The U.S. Treasury Yield Curve: 1961 to the Present


 Corey Woods
 3 years ago
 Views:
Transcription
1 Finance and Economics Discussion Series Divisions of Research & Saisics and Moneary Affairs Federal Reserve Board, Washingon, D.C. The U.S. Treasury Yield Curve: 1961 o he Presen Refe S. Gurkaynak, Brian Sack, and Jonahan H. Wrigh 68 NOTE: Saff working papers in he Finance and Economics Discussion Series (FEDS) are preliminary maerials circulaed o simulae discussion and criical commen. The analysis and conclusions se forh are hose of he auhors and do no indicae concurrence by oher members of he research saff or he Board of Governors. References in publicaions o he Finance and Economics Discussion Series (oher han acknowledgemen) should be cleared wih he auhor(s) o proec he enaive characer of hese papers.
2 The U.S. Treasury Yield Curve: 1961 o he Presen * Refe S. Gürkaynak Brian Sack and Jonahan H. Wrigh ** June 6 Absrac The discoun funcion, which deermines he value of all fuure nominal paymens, is he mos basic building block of finance and is usually inferred from he Treasury yield curve. I is herefore surprising ha researchers and praciioners do no have available o hem a long hisory of highfrequency yield curve esimaes. This paper fills ha void by making public he Treasury yield curve esimaes of he Federal Reserve Board a a daily frequency from 1961 o he presen. We use a wellknown and simple smoohing mehod ha is shown o fi he daa very well. The resuling esimaes can be used o compue yields or forward raes for any horizon. We hope ha he daa, which are posed on he websie hp:// and which will be updaed periodically, will provide a benchmark yield curve ha will be useful o applied economiss. * We are graeful o Oliver Levine for superlaive research assisance and o Brian Madigan, Vincen Reinhar and Jennifer Roush for helpful commens. All remaining errors are our own. All of he auhors were involved in yield curve esimaion a he Federal Reserve Board when working a ha insiuion. The views expressed in his paper are solely he responsibiliy of he auhors and should no be inerpreed as reflecing he views of he Board of Governors of he Federal Reserve Sysem or of any oher employee of he Federal Reserve Sysem. ** Gürkaynak: Deparmen of Economics, Bilken Universiy, 68 Ankara, Turkey; Sack: Macroeconomic Advisers, LLC, Washingon DC 6; Wrigh: Federal Reserve Board, Washingon DC 551; () ;
3 1. Inroducion The U.S. Treasury yield curve is of remendous imporance boh in concep and in pracice. From a concepual perspecive, he yield curve deermines he value ha invesors place oday on nominal paymens a all fuure daes a fundamenal deerminan of almos all asse prices and economic decisions. From a pracical perspecive, he U.S. Treasury marke is one of he larges and mos liquid markes in he global financial sysem. In par because of his liquidiy, U.S. Treasuries are exensively used o manage ineres rae risk, o hedge oher ineres rae exposures, and o provide a benchmark for he pricing of oher asses. Wih hese imporan funcions in mind, his paper akes up he issue of properly measuring he U.S. Treasury yield curve. The yield curve ha we measure is an offherun Treasury yield curve based on a large se of ousanding Treasury noes and bonds. We presen daily esimaes of he yield curve from 1961 o 6 for he enire mauriy range spanned by ousanding Treasury securiies. The resuling yield curve can be expressed in erms of zerocoupon yields, par yields, insananeous forward raes, or n bym forward raes (ha is, he myear rae beginning n years ahead) for any n and m. Secion of he paper reviews all of hese fundamenal conceps of he yield curve and demonsraes how hey are relaed o each oher. Secion 3 describes he specific mehodology ha we employ o esimae he yield curve, and Secion 4 discusses our daa and some of he deails of he esimaion. Secion 5 shows he resuls of our esimaion, including an assessmen of he fi of he curve, and secion 6 demonsraes how he esimaed yield curve can be used o calculae he yield on synheic Treasury securiies wih any desired mauriy dae and coupon rae. As an applicaion of his 1
4 approach, we creae a synheic offherun Treasury securiy ha exacly replicaes he paymens of he onherun enyear Treasury noe, allowing us accuraely o measure he liquidiy premium on ha issue. Secion 7 offers some concluding houghs. The daa are posed as an appendix o he paper on he FEDS websie.. Basic Definiions This secion begins by reviewing he fundamenal conceps of he yield curve, including he necessary bond mah. I hen describes he specific esimaion mehod employed in his paper..1 The Discoun Funcion and ZeroCoupon Yields The saring poin for pricing any fixedincome asse is he discoun funcion, or he price of a zerocoupon bond. This represens he value oday o an invesor of a $1 nominal paymen n years hence. We denoe his as d ( n ). The coninuously compounded yield on his zerocoupon bond can be wrien as y ( n) = ln( d ( n))/ n, (1) and conversely he discoun funcion can be wrien in erms of he yield as d ( n) = exp( y ( n) n). () Alhough he coninuously compounded basis may be he simples way o express yields, a widely used convenion is o insead express yields on a couponequivalen or bondequivalen basis, in which case he compounding is assumed o be semiannual insead of coninuous. For zerocoupon securiies, his involves wriing he discoun funcion as
5 d ( n) = 1 ce n (1 + y / ), (3) where ce y is he couponequivalen yield. One can easily verify ha he coninuously compounded yield and he couponequivalen yield are relaed o each oher by he following formula: y ce = ln(1 + y / ). (4) Thus, i is easy o move back and forh beween coninuously compounded and couponequivalen yields. The yield curve shows he yields across a variey of mauriies. Concepually, he easies way o express he curve is in erms of zerocoupon yields (eiher on a coninuously compounded basis or a bondequivalen basis). However, praciioners insead usually focus on couponbearing bonds.. The ParYield Curve Given he discoun funcion, i is sraighforward o price any couponbearing bond by summing he value of is individual paymens. For example, he price of a couponbearing bond ha maures in exacly n years (paying $1) is as follows: n P( n) = ( c/ ) d ( i/ ) + d ( n), (5) i= 1 3
6 where c / is he semiannual coupon paymen on he securiy ha is, i has a saed annual coupon rae of c. 1 Of course, for couponbearing bonds he yield will depend on he coupon raes ha are assumed. One popular way o express he yields on couponbearing bonds is hrough he concep of par yields. A par yield for a paricular mauriy is he coupon rae a which a securiy wih ha mauriy would rade a par (and hence have a couponequivalen yield equal o ha coupon rae). The yield can be deermined from an equaion similar o (5), only seing he price of he securiy equal o $1: n p y ( n) 1 = d ( i /) + d ( n ), (6) i= 1 p where we have replaced he coupon rae wih he variable y ( n ) o denoe he nyear par yield. Solving equaion (6), he par yield is hen given by: y p ( n) = (1 d ( n)). (7) n d (/) i i= 1 The par yields from equaion (7) are expressed on a couponequivalen basis. A coninuously compounded version of his can be derived by assuming a bond pays ou a coninuous coupon rae, in which case he par yield wih mauriy n, y pcc, ( n ), is given by: y pcc, 1 d ( n) ( n) =. (8) n d () i di 1 Because he bond maures in exacly n years, i is assumed o make is coupon paymen oday. Thus, he endofday price of he bond includes no accrued ineres. We will have o address accrued ineres in he pricing of individual Treasury securiies below. For simpliciy, his formula again assumes ha a coupon paymen has jus been made and he nex coupon is a full coupon period away, so ha here is no accrued ineres. 4
7 Zerocoupon yields are a mahemaically simpler and more fundamenal concep han par yields. However, one advanage of expressing he yield curve in erms of par yields is ha financial marke paricipans ypically quoe he yields on couponbearing bonds. Mos financial commenary focuses on individual Treasury securiies, mos ofen he onherun issues he mos recenly issued securiies a each mauriy. These securiies rade near par (a leas iniially) and have shorer duraion (owing o he posiive coupon) han zerocoupon yields wih he same mauriies. 3 Of course, he choice of wheher o focus on zerocoupon yields or par yields is simply a choice of he manner o presen he yield curve once esimaed; hese are alernaive ways of summarizing he informaion in he discoun funcion. In fac, he yield curve can be used o compue he yield for a securiy wih any specified coupon rae and mauriy dae an approach ha we will use below o analyze individual securiies..3 Forward Raes The yield curve can also be expressed in erms of forward raes raher han yields. A forward rae is he yield ha an invesor would agree o oday o make an invesmen over a specified period in he fuure for myears beginning n years hence. These forward raes can be synhesized from he yield curve. Suppose ha an invesor buys one n+ m year zerocoupon bond and sells d ( n+ m) / d ( n) nyear zerocoupon bonds. Consider he cash flow of his invesor. Today, he invesor pays d ( n+ m) for he bond being bough and receives d ( n+ m) d ( n ) = d ( n + m ) for he bond being sold. These cash d ( n) 3 We inroduce he concep of duraion in secion.4 below. The coupon rae for an onherun issue is se afer he aucion a he highes level a which he securiy rades below par. Because Treasury ses coupons in incremens of 1.5 basis poins, his process leaves he issues rading very near par immediaely afer he aucion. 5
8 flows, of course, cancel ou, so he sraegy does no cos he invesor anyhing oday. Afer n years, he invesor mus pay dn ( + m)/ dn ( ) as he nyear bond maures. Afer a furher m years, he invesor receives $1 as he n+ myear bond maures. Thus, his invesor has effecively arranged oday o buy an myear zerocoupon bond n years hence. The (coninuously compounded) reurn on ha invesmen, deermined by he amoun dn ( + m)/ dn ( ) ha he invesor mus pay a ime n o receive he $1 paymen a ime n+m, is wha we will refer o as he nbym forward rae, or he myear rae beginning n years hence. The forward rae is given by he following formula: 1 d ( n+ m) 1 f( nm, ) = ln( ) = (( n+ my ) ( n+ m) ny( n) ), (9) m d ( n) m wih he las equaliy following from (). Taking he limi of (9) as m goes o zero gives he insananeous forward rae n years ahead, which represens he insananeous reurn for a fuure dae ha an invesor would demand oday: f( n,) = lim m f( n, m) = y( n) + ny ( n) = ln( d( n)), (1) n where he las equaliy again uses equaion (). Noice ha (1) implies ha he yield curve is upward (downward) sloping whenever he insananeous forward rae is above (below) he zerocoupon yield a a given mauriy. One can hink of a erm invesmen oday as a sring of forward rae agreemens over he horizon of he invesmen, and he yield herefore has o equal he average of n hose forward raes. Specifically, from equaion (1), ln( d( n)) = f( x,) dx, and so, from equaion (), he nperiod zerocoupon yield (expressed on a coninuously compounded basis) is given by: 6
9 1 n y( n) = f( x,) dx n. (11) Likewise we can wrie y ( n ) as he average of oneyear coninuously compounded forward raes: 1 n y( n) = Σi= 1 f( i 1,1). (1) n Thus, given a complee range of forward raes, one can calculae he complee yield curve from equaions (11) and (1), or, conversely, given he complee yield curve, one can calculae all he forward raes from equaions (9) and (1). Yields and forward raes are simply alernaive ways of describing he same curve. By using forward raes, we can summarize he yield curve in some poenially more informaive ways. For example, he enyear Treasury yield can be decomposed ino oneyear forward raes over ha enyear horizon. As we will discuss below, nearerm forward raes end o be affeced by moneary policy expecaions and hence cyclical variables, while longererm forwards insead are deermined by facors seen as more persisen or by changes in risk preferences. The enyear yield meshes hese wo ypes of influences ogeher, whereas i may be easier o inerpre ha yield when one considers he nearerm and disan forward raes separaely. Indeed, former Fed Chairman Greenspan ofen parsed he yield curve ino is various forward componens (see for example his February and July 5 Moneary Policy Tesimonies). Similarly, Gürkaynak, Sack, and Swanson (5) frame heir discussion of he responsiveness of he yield curve o macroeconomic news in erms of forward raes, poining o he fac ha disan forward raes appear o respond o incoming daa (which hey associae wih movemens in longerm inflaion expecaions). 7
10 Lasly, one can also compue forward raes for fuure invesmens ha have coupon paymens. A par forward rae is he coupon rae ha one would demand oday o make a $1 invesmen a ime n and o receive back $1 in principal a ime n+m along wih semiannual coupons from ime n+½ o ime n+m, assuming ha n and n+m are p coupon daes. Le f ( nm, ) denoe his nbym par forward rae (expressed wih semiannual compounding). An invesor can synhesize his par forward rae agreemen p by selling one nyear zero coupon bond and buying f ( n, m ) / of n+ 1/, n+ 1,... n+ myear zerocoupon bonds and one more n+m year zerocoupon p bond, where f ( nm, ) is se so as o ensure ha he ne cash flow oday is zero. This implies ha p m f ( n, m) d( n) Σ i= 1d( n+ i/) d( n+ m) =. (13) Solving his equaion gives he formula for he nbym par forward rae: f ( d ( n) d ( n+ m)) ( n, m) =. (14) d ( n+ i/) p m i= 1 Whereas coninuously compounded zerocoupon yields can be wrien as he average of he corresponding coninuously compounded forward raes, as in equaions (11) and (1), we canno simply wrie par yields as averages of he consiuen par forward raes. However, Campbell, Lo and Mackinlay (1997) and Shiller, Campbell and Schoenholz (1983) show, using a loglinear approximaion, ha p 1 ρ n i p y ( n) Σi 1ρ f ( i 1,1) n =, (15) 1 ρ p where ρ = 1/(1 + y ( n)), he analog of equaion (1) for par raes. 8
11 .4 Duraion and Convexiy Before moving on o yield curve modeling and esimaion, we inroduce a couple of key conceps for he yield curve: duraion and convexiy. Duraion is a fundamenal concep in fixedincome analysis. Much of he value of a couponbearing securiy comes from coupon paymens ha are being made before mauriy, so he effecive ime ha invesors mus wai o receive heir money is shorer han he mauriy of he bond. The Macaulay duraion of a bond is a weighed average of he ime ha he invesor mus wai o receive he cash flows on a couponbearing bond (in years): n 1 ic [ ( /) ( )] ( ) i 1 D = d i + nd n. (16) P n = Zerocoupon bonds have duraion equal o he mauriy of he bond, bu couponbearing securiies have shorer duraion. For a given mauriy, he higher he coupon rae is, he shorer he duraion. Closely relaed o his concep is he modified duraion of a bond, D MOD, which is defined as he Macaulay duraion divided by one plus he yield on he bond (assuming semiannual compounding): D D =. (17) + MOD y 1 ce I can be shown ha he derivaive of he log price of a bond wih respec o is yield is simply DMOD. Thus, modified duraion provides he sensiiviy (in percen) of he value of a bond o small changes in is yield. A relaed concep is ha of convexiy. Modified duraion measures he sensiiviy of he log price of a bond o changes in yield, bu i is accurae only for small changes in 9
12 yield. The reason i is no accurae for large changes in yield is ha he relaionship beween prices and yields is nonlinear: he capial gain induced by a decline in he yield is larger han he capial loss induced by an equalsized increase in he yield. Convexiy capures his nonlineariy. To a secondorder approximaion, he change in he log price of he bond is given by: 1 dlog( P) D dy ( dy) = mod + κ, (18) 1 d P where κ = is he convexiy of he bond. Convexiy has implicaions for he shape P dy of he yield curve ha will be an imporan consideraion in he choice of our mehodology for esimaing he yield curve. In paricular, convexiy ends o pull down longererm yields and forward raes, an effec ha increases wih uncerainy abou changes in yields. Consider, for example, an increase in he uncerainy abou a longerm ineres rae ha is symmeric in erms of he possible basispoin increase or decrease in yield. For a given level of he yield, his ends o increase he expeced oneperiod reurn on he bond because of he asymmery noed above ha he capial gain from a fall in he yield is greaer han he capial loss from a rise in he yield. Formally, consider he expeced value of he nperiod zerocoupon bond one period ahead, which we can wrie as E[ d+ 1( n)] = E[exp( y+ 1( n) n)]. By Jensen's inequaliy, we have: E [ d ( n)] = E [exp( y ( n) n)] > exp( E [ y ( n)] n). (19) In oher words, he expeced value is higher han he value ha would be associaed wih he expeced yield nex period. 1
13 Markes, of course, recognize his effec and incorporae i ino he pricing of he yield curve. In paricular, he convexiy effec ends o push down yields, as invesors recognize he boos o expeced reurn from he convexiy erm and hence are willing o pay more for a given bond. This effec ends o be larger for bonds wih longer mauriies, giving he yield curve a hump shape ha is discussed a greaer lengh below. 3. Yield Curve Esimaion If he Treasury issued a full specrum of zero coupon securiies every day, hen we could simply observe he yield curve and have a complee se of he yields and forward raes described in he previous secion. Tha, unforunaely, is no he case. Treasury has insead issued a limied number of securiies wih differen mauriies and coupons. Hence, we usually have o infer wha he yields would be across he mauriy specrum from he prices of exising securiies. For each dae, we know he prices (and herefore yields) of a number of Treasury securiies wih differen mauriies and coupon paymens. Accouning for he differences in mauriies and coupons is no a problem; he esimaion will simply view couponbearing bonds as baskes of zerocoupon securiies, one for each coupon paymen and he principal paymen (as described above). 4 The more significan problem is he fac ha we do no have securiies a all mauriies. To come up wih yields across he complee mauriy specrum, we have o inerpolae beween he exising securiies. This exercise is wha consiues yield curve esimaion. 4 Coupon securiies simply bundle ogeher all of hese individual paymens. Unbundling hese paymens is precisely he purpose of he Treasury STRIPS program, in which each coupon and he principal can be individually raded. See Sack () for an overview. 11
14 In embarking on his exercise, one is immediaely confroned by an imporan issue: how much flexibiliy o allow in he yield curve. Pu differenly, one has o decide wheher all observed prices of Treasury securiies exacly reflec he same underlying discoun funcion. This is surely no he case: Idiosyncraic issues arise for specific securiies, such as liquidiy premia, hedging demand, demand for deliverabiliy ino fuures conracs, or repo marke specialness (which is ofen relaed o he oher facors). Moreover, some variaion across securiies could arise from bidask spreads and nonsynchronous quoe imes, hough we believe ha hese effecs are quie small in our daa (described below). In any case, i is desirable (and in fac necessary) o impose some srucure on he yield curve o smooh hrough some of his idiosyncraic variaion. However, one can choose differen mehods ha vary in erms of how much flexibiliy is allowed. One can esimae a very flexible yield curve which would fi well in erms of pricing he exising securiies correcly, bu do so wih considerable variabiliy in he forward raes. Or, one could impose more smoohness on he shape of he forward raes while sacrificing some of he fi of he curve. The more flexible approaches end o be splinebased mehods ha involve a large number of esimaed parameers, while he more rigid mehods end o be parameric forms ha involve a smaller number of parameers. The choice in his dimension depends on he purpose ha he yield curve is inended o serve. A rader looking for small pricing anomalies may be very concerned wih how a specific securiy is priced relaive o hose securiies immediaely around i. Suppose, for example, ha he yield curve has a dip in forward raes beginning, say, in year eigh ha is associaed wih he fac ha securiies in ha secor are he cheapeso 1
15 deliver ino he Treasury fuures conrac (an example we will show below). The rader, in assessing he value of an individual securiy in ha secor, would probably wan o incorporae ha facor ino his relaive value assessmen, and hence he would wan o use a yield curve flexible enough o capure his variaion in he forwards. By conras, a macroeconomis may be more ineresed in undersanding he fundamenal deerminans of he yield curve. Because i is difficul o envision a macroeconomic facor ha would produce a brief dip in he forward rae curve eigh years ahead, he may wish o use a more rigid yield curve ha smoohes hrough such variaion. Our primary purpose in esimaing he yield curve is o undersand is fundamenal deerminans such as macroeconomic condiions, moneary policy prospecs, perceived risks, and invesors risk preferences. Considering his purpose, we will employ a parameric yield curve specificaion. As will be seen below, his specificaion will allow for very rich shapes of he forward curve while largely ruling ou variaion resuling from a small number of securiies a a given mauriy. Our approach follows he exension by Svensson (1994) of he funcional form ha was iniially proposed by Nelson and Siegel (1987). The NelsonSiegel approach assumes ha insananeous forward raes n years ahead are characerized by a coninuous funcion wih only four parameers: f ( n,) = β + β exp( n/ τ ) + β ( n/ τ )exp( n/ τ ). () Wih his funcion, insananeous forward raes begin a horizon zero a he level β + β1 and evenually asympoe o he level β. In beween, forward raes can have a hump, wih he magniude and sign of he hump deermined by he parameer β and he locaion of he hump deermined by he parameer τ 1. 13
16 Below we will show some resuls ha allow us o inerpre he shape of he forwards ha resul from his funcional form. Bu a his poin, i is worh making a few noes. We can always inerpre forward raes as having wo componens: expeced fuure shorerm ineres raes and a erm premium. Under NelsonSiegel, he forward raes will end o sar a he curren shorerm rae ha is largely deermined by he curren moneary policy seing (he saring poin), will be governed a inermediaehorizons by expecaions of he business cycle, inflaion, and corresponding moneary policy decisions (he hump), and will end up a a seadysae level (he asympoe). I urns ou, however, ha his yield curve has difficuly fiing he enire erm srucure, especially hose securiies wih mauriies of weny years or more. The reason is convexiy. As discussed in secion above, convexiy ends o pull down he yields on longererm securiies, giving he yield curve a concave shape a longer mauriies (as will be seen below). The NelsonSiegel specificaion, while fiing shorer mauriies quie well, ends o have he forward raes asympoe oo quickly o be able o capure he convexiy effecs a longer mauriies. For ha reason, we insead use he more flexible approach described in Svensson (1994). This approach assumes ha he forward raes are governed by six parameers according o he following funcional form: f ( n,) = β + β exp( n/ τ ) + β ( n/ τ )exp( n/ τ ) + β ( n/ τ )exp( n/ τ ). (1) In effec, his specificaion adds wo new parameers (he las erm in he equaion) ha allow a second hump in he forward rae curve. The yield curve collapses o Nelson Siegel when β 3 is se o zero. However, as we will see below, he yield curve ypically needs a second hump, one ha usually occurs a long mauriies, o capure he convexiy 14
17 effecs in he yield curve. Inegraing hese forward raes gives us he corresponding zerocoupon yields: n n n 1 exp( ) 1 exp( ) 1 exp( ) τ τ n τ n y ( n) = β + β + β [ exp( )] + β [ exp( )], () n n τ n 1 τ τ τ τ 1 1 and from hese yields one can compue he discoun funcion a any horizon. Thus, for a given se of parameers, he Svensson specificaion characerizes he yield curve and discoun funcion a all mauriies. The discoun funcion can hen be used o price any ousanding Treasury securiy wih specific coupon raes and mauriy daes. In esimaing he yield curve, we choose he parameers o minimize he weighed sum of he squared deviaions beween he acual prices of Treasury securiies and he prediced prices. The weighs chosen are he inverse of he duraion of each individual securiy. To a rough approximaion, he deviaion beween he acual and prediced prices of an individual securiy will equal is duraion muliplied by he deviaion beween he acual and prediced yields. Thus, his procedure is approximaely equal o minimizing he (unweighed) sum of he squared deviaions beween he acual and prediced yields on all of he securiies. Of course, his is jus one of many specificaions ha we could have chosen. A number of oher papers insead use splinebased mehods, including Fisher, Nychka, and Zervos (1995), Waggoner (1997), and McCulloch (1975, 199). These mehods generally allow for more variaion in he forward rae curve (hough he degree of flexibiliy can be conrolled in he specificaions). However, ha flexibiliy may come wih some coss. Bliss (1996) compares a number of esimaion mehods and finds ha parsimonious specificaions such as he NelsonSiegel mehod perform favorably relaive 15
18 o some of he more flexible mehods. In addiion, Sack () demonsraes some of he esimaion difficulies ha can arise under more flexible approaches for esimaing he U.S. erm srucure. 4. Daa and Esimaion Issues We employ he Svensson mehodology for esimaing our benchmark yield curve. In our view, his mehod srikes an appealing balance beween being flexible enough o fi he U.S. yield curve well and being parsimonious enough o avoid overfiing he idiosyncraic variaion in he yields of individual securiies. As described above, we esimae he six parameers, using maximum likelihood, o minimize he sum of he squared deviaions beween he acual prices of Treasury securiies and he prediced prices, where he prices are weighed by he inverse of he duraion of he securiies. Our underlying quoes on Treasury securiies come from wo primary sources. For he period from 14 June 1961 o he end of November 1987, we rely on he CRSP daily Treasury file, which provides endofday quoes on all ousanding Treasury securiies. Since December 1987, we use Treasury quoes provided by he Federal Reserve Bank of New York (FRBNY), which is a proprieary daabase consruced from several sources of marke informaion. 5 An immediae issue ha arises is deermining he se of securiies o be included in he esimaion. The Treasury securiies ousanding a any poin in ime can differ in many dimensions, including heir liquidiy and heir callable feaures. Our goal is o use a se of securiies ha are similar in erms of heir liquidiy and ha do no have special 5 We are no permied o release eiher he underlying CRSP daa or he FRBNY daa. 16
19 feaures (such as being callable) ha would affec heir prices. In oher words, we would ideally have securiies ha only differ in erms of heir coupons and mauriies. To ha end, we include in he esimaion all ousanding Treasury noes and bonds, wih he following excepions: (i) We exclude all securiies wih opionlike feaures, including callable bonds and flower bonds. 6 (ii) We exclude all securiies wih less han hree monhs o mauriy, since he yields on hese securiies ofen seem o behave oddly. This behavior may parly reflec he lack of liquidiy for hose issues and segmened demand for shorerm securiies by paricular invesor classes. (iii) We also exclude all Treasury bills ou of concern abou segmened markes. Indeed, Duffee (1996) showed ha bill raes are ofen disconneced from he res of he Treasury yield curve, perhaps owing o segmened demand from money marke funds and oher shorerm invesors. (iv) We begin o exclude wenyyear bonds in 1996, because hose securiies ofen appeared cheap relaive o enyear noes wih comparable duraion. This cheapness could reflec heir lower liquidiy or he fac ha heir high coupon raes made hem unaracive o hold for axrelaed reasons. 7 (v) We exclude he wo mos recenly issued securiies wih mauriies of wo, hree, four, five, seven, en, weny, and hiry years for securiies issued in 198 or laer. These are he onherun and firs offherun issues ha ofen rade a a premium o 6 Flower bonds were securiies wih low coupons ha could be redeemed a par for he paymen of esae axes. 7 To avoid an abrup change o he sample, we allow heir weighs o linearly decay from 1 o over he year ending on January,
20 oher Treasury securiies, owing o heir greaer liquidiy and heir frequen specialness in he repo marke. 8 Earlier in he sample, he concep of an onherun issue was no well defined, since he Treasury did no conduc regular aucions and he repo marke was no well developed (as discussed by Garbade (4)). Our cuoff poin for excluding onherun and firs offherun issues is somewha arbirary bu is a conservaive choice (in he sense of poenially erring on he side of being oo early). (vi) Oher issues ha we judgmenally exclude on an ad hoc basis. For example, here were large and persisen failsodeliver in he May 13 3⅝ percen enyear noe, well afer i ceased o be eiher he onherun or firs offherun enyear securiy. Wih he securiy persisenly rading around he fails rae in he overnigh repo marke, he yield on he securiy in he cash marke was driven down. Thus, we dropped he securiy for some ime o avoid having our yield curve disored by he idiosyncraic dislocaion of his issue. These resricions imply ha we are esimaing an offherun Treasury yield curve, one for which he liquidiy of he included securiies should be relaively uniform. The liquidiy implici in our curve should be regarded as adequae, hough far shor of he remarkable liquidiy of onherun issues. The ranges of mauriies available for esimaion over our sample are shown graphically in Figure 1, which akes he same form as a figure repored by Bliss (1996). The dae is shown on he horizonal axis, he remaining mauriy is shown on he verical axis, and each ousanding Treasury coupon securiy is represened by a do showing is 8 Some simple saisics on rading volume highligh jus how differen he onherun issues are from oher Treasury issues. According o Sack and Elsasser (4), he weekly urnover rae for offherun Treasury securiies in 3 (ha is, weekly rading volume as a percen of ousanding deb) was abou percen, while i was a remarkable 14% for onherun issues. 18
Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.
Graduae School of Business Adminisraion Universiy of Virginia UVAF38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised
More informationYTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment.
. Two quesions for oday. A. Why do bonds wih he same ime o mauriy have differen YTM s? B. Why do bonds wih differen imes o mauriy have differen YTM s? 2. To answer he firs quesion les look a he risk srucure
More informationA Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
More informationMorningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion
More informationMACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR
MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR The firs experimenal publicaion, which summarised pas and expeced fuure developmen of basic economic indicaors, was published by he Minisry
More informationPrincipal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.
Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More informationTable of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities
Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17
More informationChapter 9 Bond Prices and Yield
Chaper 9 Bond Prices and Yield Deb Classes: Paymen ype A securiy obligaing issuer o pay ineress and principal o he holder on specified daes, Coupon rae or ineres rae, e.g. 4%, 5 3/4%, ec. Face, par value
More information11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic DS dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuingedge
More informationI. Basic Concepts (Ch. 14)
(Ch. 14) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing
More informationINTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES
INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchangeraded ineres rae fuures and heir opions are described. The fuure opions include hose paying
More informationChapter 6: Business Valuation (Income Approach)
Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he
More informationChapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
More informationPresent Value Methodology
Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer
More informationWhy Do Real and Nominal. InventorySales Ratios Have Different Trends?
Why Do Real and Nominal InvenorySales Raios Have Differen Trends? By Valerie A. Ramey Professor of Economics Deparmen of Economics Universiy of California, San Diego and Research Associae Naional Bureau
More informationA Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM)
A Brief Inroducion o he Consumpion Based Asse Pricing Model (CCAPM We have seen ha CAPM idenifies he risk of any securiy as he covariance beween he securiy's rae of reurn and he rae of reurn on he marke
More informationTHE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS
VII. THE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS The mos imporan decisions for a firm's managemen are is invesmen decisions. While i is surely
More informationTerm Structure of Prices of Asian Options
Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 111 Nojihigashi, Kusasu, Shiga 5258577, Japan Email:
More informationGraphing the Von Bertalanffy Growth Equation
file: d:\b1732013\von_beralanffy.wpd dae: Sepember 23, 2013 Inroducion Graphing he Von Beralanffy Growh Equaion Previously, we calculaed regressions of TL on SL for fish size daa and ploed he daa and
More informationLEASING VERSUSBUYING
LEASNG VERSUSBUYNG Conribued by James D. Blum and LeRoy D. Brooks Assisan Professors of Business Adminisraion Deparmen of Business Adminisraion Universiy of Delaware Newark, Delaware The auhors discuss
More informationHedging with Forwards and Futures
Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buyside of a forward/fuures
More informationNikkei Stock Average Volatility Index Realtime Version Index Guidebook
Nikkei Sock Average Volailiy Index Realime Version Index Guidebook Nikkei Inc. Wih he modificaion of he mehodology of he Nikkei Sock Average Volailiy Index as Nikkei Inc. (Nikkei) sars calculaing and
More informationII.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal
Quarerly Repor on he Euro Area 3/202 II.. Deb reducion and fiscal mulipliers The deerioraion of public finances in he firs years of he crisis has led mos Member Saes o adop sizeable consolidaion packages.
More informationThe Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas
The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he
More informationEquities: Positions and Portfolio Returns
Foundaions of Finance: Equiies: osiions and orfolio Reurns rof. Alex Shapiro Lecure oes 4b Equiies: osiions and orfolio Reurns I. Readings and Suggesed racice roblems II. Sock Transacions Involving Credi
More informationWhat is a swap? A swap is a contract between two counterparties who agree to exchange a stream of payments over an agreed period of several years.
Currency swaps Wha is a swap? A swap is a conrac beween wo counerparies who agree o exchange a sream of paymens over an agreed period of several years. Types of swap equiy swaps (or equiyindexlinked
More informationOption PutCall Parity Relations When the Underlying Security Pays Dividends
Inernaional Journal of Business and conomics, 26, Vol. 5, No. 3, 22523 Opion Puall Pariy Relaions When he Underlying Securiy Pays Dividends Weiyu Guo Deparmen of Finance, Universiy of Nebraska Omaha,
More informationJournal Of Business & Economics Research September 2005 Volume 3, Number 9
Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy YiKang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More informationOne dictionary: Native language  English/English  native language or English  English
Faculy of Social Sciences School of Business Corporae Finance Examinaion December 03 English Dae: Monday 09 December, 03 Time: 4 hours/ 9:003:00 Toal number of pages including he cover page: 5 Toal number
More informationRevisions to Nonfarm Payroll Employment: 1964 to 2011
Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm
More informationIndividual Health Insurance April 30, 2008 Pages 167170
Individual Healh Insurance April 30, 2008 Pages 167170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
More informationSupplementary Appendix for Depression Babies: Do Macroeconomic Experiences Affect RiskTaking?
Supplemenary Appendix for Depression Babies: Do Macroeconomic Experiences Affec RiskTaking? Ulrike Malmendier UC Berkeley and NBER Sefan Nagel Sanford Universiy and NBER Sepember 2009 A. Deails on SCF
More informationINVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS
INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS Ilona Tregub, Olga Filina, Irina Kondakova Financial Universiy under he Governmen of he Russian Federaion 1. Phillips curve In economics,
More informationBALANCE OF PAYMENTS. First quarter 2008. Balance of payments
BALANCE OF PAYMENTS DATE: 20080530 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se
More informationMarket Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand
36 Invesmen Managemen and Financial Innovaions, 4/4 Marke Liquidiy and he Impacs of he Compuerized Trading Sysem: Evidence from he Sock Exchange of Thailand Sorasar Sukcharoensin 1, Pariyada Srisopisawa,
More information4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
More informationEconomics 140A Hypothesis Testing in Regression Models
Economics 140A Hypohesis Tesing in Regression Models While i is algebraically simple o work wih a populaion model wih a single varying regressor, mos populaion models have muliple varying regressors 1
More informationMeasuring macroeconomic volatility Applications to export revenue data, 19702005
FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a
More informationLIFE INSURANCE WITH STOCHASTIC INTEREST RATE. L. Noviyanti a, M. Syamsuddin b
LIFE ISURACE WITH STOCHASTIC ITEREST RATE L. oviyani a, M. Syamsuddin b a Deparmen of Saisics, Universias Padjadjaran, Bandung, Indonesia b Deparmen of Mahemaics, Insiu Teknologi Bandung, Indonesia Absrac.
More informationThe Grantor Retained Annuity Trust (GRAT)
WEALTH ADVISORY Esae Planning Sraegies for closelyheld, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business
More informationTEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS
TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.
More informationVector Autoregressions (VARs): Operational Perspectives
Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101115. Macroeconomericians
More informationSPECIAL REPORT May 4, Shifting Drivers of Inflation Canada versus the U.S.
Paul Ferley Assisan Chief Economis 4169747231 paul.ferley@rbc.com Nahan Janzen Economis 4169740579 nahan.janzen@rbc.com SPECIAL REPORT May 4, 2010 Shifing Drivers of Inflaion Canada versus he U.S.
More informationMarkit Excess Return Credit Indices Guide for price based indices
Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semiannual
More informationThe Identification of the Response of Interest Rates to Monetary Policy Actions Using MarketBased Measures of Monetary Policy Shocks
The Idenificaion of he Response of Ineres Raes o Moneary Policy Acions Using MarkeBased Measures of Moneary Policy Shocks Daniel L. Thornon Federal Reserve Bank of S. Louis Phone (314) 4448582 FAX (314)
More informationDOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR
Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 33 DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Ahanasios
More informationRisk Modelling of Collateralised Lending
Risk Modelling of Collaeralised Lending Dae: 4112008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies
More informationCan Individual Investors Use Technical Trading Rules to Beat the Asian Markets?
Can Individual Invesors Use Technical Trading Rules o Bea he Asian Markes? INTRODUCTION In radiional ess of he weakform of he Efficien Markes Hypohesis, price reurn differences are found o be insufficien
More informationDynamic Option Adjusted Spread and the Value of Mortgage Backed Securities
Dynamic Opion Adjused Spread and he Value of Morgage Backed Securiies Mario Cerrao, Abdelmadjid Djennad Universiy of Glasgow Deparmen of Economics 27 January 2008 Absrac We exend a reduced form model for
More informationThe yield curve, and spot and forward interest rates Moorad Choudhry
he yield curve, and spo and forward ineres raes Moorad Choudhry In his primer we consider he zerocoupon or spo ineres rae and he forward rae. We also look a he yield curve. Invesors consider a bond yield
More informationPrice elasticity of demand for crude oil: estimates for 23 countries
Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh
More informationTHE PERFORMANCE OF OPTION PRICING MODELS ON HEDGING EXOTIC OPTIONS
HE PERFORMANE OF OPION PRIING MODEL ON HEDGING EXOI OPION Firs Draf: May 5 003 his Version Oc. 30 003 ommens are welcome Absrac his paper examines he empirical performance of various opion pricing models
More informationDoes Option Trading Have a Pervasive Impact on Underlying Stock Prices? *
Does Opion Trading Have a Pervasive Impac on Underlying Sock Prices? * Neil D. Pearson Universiy of Illinois a UrbanaChampaign Allen M. Poeshman Universiy of Illinois a UrbanaChampaign Joshua Whie Universiy
More informationReturn Calculation of U.S. Treasury Constant Maturity Indices
Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion
More informationChapter 8 Student Lecture Notes 81
Chaper Suden Lecure Noes  Chaper Goals QM: Business Saisics Chaper Analyzing and Forecasing Series Daa Afer compleing his chaper, you should be able o: Idenify he componens presen in a ime series Develop
More informationMonetary Policy & Real Estate Investment Trusts *
Moneary Policy & Real Esae Invesmen Truss * Don Bredin, Universiy College Dublin, Gerard O Reilly, Cenral Bank and Financial Services Auhoriy of Ireland & Simon Sevenson, Cass Business School, Ciy Universiy
More informationInvestor sentiment of lottery stock evidence from the Taiwan stock market
Invesmen Managemen and Financial Innovaions Volume 9 Issue 1 YuMin Wang (Taiwan) ChunAn Li (Taiwan) ChiaFei Lin (Taiwan) Invesor senimen of loery sock evidence from he Taiwan sock marke Absrac This
More informationUNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES. Nadine Gatzert
UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES Nadine Gazer Conac (has changed since iniial submission): Chair for Insurance Managemen Universiy of ErlangenNuremberg Lange Gasse
More informationcooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)
Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer
More informationChapter 6 Interest Rates and Bond Valuation
Chaper 6 Ineres Raes and Bond Valuaion Definiion and Descripion of Bonds Longerm debloosely, bonds wih a mauriy of one year or more Shorerm debless han a year o mauriy, also called unfunded deb Bondsricly
More informationForeign Exchange and Quantos
IEOR E4707: Financial Engineering: ConinuousTime Models Fall 2010 c 2010 by Marin Haugh Foreign Exchange and Quanos These noes consider foreign exchange markes and he pricing of derivaive securiies in
More informationChapter 4: Exponential and Logarithmic Functions
Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion
More informationWhy Did the Demand for Cash Decrease Recently in Korea?
Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationRecovering Market Expectations of FOMC Rate Changes with Options on Federal Funds Futures
w o r k i n g p a p e r 5 7 Recovering Marke Expecaions of FOMC Rae Changes wih Opions on Federal Funds Fuures by John B. Carlson, Ben R. Craig, and William R. Melick FEDERAL RESERVE BANK OF CLEVELAND
More informationChapter 1.6 Financial Management
Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1
More informationAppendix D Flexibility Factor/Margin of Choice Desktop Research
Appendix D Flexibiliy Facor/Margin of Choice Deskop Research Cheshire Eas Council Cheshire Eas Employmen Land Review Conens D1 Flexibiliy Facor/Margin of Choice Deskop Research 2 Final Ocober 2012 \\GLOBAL.ARUP.COM\EUROPE\MANCHESTER\JOBS\200000\22348900\4
More informationSPEC model selection algorithm for ARCH models: an options pricing evaluation framework
Applied Financial Economics Leers, 2008, 4, 419 423 SEC model selecion algorihm for ARCH models: an opions pricing evaluaion framework Savros Degiannakis a, * and Evdokia Xekalaki a,b a Deparmen of Saisics,
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College  Physics 2426  Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationSEASONAL ADJUSTMENT. 1 Introduction. 2 Methodology. 3 X11ARIMA and X12ARIMA Methods
SEASONAL ADJUSTMENT 1 Inroducion 2 Mehodology 2.1 Time Series and Is Componens 2.1.1 Seasonaliy 2.1.2 TrendCycle 2.1.3 Irregulariy 2.1.4 Trading Day and Fesival Effecs 3 X11ARIMA and X12ARIMA Mehods
More informationFourier Series Solution of the Heat Equation
Fourier Series Soluion of he Hea Equaion Physical Applicaion; he Hea Equaion In he early nineeenh cenury Joseph Fourier, a French scienis and mahemaician who had accompanied Napoleon on his Egypian campaign,
More informationIf You Are No Longer Able to Work
If You Are No Longer Able o Work NY STRS A Guide for Making Disabiliy Reiremen Decisions INTRODUCTION If you re forced o sop working because of a serious illness or injury, you and your family will be
More informationRepresenting Periodic Functions by Fourier Series. (a n cos nt + b n sin nt) n=1
Represening Periodic Funcions by Fourier Series 3. Inroducion In his Secion we show how a periodic funcion can be expressed as a series of sines and cosines. We begin by obaining some sandard inegrals
More informationHouse Price Index (HPI)
House Price Index (HPI) The price index of second hand houses in Colombia (HPI), regisers annually and quarerly he evoluion of prices of his ype of dwelling. The calculaion is based on he repeaed sales
More information4.8 Exponential Growth and Decay; Newton s Law; Logistic Growth and Decay
324 CHAPTER 4 Exponenial and Logarihmic Funcions 4.8 Exponenial Growh and Decay; Newon s Law; Logisic Growh and Decay OBJECTIVES 1 Find Equaions of Populaions Tha Obey he Law of Uninhibied Growh 2 Find
More informationSmall and Large Trades Around Earnings Announcements: Does Trading Behavior Explain PostEarningsAnnouncement Drift?
Small and Large Trades Around Earnings Announcemens: Does Trading Behavior Explain PosEarningsAnnouncemen Drif? Devin Shanhikumar * Firs Draf: Ocober, 2002 This Version: Augus 19, 2004 Absrac This paper
More informationTax Externalities of Equity Mutual Funds
Tax Exernaliies of Equiy Muual Funds Joel M. Dickson The Vanguard Group, Inc. John B. Shoven Sanford Universiy and NBER Clemens Sialm Sanford Universiy December 1999 Absrac: Invesors holding muual funds
More informationDYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS
DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper
More informationForecasting, Ordering and Stock Holding for Erratic Demand
ISF 2002 23 rd o 26 h June 2002 Forecasing, Ordering and Sock Holding for Erraic Demand Andrew Eaves Lancaser Universiy / Andalus Soluions Limied Inroducion Erraic and slowmoving demand Demand classificaion
More informationJournal of Financial and Strategic Decisions Volume 12 Number 1 Spring 1999
Journal of Financial and Sraegic Decisions Volume 12 Number 1 Spring 1999 THE LEADLAG RELATIONSHIP BETWEEN THE OPTION AND STOCK MARKETS PRIOR TO SUBSTANTIAL EARNINGS SURPRISES AND THE EFFECT OF SECURITIES
More informationMarket Analysis and Models of Investment. Product Development and Whole Life Cycle Costing
The Universiy of Liverpool School of Archiecure and Building Engineering WINDS PROJECT COURSE SYNTHESIS SECTION 3 UNIT 11 Marke Analysis and Models of Invesmen. Produc Developmen and Whole Life Cycle Cosing
More informationCommon Risk Factors in the US Treasury and Corporate Bond Markets: An Arbitragefree Dynamic NelsonSiegel Modeling Approach
Common Risk Facors in he US Treasury and Corporae Bond Markes: An Arbiragefree Dynamic NelsonSiegel Modeling Approach Jens H E Chrisensen and Jose A Lopez Federal Reserve Bank of San Francisco 101 Marke
More informationReal Return Bonds, Inflation Expectations, and the BreakEven Inflation Rate Ian Christensen, Frédéric Dion, and Christopher Reid
Bank of Canada Banque du Canada Working Paper 200443 / Documen de ravail 200443 Real Reurn Bonds, Inflaion Expecaions, and he BreakEven Inflaion Rae by Ian Chrisensen, Frédéric Dion, and Chrisopher
More informationUnderstanding Sequential Circuit Timing
ENGIN112: Inroducion o Elecrical and Compuer Engineering Fall 2003 Prof. Russell Tessier Undersanding Sequenial Circui Timing Perhaps he wo mos disinguishing characerisics of a compuer are is processor
More informationThe naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1
Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces imeseries smoohing forecasing mehods. Various models are discussed,
More informationA Note on the Impact of Options on Stock Return Volatility. Nicolas P.B. Bollen
A Noe on he Impac of Opions on Sock Reurn Volailiy Nicolas P.B. Bollen ABSTRACT This paper measures he impac of opion inroducions on he reurn variance of underlying socks. Pas research generally finds
More informationChabot College Physics Lab RC Circuits Scott Hildreth
Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard
More informationWhen Is Growth ProPoor? Evidence from a Panel of Countries
Forhcoming, Journal of Developmen Economics When Is Growh ProPoor? Evidence from a Panel of Counries Aar Kraay The World Bank Firs Draf: December 2003 Revised: December 2004 Absrac: Growh is propoor
More informationCBOE VIX PREMIUM STRATEGY INDEX (VPD SM ) CAPPED VIX PREMIUM STRATEGY INDEX (VPN SM )
CBOE VIX PREIU STRATEGY INDEX (VPD S ) CAPPED VIX PREIU STRATEGY INDEX (VPN S ) The seady growh of CBOE s volailiy complex provides a unique opporuniy for invesors inen on capuring he volailiy premium.
More informationWHAT ARE OPTION CONTRACTS?
WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be
More informationLongRun Stock Returns: Participating in the Real Economy
LongRun Sock Reurns: Paricipaing in he Real Economy Roger G. Ibboson and Peng Chen In he sudy repored here, we esimaed he forwardlooking longerm equiy risk premium by exrapolaing he way i has paricipaed
More informationABSTRACT KEYWORDS. Term structure, duration, uncertain cash flow, variable rates of return JEL codes: C33, E43 1. INTRODUCTION
THE VALUATION AND HEDGING OF VARIABLE RATE SAVINGS ACCOUNTS BY FRANK DE JONG 1 AND JACCO WIELHOUWER ABSTRACT Variable rae savings accouns have wo main feaures. The ineres rae paid on he accoun is variable
More informationThe impact of Federal Reserve asset purchase programmes: another twist 1
Jack Meaning jm583@ken.ac.uk eng Zhu feng.zhu@bis.org The impac of ederal Reserve asse purchase programmes: anoher wis 1 This aricle examines he effeciveness of recen ederal Reserve asse purchase programmes.
More informationTwo Compartment Body Model and V d Terms by Jeff Stark
Two Comparmen Body Model and V d Terms by Jeff Sark In a onecomparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics  By his, we mean ha eliminaion is firs order and ha pharmacokineic
More informationFinance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C.
Finance and Economics Discussion Series Divisions of Research & Saisics and Moneary Affairs Federal Reserve Board, Washingon, D.C. Volailiy, Money Marke Raes, and he Transmission of Moneary Policy Seh
More informationDescription of the CBOE S&P 500 BuyWrite Index (BXM SM )
Descripion of he CBOE S&P 500 BuyWrie Index (BXM SM ) Inroducion. The CBOE S&P 500 BuyWrie Index (BXM) is a benchmark index designed o rack he performance of a hypoheical buywrie sraegy on he S&P 500
More informationFinance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C.
Finance and Economics Discussion Series Divisions of Research & Saisics and Moneary Affairs Federal Reserve Board, Washingon, D.C. The Effecs of Unemploymen Benefis on Unemploymen and Labor Force Paricipaion:
More information