WARNING: LONG POST
Since there have been some questions about hedging of MBS securities lately, I am trying to write down some thoughts to explain the key difference btw two bond hedge for MBS and the standard duration hedge.
MBS securities have, at least, two distinct properties that make them ‘undesirable’.
1. CONVEXITY PROBLEM: They have call option which again gives negative convexity when interest decreases while standard (non-callable) bonds only displays positive convexity which is desirable when interest goes down. Positive convexity is good then because it accelerates the price increase of the bonds while negative convexity prevents the price to increase.
When interest increases, MBS displays positive convexity like non-callable bonds (probably a little more positive convexity but it is not our main focus here). Because of this asymmetry, MBS is seen to be market directional. It means that the price change is more than ‘comparable securities’ in one way, while it is less (or similar) to market the other way, thus more preferrable depending on direction of the market.
Take the example in the book, a parallel (level) change
Interest up Interest down
Fannie Mae 5%: -1.339 1.208
Similar duration: -1.36 1.379
Notice that I have switched the order of the similar duration bond than in the book since this is NOT a hedge, i.e. Interest up, the duration hedge value is up 1.36, but the value of the bond is down -1.36 since you short the hedge.
Observe the absolute change: MBS interest down < MBS interest up < bond interest up < bond interest down. MBS, because of the convexity, displays less price change, thus less “duration” than it “should”.
Therefore, if you choose to hedge MBS by using similar duration bond, you have used too much duration than you should –> net position (MBS + hedge) too much negative duration.
Remember duration only help with small change in interest rate (e.g., a few bps, while here the typical change is 24.3 bps). For this relative large change in rate, convexity plays a larger role.
If interest down –> you ‘lose’ on the net position
If interest up –> you ‘earn’ on the net position.
Neither is ‘desirable’ when you want to hedge. You want your position to net zero change from your target.
So the simplest solution is just to lower the duration of the hedge to compensate for the convexity at this typical large parallel change (24.3 bps) ?
Yes, and no.
Yes: lower the duration of the (duration based) hedge will help, but it is not enough
For the curious, I show below ONE way of doing it. SKIP it if it is too much
————-> SKIP THIS IF YOU ARE NOT INTERESTED
One solution is to use a modified duration hedge, but instead of at the 1bps change, use the typical 24.3 bps price change instead.
Choose a combination of futures having similar duration as the standard duration of the MBS (5.5) and try to see what hedging ratio you have.
If I choose .5565 of 2 year and and (1-.5565) of 10 year futures to get me a mixture of approx 5.5 in duration (thus match the MBS duration) and try to see what ratio of this mix to hedge against a TYPICAL level change in MBS thus compensate also for the convexity, i.e. solve for
x* .5565* .418 + x* (1- .5565)* 1.687 = 1.274
I get x = 1.29
Using the given DV01 (2 year and 10 year), I get the effective duration of the hedge = 1.29* ( 0.0186* .5565 + .067* (1- .5565)) /99.126/10 000 = 5.25 –> effective duration is lower than the indicated 5.5).
If you don’t get the math, don’t worry. I just want to show that even using the standard duration hedge, but using the TYPICAL price movement of a parallell shift (here AVERAGE 1.274 for a TYPICAL 24.3 basis point shift) instead of the DV (using only 1 bps shift: NOT TYPICAL, TOO small to be realistic) would give you a lower effective duration hedge since you have compensated for the convexity as I said earlier
——————————-> END SKIP
HOWEVER,
No: but it alone is not effective enough, which brings me to the second problem of MBS.
2. TWIST PROBLEM: MBS also are also more sensitive to non-parallel shift (twist) in interest rate than standard bonds.
This has to do with the MBS reacts differently to changes in interest in different maturities (key rate maturities). It is caused by the barbell nature of the portfolio combined with the call option. MBS portfolio and in particular its derivatives (IO and PO) are very sensitive to key durations, not only durations, as shown in the exhibits.
Therefore, to be an effective hedge, one must take into account this twist change as well.
One way is to combine a long duration position (here 10 year futures) and a short term position (here 2 year futures) that also match the change of price in twist since the 2 year reacts more to a short duration change while the 10 year reacts more to a long duration change.
This new combination is different from the standard duration -based hedge where you only try to match the DOLLAR DURATION and the DURATION of portfolio.
I.e., not combine the 2 and 10 to match the 5.5 duration of the MBS as you would with a standard duration match but mix it in a different way, so that the change of the combo compensate not only at TYPICAL paralllel shift but also TYPICAL TWIST shift.
It gives you a 2 two-variable equations (instead of just one equation as I explained in the skipped area):
Equation 1: change of hedge at typical parallel change
Equation 2: change of hedge at typical twist change
Solve the two equations and you get your two bond hedge that would compensate correctly (i.e., remove the market direction) both with TYPICAL TWIST AND PARALLEL changes.
At last, some general comments:
1. Use search function, there are normally many similar answers. Market direction concept has been explained several times earlier.
2. My advice to all is to hold off for now the complex questions. Try to solve your exam questions. Understand/consolidate your basic understanding first and how to apply those new concepts (refresh what it means to hedge by duration, how do you do that, how do you do two bond hedge). Once you have done so, then delve into the intricacies (the why’s)
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