McLeod81 Wrote: ------------------------------------------------------- > I would say there’s a 99.7% chance that this won’t > be on the exam. Yeah? What is your confidence interval? Too tight I bet…you overconfident forecaster.
Well at least I’m not falling into the prudence trap.
this question is good, but it really does not answer the question here. The question is how PO and IO vary when you vary different key rates. You argument here has no time dimension. McLeod81 Wrote: ------------------------------------------------------- > Null&Nuller, you had it right the first time and > it looks like Schweser is ass-backwards on these: > > PO’s respond VERY positively to decreasing > interest rates on the short end because > prepayments dramatically accelerate the repayment > of principal. If the entire discount from par is > repaid immediately, you win. > > IO’s are nothing but interest payments. The ideal > situation for an IO holder is that the bond is NOT > repaid at any point, and they end up receiving > interest for the entire length of the loan. There > is now principal involved, so the longer you > receive interest the better. If the loan is > repaid immediately, you get nothing. This is why > IO’s move WITH interest rates at levels below the > coupon rate. > > Once interest rates are sufficiently high, IO’s > start to act like normal annuities (positive > duration) because the chance of prepayment fall. > > From Fabozzi “CMO’s and Stripped MBS”: > > “If mortgage rates decline below the coupon rate, > prepayments are expected to accelerate. This > results in a deterioration of the expected CF for > an IO. The net effect is typically a decline in > the price of an IO.” > > “Thus we see an interesting characteristic of an > IO: It’s price tends to move in the same direction > as the change in mortgage rates. This effect > occurs 1) when mtg rates fall below the coupon > rate and 2) for some range of mtg rates above the > coupon rate.” > > “When mtg rates decline below the coupon rate, > prepayments are expected to speed up, accelerating > payments to the PO holder. The result is that the > price of a PO will increase when mtg rages > decline.” > > “When mtg rates rise above the coupon rate, > prepayments are expected to slow down. Coupled > with a higher discount rate, the price of a PO > will fall when mtg rates rise”.
McLeod81 explained that PO and IO is very sensitive to rate change when the interest rate is around the coupon rate. I will try to explain the sensitivity to different KEY rates based on my understanding. Please let me know if any mistake.
Let’s think about the person (borrower) who got a mortgage from the bank, say, 25-yr mortgage and started to make monthly payment to the bank. The monthly payment can be divided into “pricipal payment” and “interest payment”. At the beginning, the interst payment is relatively large, since the remainning balance is quite high. Given the fixed monthly payment, the principal component at the beginning will be quite samll. (Remember the interest payment = remaining balance * mortgage rate, and pricipal payment = monthly payment - interest payment).
The bank then pass through the payment to the investors. The PO holder will get the pricipal payment, and the IO holder will get the interest payment. Cash flow for the IO holder is high in the earlier years and gradually decline, while it will start from low level and keep increasing for PO investor.
Now there’s an interest rate twist. If the 1-yr interest rate decrease while all other key rates remains the same, what will the borrower do? Basically nothing. He will still make the regular payments. For the IO investor, he will get the original scheduled amount, but with lower discount rate, which makes the IO more valuable and indicates a “normal” (positive) key rate duration. However, the PO investor will be sad. The reason he invested into PO is that he expected yield curve to be more “inverted”. The demand of PO tranche will decline when the short-term interest rate drop and the yield curve to be more “normal”, and thus the PO appears a little bit negative duration (abnormal) to short-term rate.
What will happen if the 10yr interest rate drop a lot while all other rates remain unchanged? Since the mortgage rate is highly correlated to the long-term (e.g. 10yr) interest rate, the mortgage rate will drop. Of coz the borrower will refinance at current rate and pay all the remaining balance of original mortgage at once. The PO investor will be more than happy to recieve the amount which he expected to receive 25yrs later. But the IO investor lose everything because there won’t be any future cash inflow at all. So the PO shows significantly high positive (normal) duration for long-term rates. And IO has a high negative (abnormal) duration for long-term rates.
The chart is here.
In schweser its written in proffesor note (Book 3 26c) . Negative key rate duration imples that values move in same direction as in the key rate interest rate.
In 26c it says that PO has negative key rate duration whcih means that if Interet rate decline PO will decrease. But actually when interst decline PO Increase.