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# P-Strips & C-Strips

#### nichas

##### New Member
Tuckman says "when reconstituting a bond, any C-STRIPS maturing on a particular coupon payment date may be used as that bond's coupon payment" & "P-STRIPS created from the stripping of a particular bond may
be used to reconstitute only that bond."

I failed to understand this difference between P-strip & C-Strip, principal and coupon part of a particular coupon bond.

Thanks

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi nichas,

It looks like you viewed this already: http://www.bionicturtle.com/learn/article/treasury_strips_4_min_screencast/

Think of two Treasuries, A & B, with same coupons. Both get stripped.
The principal (P) on A gets a different CUSIP # than the principal (P) on B.
But the coupons strips that mature on the same date get the same CUSIP (so they are "fungible" to use Culp's term for a liquid security).

Now reconstitute, say treasury A: you must use the 'P' from 'A' but regarding the coupons (with the same CUSIPs), it won't matter if they are from A or B b/c they have the same CUSIP

maybe this is better: http://www.riskglossary.com/link/treasury_strips.htm

David

#### nichas

##### New Member
Thanks David,
Perfect!
You are a very good teacher I must say.
I did read the first link mentioned above, its good.

One more doubt I have. In the comparison of advantages and disadvantages of stripping a coupon bond
how are zero coupon bonds more sensitive to interest rate than coupon bonds. One example may help.

Thanks,
nichas.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
thanks, i've spent maybe too much time in the tuckman

sure, that goes to duration. The present value (PV) of $100 10-year zero has only the one lump sum (100) discounted to today; it's value = (100)EXP[(-r)(10)]. Due to "length" until receipt, the PV fluctuates greatly with changes in the rate (its Macaulay duration = 10 years). Now add coupons: the PV is now a function of several "embedded" zeros where the coupons are less sensitive because they arrive earlier; less time until receipt. So the coupons bring down (dilute) the bond's duration. Only a zero can have Maucaulay duration = time to maturity. the other advantage he mentions might be even more signifacent "immunization" - like pensions funds match assets/liabilities, the adv of a zero is you focus the cash receipt when you'll need it and you don't have to fret the "reinvestment risk" of the coupons... David #### nichas ##### New Member Thanks David, Got it! #### minnie ##### New Member hello,david! I have one question , why shorter term C-strips tend to tade rich,and longer term C-strips tend to tade cheap? thank you ! #### nichas ##### New Member Hi Minnie, Say we have 3 C-strips over a period of 1.5 years. The first strip's present value (maturing after 6 months) when discounted today will be more than the second C-strip's PV (maturing after an year) Same will be the case between the 2nd C-strip and 3rd strip(maturing after an year and half) So PV of 1st Cstrip > PV of 2nd Cstrip > PV of 3rd Cstrip and so on.. hence short term Cstrips trade rich and long term trade cheap... Correct me David if I am wrong. #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Sachin, I agree with your illustration in the context of a "pricing framework;" i.e., you explain why the PV [near term C STRIP] ought to be lower than PV [distant C STRIP]. But when Tuckman says the near term C STRIP "trades rich," he means that its (observed or empirical) market price is greater than the price you would expect (by inferring discount/spot rates that are bootstrapped from traded Treasuries). In his case, it's a "violation" of no arbitrage (one price law), but in a world absent friction and fully liquid. So, I don't *why* know Tuckman finds this. He suggests (or says) that illiquidity is responsible for differences between pricing framework and empirical prices. But it doesn't really answer the question *if* the mispricing pattern is persistent. Illiquidity, to my thinking, would cause either random variation (sometimes rich, sometimes cheap) or, more likely, a persistently cheap price for illiquidity (these are pretty illiquid), but not the pattern shown. A predictable persistence could be due to something technically persistent like traders always tend to buy more (demand more) short term c strips. But for myself, as it's an empirical observation, I don't struggle with it (nor do I assume Tuckman's 2001 data is correct today?!) only because it reminds me of, and maybe this isn't the greatest analogy, how the market price of a closed end mutual fund varies from its NAV. There maybe isn't a great fundamental explanation, as ultimately price is set be supply/demand. but great question, it's been in the curriculum for a long while and it's the first time i've been asked about it. Nice! David #### minnie ##### New Member Thank you ,DAVID and NICHAS! I have another problem when reading TUCKMAN's book. Chapter 4 : How to calculate or determine flat price ? because "full price = flat price + AI(4.1)=PV(future cash flows),which discounted by yield rate(4.13) , flat price = PV(future cash flows) - AI ,Is that right? #### yuqingmi ##### New Member Hi David, I just started reading Tuckman and (immediately) have 2 questions, please help ~~ Thanks! 1. Under what circumstances would the bonds be reconstituted? Why reconstituting a bond? 2. It is written that "P-Strips created from the stripping of a particular bond may be used to reconstitute only that bond. This difference implies that P-strips inherit the chepaness or richness of the bonds from which they are derived" my question is: What does it mean by "P-strips inherit the chepaness or richness of the bonds from which they are derived?" Thanks! #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Hi yuqingmi, 1. As a reconstitution is reverse-stripping (trader deliver multiple zeros and gets back a coupon bond), I agree its need is less obvious. Stripping is explained by an appetite for zero coupon bonds. But recon, just to my knowledge (I don't have practical experience here), is largely an arbitrage play: if dealer sees his/her bundle of matching strips is trading rich, can sell them in exhange for recon bond and make a small arbitrage profit. So, i'm only aware of an arbitrage motive. Systemically, the existence of this market (i.e., the ability of traders to arbitrage the price difference) tends to keep them close. Just the "threat" of recon market helps makes the STRIP market efficient. 2. The bond's predicted value, given by a pricing framework, is X. If the bond's *observed* market price > X, the bond is "trading rich"; If observed price < X, bond is trading cheap. (Trading rich or cheap is a violation of his "law of one price." The trade cheap/reach will always be hard to attribute because, by definition, what explains it is outside the model/pricing framework. Tuckman thematically attributes trading rich/cheap to lack of, or an excess of, liquidity which seems to me consistent with much research). So, first he is saying, long term Treasury (coupon) bonds tend to trade rich (market price > price implied by model). He explains this primarily by a extra liquidity; i.e., lack of liquidity would lead to a discount, "excess" liquidity leads to a premium. But again, i would tread the observation of trading cheap/rich as an observed phenomenon, which may change. Ultimately, supply/demand creates "trade rich, trade ceap" Second, see thread above about fungible or not fungible. The C-STRIPS are fungible (any matching Treasure can be used); but the P-STRIPS must strip/reconstitute only with their matching Treasury. Therefore, a C-STRIP will price *efficiently* in the ocean of matching coupons, but the P-STRIP is linked to its bond (less efficiently if you will). If you think about the recon arbitrage above, and you hold a P-STRIP, since it reconstitutes only into its matching bond, your arbitrage is a function of relationship only with that bond price. So, if it is rich, your STRIP will tend to be rich (or, if the P-STRIP starts to diverge too much from it's matching bond, which it is "married to", unlike the C-STRIP, an arbitrage becomes possible). Hope that helps, great questions! David #### yuqingmi ##### New Member Hi David, Thank you for the useful and insightful reply! Thanks! #### Francesca ##### New Member Hi David, I have also few questions relating to Tuckman. 1- what's the difference between the structure of a Treasury coupon bonds and a Treasury P-strip and C-strip? 2-what's teh difference yield curve calculations yield using P-strip and C-strip? In chapter 7, I don't understand the definition of the key rate 01 and the difference with key rate duration? Thanks, Francesca #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Hi Francesca, 1. You might find this helpful: a 4-min screencast I did on these here. STRIPS are the zero-coupon bonds extracted from the coupon-bearing Treasuries. 2. The KR01 is to key rate duration as DV01 is to duration. Duration is measure of price change given a PARALLEL 1% shift in the yield curve. Key rate duration is similar, except it is the price change (in %) given only a NON-PARALLEL SHOCK to the key rate. DV01 is the price change ($) given a 1 basis point PARALLEL yield curve shift, whereas KR01 is the price change ($) given a 1 bps non parallel shock to only the key rate. I recommend you get comfortable first with Duration and DV01. And, please note, these are more similar than different (both are linear sensitivities), the difference is really units: DV01 = Price*Duration/10,000. This shows how duration/DV01 are close cousins. Okay, then see that KR01, key rate duration are similar but except for the assumption of a parallel shift in the entire yield curve, we ask for only a shift (shock) to the key rate (and the neighboring rates, whatever is the rule) Hope that helps. David #### Francesca ##### New Member thanks David!! Really helpful!!! Francesca #### Nikjam ##### New Member Hi David, Just started reading Tuckman and I am confused with STRIPS.Read the posts for year 2008 but I still have some basic doubts. Lets take an example of 5-year$10000 US Treasury Bond with annual coupon rate 5% .Now on stripping this would give 1 P-STRIP & 10 C-strips.What I am unclear about is:
1 I will have to pay $10000 for C-strip.Now the one that matures in 6 months gives me 2.5%, the one that matures after a year gives 5% the one that matures after a year gives 7.5% and so on.So that means$10000 paid gives $10250 after 6 months and$10000 paid gives 10500 after 1 year and so on.But the $10000 invested in P-STRIP gives$10500 after 5-years.So on comparision with the returns that C-STRIPS yield in a shorter duration why will a Investor invest in P-STRIPS?
Or is it that the P-STRIPS are issued at present value and they lead to a payment of the par value at the time of maturity like the normal Treasury bonds?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Nikjam,

Your last sentence is true: STRIPS are zero coupon bonds so they must be issued at a discount (and, they will trade at discount, generally getting "pulled to par" as maturity nears). I input the Tuckman XLS here (we like to collect these!):

http://sheet.zoho.com/public/btzoho/cstrips

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