Central Bank Intervention and Exchange Rate Volatility (Empirically Testing Conflicting Results)

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1 Cenral Bank Inervenion and Exchange Rae Volailiy (Empirically Tesing Conflicing Resuls) Econ 11C Term Paper Professor Ai-Ru Cheng 1/16/07 by Sanchia Mukherjee Vladyslav Sushko 1

2 Table of Conens: 1. Inroducion Measuring Volailiy Limiaion of GARCH Decomposiion of Volailiy Mehodology for Exracing Jump Componen Conflicing Resuls in Lieraure Daa Descripion Daa Issues Mehodology Resuls Conclusion References... 15

3 1. Inroducion In inernaional economics, he poenial effec of Cenral Bank Inervenion (CBI) on exchange rae behavior has been an imporan issue of debae since he end of Breon Woods Sysem. A large body of lieraure examines he relaion beween CBI and exchange rae volailiy. This issue is also crucial o finance, because volailiy is fundamenal o pricing financial asses. Some resuls documened in empirical finance lieraure show ha inervenions end o increase exchange rae volailiy in he shor run (Beine e al., 00; Baillie and Oserberg, 1997; Bonser-Neal and Tanner, 1996), or move he exchange rae in he wrong direcion (Baillie and Oserberg, 1997). Ye some empirical sudies in inernaional economics show ha CBI can acually decrease exchange rae volailiy in he shor-run (Waanabe and Harada, 004). These are moivaed by he noion ha one of cenral bank s objecives may be o sabilize he marke, hus i will inervene in such a fashion as o decrease exchange rae volailiy. This is a odds wih mos financial lieraure ha reas CBI like any oher shock implying ha inervenion emporarily increases boh volailiy and rading volume. Two branches in he microsrucure heory ha advocae a posiive relaion beween CBI and marke volailiy are Invenory Approach and Informaion Approach (Dominguez, 003). The invenory branch examines he quesion of wha happens when orders o buy and sell are no always balanced in he seleced ime period. One simple predicion of invenory models is ha since a dealer will sell if he has long invenory and buy if he has shor invenory, here should be mean reversion in prices due o invenory effecs. This migh be a resul of inervenion. Theory predics ha his mean reversion will ake place 3

4 unil change in he porfolios due o inervenion are rebalanced. The informaion branch focuses on he quesion of how prices may be affeced by he fac ha raders in he marke may have differen informaion. In his case, dealer s posiion is speculaive. Being in he middle of many raders, he rader knows ha some raders have beer informaion relaive o him. The informed raders will buy when he price is very low and buy when price is high. Traders know ha hey will lose when rading wih informed raders. Therefore, in order o remain solven hey have o offse he loses by making gains by dealing wih uninformed raders. This will increase he volume of ransacion in he marke and affec he relaive price, which is exchange rae. Again, le us consider he case ha some raders (informed) know ha cenral bank is inervening one hour prior o public release of he inervenion informaion. Then predicing he movemen in he exchange rae hey eiher buy or sell currency. This will increase he ransacion volume and volailiy and also change he efficacy of inervenion operaions.. Measuring Volailiy Based on his heoreical framework, imporance of CBI on exchange rae and is effeciveness are examined. There are hree main approaches o measure asse price volailiy: GARCH, (Baillie and Oserberg, 1997), Implied volailiy from opion prices (Dominguez 1998, Bonser-Neal and Tanner, 1996), and Realized volailiy (Beine, Lauren, and Palm 005, Dominguez 004). 4

5 .1 Limiaion of GARCH The use of GARCH model has an imporan limiaion. I is widely known fac ha he shocks o exchange rae volailiy are highly persisen. As we incorporae CBI in he volailiy model hen i becomes equivalen o assuming ha he effecs of inervenions are also persisen. In he case when he effecs are ransiory he model would no be valid anymore.. Decomposiion of Volailiy In order o overcome he problem of volailiy clusering, he lieraure reas volailiy in erms of wo componens: Shor-erm (jump) componen, and Long-erm (persisen) componen. Engle and Lee (1999) considered he marke prices of raded sock opions wih a range of opion expiraions and invesigaed he erm srucure of implied volailiies. They found ha sock reurn volailiy could be decomposed ino wo dominan scenarios in foreign exchange marke. The dominan effec moves parallel o implied volailiy, bu he ampliude is much greaer for he shor mauriies. The volailiy of shor-erm volailiy is much greaer han long-erm volailiy. The erm srucure of implied volailiy can change slope wihin a shor period of ime as he shor-erm volailiy can move from abnormally low o abnormally high and i shows disconinuiies in he underlying price process, herefore, i is ermed as jump componen. On he oher hand, he long horizon volailiy is highly persisen and coninuous and ermed as coninuous componen in Financial Economics. The decomposiion of volailiy ono shor-run (jump) and long-run (coninuous) componens makes i well suied for various economic and asse pricing hypohesis. 5

6 Time series inervenion lieraure uses wo differen approaches o decompose exchange rae volailiy. One is o esimae he volailiy using Componen GARCH (Waanabe, Harada, 004). This mehod simulaneously esimaes he effecs of inervenion on shor-run and long-run componens of exchange rae volailiy wihou explicily observing hese componens. Calling hese GARCH shor-run and GARCH long-run, he laer includes an inercep erm, and he lef-hand side of boh mus sum o he realized exchange rae volailiy. Componen GARCH model will be addressed in more deail in our mehodology secion. The second approach uses he concep of bi-power variaion o explicily decompose realized volailiy ino persisen componen and jump componens hen esimaes inervenion effecs using ARIMA models (Beine e al., 006). Whereas in radiional heory of financial economics he variaion of asse prices is measured by looking a sums of squared reurns calculaed over small ime periods, more recenly Barndorff-Nielsen and Shephard (004) inroduced a parial generalizaion of quadraic variaion called bi-power variaion (BPV). They showed ha in some cases relevan o financial economics, BPV could be used o spli up he individual componens of quadraic variaion ino he coninuous par of prices and ha due o jumps. In urn, he bi-power variaion process can be consisenly esimaed using an equally spaced discreizaion of financial daa. This esimaor is called he realized bi-power variaion process. 6

7 .3. Mehodology for Exracing Jump Componen We follow Beine e al. (006) o explain he basic process of exracing jump componen from realized volailiy. This mehodology was developed by Andersen, Bollerslev, and Diebold (1998, 001, 005) and Barndorff, Nielsen, and Shephard (00). The movemen of asse prices in ime can be approximaed wih he following sochasic differenial process: dp ( ) = µ ( ) d + σ ( ) dw ( ) + κ ( ) dq( ) 0 T (1) Equaion (1) is also referred o as coninuous-ime jump diffusion process (Beine e al., 006). Here, p() is he log of asse price wih mean μ(), coninuous volailiy σ(), and disconinuous jumps κ(). Coninuous volailiy follows Brownian moion W() and he jump has a Poisson disribuion. I follows ha he inegraed volailiy of his asse price (i.e. he sum of square reurns) beween ime 0 and ime is: σ ( s) ds + < s [ r, r] = κ 0 0 ( s) () The realized daily volailiy, RV +1 (Δ), is jus he sum of corresponding inraday discreely sampled Δ-period reurns. If he inraday daa is obained a 5 minue inervals, hen 1/ Δ = 88, hen number of daily daa poins. If follows ha in he limi (as Δ 0) realized daily volailiy approaches coninuously aggregaed sum of square reurns: RV + 1 ( ) + σ ( s) ds + κ ( s) 1 < s + 1 (3) 7

8 In order o exrac jump componens from realized volailiy Beine e al. (006) esimae realized bi-power variaion, BV +1 (Δ), which is defined as he sum of he produc of adjacen absolue inraday reurns sandardized by a consan (Beine e al., 006): 1/ + 1 j = BV ( ) µ 1 r + j, r + ( j 1), (4) where μ 1 (/π) 1/ is he mean of he absolue value of sandard normally disribued random variable. Since reurns from wo adjacen ime periods share he persisen volailiy bu no he sporadic jumps, i follows from (4) ha bi-power variaion provides a reasonable proxy for he persisen componen of he volailiy. Furhermore, Barndorff- Nielsen and Shephard (004, 005) shows ha: BV ( ) σ ( s) ds (5) Since realized volailiy, RV +1 (Δ), and bi-power volailiy, BV +1 (Δ), can be direcly calculaed from observaions of he asse s price, i follows ha he unobservable jump componen can be approximaed as he difference of he wo: RV + 1 ( ) BV + 1( ) κ ( s) < s + 1 (6) Equaion (6) complees he basic overview of he jump exracion process from he realized volailiy of asse reurns. 8

9 3. Conflicing Resuls in Lieraure In conducing lieraure review we found wo recen sudies ha aemp o overcome limiaions of GARCH in assessing he effecs of CBI on exchange rae volailiy. The firs sudy is by Waanabe and Harada (004) who use componen GARCH model and esimae he effecs of CBI on he implied long-run (persisen) and shor-run (ransiory) componens of exchange rae volailiy. They use daa on daily closing spo price of New York marke for yen/dollar exchange rae from April 1, 1991 o March 31, 003. The auhors find no significan effec of BOJ s inervenion on long-run volailiy and significan negaive effec on shor-run volailiy of Yen/Dollar exchange rae in he second half of he sample period. The second sudy is by Beine e al. (006) who exrac he jump componens using bi-power variaion approach described in he previous secion and esimae he effecs of CBI on realized volailiy, is coninuous componen, he disconinuous jump componen using ARFIMA model. Unlike Waanabe and Harada (004) hey use inraday daa on Yen/Dollar exchange rae from Jan,1987 o Oc 1, 004. Beine e al. also ge rid of he rading days when here is low rading aciviy, holidays and weekends. These auhors find posiive a posiive effec of CBI on persisen and jump componens of volailiy, wih he effec on jump componen also highly significan. The resuls of Waanabe and Harada (004) and Beine e al. (006) presen a conradicion. One possible reason for his may simply be he difference in daa frequencies (daily versus inraday). If no, hen one of he models is no decomposing he exchange rae volailiy correcly. In he res of he paper we address hese conflicing 9

10 resuls by esimaing boh models, componen GARCH and realized volailiy ARIMA, wih uniform daa. 4. Daa Descripion We use daily closing spor Yen/Dollar exchange rae daa from 1 April, 1991 o 31 March 004 (provided by Professor Ai-Ru Cheng). Figure 1 Yen/Dollar exchange rae for his ime period. This daa has been conrolled for missing and low volume rading days corresponding o weekends and holidays. The realized volailiy of our daase has been already decomposed ino he coninuous (bi-power) componen and he jump componen. These are ploed in figure. Finally, we use official daily Bank of Japan inervenion daa from 13 May 1991 o 16 March 004. During his period Bank of Japan inervened in Yen/Dollar foreign exchange marke a oal of 348 imes (days), each ime wih sales of 30 billion Yen. Bank of Japan haled is inervenion policy in 004. Figure 1: Yen/Dollar exchange rae over he sample period 10

11 Figure : Decomposed exchange rae volailiy over he sample period Figure 1 shows a prolonged period of appreciaion of he Yen beween March 1990 and November 1995, followed by depreciaion of almos equal magniude from December 1995 unil he spring of This mean-reversal process is repeaed again on a smaller scale beween November 1997 and Ocober 001. Figure shows a subsanial spike in volailiy during he rough (Yen/Dollar exchange rae a is lowes) preceding December 1995 and an even greaer volailiy in he spring of 1998 when anoher rend reversal in Yen/Dollar exchange rae ook place. 11

12 4.1 Daa Issues There are wo poenial sources of problems wih our daa. Firs and foremos, our obained esimaes for Bank of Japan inervenion are a odds wih hose presened in he lieraure. Specifically, Waanabe and Harada (004) repor official Bank of Japan inervenion daa o show ha while mos inervenion episodes are indeed sales of Yen, hey are no all of equal magniude of 30 billion as in ou sample. This can poenially have profound effec on our resuls. We parially overcome his defec in daa by using dummy variable in our model o indicae an inervenion episode. Second, because our daa is sampled a daily frequencies, he bi-power volailiy may no longer have he necessary asympoic properies o be an accurae esimae of he consisen volailiy componen. 5. Mehodology We aemp o replicae componen GARCH and realized volailiy ARFIMA mehodologies of Waanabe-Harada (004) and Beine e al. (006) respecively. By applying boh esimaion echniques o he same daa we hope o reconcile he conradicory conclusions of he above auhors wih respec o CBI effec on exchange rae volailiy. Firs we use maximum likelihood o esimae he following componen GARCH (1,1): σ = σ + σ l, s, σ + θ s, = α σ s + β ( ε σ 1 1), 1 σ + θ l, = ω + ρ σ l, 1 + ϕ ( ε 1 σ 1) S I L I (7) (8) (9) 1

13 where σ s and σ l are shor-run (jump) and long-run (persisen) componens of he realized volailiy σ and I is a dummy variable ha akes on a value of 1 if here was CBI in period and is zero oherwise. The inercep ω in equaion (9) is consisen wih Engle and Lee (1999) reasoning for long-horizon volailiy. Since long-run volailiy componen is highly persisen compared o he shor-run componen, our esimaions should yield ρ > α. However, we are specifically ineresed in esimaing he coefficiens on inervenion dummies, θ S and θ L. If inervenion causes jumps in volailiy as he heory predics, hen θ S should be posiive and significan. We also aemp o replicae Beine e al. (006) mehodology only his ime using daily closing spo raes insead of inraday observaions. We esimae he following ARFIMA (1, d, 0) model: (1 ] d ρ L)(1 L) [log( σ ) µ = ε + θ I (10) (1 ] d ρ L)(1 L) [log( σ l, ) µ = ε + θ L I (11) Here L is a lag operaor, ρ is once again a persisency measure, and d is he fracional inegraing parameer. In his model σ is once again realized volailiy, however σ l is he bi-power volailiy calculaed direcly from daa via he process described in secion.3. Again, we are ineresed in esimaing θ and θ L. If CBI causes jumps in volailiy bu does no affec is permanen componen hen we would expec θ o be posiive and significan and θ L o be insignifican. 13

14 6. Resuls Table 1: Componen GARCH (1,1) Resuls Coefficien MLE Value Coefficien MLE Value α ρ β θ S φ θ L ω Table 1 illusraes esimaion resuls of componen GARCH. Indeed wih a persisence erm esimaed a.096 for he long-run componen, compared o for shor-run componen, he specificaion seems correc in decomposing realized volailiy. Moreover, θ S = and θ L = confirm our expecaions ha CBI produces volailiy jumps. These resuls are a odds wih Waanabe and Harada (004) who found ha inervenion in foreign exchange markes by he Bank of Japan reduced volailiy in he shor-run. Nex we repor resuls for our esimaion of inervenion effecs on volailiy using Beine e al. (006) mehodology. Firs we esimae he fracional inegraion parameer, d, using Geweke/Porer- Hudak (GPH, 1983) mehod. Our esimaed d is.4104 wih sandard error of.059. Thus we see ha realized volailiy in our daa exhibis long-memory consisen wih lieraure on exchange rae volailiy. Unforunaely, since we conduced his par of he esimaion in STATA, we were unable o apply his precise value of fracional inegraion parameer o our ARIMA model. Insead we esimae a regular ARIMA (1,1,0). Table repors coefficien esimaes wih z-sas in parenhesis. The esimaed values of θ and θ L are posiive and significan, suggesing ha CBI increases exchange rae volailiy. 14

15 Furhermore, θ is wice as large as θ L indicaing ha he effec of inervenion on bipower volailiy is much smaller han on realized volailiy. Since he effec on realized volailiy, θ, is an average of θ L and he jump effec, his means ha he effec of CBI mus be even larger on he jump componen: approximaely 3 imes as large as θ L according o our resuls. Table : ARIMA (1,1,0) Esimaion Resuls Dependen Variable σ σ l, d 1 1 ρ (-07.89) ( ) θ (8.39).0000 (8.71) Log likelihood Conclusion Alhough slighly miss-specified, our ARIMA resuls confirm he findings of Beine e al. (006) ha CBI causes significan volailiy jumps. Moreover, hey are consisen wih our resuls from componen GARCH esimaion conduced using Waanabe and Harada (004) mehod. From his we conclude ha he discrepancy beween he wo sudies was caused by differences in daa and no he underlying mehodologies. References Andersen, T. G., Bollerslev T., Diebold F. X.., and Labys P., 1999: Realized Volailiy 15

16 and Correlaion, L.N. Sern School of Finance Deparmen Working Paper 4. Barndorff-Nielsen, O., and Shephard N., 004. Power and Bipower Variaion wih Sochasic Volailiy and Jumps (wih Dis- cussion), Journal of Financial Economerics,, Beine 00. Cenral bank inervenion and foreign exchange raes: New evidence from FIGARCH esimaions. Journal of Inernaional Money and Finance 1, Beine M., Lahaye J., Lauren S., Neely C. and Palm F.C., 006. Cenral Bank Inervenion and Exchange Rae Volailiy, Is Coninuous and Jump Componens. Federal Reserve Bank of S. Louis Working Paper Baillie, R.T., Oserberg, W.P., Why do Cenral Banks Inervene?, Journal of Inernaional Money and Finance, 16, Beine, M., Lauren S. and Palm F., 005. Cenral Bank Forex Inervenions Assessed Using Realized Momens. Journal of Inernaional Financial Markes, Insiuions and Money. Bonser-Neal and Tanner, Cenral bank inervenion and he volailiy of foreign exchange raes: Evidence from he opions marke. Journal of Inernaional Money and Finance 15, Dominguez K.M., Cenral bank inervenion and exchange rae volailiy. Journal of Inernaional Money and Finance, 17, Dominguez K.M., 003. The Marke Microsrucure of Cenral Bank Inervenion, Journal of Inernaional Economics, 59, Dominguez K.M., 004. When Do Cenral Banks Inervenions Influence Inra-daily and Longer-erm Exchange Rae Movemens. NBER working paper 9875 Engle, R.F., Lee, G.G.J., A long-run and shor-run componen model of sock reurn volailiy. In: Engle, R., Whie, H. (Eds.), Coinegraion, Causaliy and Forecasing. Oxford Univ. Press, Oxford, UK, Waanabe T. and Harada K., 004. Effecs of Bank of Japan s Inervenion on Yen/Dollar Exchange Rae Volailiy. Journal of Japanese and Inernaional Economics, 0,