CFAI text V4 : 2nd paragraph (entire paragraph) on P.166 & Exhibit 3 on P.167 [When interest rates rise, we see -------------------------- offsets part of the depreciation.] By examining Exhibit 3, you will find that if I/R > Yo and if I/R rises, the decline in value of MBS with negative convexity will be more than the decline in value of bonds with positive covexity (e.g., Treasury). This seems discrepant with the statements in above-mentioned. paragraph. Am I missing something ? Anyone can explain / clarify ?
AMC, do you have schweser notes? in the notes 3, P116, fig2. and 1st line of P117 when yield >coupon rate i (i.e. y0 in the CFAI text V4 Exhibit 3 on P.167 ). the MBS have positve convexity, because the call option is out-of the -money, it acts almost like the non-callable bond. the exhibit 3 on P167 is a little missleading.
the exhibit 3 shows the positive & negative convexity and duration changes. no saying MBS is always negative convexity when I/R>Yo. the best illusion of Price-yield relation of MBS is exhibit 1 on P164 FAI text V4.
annexguy, Oh, yes. exhibit 1 on P164 CFAI text V4 is the correct one. TKVM !
AMC, You should not look at negative convexity part. BTW, exhibit 3 does not mean to explain the 2nd paragraph, but the 3rd paragraph. My question on 2nd paragraph is: Is the positive convexity for MBS greater than the convexity for Treasury when I/R rises?
lzhao Wrote: ------------------------------------------------------- > My question on 2nd paragraph is: > Is the positive convexity for MBS greater than the > convexity for Treasury when I/R rises? Yes, this is my another question ! Any other comment ?
I think the positive convexity shall be same as that of comparable option-free bonds if Yo > C/R because prepayment option becomes worthless.
[The net effect is that ----------offsets part of the depreciation.] in 2nd paragraph I guess this is under the situation of Yo < C/R. If I am wrong, please correct me.
AMC Wrote: ------------------------------------------------------- > lzhao Wrote: > -------------------------------------------------- > ----- > > My question on 2nd paragraph is: > > Is the positive convexity for MBS greater than > the > > convexity for Treasury when I/R rises? > my guess is positive convexity for MBS < convexity for Treasury when I/R rises, and I/R>Yo. reason: Value of MBS=value of Treasury - Value of prepayment option. when I/R rises, and I/R>Yo, Value of prepayment option is very small , almost worthless, but still have a little time value (e.g. AMC wins 100million lottery and pays off the mortgage right now. ) . so Value of MBS
annexguy, Your comments are very interesting. I just do not understang the actual meaning of “a same-duration Treasury securities”. If I/R < C/R, it is quite imposible that the duration of a MBS will be same as that of a Treasury bond. The statements in this paragraph are vague to me.
“a same-duration Treasury securities”. even MBS’s duration is hard to measure, it still possible to measure and find another T-Bond have same duration. because the prepayment option affects very little. Whyisn’t possilbe that a MBS will be same as that of a Treasury bond? Duration is wieghted ave. future cashflow timing. bond’s exact cashflow won’t be same as MBS, but the weight ave. future cashflow timing is possible.
Annexguy, To align with 2nd paragraph AMC refers to, you should reason with the change of bond value, not the value itself.
lzhao Wrote: ------------------------------------------------------- > Annexguy, > To align with 2nd paragraph AMC refers to, you > should reason with the change of bond value, not > the value itself. are you referring to this formula? Value of MBS=value of Treasury - Value of prepayment option I don’t know why it is not “the change of bond value”, but it is from the CFAI text.
Formulat is correct, but the reasoning should be based on changes of each variable in the formula.