Can someone please help me out here… I understand the entire MBS topic with the exception of the hedging aspect including the 2 bond hedge. Anyone have time to perhaps go over an example in detail with some explanation as I find the Schweser material too abstract in this area. Any help would be really appreciated!!! PJStyles
PJ, I would love to help you with the math but at work, so no can do. The problem with hedging MBS is that due to the Negative Convexity the hedge will underperform when using Treasuries in the Negative convexity region…but in the Positive convexity region the hedge will perform in line. Remember. MBS has Negative Convexit. Treasuries do not. Hence there lies the problem.
Let me take a stab at this…little slow at work. Not only MBS has negative convexity to worry about, MBS is more sensetative to yield curve twist than bullet bonds. However, you can’t really use MBS to hedge MBS, we only have treasure bond/future to hedge MBS. So, use one bond is insufficent to hedge MBS, since it doesn’t address the yield curve twist. When we talk about yield curve twist, what should jump into your mind should be key-rate duration===>several key points on the yield curve. Therefore introduce the idea of using 2 bond to hedge MBS, one to address the short-end, another to address the long-end. For exam purpose, I will think(90% sure) that they will give you the numbers. They will give you two sets up number, given a rate change(short-term rate), how the short-end bond, long-end bond, and MBS will react to the change. Then given another rate change (long-term rate), how the short-end bond, long-end bond, and MBS will change in price. Then you set up your 2X2 equation to solve for number of short-bond you need, and number of long-bond you need.
THat’s right they will give you the Increase/Decrease for Yield Level and Increase/Decrease for Yield Twist…calculate the ABSOLUTE Average of the 2 (if they are nice they will just give this number), and set them equal to the MBS Average.
Ok, I snuck this one in with time…You’re luck; Let’s pretend that the Absolute Average Price Changes are provided as such: Yield Level Yield Twist MBS 1.50 0.25 2Y Treas 0.50 0.30 10Y Treas 1.75 0.40 Now setup equations as follows: -1.50 = 0.50*w2 + 1.75*w10 -0.25 = 0.30*w2 + 0.40*w10 You want the MBS’s values to be negative b/c you are hedging. Now solve: -1.50 -1.75*w10 = 0.50*W2 W2 = -3 – 3.5*w10 Now input w2 into the other equation -0.25 = -0.30(-3-3.5*w10)+0.40*w10 -0.25 = 0.90 + 1.05*w10 + 0.40*w10 -1.15 = 1.45w10 W10 = -07931 Now solve for W2 -1.50 = 0.50*w2 + 1.75*(-0.7931) -0.1121 = 0.50*w2 W2 = -0.2242 So you will Sell -0.7931 10Y Treasures and Sell -0.2242 2Y Treasuries. Of course these amounts would be multiplied by the Notionals…. Does that help. If they give you price changes…You want the Absolute Average, for instance if original price is 100, and we increase 100bps and it goes to 98.5 and then we decrease by 100bps and it goes to 101.5, the Absolute Average price change is +1.50.
AWESOME… I’ve printed this thread out. WS’ explanation along with your example should make getting through this so much easier. Thanks guys.
PJStyles…let me confuse you a little( not really), if you change the sign on those 2 equations, you will get the same answer. Just make sure your 2 bonds has different sign than your MBS.
“possibly” not true WS…I thought I recall seeing a problem where they were short say a 10y, but Long a 2Y in the CFAI texts… I dont have it on me so I can’t check. To be safe I would include the (-) signs, that’s just me. 
I actually get this now… and followed the example in Schweser quite easily. This post has been a huge help. However, I did notice that the LOS does not mention anything about “Evaluating” which makes me believe we won’t be asked to calculate anything relating to a 2 bond hedge but rather explain why it’s important and why duration matching is not a suitable hedging strategy for MBS.
bigwilly Wrote: ------------------------------------------------------- > “possibly” not true WS…I thought I recall seeing > a problem where they were short say a 10y, but > Long a 2Y in the CFAI texts… I dont have it on > me so I can’t check. > > To be safe I would include the (-) signs, that’s > just me. REALLY??? So, it is possible to construct a hedge with long&short position on the short-bond and long-bond? I am trying to picutre how that would work…would they cancel out each other some, then the remaining net effect (positive or negative) applies toward to MBS (just thinking out loud).
I guess if the twist in the yield curve was very pronounced or something…I dont know this is off of memory, I’m review SS6 today, SS8 won’t be until Sunday or most likely Monday b/c of weekend obligations 
Dont forget to add options to adjust for cupsy coupon!
Take your cupsy coupon and stick it, just kidding CSK. Cuspy coupon is the tangent line to the curve, but what exactly is it again… I can’t beleive i can’t remember exactly what it is.
^LOL, LOL, LOL
Which LOS includes the word calculate or similar ? Do we have to be able to derive a 2 hedge bond ?
No we don’t… It’s not in any of the LOS’.
Be careful, becuase Demonstrate equals Calculate b/c Macro is Demonstrate and we had to calculate on Mock.
that brings me to the question of Modified dietz with tax adjustment…
Fack tax adjustment, that’s how I roll