annexguy, I think in R31, two-bond hedge is discussed from P.174. Before that, traditional (duration-based) hedge which use futures to hedge and other risks are discussed. Duration will change if covexity changes. Since there are some limits of traditional (duration-based) hedge, so two-bond hedge is introduced. Above are my understandings. if I am wrong, please correct me.
read cfai text book, which helps more than schwesser like a lot of guys pointed out. i think it depends on how convexity is going to do to durations, say the yield moved from + convexity to - convexity zone, the lower horizon needs extra duration, buy short term treasury, sell long term treasury. it the yield moves in the + convexity zone only, sell 2 treasury. don’t know what to do if the yield moves in - convexity zone. hope it’s a numerical question on the exam.
Yes, I am confused by “how to use two-bond hedge”. I just know that two-bond hedge shall be used to hedge “twist” of yield curve risk. Anyone can advise ?
Both DUR hedge and 2 bond hedge are for hedging interest rate change Duration hedge ie. matching $DUR of MBS and Treasury -> no problem when interest rate rise (both exhibit positive convexity) -> hedge loss when interest rate fall (MBS exhibit negative convexity and Treasury exhibit positive convexity) Two bond hedge ie. matching the price change of 2 year and 10 years treasuries with MBS. -> hedge virtually all interest rate change (twist or level).
B_C, My understandings are : 1. DUR hedge : only hedge parallel shift of yield curve A. Interest rate rise (both exhibit positive convexity) Sell futures B. Interest rate fall (MBS: - convexity, Treasury : + convexity) Sell futures : loss Buy futures : Hedge can be archieved (may be not perfect) 2. Two-bond hedge : hedge both parallel shift & twist of yield curve (not only twist) Your advice regarding two-bond hedge (matching the price change of 2 year and 10 years treasuries with MBS) is much appreciated.
For Two bond hedge. we match the price change of 2 year and 10 years treasuries with MBS under “level” or twist" yield curve change. P change(NH1)+Price change(NH2) = -P change (MBS) when level change P change(NH1)+Price change(NH2) = -P change (MBS) when twist change, => solve for NH1 and NH2 => hedge virtually all interest rate change (twist or level).
Correct. Duration hedge will hedge away parallel SHIFTS in the yield curve Two Bond hedge will hedge away TWISTS and parallel SHIFTS in the yield curve Two Bond Hedge requires 3 instruments 2Y T 10Y T MBS Look up the circa 10-step calc at the end of the chapter. It’s pretty simple once you go through the worked example. For each of the 3 instruments, Calculate price change for a Twist For each of the 3 instruments, Calculate avg price change for a Twist For each of the 3 instruments, Calculate price change for a Level shift For each of the 3 instruments, Calculate avg price change for a Level shift Set simultaneous equations Solve simulataneous equations to work out H2 and H10 If H2 or H10 are -ve, the short them, otherwise long them
Regarding DUR hedge : only hedge parallel shift of yield curve -> correct But as you are longing MBS => interest rate parallel shift are hedged by shorting Treasuries or sell treasury futures (no matter whether the interest rate rise or fall). Not long. This is different from duration hedging on prepayment risk. “The hedging principle is that the change in the value of the mortgage security position for a given basis point change in interest rates will be offset by the change in the value of the Treasury position for the same basis point” quoted from the text book
B_C Wrote: ------------------------------------------------------- > Regarding DUR hedge : only hedge parallel shift of > yield curve -> correct > > But as you are longing MBS => interest rate > parallel shift are hedged by shorting Treasuries > or sell treasury futures (no matter whether the > interest rate rise or fall). Not long. This is > different from duration hedging on prepayment > risk. > > “The hedging principle is that the change in the > value of the mortgage security position for a > given basis point change in interest rates will be > offset by the change in the value of the Treasury > position for the same basis point” quoted from the > text book in one word, either DUR hedge or 2-bond hedge , it is normally short the future.
I got concepts about MBS hedging mainly from 2009 Schweser (note/q-bk). 2009 Schweser note of this reading was very much simplified and did not discuss 2-bond hedging very clearly. I am confused again and do not know if those concepts are correct. CFAI’s 2009 LOS(e) is deleted this year. I don’t know Schweser 2010 note of this reading is futher simplified.
CFAI 2010 LOS still has 2-bond hedge. You may refer to CFAI textbook for details.
B_C, Do you mean that my following concepts are wrong (from your previous post) ? DUR hedge : Interest rate rise (both exhibit positive convexity) => Sell futures Interest rate fall (MBS: - convexity, Treasury : + convexity) => Sell futures : will incur loss => Buy futures : Hedge can be archieved (may be not perfect) Your advice will be appreciated !
I asked this topic to schweser insturctor. for your ref. To hedge MBS’s interest rate risk, can the Duration based hedge used when MBS has positive Duration like normal bond. shall I short or long a future? TKS! CFA, CAIA - Level 3 Manager: When rates are high and negative convexity os not a factor, you can follow a “normal” hedging strategy. To hedge MBS’s interest rate risk, I have following thoughts, but not very sure, pls help. Two-bond hedge ,hedges both parallel shift & twist of yield curve . in the samples of notes, managers take short position of 2 bonds in notes’ example. can we see to hedge interesr rate risk, always short the future w/Two-bond hedge. CFA, CAIA - Level 3 Manager: Not always both short. Depends on the current level of rates, the shape of the yield curve, and the yield on the MBS. You could be long and short. Remember that Treasuries have positive convexity (the usual shape of the bond yield/price curve and MBS have a segment that exhibits negative convexity.
annexguy, So what shall be correct ?
AMC Wrote: ------------------------------------------------------- > annexguy, > > So what shall be correct ? all depends. not always short. and 2-bond hedge is best option for MBS. BTW, this afternoon, I did the 2009 CFAI sample exams version 1,2,3 purchased from CFAI website before 2009 exam, not the one free downloaded from CFAI this year. In the sample exam version 2, Yun Fan Case Scenario Q7-12 covers lots of area of this thread. It helps me understand them better.
annexguy, If you don’t mind, would you please send the 2009 CFAI sample exams version 2,3 purchased from CFAI website last year to my e-mail address : smkuo@aamcc.biz I purchased version 1 only last year. Thanks in advance.
AMC, As far as I understand… For two bond hedge. Your position can be short / long depends on whether the NH10yr and NH2yr you solved is positive or negative For DUR hedge. Your position should be short futures on treasuries as long as you are longing the MBS not shorting MBS. without considering the convexity problem…then… If interest rate rise => MV of both MBS and Treasuries fall => Gain from treasuries future offset MBS fall. If interest rate fall => MV of both MBS and treasuries rise => Gain from MBS offset future loss. => your position is hedged. But as we have discussed. This is not a good hedge due to convexity problem.
“The interest rate risk of a mortgage security corresponds to the interest rate risk of comparable Treasury securities (i.e., a Treasury security with the same dura- tion). This risk can be hedged directly by selling a package of Treasury notes or Treasury note futures.” quoted from the text book.
AMC Wrote: ------------------------------------------------------- >check your email.
Why does my PC upload the post so slow? never happened when L1 and L2. same thing on your PC?