of the remaining principal balance, this means the customer will pay more interest. does that make sense so far? and if so, how does paying more interest translate into a higher pv? thx!

Ya I thought about your last point, think its because cashflow now is higher because of the higher interest, therefore PV increases, but would this not be offset by the lower pre-payment cash flow