PO/IO MBS duration

This question has been discussed before but no one has come up with a clear reason to this and that is: why does a PO strip show negative duration when IR move down at the shorter end of the yield curve? Completely boggled as to why. I’m hoping someone can take a stab at it.

I know the POs should increase in value as IR move down as people will prepay their mortgage therefore an investor getting his investment back earlier + discounted back at a lower rate which on a PV basis is better. So is this not a positive thing? Not sure.

if the po had not been refinanced and stayed its course for the entire time from the investor’s perspective - he would have earned more over the life of the MBS. Now a) the investor gets all the money back at once. so he misses out on all the future earnings that he might have gotten. b) he needs to now invest the proceeds in a lower interest rate environment. from the perspective of the investor - his time to recoup the cash flows has sharply reduced - which is negative duration. Essentially he just receives the entire investment, no chances of any “interest earned” at all.

the Interest portion is high during the first few years and the principal less for mbs securities…so the duration of the IO is less than the duration of the PO. when interest rates drop and prepayments come in, the investor in PO gets his cash sooner + his discount rate is lower…combined with these two effects the % of price goes up which in terms of duration will be positive…since duration = - dP/(dy*P)… the assumption in this equation is that the rate shifts are parallel… but if the rates are changing individually i.e one rate at a time, then the PO exhibits negative duration for short end of the curve… the reason for this is that when the short end rates are lowered, you are not assuming that the mortgage rate is lowered as well, you are just assuming that the steepness of the curve increases and this usually results in higher mortgage rates and lower prepayments and cashflows further out resulting in negative duration… this is not the case with the parallel shifts where the assumption is that the mortgage rates drop as well since the slope of the curve is constant… mortgage rates are usually estimated as short term rate + constant* slope between the short term and long term rate…so even if the short term rate goes down the slope could go the other way increasing the mortgage rates… hope this helps…

It makes more sense now. Thanks for the timely responses everyone - appreciate it. I failed level 3 last summer and I’m trying to pull out all the stops this year. I see why the assumption is assumes there is a parallel change in IR given the model for duration works best for parallel changes in rates. I see how the mortgage rates drops for parallel changes based on the formula you mention in your post above and if for non-parallel changes in rates, we cannot assume that mortgage rates drop also to induce people to prepay their mortgages. So this results in the positive duration for parallel changes turning into negative duration for key rate changes as yields decrease.

I would really like to see some evidence that long term mortgage rates go up when short term interest rates go down. I just don’t believe it. I’ve seen this stuff about negative short term key rate duration before but, for example, I have never been able to find a reference to it on a Google search. Just people asking about it. Anybody got some vaguely reliable source for this? (No offense intended to seeki - s/he could be right)

I worked at a bank early on in my career and had to be invovled in pricing loans, etc. If a yield curve steepens, and short term rates either drop (through central bank omo’s or lowering the ffr) or simply stay constant, the tens, twenties, and thirties increase this will most certainly get reflected in the pricing of mortgage rates that a bank will quote as most of the ALM departments are going to set policy pricing on these as benchmarked to a treasury of similar maturity as the loan plus some spread depending on what they are trying to do in managing the loan portfolio, what interest rate risk currently looks like for the bank and various other funding sources and associated costs for those. I don’t have any sources and don’t have time to do that, so it’ll just have to be anecdotal evidence.

I don’t think you are following the discussion. First off, key rate duration means the sensitivity to an interest rate move when just the key rate moves and all otehr rates are held constant. The OP is sugeesting that if short rates decrease and all other rates remain constant that PO strips will decrease in value. Then Seeki said that it’s because mortgage rates will rise even though none of those benchmark rates rise thus making the prepayment rate go down. Seeki then says that mortgage rates are based on some semi-plausible formula. Everyone knows that mortgage rates follow long-term rates. It’s PO strips running in the counter-intuiitive direction that is being asked here (PO strips have highly positive long term key rate durations).

Joey, I’m following the discussion, and I understand key rate duration, I may have simply misunderstood a comment you had made two posts up: " would really like to see some evidence that long term mortgage rates go up when short term interest rates go down. I just don’t believe it." Perhaps I just read this wrong or misinterpreted what you wrote but to me it did seems as if you were saying you could not imagine a situation where short term rates (read: the short end of the treasury curve) going down and long term rates going up and thus any other rate product tied to that rate. That is what my repsonse is geared towards. I think the question on negative duration on POs is already stated, so I’m jsut stopping here. I can see this quickly deteriorating into an argument over nothing and I don’t want to do that. Besides you’re clearly smarter than I and as I’m struggling through this final level I might have a question at some point that I would need your help on. Not trying to step on any toes here, guess I just misunderstood. Pardon me.

Yep - no harm no foul.

the key rate duration that’s in the cfa material is from the fabozzi’s book/paper…i don’t know when it was published but that was the relationship back then. you just have to run the regressions and see what the current relationship is. i work at the mbs desk and the 2 year rate + the slope of the 10-2 year rate is what describes the mortgages rates the best if a linear system is assumed… I don’t believe that the key rate durations will always be what cfa/fabozzi published and they might change based on the interest rate regime…