Aimee Wrote: ------------------------------------------------------- > I can give you my summary but I don’t know if it > will make a ton of sense since I wrote it to > remind myself of what was written there. I would > highly recommend cracking open the CFA book and > reading the 3 or 4 pages on it, its not tough to > do. They will have to give us the average price > changes, there’s no way they could ask us to come > up with those in the exam. Anyways, here’s what I > wrote: > > Two-bond hedge: > Step 1: Given assumed change in level of IRs, > determine average absolute price change per $100 > of mortgage security and 2yr/10yr bond. > Step 2: Given assumed change in twist of IRs, > determine average absolute price change per $100 > of mortgage security and 2yr/10yr bond. > Step 3/4: Set up two equations to determine > amount in each instrument to take per $1 MS: > > Level: (Amt in 2yr)(avg price change) + (Amt in > 10yr)(avg price change) = - avg price change > mtg > Twist: (Amt in 2yr)(avg price change) + (Amt in > 10yr)(avg price change) = - avg price change > mtg > > > > Example: Mgr simulates w/MC how $100 of mtg > security will change for given yield change and > forecasted twist. > Results: > > For Level: > Avg price change > Mtg .75 > 2 yr .24 > 10 yr 1.80 > > For Twist: > Avg price change > Mtg .32 > 2 yr .15 > 10 yr .60 > > > (weight 2yr)(.24) + (weight 10yr)(1.80) = -.75 > (weight 2yr)(.15) + (weight 10yr)(.60) = -.32 > > Solve Aimee, you’re my hero. I was gonna do a Sponge and just hope that this wouldn’t show up, but it seems beyond simple. Thanks very much for that breakdown; took about two minutes to “master” this concept based off of your notes.
Amy thanks for reviving this topic. Was a bit rusty on it and am nice and refreshed now. One thing to pay attention to as well is that the hedge amount for the 10yr and 2yr is based on the par value of MBS. (I can see CFAI putting in a couple of different amounts and having to pick) Also 4 things that are needed to be effective. a) yield curve shifts are reasonable b) prepayment model does a good job at estimate c) volatility assumptions are realized with Monte Carlo d) AVG price changes is good approximation.
I am sorry but I don’t understand what does the 2 tables on CFAI text V4. P.182 means. It seems to be the most important conclusion of the calculation. Can anyone explain ?
I think it’s meant for illustration. It showing that if you did a pure duration hedge you would have some big errors associated with it (looking at it in hindsight) The box below is showing the effectiveness of a 2 bond Hedge and it’s error at -.02. Much better result than the duration hedge. (because of the issues with convexity)
GMofDen, TKVM !
GMofDen gets at the heart of the LOS (LOS 31 D for those keeping score), IMHO. Nowhere does it say we have to calculate the hedge, just compare & contrast duration hedges with “interest rate sensitivity” approaches (ie, the 2 bond hedge) to hedging MBS. If this is tested is seems like it would be one of those “agree/disagree” with someone’s statement type questions. To properly hedge interest rate risk, the manager must know (1) how the yield curve will change over time, and (2) incorporate the effects of the changes in the yield curve on the prepayment option. If a duration hedge is used and interest rates increase, the gain on the hedge may exceed the loss on the bond. The opposite occurs if rates fall. Thus duration hedges are imperfect hedges and suggest MBS are “market directional”. A 2 bond hedge removes virtually all “market directionality” in an MBS, when the likely level & twist in the yield curve are accounted for (along with 3 other assumptions). The 2 bond hedge may outperform the long position in the MBS in certain instances, but the carry (higher yield income in the MBS vs. the Treasury) more than offsets this under performance in the hedge.
Try asking any of last year’s repeaters if they think knowing the calculation is necessary…
sjuhawk Wrote: > If a duration hedge is used and interest rates > increase, the gain on the hedge may exceed the > loss on the bond. The opposite occurs if rates > fall. Would you please explain tangibly/detailedly ? Thanks !
AMC, This is what those tables n p.182 are about. Table 1 shows you what happens to the price of the security and the duration hedge when there is a parallel shift in the yield curve. The error term tells you whether the hedge was successful. The +0.09 indicates the Duration hedge made money when rates went up. When rates went down however, the Duration Hedge lost 0.16. Table 2 shows you that same information for the 2 Bond Hedge. The 2 Bond hedge lost 0.02 when rates moved up and when rates moved down. However, the 2 Bond hedge did not lose you money because in a 2 bond hedge you are long the MBS and short at least one Treasury bond. Because you are long an MBS you are collecting the interest which is higher than the interest payment on a Treasury, and more than offsets that 0.02 loss on the hedge position. Hope that helped.
sjuhawk, TKVM for your tangible/detailed explanation !