To hedge interest rate risk of MBS, which of the following shall be correct ? Selling Treasury futures or buying Treasury futures ?

Both, depending on whether you want to increase or decrease duration. Correct?

Any other response ?

i think it depends which way interest rates are expected to move. So for example, if interest rates are expected to decrease, since MBS exhibit negative convexity, their price will not rise as much …so it is better to opt a solution mirroring selling of MBS > sell futures? im not too sure with this though

as per my understanding, when rates decline MBS seurities with -ve convexity register inreased pre-payments taking place. hence duration will decline more than expected. To hedge our int. rate exposure of MBS, we should go long treasury futures. Alternatively, when rates increase, duration of MBS will Inrease more than expected (as prepayments will slow or be almost NIL) and hence we should hedge by going short treasury futures.

Yes, you are right. But it seems that some solutions in q-bk are discrepant.

schweser notes3, p120. bottom professor’s note:a two-bond hedge refer to selling short 2 bonds or taking a short in futures on the bonds. P121, 1st line. the mgr use a two-bond hedge to hedge the risk associated with both increase and decrease in interest rate + forecasted twist. P123, last line. take short position of 2 bonds. Hedging is a case of interest rate risk control where manager seeks to completely offset dollar price change in the MBS by taking opposite position in an appropriate hedging tools which will produce the same dollar price change amount in opposite direction. i.e. MBS increases $10, hedging tools decrease $10. no matter how interest rate or MBS value will change. CFAI text, V4,P177, Illustrations of two-bond hedge. they are very interesting. 1st example, Long one bond, short the other 2nd example, short 2 bonds. I guess short will be better answer. AMC, can you give more details about Q-bank’s solutions?

annexguy, I went back to review the question in q-bk and its solution. It was my mis-undestanding which caused my confusion. The comments from level3aspirant shall be correct. But I will like to revise his comments a little bit to be as follows. When rate declines to be lower than the C/R of MBS (or its price rises above its par value), the MBS will exhibit negative convexity due to inreased pre-payments, hence duration will decline more than expected. To hedge I/R risk of MBS, we should go long (buy) treasury futures. Alternatively, when rate rises above C/R of MBS (or its price fall below its par value), duration of MBS will Inrease more than expected (as prepayments will slow or be almost zero), then we should hedge by going short (sell) treasury futures. Correct me if am wrong !

annexguy, Util now, what I am talking about is duration-based hedge. Two-bond hedge shall be another story.

given the complications of MBS, using only a duration-based framework won’t be adequate for hedging MBS. 1.for MBS w/negative convexity, duration-based hedge that removes the risk associated w/interest rate rising can produce loss on hedged position when rate decreasing. 2.duration-based hedge can’t effectively deal w/ observed patterns of yield curve changes over time and the effect yield curve changes have on the propensity for the prepayment by homeowners. In reading 31 , only introduced Two-bond hedge for MBS. Also,When rate declines to be lower than the C/R of MBS (or its price rises slowly), the MBS will exhibit negative convexity due to inreased pre-payments, the MBS price rises slower than bond is mainly due to negative convexity, not Duration.

In Reading 30, the duration-based hedge is introduced . and duration-based hedge is for normal bond , not MBS. and it need the current duration and a target duration, and DD of future contract. # contract=[DD(T)-DD§]/DD(f) Long or short future contract is depends on the relative value of DD(T) to DD§, not the forecast of interest rate. AMC, can you find any words in notes to support your theory of long or short?

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.