Does Mortgage Hedging Raise Long-Term Interest Rate Volatility? *

Transcription

1 Preliminary Draf: Please do no quoe wihou he auhors' permission. Does Morgage Hedging Raise Long-Term Ineres Rae Volailiy? * by Yan Chang, Douglas McManus and Buchi Ramagopal Freddie Mac Office of he Chief Economis 8 Jones Branch Drive McLean, VA July 4 * The auhors are graeful o Frank Nohaf, Ed Golding, and Peer Zorn for heir suggesions and insighs. We would like o hank Jorge Reis, Mich Pos and Jim Berkovec for heir commens. Bob Winaa helped wih he consrucion of he daa se and hanks o Mura Karakur for his insighs ino swapions volailiy. The views presened are hose of he auhors and no of Freddie Mac. We are responsible for he remaining errors.

2 Absrac Does Morgage Hedging Raise Long-Term Ineres Rae Volailiy? This paper eamines he impac of morgage hedging aciviies on ineres rae volailiy. A recen analysis by Perli and Sack (3) provides a framework for evaluaing his quesion and along wih esimaes of he een o which hedging by agens in he morgage marke amplifies ineres rae volailiy. We evaluae he amplificaion issue by considering a wider range of ineres rae derivaives and implemening differen measures of hedging inensiy o isolae he sources ha migh be conribuing o volailiy. By considering a rolling window over which we obain maimum likelihood esimaes of key parameers we show ha he een o which morgage hedging deermines volailiy is driven compleely by wo episodes: he collapse of LTCM and he marke reacion in he afermah of he 9/ ragedy. We conclude ha i is difficul o make he case ha hedging by morgage marke paricipans is responsible for eacerbaing volailiy.

3 . Inroducion Volailiy is an ever-presen feaure of financial markes. Recen hisory has evidenced several episodes of heighened volailiy. Evens such as he Russian deb crisis, he collapse of LTCM, and he disrupion of he Asian markes in he lae 99 s have all been responsible for periods of heighened volailiy. While such volailiy can be viewed from a macroeconomic perspecive as he source of economic insabiliy, from a complee markes perspecive, his volailiy represens he efficien funcioning of markes in he face of uncerainy. Over he pas wo decades, markes, insiuions, and pracices have been eamined as possible sources of ecessive volailiy. This paper eamines he possible role of morgage hedging in creaing volailiy in ineres rae markes. Saring in 99, 3-year fied morgage raes declined from a high of.5% o a low of 5.% in June of 3. This decline in raes led households o refinance heir morgages in record numbers. The refinancing aciviy peaked during he years of , 998 and mos recenly, in 3. By he end of 3, up o 4-45% of he $7. rillion single-family deb ousanding was financed, in 3 alone. The volume of refinancing aciviy in 3, for eample, led o more han hree rillion dollars of morgage deb ousanding o be re-sruck a lower raes. Despie he huge volume, he US morgage marke managed o respond fleibly, providing homeowners he benefi of lower raes. The decline in raes and he re-sriking of morgage deb has led an increasing number of morgage marke paricipans such as originaors, morgage-servicers, and porfolio managers o manage he risks associaed wih his secular decline in raes. Since fied rae morgages have posiive duraion and negaive conveiy, marke paricipans can choose a miure of saic and dynamic hedging sraegies o miigae he associaed ineres rae risk. Saic hedging of morgage ineres rae risk can be accomplished by issuing callable deb or hrough he synhesis of callable deb engineered by he purchase of swapions. Dynamic hedging, on he oher hand, calls for he consan managemen of he relaive duraions of he asses and liabiliies, ypically hrough swap ransacions. Counerparies o hese derivaive ransacions have diversified books of business and can consequenly manage hese risks. However, hey also serve as inermediaries in he marke for hese ransacions by idenifying ohers paries ha migh naurally offse hese morgage marke risks. The naure and magniude of morgage hedging aciviies has raised he issue of is impac on marke ineres raes. Several approaches have been aken o his problem. Naranjo and Toevs () sugges ha large morgage marke paricipans reduce volailiy in morgage raes as a resul of heir paricipaion in he marke. Alernaively, anoher characerizaion by Perli and Sack (3) suggess ha morgage hedging raises long-erm rae volailiy. The argumen of Perli and Sack suggess ha he ools of financial engineering, as applied o morgage risk managemen migh be responsible for heighened volailiy. This paper invesigaes his claim. The issue of wheher raional speculaors or risk managemen frameworks can desabilize prices or eacerbae volailiy has been a subjec of coninued research. One posiion, saring wih Friedman (953) is ha raional speculaors ac o sabilize asse prices. In Friedman s view Speculaors who desabilized prices by, on average, buying when prices were high and selling when hey were low would find his unsusainable and be eliminaed from he marke. The more 3

4 raional speculaors who moved prices back oward fundamenals would eliminae such speculaors, who are less han raional and moved prices away from fundamenals. Alernaively, several recen researchers have developed heoreical eamples in which rading aciviies can desabilize prices. In hese eamples, raional speculaors migh no easily sabilize asse prices even when hey have access o idenical informaion, and have idenical priors as shown by Har and Kreps (986). Similarly, DeLong, Schleifer, Summers and Waldmann (99) also show, for eample, ha invesors wih erapolaive epecaions, hose who chase rends, or have sop-loss orders in place, all of which could be characerized as posiive feedback invesmen sraegies, migh conribue o desabilizing marke movemens. Argumens similar o hose of desabilizing speculaion have been used o make he case ha risk managemen in general, or porfolio insurance in paricular, conribues o greaer volailiy in raes or asse prices. Porfolio insurance, for eample, according o he Brady Repor, was considered o have been he eacerbaing facor in he crash of 987. In a similar vein, he Value-a Risk (VaR) mehodology has also been blamed for amplifying volailiy (See Persaud () and Dunbar ()). The argumen is ha shocks migh raise volailiy iniially, leading o a breach of VaR posiions and require invesors o raise he amoun of allocaed capial; oherwise invesors would be required o liquidae some par of heir porfolios. I furher raises he possibiliy ha large insiuions ha eceed predeermined VaR measures (deermined inernally by managemen or, eernally by a regulaor) migh hen simulaneously sell he same asse a he same ime, creaing higher volailiy and correlaions, which amplify he iniial effec, forcing addiional sales. However, Jorion () claims ha such criicisms relaing o he VaR framework have been misplaced. In effec, he argumen presened by Perli and Sack is ha when raes rise, morgage hedgers sell off Treasuries eiher direcly or synheically hrough swaps furher amplifying he increase in raes. Conversely, in response o declining raes morgage hedgers will purchase long duraion asses, amplifying he decline in raes. The magniude of he amplificaion effecs will depend on he degree o which morgage hedgers adop dynamic raher han saic hedging sraegies. Underlying heir argumen is he assumpion ha some consan proporion of morgage ineres rae risk is acively managed hrough dynamic raher han saic hedging sraegies. While he argumens presened by Perli and Sack are appealing, heir amplificaion proposiion i.e., morgage hedging amplifies rae movemens, is similar o argumens ha have been made in differen seings. A recen line of argumen ha has been proposed, wih he implicaion of eliminaing he need o dela hedge, is o push for he adopion of adjusable rae morgages. While i would eliminae he need on he par of large morgage holders o dela hedge, i ignores he possible impac on individual homeowners and he fac ha hey may no be in a posiion o efficienly manage such ineres rae risk as evidenced by higher ARM defaul raes for oherwise idenical morgages. I is in fac ironic ha ARMs are being proposed as an alernaive o fied rae morgages in he US marke a a poin when counries such as he UK see he prevalence of ARMs as being one of he reasons for heir boom-bus housing cycles, which increases he ampliude of heir business Jorion () 4

5 cycles. The review of he housing marke in he UK by David Miles (4) highlighs he need for he UK housing marke o inroduce longer erm morgages wih prepaymen opions, much like hose in he US morgage marke. Sill, he quesion remains as o wheher or no dela hedging by morgage marke paricipans creaes volailiy, and if so, he een o which his is he case. Ulimaely, he issue of impac of morgage hedging and he impac on volailiy is one ha has o be deermined empirically. In he ineres of consisency, we use a framework idenical o ha of Perli and Sack and lay ou he framework in secion. The daa along wih resuls of he firs sage regression are described in secion 3. The resuls of he firs par of he empirical eercise, measuring he een o which morgage hedging eacerbaes volailiy is presened in secion 4. The final argumens and summary of resuls are presened in he conclusion.. The Model The underlying inuiion of he framework uilized is ha changes in he long-erm raes are driven by a daa generaing process. The shocks generaed by his process emanae from moneary policy innovaions, news and changes in risk preferences. The long-erm rae in quesion is he en-year swap rae and changes in his rae beween ime and +n are generaed by a fundamenal shock ε (, + n). The changes in he en-year swap rae are characerized as: (, + n) = ε(, n) r γ + () In his seing, he fundamenal shock ε (, + n) is eacerbaed by a facor γ, whose value is known a ime and whose magniude is deermined by he degree of morgage hedging aciviy. This amplificaion facor is supposed o characerize he sae of he morgage marke a he beginning of he period. I akes on a value ha could be close o one if he een of prepaymen risk is low, and values ha are higher values if prepaymen risk is greaer. Thus shocks, during periods of high prepaymen risk are amplified and shocks during periods of low prepaymen risk are dampened. Using he specificaion in (), he variance of he ineres rae is characerized as: σ = γ σ. () r, ε, The epression describes he second momen of he en-year swap rae as a funcion of he second momen of he fundamenal shock and he amplificaion facor. The condiional variance of he fundamenal shocks is described as following an AR() process: σ + u. (3) ε, = α + ασ ε, Using equaion () o rewrie las period s fundamenal variance as raio of las period s variance of he swap rae o he amplificaion facor and using (3), equaion () is epressed as: 5

6 γ σ + r, = αγ + α σ r, γ u (4) γ During periods of higher prepaymen risk when γ is higher i raises he average level of volailiy, he firs erm on he righ hand side of (4), will be higher. The second erm above highlighs he auocorrelaion of volailiy, and hird erm describes he volailiy of volailiy effec. This erm describes he fac ha, as Perli and Sack poin ou, shows ha changes in epeced volailiy are greaer when prepaymen risk is high. The framework for deermining he magniude of he amplificaion facor γ, is described as: γ = + βx, (5) where X is a measure of hedging inensiy. When here is no hedging pressure he value of γ is one, and higher when here is an increased need for greaer morgage marke hedging. Various proies of morgage marke hedging needs are considered and we discuss hem furher in he ne secion which discusses daa. Using he specificaion for he hedging amplificaion facor in (5), (4) can be rewrien as β σ + + X r, = α + αβx + α σ r, + ( βx ) u. (6) + βx The final version of he specificaion uses a lagged value of he hedging proy and implemens he following epression o avoid he endogeneiy problem. The implemened version for he esimaion eercise is σ X ) u (7) r, = α + αβ + ασ r, + ( + βx The produc of he parameers α β provide a measure of he degree of sensiiviy of volailiy o changes in hedging inensiy. A version of he equaion is used for he esimaion eercise using OLS, however i involves ignoring he heeroscedasiciy induced by he las erm, which is he volailiy of volailiy effec. However, in is curren form, (7) is esimaed using he maimum likelihood framework, where he likelihood funcion is given by: ( X ) ( ( + ) ) σ α βx α σ L( α, α, β, υ) = ln υ( + β ) r, r, (8) υ 6

7 3. The Daa Volailiy in financial markes is ypically measured in one of wo ways. The firs eamines he e-pos hisorical volailiy of raes. The second uses he financial derivaive pricing models o ascerain he e-ane volailiies consisen wih derivaive asse prices. This paper, like Perli and Sack, will focus on he volailiies implied by he prices of swapion derivaive conracs. These implied volailiies are he resul of applying Blacks (976) model of ineres rae opion pricing o ranslae marke daa on prices o volailiy. The Perli and Sack mehodology seeks o eplain shor-erm movemens in volailiies unrelaed o longer-erm shifs in he underlying ineres rae process. To implemen his measure hey derive he residual componen of shor-erm volailiy orhogonal o long-erm volailiy. This sep involves regressing a squared measure of shor-erm implied volailiy on squared values of longer-erm implied volailiy, and using he residual as he dependen variable in he analysis. The residualη in (9) below measures he par of shor-erm volailiy no eplained by long-erm volailiy: σ, + η, (9) r (3m y) = ψ + ψ σ r, (y y) where σ r, (3m y) is he square of he implied volailiy of a hree-monh swapion on a enyear swap. Similarly, σ r, (y y) is he square of he implied volailiy on a wo-year opion on a en-year swap. The resuls from (9) are used o build he orhogonalized measure of variance, which is consruced as follows: σ r, = η + σ r, (3m y ), () where η is he ime series of residuals and σ r, (3m y) is he sample average of he variance of he 3 monh year swapions. We use ime series on he implied volailiy for five swapions: 3monh 5 year, 3 monh year, 6 monh 5 year and 6 monh year. The implied volailiies are measured in basis poins (bps.), i.e. h of one percen. The sources for he opion volailiies were he Salomon Smih Barney s Yield Book online service or Perli and Sack. The ime series for each of hese volailiies was consruced as he produc of daily rae volailiy and he appropriae forward rae. 3 The descripive saisics for he variables used and heir definiions are described below in Table. Swapions are opions conracs on a swap. These conracs provide he holder wih an opion o ener ino a swap a some poin in he fuure. The quoed prices of hese conracs are in volailiy unis, he marke deermined value of e-ane volailiy. 3 Basis poin volailiy for he 3 monh year swapion equals he produc of he rae volailiy for he 3 monh year and he 3 monh forward en year raes. 7

8 Table : Definiions and Descripive Saisics for Variables used in he Analysis: 997: 3:5 4 Variable Definiion Source Frequency Mean Sandard Deviaion Duraion eposure o be covered as Daa used in a resul of a shock a any poin in he Perli and Weekly ime Sack paper Morgage Marke Conveiy 3my Implied Volailiy 6my Implied Volailiy yy Implied Volailiy y5y Implied Volailiy 3m5y Implied Volailiy 6m5y Implied Volailiy Annual basis poins (bps.) implied volailiy. Annual basis poins (bps.) implied volailiy. Annual basis poins (bps.) implied volailiy. Annual basis poins (bps.) implied volailiy. Annual basis poins (bps.) implied volailiy. Annual basis poins (bps.) implied volailiy. Daa used in he Perli and Sack paper Salomon Smih Barney series from YieldBook Salomon Smih Barney series from YieldBook Salomon Smih Barney series from YieldBook Salomon Smih Barney series from YieldBook Salomon Smih Barney series from YieldBook Weekly Weekly Weekly.5.38 Weekly Weekly Weekly.53.5 The firs wo variables described in Table, morgage marke conveiy and he conveiy of he fied income universe, measure he conveiy eposure in erms of he magniude of swaps ha would have o be raded o remain duraion neural in he presence of a rae shock ha is ypically 5 bps. We use he weekly observaions on he morgage marke conveiy measure, obained from Perli and Sack o replicae heir resuls. The remaining si weekly series measure implied volailiy of boh shor and long-erm swapions. Figure displays boh shor and long volailiy series. In eamining he daa we noiced ha he Perli and Sack long implied volailiy (yy) series deviaed from our series saring in. While he Perli and Sack series differed in hese laer monhs hey generally agreed wih our pre- daa. To check he reliabiliy of hese series we obained addiional independen volailiy daa from JP Morgan and LehmanLive.com and found ha heir daa more closely corresponded 4 The Annual basis poins (bps.) implied volailiy is divided by. In doing so we are saying consisen wih Perli and Sack (3). Marke convenion, however, would epress he implied volailiy of a 3my swapion as 6.4 basis poins. This convenion has no implicaions for he foregoing economeric eercise. 8

9 o our series han he Perli and Sack series over he o 3 period. 5 As a resul of his divergence we will consider model esimaes using boh he Perli and Sack series and he series using daa from Salomon Smih Barney. Figure : Time Series of he Perli and Sack and Our Values (Salomon Smih Barney) of Implied Volailiy Lef Hand Scale: 3monh year year year 3monh year Perli & Sack 3monh year Perli & Sack year year Salomon Smih Barney Perli & Sack Salomon Smih Barney Perli & Sack Firs we replicae he firs-sage resuls of Perli and Sack using heir series and hese findings are given in he firs row of Table. Perli and Sack use he residuals from his firs sage regression (afer adding he average squared volailiy) as he dependen variable in heir second sage regression. Noe ha we numerically replicae heir coefficien esimaes. The firs se of resuls highlighed in firs row of Table below are obained using Perli and Sack daa, whereas, all he oher resuls are obained using our implied volailiy series. I is noiceable ha using our series he value of he coefficiens and he R are all significanly lower han hose obained by Perli and Sack. 6 We hen re-esimae his firs sage using he alernaive daa series for boh shor and long volailiy. These resuls are given in he second row of Table Salomon Smih Barney 3monh year Salmon Smih Barney year year Righ Hand Scale: year year sqr 5 The specificaion suggesed in Perli and Sack requires ha he volailiy series be squared prior o he regression. The pos Perli and Sack volailiy series more closely mached he square of our volailiy series. This is suggesive of he possibiliy ha he Perli and Sack daa was updaed wih squared volailiies raher han volailiies. 6 We also noe ha afer replicaing he Perli and Sack firs-sage resuls, he R of.6 differed from he.95 value repored in he Perli and Sack paper. I is imporan o noe ha his residual volailiy is small boh in relaive and absolue magniude. The average squared volailiy is.7, of which he uneplained componen is., wih he coefficien of variaion aking a value of.9, a small magniude. In fac, i migh be argued ha his effec (of residual volailiy) is so small ha i no of any grea consequence o any policy issues ha relae o sabiliy in financial markes. 9

10 and qualiaively replicae he signs of he Perli and Sack coefficien esimaes, bu differs maerially in heir magniude. In order o evaluae he sensiiviy of he Perli and Sack findings, we perform alernaive firs sage regressions using differen swapion srucures. The hird row varies he Perli and Sack eperimen by changing he shor volailiy series o one based on 6m y swapions. The fourh row varies he Perli and Sack eperimen by shorening he long volailiy series o he y 5y swapion. The fifh and final row alers boh series, aking he 6m 5y swapion volailiy as he shor series and he y 5y series as he long series. In hese hree cases he sign and he magniude of he coefficiens are similar o wha was obained in he replicaion of he Perli and Sack model using our shor and long series. While here may be a difference beween he resuls based on he daa sources, we find ha he firs sage regressions produce similar resuls across he range of swapion volailiies ha we eplore. This suggess ha hese Perli and Sack findings are no specific o he paricular swapion conracs hey chose o eplore. I is informaive o eamine he graph of he dependen variable creaed ou of he firs sage regression. Figure plos he volailiy series creaed by adding he residual from he firs sage regression o he average squared volailiy for he shor-erm swapion. Two feaures are sriking in his graph. They are he spikes ha occur he laer half of 998 and near he end of, associaed wih he LTCM and he 9/ evens. The LTCM erema is approimaely 6.54 sandard deviaion even and he 9/ insance is a 3.77 sandard deviaion even. Since boh leas squares and Maimum Likelihood mehodologies can be highly sensiive o oulier observaions, his graph moivaes he eploraion of he sensiiviy of he Perli and Sack findings o hese sressful episodes. Wih he possibiliy of model error and parameer insabiliy, he issues remains as o wheher any variabiliy remains o be eplained. However, mos of our resuls do indicae ha (wih R ranging from.78 o.9) here may well be up o % of he variabiliy ha remains o be eplained. However, his is an issue ha we will pursue in he ne secion. Table : Regression Resuls for Shor-Term on Long-Term Implied Variance Dependen Variable Independen Variable Time Period Evaluaed R-Square 3myr yryr 997: 3:5.6 3myr yryr 997: 3: myr yryr 997: 3: m5yr yr5yr 997: 3: m5yr yr5yr 997: 3:5.943 Esimaed Parameers (p-values in Parenhesis) ϕ ϕ

11 Figure : Time Series Comparison of Perli and Our Dependen Variable.5.8 LTCM Crisis Salomon Smih Barney 9/ Effec 9/ /4/997 4/4/997 7/4/997 /4/997 /4/998 4/4/998 7/4/998 /4/99 8 /4/999 4/4/999 7/4/999 /4/99 9 /4/ Perli & Sack 4/4/ 7/4/ /4/ /4/ 4/4/ 7/4/ /4/ /4/ 4/4/ 7/4/ /4/ /4/3 4/4/3 Salomon Smih Barney Dependen Variable Perli & Sack Dependen Variable The eogenous variable used in his analysis is a proy for hedging aciviy. 7 The ineres rae risk in he universe of morgage deb is measured by he oal morgage marke duraion and conveiy. Saring from a duraion neural posiion for a given porfolio, he measure of hedging inensiy will depend on he changes in he level of duraion of morgage deb. This change in duraion will depend, in urn on he degree of conveiy, as conveiy is a measure of he rae of change of duraion. As such, conveiy serves as a reasonable proy for changes in duraion for invesors who choose o dynamically hedge changes in duraion. I is worh noing ha dynamic hedging is a reacive hedging proocol. However, mos firms use a miure of saic and dynamic hedging. When rae changes aler he duraion of asses, he porfolio can be rebalanced o a duraion neural posiion by changing he duraion of liabiliies, for eample, by he use of swaps. To he een ha firms anicipae hedging needs and eliminae some or all of he conveiy eposure hrough he use of swapions o offse he negaive conveiy inheren in he morgage universe, he residual negaive conveiy would be he appropriae measure of hedging inensiy. However, residual pos-hedging conveiy is unobservable and so he analysis uses morgage marke conveiy. If firms change heir mi of dynamic and saic hedging during he sample period, his could diminish he prediciveness of his regressor. 7 Perli and Sack consider hree proies for hedging. Since hey indicae ha conveiy is he mos robus and indicaive measure of hedging inensiy, we resric our aenion o his proy.

12 The series for conveiy used in his paper is he same as ha used by Perli and Sack. I provides a weekly measure of en-year swap equivalens needed o swap ou he changes in duraion resuling from changes in raes during he same period. 8 We also use a broader measure of conveiy for he fied income universe laer in he esimaion eercise, o provide a measure of he impac of he hedging needs of he fied income universe. An addiional variable describing he magniude of he conveiy of he enire fied income universe is used, and i measures he conveiy of he all of he ousanding fied income securiies in he Broad Invesmen Grade (BIG) inde. While he measure of conveiy is of monhly frequency i does provide measure agains which one can conras he conveiy of he morgage universe and provide insigh ino he een o which hedging in he fied income universe migh be conribuing o volailiy. When using his series o eamine specific conribuion of morgages relaive o he enire marke, we will conver he morgage marke conveiy and implied volailiies o monhly observaions Impac of Morgage Hedging on Volailiy Perli and Sack measure he impac of morgage hedging on volailiy by regressing he consruced residual shor-erm volailiy variable on a proy for morgage marke hedging, he oal morgage marke conveiy. Firs, we replicae he Perli and Sack second-sage analysis and obain coefficiens ha are idenical and are presened in he firs shaded row of Table 3. We hen eend he second-sage analysis o differen swapion srucures. Using hree oher swapion volailiies for he same sample period ( 6myr, 3m5yr, and 6m5yr) we find ha we are able o obain he esimaes of he coefficiens α and α ha are nearly idenical and significan. For he parameer of ineres, α β, he sign is in agreemen wih he resuls of Perli and Sack for all of he swapion srucures, bu he magniude is subsanially reduced. We find ha he esimaes do no appear significan, bu because he sandard errors are no adjused for heeroscedasiciy, he reliabiliy of inferences drawn is quesionable. Table 3: Regression Resuls for Orhogonalized Implied Variance Dependen Variable Time Period Evaluaed 3myr 997: 3:5 6myr 997: 3:5 3m5yr 997: 3:5 Morgage Marke Conveiy As Independen Variable Esimaed Parameers (p-values in Parenhesis) α α α β (.) (.) (.) (.) (.) (.4) (.) (.) (.) 8 Ten-year swap equivalens are a sandard measure of he number of dollars of his conrac ha mus be used o eliminae a duraion eposure. 9 Eplanaion of how you manage o produce monhly volailiy numbers.

13 6m5yr 997: 3: (.) (.) (.) We move ne o he esimaion of he parameers using MLE wih he specificaion described in (8). The MLE will be boh efficien and provide a basis for asympoically valid inference. The resuls for his eercise are described in Table 4 below. Wih he MLE esimaion eercise we are esimaing four parameers: α, α, β and υ, and he parameer of ineres is β, he amplificaion parameer. For all of he swapion srucures for his sample period, we find ha he coefficiens are all highly significan and closely approimae he resuls of Perli and Sack. Table 4: MLE Resuls for Orhogonalized Implied Variance Dependen Variable Time Period Evaluaed 3myr 997: 3:5 6myr 997: 3:5 3m5yr 997: 3:5 6m5yr 997: 3:5 Morgage Marke Conveiy As Independen Variable Esimaed Parameers (p-values in Parenhesis) α α β υ (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) One imporan es of a models validiy is parameer sabiliy. Inuiively, here maybe srucural differences beween periods wih low levels of hedging aciviy as compared wih periods of high levels of hedging aciviy. For eample, in periods where he demand for hedging is low, risk managers may increase he proporion of hedging accomplished hrough saic hedges. We proceed o eamine his issue by segmening he sample period ino a period when he MBA Refi-inde was low and wih epeced low levels of hedging aciviy and, a period when he MBA Refi-inde was high and volaile, implying greaer hedging pressures. For his purpose we spli he sample period ino wo sub-samples, 997: : and : 3:5, and esimae he model for hese wo sub-periods. I is here ha we find a resul ha is couner-inuiive. During a period when he refi-incenives were low and when we migh have epeced o find ha he amplificaion parameer β o be low in magniude, ye we find i be o high no only for he 3myr swapion srucure, bu for all of he ohers as well. Furhermore he esimaes all have high p-values and -saisics. Equally We idenified a problem wih he specificaion of he Likelihood in he original Perli and Sack analysis, and correced i for he esimaes provided in Table 4. The correced Likelihood esimaes did no maerially differ. A derivaion of he correced Likelihood can be found in Appendi A. 3

14 couner-inuiive, for he period : 3:5, when he MBA refi-inde was high and hedging pressures were grea, we find ha he values of he amplificaion parameer β implied ha higher levels of hedging acually lowered volailiy. Furhermore hese resuls are highly saisically significan. Were he original Perli and Sack specificaion correc, we would be unlikely o observe his magniude of parameer insabiliy. Table 5: MLE Resuls for Orhogonalized Implied Variance Dependen Variable 3myr 6myr. 3m5yr 6m5yr Time Period Evaluaed 997: : : 3:5 997: : : 3:5 997: : : 3:5 997: : : 3:5 Morgage Marke Conveiy As Independen Variable Esimaed Parameers (p-values in Parenhesis) α α β υ (.5) (.) (.) (.) (.5) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.4) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) (.) To furher refine our undersanding of he parameer insabiliy in he Perli and Sack model, we eamine he parameer esimaes of a rolling window. Specifically we ake 3 week inervals saring wih he firs dae 997: and esimae he model parameers for each of daa window. If he model were correcly specified, hese esimaes would be consan, ecep for sampling error. Alernaively, if he sabiliy were caused by an oulier in he daa, we would see subsanial movemen in he parameer esimaes as he oulier daa poins move ino or ou of he sample window. Figure 3 below plos he amplificaion parameer esimae β as a funcion of he sar dae of he 3 week window. This graph ehibis wo srong disconinuiy poins, one a abou 3/3/997 and he oher a abou 9/3/998. These wo poins correspond o insances in which marke disrupions brough abou by LTCM ener and ei, respecively, from he sample window. Furher, removing he few daa observaions associaed wih LTCM marke disrupion and reesimaing, resuls in coefficien esimaes ha shif from being variable and negaive o posiive, consan and frequenly saisically significan. 4

15 Figure 3: Changing MLE Esimaes of Sensiiviy Parameer LTCM Effec Saring Poin LTCM Effec Ending Poin 9/ Effec Saring Poin 9/ Effec Ending Poin /3/997 4/3/997 7/3/997 /3/997 /3/998 4/3/998 7/3/998 /3/998 /3/999 4/3/999 7/3/999 /3/999 /3/ 4/3/ 7/3/ /3/ Wih spikes Wihou wo spikes 6. Conclusion Undersanding volailiy and is deerminans is an imporan open issue. The possibiliy ha risk miigaion sraegies could have he uninended consequence of increasing he amplificaion of eogenous shocks o financial markes raises imporan policy quesions. Perli and Sack ask an imporan quesion relaing o morgage risk managemen implicaions for ineres rae volailiy. Their analysis focused on eplaining he componen of shor-erm volailiy unrelaed o movemens in long-erm volailiy. While heir empirical findings ha linked morgage hedging o increased volailiy were an arifac of several oulier observaions in he daa, correcing heir analysis by dropping periods associaed wih he LTCM crisis and 9/, generae esimaes ha sugges here is lile impac o he volailiy from morgage hedging. Indeed, over some periods he hedging aciviy appears o miigae some of he marke volailiy. While his analysis represens a sep owards beer undersanding he linkage beween hedging aciviies and financial sabiliy, we believe ha a more srucural approach o his problem is needed. The erm srucure of volailiy, for eample, would sugges an alernaive empirical approach o obaining informaion abou shor-erm volailiy unrelaed o long-erm volailiy movemens han was aken in he Perli and Sack firs sage regression. Furher, he componen of shor-erm volailiy no eplained by movemen in long-erm volailiy is small in boh 5

16 absolue and relaive magniude. Any heory ha has policy relevance needs o eplain maerial movemens in marke volailiy. 6

17 Appendi For a variable ha follows normal disribuion N( µ, σ ), wih mean µ and variance σ, he likelihood funcion, or he densiy funcion, is as follows: ( ( µ ) L = f ) = ep( ). σ (π ) σ The log-likelihood funcion is he resul of aking naural log on boh sides of he above equaion: log L = ln π lnσ ( µ ). σ To maimize log L is o maimize lnσ ( µ ). σ From equaion (7) we have: σ = α + α β X + α σ + β X ) u. r, r, ( + We can use ε o denoe he amplified error erm, wihε = ( + βx ) u disribuion N(, V ( β X ) ). + Our variable here is σ r,, wih. ε follows normal σ = V ( + βx ) and ( = α + βx ) + ασ r, µ. Subsiue hese erms ino he log-likelihood funcion, we have: L( α ) ( ( ) ) ( ( ) ), α, β, υ = ln υ + βx σ r, α + βx ασ r,, insead υ ( + βx ) of L( α ) ( ( ) ) ( ( ) ), α, β, υ = ln υ + βx σ r, α + βx ασ r, as in equaion (8). υ 7

18 References De Long, Bradford, Andrei Schleifer, Lawrence H. Summers and Rober J. Waldmann, Posiive Invesmen Feedback Sraegies and Desabilizing Raional Speculaion, Journal of Finance, v. lv, no., June 99. Dunbar, Nicholas, Invening Money: The Sory of Long-Term Capial Managemen and he he Legends Behind I, John Wiley & Sons; New Ediion. Friedman, Milon, Essays in Posiive Economics. Chicago: Univ. of Chicago Press, 953. Har, Oliver D., David M. Kreps, Price Desabilizing Speculaion, Journal of Poliical Economy, pp , v. 94, no. 5, 986. Jorion, Phillipe, Fallacies in he Effecs of Marke Risk Managemen Sysems, Working Paper, July. Naranjo, Andy and Alden Toevs, The Effecs of Purchases of Morgages and Securiizaion by Governmen Sponsored Enerprises on Morgage Yield Spreads and Volailiy, pp , Journal of Real Esae Finance and Economics, Sep.-Dec., v. 5, iss. -3. Perli, Robero and Brian Sack, Does Morgage Hedging Amplify Movemens in Long-Term Ineres Raes? pp. 7-7, Journal of Fied Income, Dec. 3. Persaud, Avinash, Sending he Herd Off he Cliff Edge: The Disurbing Ineracion Beween Herding and Marke Sensiive Risk Managemen Pracices, Journal of Risk Managemen Pracices, Journal of Risk Finance, 59-65,. 8