Immunization target rate of return vs ytm

Sorry if this was discussed before. I could not get what this means. (SS8-Reading 27) “The immunization target rate of return is defined as total return of the portfolio assuming no change in the term structure.” Is this total return equal to Principal+Interest+Reinestment? If so how is it different than ytm? "In general, for an upward-sloping-yield curve, the immunization target rate or return will be less than the yield to maturity because of the lower reinvestment return. Conversely, a negative or downward-sloping curve will result in an immunization target rate of return greater than the yield to maturity because of the higher reinvestment return "

In most cases, we can only reinvest the coupon at the short end of the YC, given a normal shape, short end pays less than long end. That is why immunization target rate is lower than YTM.

Wow… all it needed was ws’ one little sentence to make everything clear as day for me. The last thread confused the hell out of me.

The YTM and the Immunization rate mean the same thing ( total return). the only difference is how you calculate them In YTM you assume coupons are re-invested at the YTM In Immunization, you assume coupons are re-invested either at the implied Forward rates or the Treasury Spot rates. So it’s a more realistic measure of the total return you might be able to get. They will both be equal if the yield curve is flat. For the second part of your question, I am not sure how the re-investment return is lower if the yield curve is upward sloping ? Did not make sense to me when I read it. The way I thought of it is from this part " … because by virtue of the passage of time, there is a return effect as the portfolio moves along the yield curve"… So, if I understand correctly, as the portfolio matures and interest rates rise (upward sloping curve) the price will decrease leading to a lower total return (Immunization rate) than the YTM.

ymmt, I am still damn confused about why PO or IO exhibit negative duration during their early phase. (I am confused enough that I don’t even know my question is stated correctly). It was few post back, your desk confirmed that fact they were indeed negative.

5/11 and 8/11 strips are currently lower in price (12:56PM), and you’ll notice that the front end of the curve has fallen significantly more than the 5 yrs yields. Evidence that lower partial durations have a negative effect on zeros?

ymmt Wrote: ------------------------------------------------------- > 5/11 and 8/11 strips are currently lower in price > (12:56PM), and you’ll notice that the front end of > the curve has fallen significantly more than the 5 > yrs yields. Evidence that lower partial durations > have a negative effect on zeros? Yeah, indeed.

Thank you all. mo34, this comparison of immunization rate of return and ytm is very helpful.

The reason why POs exhibits negative convexity is becuase they are like callable bonds in the sense that the mortgage borrowers are the POs issuers. They borrow money like the bond issuers do. With that in mind, wouldn’t callable bonds and mortgage loans be somewhat alike in that the mortgage payers have the right to prepay the loans much like bond issuers can call the bonds back? If we all agree the above, then since callable bonds have negative convexity because they are likely to be called at the lower rates and reissue the bonds making the price of the callable bonds “capped” at lower rates (who will buy callable bonds at a price above the callable price when rates are low and they are likely to be called) and thus negative convex, so do mortgage borrowers are likely to prepay the loans at lowe rrates and reborrow. I would also add that since PO are principal payments only, they would exhibit more significant negative convexity than regular callable bonds.

mo34 Wrote: ------------------------------------------------------- > The YTM and the Immunization rate mean the same > thing ( total return). the only difference is how > you calculate them > > In YTM you assume coupons are re-invested at the > YTM > > In Immunization, you assume coupons are > re-invested either at the implied Forward rates or > the Treasury Spot rates. So it’s a more realistic > measure of the total return you might be able to > get. > > They will both be equal if the yield curve is > flat. > Ah, this is great. I was confused on how you get Target Rate. Whether it was a YTM (sort of, but not quite), an IRR (sort of, but not quite), or whatever. This clears it up. > For the second part of your question, I am not > sure how the re-investment return is lower if the > yield curve is upward sloping ? Did not make sense > to me when I read it. The way I thought of it is > from this part > > " … because by virtue of the passage of time, > there is a return effect as the portfolio moves > along the yield curve"… > > So, if I understand correctly, as the portfolio > matures and interest rates rise (upward sloping > curve) the price will decrease leading to a lower > total return (Immunization rate) than the YTM. This gets to WS’s point. When you reinvest, you’ll be reinvesting at the short end of the curve, which, if upward sloping, won’t be paying you as much as the long end. I guess it depends somewhat on what your theory is about yield curve shape. If it’s a pure expectations theory (that long term rates just predict the short term rate that far into the future), then you’d expect to reinvest at more or less the same number. If there is a liquidity premium (or more accurately, a term premium) for holding the money at the long end, then you won’t be getting that at the short end when you reinvest. Oh dear, I need to review this. There was once a time when it was clear to me.

chuliu Wrote: ------------------------------------------------------- > The reason why POs exhibits negative convexity is > becuase they are like callable bonds in the sense > that the mortgage borrowers are the POs issuers. > They borrow money like the bond issuers do. With > that in mind, wouldn’t callable bonds and mortgage > loans be somewhat alike in that the mortgage > payers have the right to prepay the loans much > like bond issuers can call the bonds back? > > If we all agree the above, then since callable > bonds have negative convexity because they are > likely to be called at the lower rates and reissue > the bonds making the price of the callable bonds > “capped” at lower rates (who will buy callable > bonds at a price above the callable price when > rates are low and they are likely to be called) > and thus negative convex, so do mortgage borrowers > are likely to prepay the loans at lowe rrates and > reborrow. > > I would also add that since PO are principal > payments only, they would exhibit more significant > negative convexity than regular callable bonds. chuliu, the material talks of negative duration and not negative convexity.

On the PO/IO duration question: POs are purchased at a discount and the rate of return depends on how quickly the underlying mortgages are repaid. The faster the repayment, the higher the rate of return. If mortgage rates decline, prepayments will increase, improving the PO’s cash flow and increasing its value (positive duration – rates down, price up). IOs, in contrast, receive payments based only on the amount of mortgage principal outstanding. When mortgage rates go down, prepayments increase, reducing outstanding principal, thereby reducing the interest paid on outstanding principal, thereby reducing cash flows to the IOs, thereby reducing their value (negative duration – rates down, price down). If rates go down enough, an IO investor may not recoup their principal even if the IO is held to maturity. I think the main point in this part of the SS9 reading is just to highlight the importance of key rate durations/yield curve risk for MBSs, not necessarily to have us memorize the properties of PO/IO securities (though nothing would surprise me). For example, while POs have positive duration, they actually have negative key rate duration on the short end of the curve. No, I don’t know exactly why that is, but I’m guessing it has something to do with the fact that mortgages are priced off the long end of the curve, so a change in short rates won’t do much to prepayments but will affect the available reinvestment rate. But given how much else in the curriculum I have no clue on, at this late date, I’m not going to spend the time to figure out the rest of this particular puzzle… BTW, all the stuff in the first 2 paragraphs is explained in Fabozzi, p380.