Reading 31, Volume 4 of CFAI text Duration-based hedge means “shorting Treasury securities” or “selling Treasury futures” ? Why duration-based hedge is not appropriate for hedging MBS ? Is duration-based hedge appropriate for hedging MBS when the MBS exhibits positive convexity ? Thanks in advance !
I was confused by these too, now my understandings are : Since when MBS exhibits negative convexity, it has negative or less positive duration duration. To make the negative or less positive duration duration to be positive or more positive as that of option-free bonds, the duration of the MBS shall be increased (not reduced), while shorting Treasury securities or selling Treasury futures will reduce the duration of the hedged MBS further which will be even worse. It seems that it is appropriate to hedge the MBS by shorting Treasury securities or selling Treasury futures when it exhibits positive convexity. I am not sure if I am right. Please correct me !
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)
elcfa, Thank you very much for kindness/patience/advices in answering to my question. I think need time to digest those materials supplied by you. But I am curious if what AMA said are correct or not, can you confirm ? Thanks again !
AMA Wrote: ------------------------------------------------------- > I was confused by these too, now my understandings > are : > > Since when MBS exhibits negative convexity, it has > negative or less positive duration duration. To > make the negative or less positive duration > duration to be positive or more positive as that > of option-free bonds, the duration of the MBS > shall be increased (not reduced), while shorting > Treasury securities or selling Treasury futures > will reduce the duration of the hedged MBS > further which will be even worse. > Not sure, what AMA means here, but as I wrote earlier: if you use duration-based hedge, your hedge should have LOWER duration than the duration of the MBS because of the effect of convexity on the TYPICAL (parallel) rate changes (in the example 24.3 bps which is larger than just a few bps). For change of a few bps where convexity does not matter much, you can use a hedge matching duration of the MBS, but this sceneario is not realistic since the typical rate change is much more (24.3 bps) thus you have to lower the duration to compensate for the convexity. > It seems that it is appropriate to hedge the MBS > by shorting Treasury securities or selling > Treasury futures when it exhibits positive > convexity. Depends on the typical rate change to see whether convexity (even with positive) is a problem or not. Even convexity is not a problem, TWISt problem is still there, thus you need to use two bond hedge anyway to hedge properly. Fortunately, I don’t think it is a problem for the exam. In the exam, you will be given an MBS and ask to hedge using two bonds --> just understand how to solve the equations. Check the LOS to make sure.
elcfa, Thank you so much for your futher response ! Very sorry, 3 more questions : 1. Is it that duration-based hedge just means adjusting duration by “buy/sell Treasury bonds” or “long/short Treasury futures” ? 2. Is it that convexity can not be hedged by duration-based hedge ? 3. Adjusting DURATION = Adjusting DOLLAR DURATION ? Thanks !
alta168 Wrote: ------------------------------------------------------- > elcfa, > > Thank you so much for your futher response ! Very > sorry, 3 more questions : > > 1. Is it that duration-based hedge just means > adjusting duration by “buy/sell Treasury bonds” or > “long/short Treasury futures” ? > Yes. You can also do that by buying/selling another bond portfolio, though it is most effective/convenient using T-bonds or T futures. > 2. Is it that convexity can not be hedged by > duration-based hedge ? > Not effectively. > 3. Adjusting DURATION = Adjusting DOLLAR DURATION > ? > Yes and no. Don’t think you understand the two concepts correctly. I think you should revise the definition of those concepts to differentiate the difference between them. > Thanks !
elcfa Wrote: ------------------------------------------------------- > At last, some general comments: > > 1. Use search function, there are normally many similar answers. Market direction > concept has been explained several times earlier. Thanks a lot for your detailed explanation regarding “duration-based hedge”. Actually, I tried to search some messages about MARKET-DIRECTION on this forum a few weeks ago, but only an indication of “NO RESULTS WERE FOUND”. Anyway, your advice is appreciated !
elcfa Wrote: ------------------------------------------------------- > alta168 Wrote: > -------------------------------------------------- > > 3. Adjusting DURATION = Adjusting DOLLAR DURATION ? > > Yes and no. Don’t think you understand the two concepts correctly. I think you should > revise the definition of those concepts to differentiate the difference between them. If you don’t mind, would you please kindly asdvise when will be “Yes” and when will be “No” ? I have same question because I found that it is said in the 1st line on P30 of Vol 4 of CFAI text that “portfolio rebalancing (adjusment) is required to keep the portfolio DURATION syncronized with the horizion date” but without an intoduction or example regarding how to rebalance (adjust) the portfolio’s duration to keep the portfolio’s DURATION to be same as the horizion date. However, subsequently in 4.1.1.5 and example 6/7, the rebalancing of the portfolio’s DOLLAR DURATION is addressed. If rebalancing of the DURATION is not equivalent to the rebalancing of the DOLLAR DURATION, then how to rebalance the portfolio’s DURATION ? Thanks in advance !
dollar duration = duration* portfolio value* 0.01 you can have duration unchanged but dollar duration changed or vice versa. The example 6 and 7 show exactly that: duration of the portfolio remains unchanged but the dollar duration is adjusted after you have added more value to the portfolio (so that the dollar duration changed to a target value). Reading “Fixed income portfolio mgnt part II” shows how to adjust duration using futures by calculating dollar duration.
elcfa, Thank you very much for your quick reply ! I am very sorry that I did not ask my question clearly. My question shall be : Can we rebalance duration and dollar duration simultaneouly ? Your advices are really appreciated and thank you for your patience !
Look at the formula dollar duration = duration* portfolio value* 0.01. If you change duration while keeping portfolio value intact (e.g., sell a bond and buy another bond with a similar value but a different duration), you change the duration and dollar duration of the portfolio at the same time. Same thing if you add T bond futures (portfolio value not changed, but total duration thus dollar duration increased). seriously man: if you get stuck in such basic questions so often, I would consider attend an instructor-led course where you can ask (and get answers for) such questions much more effectively instead spinning your wheel and wasting your time in a forum like this. It will also help you focus on the most essential material instead of worrying to understand about every sentence in the CFA books.
elcfa Wrote: ------------------------------------------------------- > Look at the formula dollar duration = duration* portfolio value*0.01. > If you change duration while keeping portfolio value intact (e.g., sell a bond and buy another > bond with a similar value but a different duration), you change the duration and dollar > duration of the portfolio at the same time. Same thing if you add T bond futures (portfolio > value not changed, but total duration thus dollar duration increased). I guess what AMA meant here is : Can we rebalance duration and dollar duration simultaneouly “in an immunization” ? Also an extended question is : Which one (duration or dollar dulation) shall be rebalanced “in an immunization” ? Maybe you can refer to his messages in another post of “R28 : Rebalancing”.
I would think again - you are going overboard here. What do you want controlled? Do you want the Duration controlled (which actually means nothing - this is just a unit of time) or do you want the Dollar Duration controlled (in a Portfolio sense - this does have meaning - since it is a direct reflection of the Portfolio’s value). Is it just my feeling? It looks like (seeing the language and style on the posts) that AMA and alta168 are two alter egos… One posts the other counter questions)
cpk123 Wrote: ------------------------------------------------------- > Is it just my feeling? > It looks like (seeing the language and style on > the posts) that AMA and alta168 are two alter > egos… One posts the other counter questions) Haha, good catch CP. AMA (and alta168), I suspect, are incarnations of AMC who also bombarded the forum with similar questions last year. AMC then AMA: I guess AMB was stillborn :-).
cpk123 & elcfa, I am sorry that I am new in this forum and I don’t know AMA, AMC…at all. It’s good for me to have discussions so that we can have better undertanding of those materials in CFA curriculum and your responses are much appreciated. Just for reference, I am in Asia.
Since this topic is on Reading 31, I don’t understand the following statement on page 169: "Recall that by hedging interest rate risk, a manager synthetically creates a Treasury bill and therefore earns the return on a Treasury bill. " I do not recall prior reading that showed hedging interest rate risk means synthetically creating a Treasury Bill. Can someone point me to the relevant chapter prior to Reading 31 that state so? OR is it just another sweeping statement which appears to be typical of the fixed-income statement?
this question had been asked before… as well … http://www.analystforum.com/phorums/read.php?13,1214516,1214516#msg-1214516
Thanks cpk123.
I find this Reading 31 to be worrisome. LOS31d states “compare and contrast duration-based approaches with interest rate sensitivity approaches to hedging mortgage securities.” Nothing is mentioned about calculation, evaluation or computing. Yet, the EOC question 6b showed that this LOS requires calculation on the two-bonds hedge. Getting really worried whether the LOS can be relied on or not.