Understanding Treasury Futures

Transcript

INTEREST RATES Understanding Treasury Futures Thirty-year Treasury bond futures were originally introdued on the Chiago !oard of Trade in "#$$% The &rodut line was aug'ented o(er the years by the introdution of ")-year* +-year* ,-year Treasury note and )-year .Ultra/ Treasury bond futures%" This &rodut line has e0&eriened tre'endous suess as the sale and global signifiane of U%1% Treasury in(est'ent has grown o(er the years% Today* these &roduts are utili2ed on an international basis by institutional and indi(idual in(estors for &ur&oses of both abating and assu'ing ris3 e0&osures% in(est'ents gi(en that the .full faith and redit/ of the U%1% go(ern'ent ba3s these seurities%  The seurity buyer an either hold the bond or note until 'aturity* at whih ti'e the fae (alue beo'es due; or* the bond or note 'ay be sold in the seondary 'ar3ets &rior to 'aturity% :n the latter ase* the in(estor reo(ers the 'ar3et (alue of the bond or note* whih 'ay be 'ore or less than its fae (alue* de&ending u&on &re(ailing yields% :n the 'eanti'e* the in(estor reei(es se'i-annual ou&on &ay'ents e(ery si0 'onths% Treasury Futures Avg Daily olu!e This dou'ent is intended to &ro(ide an o(er(iew of the funda'entals of trading U%1% Treasury bond and note futures% 4e assu'e only a ursory 3nowledge of ou&on-bearing Treasury seurities% Thus* we begin with a &ri'er on the o&eration of ash Treasury 'ar3ets before 'o(ing on to &ro(ide so'e detail regarding the features of the U%1% Treasury futures ontrats as well as a disussion of ris3 'anage'ent a&&liations with U%1% Treasury futures% *)))*))) ,*+))*))) ,*)))*))) "*+))*))) "*)))*))) +))*))) en(iron'ent* the 'ar3et (alue of their bonds will inrease% #F Yields Rise  T$%& Prices Fall  #F Yields Fall  T$%& Prices Rise  This in(erse relationshi& 'ay be understood when one loo3s at the 'ar3et&lae as a true aution% ssu'e an in(estor &urhases a ")-year note with a A@ ou&on when yields are at A@% Thus* the in(estor &ays "))@ of the fae or &ar (alue of the seurity% 1ubse5uently* rates rise to $@% The in(estor deides to sell the original bond with the A@ yield* but no one will &ay &ar as notes are now 5uoted at $@% Iow he 'ust sell the bond at a disount to &ar in order to 'o(e the bond% I.e., rising rates are ao'&anied by delining &ries% Falling rates &rodue the re(erse situation% :f rates fall to +@* our in(est'ent yields 'ore than 'ar3et rates% Iow the seller an offer it at a &re'iu' to &ar% Thus* delining rates are ao'&anied by rising &ries% 1hould you hold the note until 'aturity* you Or* you 'ay 5uote to the nearest ">",?th% :f our bond were to rally fro' #$-"?>,nds  by ">",?th* it 'ight be 5uoted on a ash sreen as #$-"?,% The trailing .,/ 'ay be read as ,>?ths  of ">,nd; or* ">",?th% :f the seurity rallies fro' #$-"?>,nds by >",?ths* it 'ay be 5uoted as #$-"?A% The trailing  .A/ 'ay be read as A>?ths of ">,nd or >",?ths% 1o'eti'es* 5uotation syste's use an alternate frational referene% E.g., the (alue of #$-"?, 'ight be dis&layed as #$-"?J% Or a (alue of #$-"? 'ight be dis&layed as #$-"?K%  (alue of #$-"?A 'ight be dis&layed as #$-"?L% Futures 5uotation &raties are si'ilar but not entirely idential%  5uote of #$-"?, is the sa'e no 'atter whether you are loo3ing at a ash or a futures 5uote% :t 'eans #$@ of &ar &lus "?>,nds &lus ">",?th% 'uotation Practices Cash Price (eans Deci!al %)uivalent *+ o, Par Futures 'uote Treasury note futures =,))*))) fae (alue% are traded in units of Accrued #nterest and Settle!ent Practices :n addition to &aying the 6negotiated7 &rie of the ou&on-bearing seurity* the buyer also ty&ially o'&ensates the seller for any interest arued between the last se'i-annual ou&on &ay'ent date and the settle'ent date of the seurity% s3i& date/ settle'ent on the Friday* et% 13i& or forward date settle'ents 'ay be useful in order to 'ath Treasury transation &ay'ents with ones antii&ated future ash flows at urrent 'ar3et &ries% Theoretially* there is no effeti(e li'itation on the nu'ber of days o(er whih one 'ay defer settle'ent% Thus* these ash seurities 'ay effeti(ely be traded as forward ontrats% Treasury Auction Cycle E.g., it is 8anuary ")* ,)"% Hou &urhase =" 'illion fae (alue of the "-+>?@ Treasury seurity 'aturing in Io(e'ber ,),, 6a ten-year note7 for a &rie of #$-"? 6=#$+*$?"%,+7 to yield "%?#@* for settle'ent on the ne0t day* 8anuary ""* ,)"% Treasury seurities are autioned on a regular basis by the U%1% Treasury whih ae&ts bids on a yield basis fro' seurity dealers%  ertain a'ount of eah aution is set aside* to be &laed on a nono'&etiti(e basis at the a(erage yield filled% :n addition to the &rie of the seurity* you 'ust further o'&ensate the seller for interest of =,*++?%$) arued during the +$ days between the original issue date of Io(e'ber "+* ,)", and the settle'ent date of 8anuary ""* ,)"% Prior to the atual issuane of s&eifi Treasuries* they 'ay be bought or sold on a .4:/ or .4hen :ssued/ basis% 4hen traded on a 4: basis* bids and offers are 5uoted as a yield rather than as a &rie% 0S0 Treasury Auction Schedule This interest is alulated relati(e to the +$ days basis are settled against a &rie on the atual issue date of the seurity* alulated &er standard &rieyield for'ulae% seurity* the third 'ost reently issued seurity is the .old-old/ seurity* the fourth 'ost reently issued seurity is the .old-old-old/ seurity% 1eurity dealers &urhase these seurities and subse5uently 'ar3et the' to their usto'ers inluding &ension funds* insurane o'&anies* ban3s* or&orations and retail in(estors% The 'ost reently issued seurities of a &artiular 'aturity are referred to as .on-the-run/ seurities% On-the-runs are ty&ially the 'ost li5uid and ati(ely traded of Treasury seurities and* therefore* are often referened as &riing benh'ar3s% ess reently issued seurities are 3nown to as .off-the-run/ seurities and tend to be less li5uid% s of 8anuary ""* ,)"* the 'ost reently issued ")-year note was identified as the "-+>?@ note 'aturing in Io(e'ber ,),,; the old note was the "+>?@ note of ugust ,),,; the old-old note was the "->@ of May ,),,; the old-old-old note was the ,@ of February ,),,% The Treasury urrently issues -wee3* "-wee3* ,Awee3 and +,-wee3 bills; ,-year* -year* +-year* $year and ")-year notes; and* )-year bonds on a regular shedule% :n the &ast* the Treasury had also issued seurities with a -year and ,)-year 'aturity% Further* the Treasury 'ay issue (ery short ter' ash 'anage'ent bills along with Treasury :nflation Proteted 1eurities or .T:P1%/ !eyond that* one is e0&eted to identify the seurity of interest by ou&on and 'aturity% For e0a'&le* the .,s of Q,"/ refers to the note with a ou&on of ,@ 'aturing on Io(e'ber "+* ,),"% s of 8anuary ")* ,)"* there were not any .4:/ or .when issued/ ")-year notes% 4:s ty&ially 5uoted and traded on a yield basis in antii&ation of the establish'ent of the ou&on subse5uent to the original aution% 17-Year Treasury &otes *As o, 6anuary 178 "71. year all feature% That &ratie was disontinued at that ti'e* howe(er* as the Treasury instituted its  .1e&arate Trading of Registered :nterest and Prini&al on 1eurities/ or 1TR:P1 &rogra' with res&et to all newly issued ")-year notes and )year bonds%  The Roll and ?i)uidity Clearly* traders who fre5uently buy and sell are interested in 'aintaining &ositions in the 'ost li5uid seurities &ossible% s suh* they tend to &refer onthe-run as o&&osed to off-the-run seurities% :t is intuiti(e that on-the-runs will offer su&erior li5uidity when one onsiders the .life-yle/ of Treasury seurities% Treasuries are autioned* largely to bro3er-dealers* who subse5uently atte'&t to &lae the seurities with their usto'ers% Often these seurities are &urhased by in(estors who 'ay hold the seurity until 'aturity% t so'e &oint* seurities are .&ut-away/ in an in(est'ent &ortfolio until their 'aturity% Or* they 'ay beo'e the suboffer s&read in the roll* offering the o&&ortunity to sell the old note>buy the new note; or* buy the old note>sell the new note* in a single transation% The .old note/ in our table abo(e was 5uoted at a yield of "%?$@ while the .new note/ was seen at "%?#+@% :n this ase* the roll is 5uoted at a&&ro0i'ately negati(e + basis &oints 6-)%)?@ B "%?$@ - "%?#+@7% This iru'stane runs ontrary to our ty&ial assu'&tion that traders will be willing to forfeit a s'all a'ount of yield for the &ri(ilege of holding the &ro(ision that the transations are re(ersed at ter' with the lender wiring ba3 the original &rini&al &lus interest% The borrower is said to ha(e e0euted a re&urhase agree'ent; the lender is said to ha(e e0euted a re(erse re&urhase agree'ent% Many ban3s and seurity dealers will offer this ser(ie* one the usto'er a&&lies and &asses a re5uisite redit he3% The 3ey to the transation* howe(er* is the safety &ro(ided the lender by (irtue of the reei&t of the 6highly-'ar3etable7 Treasury seurity% These re&o transations are ty&ially done on an o(ernight basis but 'ay be negotiated for a ter' of one-wee3* twowee3s* one 'onth%  third &arty ustodian is fre5uently used to add an additional layer of safety between the lender and borrower* i.e.,  a tri-&arty re&o agree'ent% O(ernight re&o rates are ty&ially 5uite low in the (iinity of Fed Funds% ny Treasury seurity 'ay be onsidered .good/ or  .general/ ollateral% 1o'eti'es when &artiular futures ontrat* as a'ended* is referred to as the  .lassi/ bond futures ontrat% :t is li3ewise te'&ting to refer to U%1% Treasury bond and note futures as .A@ ontrats%/ This too 'ay be so'ewhat 'isleading% T-bond and T-note futures are based nominally   u&on a A@ ou&on seurity% !ut in &oint of fat* the ontrat &er'its the deli(ery of any   ou&on seurity* again &ro(ided that it 'eets the 'aturity s&eifiation 'entioned abo(e% I.e., shorts are not neessarily re5uired to deli(er A@ ou&on bonds% :n fat* there 'ay be no eligible for deli(ery seurities that atually arry a ou&on of &reisely A@ at any gi(en ti'e% !eause of the rather broadly defined deli(ery s&eifiations* a signifiant nu'ber of seurities* ranging widely in ter's of ou&on and 'aturity* 'ay be eligible for deli(ery% This a&&lies with e5ual effet to ,-* -* +- and ")-year Treasury note futures; as well as the lassi and Ultra T-bond futures ontrats% seurity that is tendered by referene to the A@ futures ontrat standard% The .Prini&al :n(oie 'ount/ &aid fro' long to short u&on deli(ery 'ay be identified as the Futures 1ettle'ent Prie 'ulti&lied by the Con(ersion Fator 6CF7 'ulti&lied by ="*)))% That ="*))) onstant reflets the ="))*))) fae (alue futures ontrat si2e assoiated with 'ost Tnote and T-bond futures% Iote that the ,-year Tnote ontrat is based on a =,))*))) fae (alue a'ount% Thus* this onstant 'ust be reset at =,*))) for ,-year Treasury futures%    =      ()  $1,000 ny interest arued sine the last se'i-annual interest &ay'ent date is added to the &rini&al in(oie a'ount to e5ual the total in(oie a'ount%    =    +   6""%$+$+7* the &rini&al in(oie a'ount 'ay be alulated as follows%    = 1!1"#!!#%  0"#0##  $1,000 = $!,&" :n order to arri(e at the total in(oie a'ount* one 'ust of ourse further add any arued interest sine the last se'i-annual interest &ay'ent date to the &rini&al in(oie a'ount% Cheapest-to-Deliver The intent of the on(ersion fator in(oiing syste' is to render e5ually eono'i the deli(ery of any eligible-for-deli(ery seurities% Theoretially* the short who has the o&tion of deli(ering any eligible seurity should be indifferent as to his seletion% 9owe(er* the CF syste' is i'&erfet in &ratie as we find that a &artiular seurity will tend to e'erge as hea&est-to-deli(er/ 6CT7 after studying the relationshi& between ash seurity &ries and &rini&al in(oie a'ounts% i'&liations for basis traders who arbitrage ash and futures 'ar3ets%  basis trader will see3 out arbitrage o&&ortunities or situations where they 'ight be able to a&itali2e on relati(ely s'all &riing disre&anies between ash seurities and Treasury futures by buying .hea&/ and selling .rih/ ite's% rbitrageurs will tra3 these relationshi&s by studying the basis% The basis desribes the relationshi& between ash and futures &ries and 'ay be defined as the ash &rie less the ad &oints 'ight be shown as )>,nds% :t is also .in(erted/ in the sense that we are o'å ash less ad?@-"# e0hibited the lowest basis and* therefore* 'ay be onsidered the CT seurity% Iote* howe(er* that there are 5uite a few seurities* with si'ilar ou&ons and 'aturities* whih are near CT% :n fat* the entire uni(erse of eligible-fordeli(ery seurities features reasonably si'ilar ou&ons and 'aturities% :t is i'&ortant to identify the CT seurity to the e0tent that Treasury futures will tend to &rie or tra3 or orrelate 'ost losely with the CT% This has interesting i'&liations fro' the stand&oint of a  .basis trader/ or a hedger as disussed in 'ore detail below% 1uffie it to say at this &oint that basis trading is a fre5uent &ratie in the Treasury futures 'ar3ets% Certain ter'inology has been de(elo&ed to identify basis &ositions% One 'ay .buy the basis/ by buying ash seurities and selling futures% One 'ay .sell the basis/ by selling ash seurities and buying the CF reflets relati(e (alue then &resu'ably it will reflet relati(e (olatility or &rie 'o(e'ent as well% 9hy #s >ne #ssue CTDH :f the on(ersion fator in(oiing syste' &erfor'ed flawlessly* all eligible-for-deli(ery seurities would ha(e a si'ilar basis and be e5ually eono'i to deli(er% s suggested abo(e* howe(er* a single seurity or se(eral si'ilar seurities tend to e'erge as CT% The CF in(oiing syste' is i'&erfet beause it is i'&liitly based on the assu'&tion that - 6"7 all eligible-for-deli(ery seurities ha(e the sa'e yield; and 6,7 that yield is A@% !ut there are any nu'ber of .ash 'ar3et biases/ that i'&at u&on the yield of a Treasury seurity% Further 'athe'atial biases in the on(ersion fator alulation will tilt the field towards seurities of &artiular ou&ons and 'aturities when yields are greater than or less than the A@ ontrat standard% 9ene* we 'ay further s&ea3 of .on(ersion fator Prior to the sub&ri'e 'ortgage risis that eru&ted in ,))?* the yield ur(e has been rather flat out &ast "+ years% Thus* this fator has* as an historial 'atter* had little i'&at on the deli(ery of bonds into the )-year T-bond ontrat% More reently* howe(er* we see that the yield ur(e has generally stee&ened suh that the different between ")- and )-year yields has e0&anded to greater than "@% 1till* this fator 'ay not be terribly o(ert as it tends to be obsured by on(ersion fator biases as disussed below% ow or generally falling yields 'ay &ro(e &roble'ati to the seurity in(estor to the e0tent that a signifiant o'&onent of ones return is attributable to rein(est'ent ino'e% Cou&on &ay'ents* one reei(ed* will be rein(ested* &resu'ably at &re(ailing short-ter' rates% 4hen rein(est'ent ris3s beo'e notieable* in(estors will &refer low-ou&on seurities* generating s'all ou&ons arrying li'ited rein(est'ent ris3s* o(er high-ou&on seurities% Thus* those high-ou&on seurities 'ay beo'e CT% Bias to long duration #, yields I ;+  *i.e., loJ-coupon8 long!aturity securities Bias to short duration #, yields K ;+  *i.e., high-coupon8 short- is a defining feature of an arbitrage* Treasury basis transations li3ewise annot be onsidered an arbitrage  per se% Fre5uently the 'ost o(ert fator that ditates the 'o(e'ent of a basis trade is si'&le diretional &rie 'o(e'ent% !aturity securities CTD Driven Gy Yields "), uration is e0&lained 'ore thoroughly below but thin3 of duration as a 'easure of ris3% 4hen yields are rising and &ries are delining* in(estors will gra(itate towards less ris3y or short-duration seurities% They will want to li5uidate ris3ier long duration seurities* reating a deli(ery bias in fa(or of those long duration bonds% I.e.,  while the on(ersion fator is fi0ed* the relati(e &rie 'o(e'ent of long (s% short duration seurities 'ay be (ery different* thereby reating deli(ery biases% ")" ")" ")) ")) ")) 1hort Ouration 1eurity ong Ouration 1eurity ## ## On the other hand* when yields are delining and &ries rising* in(estors will &refer those ris3ier long duration seurities% Thus* they 'ay wish to li5uidate less aggressi(e short duration seurities* reating a deli(ery bias in fa(or of those short duration seurities% A A@ @ Consider the &eriod between Otober ,)", and early 8anuary ,)" as de&ited in our gra&hi% uring this &eriod* the &rie of the Marh ,)" Ten-year Tnote futures e0&eriened a &rie ad(ane fro' The i'&at of these wea3ening and subse5uently strengthening on(ersion fator biases 'ay be obser(ed by e0a'ining the basis for se(eral eligiblefor-deli(ery seurities% tually* the si'&le and graudual on(ergene of ash and futures &ries 'ay be the feature that is 'ost a&&arent fro' an e0a'intion of this gra&hi% )) (ar-1. 17-Yr Basis ,+) ?ong Duration Basis Rising ,)) "+) ?ong Duration Basis Falling ")) +) )       ,       ,       ,       ,       ,       "       "       "       "       "       >       >       >       >       >       "       ?       +       ,       #       >       >       "       ,       ,       )       )       >       >       >       "       "       )       )       )       "       "       " "-+>?@-,, !asis       ,       ,       ,       ,       ,       ,       "       "       "       "       "       "       >       >       >       >       >       >       +       ,       #       A       -       )       >       "       "       ,       >       "       "       >       >       >       ,       >       "       "       "       "       "       ,       "       "       "       "       ,       ,       ,             "       "       "       "       >       >       >       >       $       G       "       $       "       ,       -       >       >       >       >       "       ,       ,       ,       "       "       " "->G@-,, !asis Finally* note that ->?@-"# re'ained hea&est to deli(er throughout the &eriod in 5uestion* during whih ti'e its basis on(erged rather steadily down towards 2ero% :t is lear that the &erfor'ane of the basis is strongly dri(en by diretional &rie 'o(e'ent in the Treasury 'ar3ets% Thus* .buying the basis/ or  .selling the basis/ 'ay be 'oti(at ed by e0&etations regarding rising or falling yields% The 3ey is to get a sense of 'ar3et diretion and then identify the long or short duration seurities whose basis (alues will be i'&ated by any si2able &rie 6or yield7 'o(e'ent% #!plied Repo Rate 4e often suggest that the seurity with the lowest basis is hea&est-to-deli(er% !ut to be &erfetly orret* we 'ay &oint out that the struture of ou&on reei&ts and rein(est'ent of suh ou&on ino'e &lays so'e 6generally s'all7 &art in establishing a &artiular seurity as hea&est-to- the ->?@-"# is hea&er to deli(er relati(e to the "->@-,,% :n fat* if we san the :RRs assoiated with all seurities eligible to be deli(ered into the Marh ,)" ontrat in Table , below* we find that the :RR of )%","@ assoiated with the ->?@-"# is su&erior to all other :RRs% Thus* the ->?@-"# Treasury seurity is assoiated with the lowest basis and the highest :RR as of 8anuary ")* ,)"% s a general rule* the seurity with the lowest basis will li3ewise e0hibit the highest i'&lied re&o rate% :t is &ossible that a seurity with the lowest basis 'ay not 5uite ha(e the highest :RR beause of ash flow onsiderations% !ut this state'ent is generally true% :n any e(ent* this obser(ation onfir's the CT status of the ->?@"# as of 8anuary ")* ,)"% !y buying the basis of a Treasury seurity* or buying ash and selling futures* one beo'es obligated to 'a3e deli(ery of the Treasury in satisfation of the 'aturing futures ontrat% + Thus* buying the basis of the hea&est-to-deli(er ->?@-"# (s% a futures ontrat that 'atures two or three 'onths hene* the o&&ortunity to use the futures ontrat as a deli(ery on(eyane% Consider any disre&any with res&et to the CT to re&resent a ris3 &re'iu' of sorts% :f one buys the CT seurity and sells futures with the intention of 'a3ing deli(ery* the worst ase senario has the basis on(erging fully to 2ero and the hedger essentially lo3ing in a return e5ual to the :RR* in this ase )%","@% !ut if 'ar3et onditions should hange suh that another seurity beo'es CT* this i'&lies that the basis 'ay ad(ane* or at least fail to o'&letely on(erge to 2ero% s a result* the trader 'ay reali2e a rate of return that is in fat greater than the urrently alulated :RR% Basis >ptionality :n other words* there is a ertain degree of  .o&tionality/ assoiated with the &urhase or sale of the basis% !uying the basis is analogous to buying an o&tion whih* of ourse* i'&lies li'ited ris3% &rofile of a short o&tion &osition* thus the analogy between a short basis &osition and a short o&tion% s disussed abo(e* the basis e(en for the CT seurity tends to be in e0ess of ost of arry onsiderations% This is 'anifest in the fat that the :RR e(en for the CT is ty&ially a bit below &re(ailing short-ter' rates% This &re'iu' in the basis essentially reflets the unertainties assoiated with whih seurity 'ay beo'e CT in the future% Thus* the basis &erfor's 'uh a3in to an o&tion% i3e any other o&tion* the basis will be affeted by onsiderations inluding ter'* (olatility and stri3e &rie% The rele(ant ter' in this ase is the ter' re'aining until the &resu'ed deli(ery date (s% the futures ontrat% Mar3et (olatility affets the &robability that a rosso(er 'ay our% Rather than s&ea3 of a stri3e or e0erise &rie* it is 'ore a&&ro&riate to assess the 'ar3ets &ro0i'ity to a  .rosso(er &oint/ or a &rie>yield at whih one 'ight e0&et an alternate seurity to beo'e CT% Consider the &urhase or sale of the CT basis% The Finally* if rates are lose to the A@ futures ontrat standard* the basis for what is urrently CT 'ay be ditated by onsiderations a&art fro' on(ersion fator biases% Thus* there 'ay be signifiant rosso(ers regardless of whether rates rise or fall% !uying the CT basis under these onsiderations 'ay be onsidered a3in to the &urhase of an o&tion straddle 6i.e.,  the si'ultaneous &urhase of all and &ut o&tions7% Under these iru'stanes the basis buyer 'ay be indifferent between ad(aning or delining &ries but has an interest in seeing &ries 'o(e signifiantly in either diretion% 1elling the CT basis when rates are near the A@ ontrat standard is a3in to selling a straddle 6i.e%* the si'ultaneous sale of both all and &ut o&tions7% The basis is sold under these iru'stanes beause the trader antii&ates an essentially neutral 'ar3et% Yields K ;+ Yields L ;+ Yields I ;+ Buy CTD Basis !uy Put O&tion !uy 1traddle !uy Call O&tion Sell CTD Basis 1ell Put O&tion 1ell 1traddle 1ell Call O&tion 'anage the'% The &artiular harateristis of a ou&on-bearing seurity will learly i'&at u&on its (olatility% Two readily identifiable ways to define ou&onbearing seurities is in ter's of their 'aturity and ou&on% efining (olatility as the &rie reation of the seurity in res&onse to hanges in yield we 'ight draw onlusions as follows% ?onger (aturity  reater olatility  $igher Coupon  ?oJer olatility  ll else held e5ual* the longer the 'aturity of a fi0ed ino'e seurity* the greater its &rie reation to a hange in yield% This 'ay be understood when one onsiders that the i'&liations of yield 'o(e'ents are felt o(er longer &eriods* the longer the 'aturity% On the other hand* high ou&on seurities will be less i'&ated* on a &erentage basis* by hanging yields than low ou&on seurities% This 'ay be understood when one onsiders that high ou&on seurities return a greater &ortion of ones original Duration :f !P 'easures the absolute hange in the (alue of a seurity gi(en a yield flutuation; duration 'ay be thought of as a 'easure of relati(e or &erentage hange% The duration 6ty&ially 5uoted in years7 'easures the e0&eted &erentage hange in the (alue of a seurity gi(en a one-hundred basis &oint 6"@7 hange in yield% uration is alulated as the a(erage weighted 'aturity of all the ash flows assoiated with the bond* i.e.,  re&ay'ent of .or&us/ or fae (alue at 'aturity &lus ou&on &ay'ents* all disounted to their &resent (alue% (easuring olatility *As o, 6anuary 178 "71. "-Yr &ote .-Yr &ote <-Yr &ote Coupon (aturity ">?@ >?@ >@ ",>">" )">"+>"A ",>">"$ Duration *Yrs "%#A+ ,%#?) %?A$ BP *per !il ="#A =,#? =?A ati(ities% Effeti(e use of these ontrats* howe(er* re5uires a ertain grounding in hedge tehni5ues% Most &ointedly* one 'ay atte'&t to assess the relati(e (olatility of the ash ite' to be hedged relati(e to the futures ontrat &rie% This relationshi& is often identified as the futures .9edge Ratio/ 69R7% 9edge ratios reflet the e0&eted relati(e 'o(e'ent of ash and futures and &ro(ide ris3 'anagers with an indiation as to how 'any futures to use to offset a ash e0&osure%  on(ersion fator weighted hedge is li3ely to be 5uite effeti(e if you are hedging the hea&est-todeli(er seurity% Treasury futures will tend to &rie or tra3 or orrelate 'ost losely with the CT seurity% !ut other seurities with different ou&ons and 'aturities 'ay reat to hanging 'ar3et onditions differently% Thus* one 'ight 5uestion if you an or should do better than a CF weighted hedgeS BP 9eighted $edge The 'ost su&erfiial way to a&&roah identifiation of the a&&ro&riate hedge ratio is si'&ly to 'ath the fae (alue of the ite' to be hedged with the fae (alue of the futures ontrat% :n order to understand the 'ost effeti(e tehni5ues with whih to a&&ly a hedge* onsider the funda'ental ob@-",% *> 34 = 0"&'0 ?$&,$#0"%%%00@ = 10"!  10  Iote that the 9R B ") is signifiantly greater than the $" ontrats suggested by referene to the on(ersion fator of the "->@-,, seurity% This is due to the fat that the CT seurity arries a relati(ely short duration of A%"+ years o'&ared to the duration assoiated with the hedged seurity of ?%+?? years% :t is no oinidene that the ratio of durations is roughly e5ual to the ratio between the !P and CF hedge ratios or 6A%"+ W ?%++?7 X 6$" M ")7% I.e., the futures ontrat is &riing or tra3ing or orrelating 'ost losely with a shorter duration seurity% Conse5uently* futures &ries will reat rather 'ildly to flutuating yields% Therefore one re5uires 'ore futures to enat an effeti(e hedge% E.g.,  what would our hedge ratio be if the CT Crossover Ris:s Port,olio $edging This further suggests that* if there is a rosso(er in the CT fro' a short duration seurity to a longer duration seurity* the nu'ber of futures needed to hedge against the ris3 of delining &ries is dereased% This 'ay be a fa(orable iru'stane for the hedger who is long ash Treasuries and short futures in a ratio &resribed by the !P tehni5ue% Thus far* our disussion has entered about o'&arisons between a single seurity and a Treasury futures ontrat* a .'iro/ hedge if you will% !ut it is far 'ore o''on&lae for an in(estor to beo'e onerned about the (alue of a &ortfolio of seurities rather than fous on a single ite' within a &resu'ably di(ersified set of holdings% Consider that as &ries deline and longer duration seurities beo'e CT* one is essentially o(erhedged in a delining 'ar3et% :f on the other hand* &ries ad(ane and e(en shorter duration seurities beo'e CT* the a&&ro&riate hedge ratio will tend to inrease% Thus* the long hedger beo'es underhedged in a rising 'ar3et% 9ow 'ight one address the ris3s assoiated with a &ortfolio of seurities* i.e%* how to e0eute a .'aro/ hedgeS The sa'e &rini&les a&&ly whether hedging a single seurity or a &ortfolio of seurities% Thus* we need to e(aluate the ris3 harateristis of the &ortfolio in ter's of its !P and duration AB875BCDB : <*> ;7 E.g., assu'e that you held a =")) 'illion fi0ed ino'e &ortfolio with a !P B =?)*))) and a duration of ? This duration is si'ilar to the The returns on this benh'ar3 'ay be identified as the .ore/ or .beta/ returns assoiated with the &ortfolio% :n addition* the asset 'anager 'ay e0erise so'e li'ited degree of latitude in an atte'&t to out&erfor' the benh'ar3* or to a&ture so'e e0ess return 3nown as .al&ha/ in urrent in(est'ent &arlane% sset 'anager 'ay be authori2ed to adAB875BCDB : <*>;7 I 34 =  years and re'aining a re'aining 'aturity of not 'aturity of not less than " 'ore than  year and # years but not 'onths fro' less than , "st day of years* # deli(ery 'onth 'onths fro' but not 'ore last day of than , years deli(ery 'onth fro' last day of deli(ery 'onth :n(oie &rie B settle'ent &rie <-Year T17-Year T&ote Futures &ote Futures ="))*))) fae-(alue U%1% Treasury notes Classic Tltra T-Bond Bond Futures Futures ="))*))) fae-(alue U%1% Treasury bonds T-notes with original 'aturity of not 'ore than + years and  'onths and re'aining 'aturity of not less than  years and , 'onths as of "st day of deli(ery 'onth% T-bonds with re'aining 'aturity of at least "+ years but no 'ore than ,+ years% T-notes 'aturing at least A-K years but not 'ore than ") years* fro' "st day of deli(ery 'onth% T-bonds with re'aining 'aturity of at least ,+ years but no 'ore than ) years 0 on(ersion fator 6CF7  arued interest* CF B &rie to yield A@ ia Federal Reser(e boo3-entry wire-transfer Marh 5uarterly yle Y Marh* 8une* 1e&te'ber* ee'ber