Foreign exchange market intervention and expectations: an empirical study of the yen/dollar exchange rate

Transcription

1 Foreign exchange marke inervenion and expecaions: an empirical sudy of he yen/dollar exchange rae by Gabriele Galai a, William Melick b and Marian Micu a a Moneary and Economic Deparmen, Bank for Inernaional Selemens, CH-4002 Basel, Swizerland b Deparmen of Economics, Kenyon College, 312Ascension Hall, Gambier, Ohio 43022, Unied Saes Absrac We use official inervenion daa provided by he Federal Reserve and, recenly, he Japanese Minisry of Finance, as well as a new daa se based on Reuers news aricles on inervenion ha is perceived by FX raders. We esimae probabiliy densiy funcions (PDFs) from opion daa o describe marke expecaions. We find ha, beween 1993 and 1996, Japanese auhoriies ended o respond mainly o deviaions of he exchange rae from some implici arge levels and o a rise in marke uncerainy. Beween 1997 and 2000, he Bank of Japan mainly reaced in response o higher uncerainy. On he oher hand, he Federal Reserve inervened only in cooperaion wih he Bank of Japan. We find ha inervenion had no saisically significan sysemaic effec on he mean of yen/dollar expecaions. Consisenly, we deec no evidence ha inervenion sysemaically alered marke paricipans bias beween a sronger and a weaker dollar wih respec o he forward rae. Conrary o mos findings of he lieraure, we fail o find evidence ha inervenion was associaed on average wih higher exchange rae variabiliy. Finally, we find ha inervenion was no followed by an increase in he ails of he disribuion of exchange rae expecaions. The consensus view is ha serilized inervenion can be effecive if i is announced publicly, coordinaed across cenral banks, and mos imporanly, consisen wih underlying fiscal and moneary policies. As we are able o conrol for public announcemen and cenral bank coordinaion, our findings sugges ha inervenion during our sample period was no consisen wih underlying fiscal and moneary policy and herefore had lile influence on marke oucomes and expecaions. JEL Classificaion: C22 E41 F31 Keywords: Corresponding auhor. Tel.: ; fax: address: gabriele.galai@bis.org. (G. Galai) 1

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3 1. Inroducion This paper presens empirical evidence on he relaionship beween cenral bank inervenion and marke expecaions of he daily yen/dollar exchange rae. Over he pas years, a number of sudies have analysed he effec of inervenion on he exchange rae level as well as on he insananeous and expeced volailiy of he exchange rae of he yen/dollar, he mark/dollar and oher exchange raes. The resuls are generally mixed and depend on boh he sample period being invesigaed and he inervenion sraegies being used. This paper provides furher evidence on his issue in four ways. Firs, i focuses no only on he expeced level and variance of he exchange rae, bu on he enire disribuion of expeced exchange raes, which is derived from opion prices. The momens of his disribuion allow a more complee characerisaion of marke senimen. Second, his paper uses wo new daa ses on inervenion episodes. One daa se covers acual inervenion episodes and was recenly provided by he Japanese Minisry of Finance hrough is websie. The oher daa se conains inervenions perceived by marke paricipans and is based on Reuers repors. This daa se is more comprehensive han he daa ses based on newspaper aricles ha have been used in he lieraure. Third, his paper uses a comprehensive daa se of news abou macroeconomic variables ha helps o disinguish he effec of inervenion from ha of he arrival of oher relevan informaion. Finally, he paper also looks a wo direcions of causaliy in he relaionship beween inervenion and marke expecaions. We firs examine he reacion funcion of moneary auhoriies and esimae how changes in he momens of he expeced disribuion of fuure exchange raes affec he likelihood of cenral bank inervenion. We hen invesigae he effec of inervenion on he momens, aking accoun of he fac ha inervenion and marke expecaions are deermined simulaneously. In his paper, he empirical probabiliy densiy funcions (PDFs) of fuure yen/dollar raes are esimaed using risk reversals and a-he-money implied volailiies of one-monh OTC opions. 1 We use measures of he momens of hese disribuions he mean, variance, skewness and kurosis and 1 In his paper, he exchange rae is defined as yen per dollar. 1

4 quasi-momens such as inerquanile ranges o describe he sae of marke condiions on a paricular day. If we consider he yen/dollar exchange rae, he mean of he PDF is he raders average expecaion of he yen/dollar rae one monh ahead, i.e. he one-monh forward rae. The second momen of he PDF, he variance of he expeced exchange rae, can be used o describe how uncerain marke paricipans are on a specific day abou he yen/dollar exchange rae ha will prevail over he near fuure. Skewness can be inerpreed as a measure of marke paricipans balance of risks beween a much sronger and a much weaker dollar wih respec o he yen around he expeced fuure exchange rae. The fourh momen, kurosis, measures how fa he ails of a PDF are and indicaes he marke s view of he likelihood of very large exchange rae movemens in eiher direcion in he near fuure. The higher he probabiliy ha he marke assigns o such an exreme change (in eiher direcion) on a paricular day, he higher he kurosis of he PDF on ha day. 2 Our analysis is conduced over he period from 20 Sepember 1993 o 30 April For he purpose of his paper, cenral bank inervenions are defined as ransacions inended o influence he exchange rae. This definiion herefore excludes ransacions such as hose aimed a alering he currency composiion of he cenral bank s foreign exchange porfolio. Our resuls sugges ha during he period of dollar weakness beween 1993 and 1996, he Bank of Japan seems o have responded o deviaions of he spo exchange rae from wha raders perceived as implici arge ranges. I also appears o have inervened on average as a response o a rise in marke uncerainy, consisen wih saemens made by cenral banks in he pas ha emphasised heir aemp o calm disorderly markes. We found evidence ha beween 1997 and 2000, he Bank of Japan seems o have inervened mainly following a rise in uncerainy. During he whole sample period, he Federal Reserve inervened always in conjuncion wih he Bank of Japan. Consisen wih some of he findings in he lieraure, our regression analysis suggess ha, on average, inervenion in he yen/dollar marke had no saisically significan effec on he mean of he 2 3 High kurosis need no come exclusively from "fa ails", since i may also come from having a high proporion of observaions close o he mean (a "hick midriff"). Hence, a change in kurosis may no necessarily imply a change in he ails of he disribuion. Equivalenly, an increase in he kurosis of one of he PDFs need no imply a rise in he expeced likelihood of major moves. The sar of he sample period is dicaed by he availabiliy of opion daa necessary o esimae he PDFs. 2

5 PDF during he period under review. We also find ha, beween Sepember 1993 and April 2000, cenral bank inervenion direced a he yen/dollar exchange rae was no associaed wih a significanly higher variance of expeced fuure spo raes. This resul indicaes ha, on average, cenral bank inervenion was no followed by an increase in uncerainy in he marke abou fuure exchange rae movemens. Consisen wih our resuls for he mean, we find ha, on average, inervenion did no have a significan effec on he skewness. Hence, following inervenion in suppor of he dollar, marke paricipans did no change he weigh ha hey pu on a much sronger raher han a much weaker dollar wih respec o he forward rae. Finally, we find ha inervenion did no influence he kurosis in a significan way. In erms of inervenion sraegies, resuls for he period 1993 o 1996, when all inervenions involved dollar purchases, indicae ha a 90% or 95% confidence levels, he impac of coordinaed or officially announced inervenions was no saisically differen from ha of unilaeral inervenions. 4 Our resuls can be easily reconciled wih he consensus view on he effecs of inervenion in he foreign exchange marke. According o his view (see he lieraure review in he following secion) serilized inervenion can be effecive if i is announced publicly, coordinaed across cenral banks, and mos imporanly, consisen wih underlying fiscal and moneary policies. When cenral banks enered foreign exchange markes in a coordinaed, public fashion in he 1980s - paricularly around he Plaza or Louvre Agreemens - hese inervenions did succeed in affecing raders expecaions of fuure exchange rae movemens (see Galai and Melick (2002)). For he period under sudy in his paper, however, all of hese condiions were no me; wih he resul ha inervenion is found o have lile influence on marke oucomes and expecaions. The remainder of he paper is organised as follows. Secion 2 reviews he main conribuions o he lieraure on he effec of cenral bank inervenion and on cenral banks reacion funcions. In Secion 3, we describe our inervenion daa and daa on macroeconomic news. Secion 4 describes he opion daa and he mehod ha was used o esimae he empirical PDFs. We also discuss he inerpreaion of PDFs. In Secion 5, we firs esimae reacion funcions for he Federal Reserve and he Bank of 3

6 Japan ha relae inervenion o pas marke condiions. We hen analyse he impac of inervenion on marke expecaions. Secion 6 concludes. 2. Review of he lieraure The lieraure on he effec of inervenion in foreign exchange markes is exensive. This secion reviews some of he main conribuions for comprehensive surveys, refer o Edison (1993), Almekinders (1995), Schwarz (2000) and Sarno and Taylor (2001). 5 In he 1980s and early 1990s, aenion focused on he effec of serilised inervenion on he level of he exchange rae and on he channels hrough which i works. The resuls on he effeciveness of inervenion are mixed and depend on which exchange rae is analysed, wha sample period is sudied and he inervenion sraegy ha was used. In an influenial paper, Dominguez and Frankel (1993a) use daily and weekly official and press repor daa on inervenion direced a he yen/dollar and mark/dollar exchange raes beween 1984 and The auhors find ha inervenion had a significan impac on he exchange rae, especially when i was publicly announced and coordinaed. Laer sudies have no provided a unanimous confirmaion of Dominguez and Frankel s finding ha inervenion has an impac on exchange rae levels. Using a case sudy approach for he yen/dollar and mark/dollar exchange raes during he period , Cae e al. (1994) confirm ha inervenion influences exchange raes paricularly for coordinaed inervenions. 6 Faum (2000) and Faum and Huchinson (2002, 2003) argue in favour of an even sudy approach o examine he effec of inervenion on exchange rae changes, as mehods relying on ime series daa do no capure he sporadic occurrence of inervenion. Faum (2000) uses a non-parameric esimaion echnique o show ha during he monhs following he Plaza agreemen, inervenion by he Federal Reserve and he Bundesbank was effecive, especially when i was coordinaed. Using similar echniques, Faum and Huchison (2002, 2003) find evidence supporing he effeciveness of inervenion in he 4 5 In his paper we define as coordinaed inervenion hose episodes in which wo or more cenral banks enered he marke on he same day. For a survey of informaional aspecs of inervenion, see Bailie, Humpage and Oserberg (2000). 4

7 mark/dollar and yen/dollar markes. Io (2003) presens evidence based on Japanese Minisry of Finance daa ha inervenion in he yen/dollar marke in he second half of he 1990s was effecive. Dominguez (2003a) concludes ha recen G3 inervenion was ofen successful wih regard o boh shor and longer-erm exchange rae movemens. However, oher papers do no suppor he conclusion ha inervenion is effecive. Humpage (1988), for example, concludes ha inervenion was unable o influence he dollar s level. Baillie and Oserberg (1997) find ha over he period Augus 1985 o March 1990, Federal Reserve inervenion did no influence he mark/dollar or yen/dollar exchange raes. In erms of ransmission channels, here is now general consensus in he lieraure ha inervenion does no affec exchange raes hrough he porfolio channel, i.e. by changing he relaive ousanding supply of domesic and foreign asses and hereby of he expeced relaive reurns on hese asses. 7 There is some, bu no conclusive, evidence ha inervenion mainly works hrough he signalling channel, i.e. by he cenral bank conveying a signal o marke paricipans abou informaion on fuure fundamenals. 8 Recen work on he microsrucure of foreign exchange markes has highlighed he role of imperfec informaion as a channel hrough which inervenion migh influence exchange raes (Evans and Lyons (2001); D Souza (2002); Dominguez (2003b)). Over he pas few years, a number of sudies have focused on he effecs of inervenion on exchange rae volailiy. 9 Mos of hese papers have looked a condiional exchange rae volailiy, usually esimaed wih GARCH models. Empirical evidence suggess ha cenral bank inervenion ends o increase he condiional exchange rae volailiy. Connolly and Taylor (1994), for example, use a GARCH model o describe condiional yen/dollar volailiy and use marke daa on inervenion by he Bank of Japan. They presen evidence ha, beween 1977 and 1979, Bank of Japan inervenion was For a criical view of Cae e al s resul, see Truman (1994) and Weber (1994). Rogoff (1984) is among he firs o es he imporance of he porfolio balance channel. He finds no significan effecs of serilised inervenion hrough his channel. Frankel and Engel (1984), Lewis (1988) and a number of oher sudies, which are reviewed in deail in Edison (1993), reach a similar conclusion. By conras, Dominguez and Frankel (1993b) find some supporive evidence for he porfolio channel. An overview of he lieraure on he signalling channel is provided by Baillie, Humpage and Oserberg (2000). Sudies ha find a significan effec of inervenion hrough his channel include Dominguez (1990), Klein and Rosengren (1991), Dominguez (1993), Kaminsky and Lewis (1996) and Lewis (1995). On he oher hand, evidence provided by Dominguez (1997) suggess ha inervenion does no serve exclusively as a consisen signal of fuure moneary policy changes. Dominguez (1998) provides a good overview of his lieraure. 5

8 associaed wih an increase in condiional yen/dollar volailiy. Similarly, Baillie and Humpage (1992) find a posiive relaionship beween Federal Reserve, Bank of Japan and Bundesbank inervenion and he condiional volailiy of he mark/dollar and yen/dollar exchange raes for he period February 1987 o February Dominguez (1993), however, argues ha he impac on exchange rae volailiy depends on how cenral banks conduc inervenion. Looking a daily and weekly daa for , she finds ha inervenion ha is officially announced reduces volailiy while inervenion ha is no deeced by he marke increases volailiy. Finally, Hung (1997) finds ha inervenion can affec exchange rae volailiy hrough he noise-rading channel, i.e. by inducing noise raders o reac o changing marke condiions. A recen paper by Dominguez (2003c) examines he impac of G3 inervenion in he Deusche mark/dollar and yen/dollar markes using inra-daily and daily daa. She finds evidence of a significan impac of inervenion on exchange rae volailiy boh a he inraday and he daily frequency, alhough lile lasing effec. More recenly, daa on volailiy implied by opion prices have been used o sudy he effec of inervenion on marke paricipans assessmens of fuure exchange rae volailiy. 10 The advanage of implied volailiy over measures of volailiy compued from acual exchange rae realisaions, for example using GARCH models, is ha implied volailiy incorporaes a marke assessmen of fuure volailiy ha is no direcly observable. The idea here is ha inervenion on a paricular day may send a signal o marke paricipans abou he fuure exchange rae policy and hence influence he marke s forecass of fuure exchange rae volailiy. The evidence on he impac of inervenion on implied volailiy is mixed. Bonser-Neal and Tanner (1996) are he firs o have sudied he effec of inervenion on implied volailiy. They use daa on implied volailiies from exchange raded opions from 1985 o 1991 ogeher wih official daa on inervenion by he Federal Reserve and he Bundesbank. They also recover daa on perceived inervenion by he Bank of Japan from newspaper aricles. They find ha inervenion had a differen impac on volailiy over differen ime periods. Beween February 1987 and December 1989 (he Louvre period ), inervenion acually increased implied volailiy, while here is less evidence ha 10 The usefulness of implied volailiy from currency opions as a forecas of fuure exchange rae movemens has been documened in Figlewski (1997) and Galai and Tsasaronis (1996). 6

9 inervenion reduced exchange rae volailiy beween 1990 and Over he period 1985 o 1991 as a whole, here is no evidence ha cenral bank inervenion reduced exchange rae volailiy. Bonser-Neal and Tanner (1996) also examine wheher changes in implied volailiy Granger cause inervenion by he Federal Reserve and find lile evidence of Granger causaliy running from implied volailiy o inervenion. Murray e al. (1997) invesigae he effec of differen inervenion sraegies by he Bank of Canada on implied volailiy of he Canadian/US dollar exchange rae. In conras o Dominguez (1993) resuls, hey find ha inervenion ha was expeced or ha was unexpecedly ligh had no effec on implied volailiy, while inervenion ha was unexpeced and heavy significanly reduced implied volailiy. Dominguez (1998) looks a he effec of inervenion on boh GARCH volailiy and implied volailiy. She finds ha he effec depends on boh he sample period and he inervenion sraegy. One of her ineresing resuls is ha inervenion can lead o an increase in volailiy even if marke paricipans do no perceive i. Similarly o Bonser-Neal and Tanner (1996), she also finds ha volailiy does no Granger-cause inervenion. In summary, here is no unanimiy among empirical sudies on he size and srengh of he effec of inervenion on he level and higher momens of exchange raes. Findings vary by ime period, daa source, and esimaion mehod. In paricular, sudies ha include he Plaza and Louvre ime periods are more likely o find ha inervenion has a significan effec on he mean or he variance of he exchange rae. Those sudies ha include conrol for he simulaneous deerminaion of he inervenion decision and he exchange rae are less likely o find a significan effec for inervenion. Reviews of all of hese sudies, and commenaries by policy makers involved in inervenion, do sugges a consensus view. As Sarno and Taylor (2001) pu i official inervenion can be effecive if he inervenion is publicly announced and concered and provided ha i is consisen wih he underlying sance of moneary and fiscal policy. Former Federal Reserve and Unied Saes Treasury official Truman (2003) argues ha The evidence on he shor-run effeciveness of exchange marke inervenion is sufficien in my view o suppor he judicious use of inervenion by he Unied Saes as a supplemenary policy insrumen as long as i generally is used in a manner consisen wih oher economic policies, bu ha same evidence falls subsanially shor of demonsraing ha inervenion is a separae policy insrumen ha can be used o manage exchange raes wih any lasing effec. Edison (1993) and Almekinders (1995) survey empirical work on he deerminans of inervenion. The approach ha is generally followed in he lieraure consiss of specifying and esimaing a reacion 7

10 funcion for cenral banks. The objecives being considered include leaning agains he wind, minimising deviaions of exchange raes from some implici arge levels and reducing uncerainy. Eijffinger and Gruijers (1991) find ha, beween 1985 and 1987, he Federal Reserve and he Bundesbank inervened mainly o reduce erraic exchange rae movemens and lean agains he wind. Dominguez and Frankel (1993a) find ha beween Sepember 1985 and December 1990 he Federal Reserve and he Bundesbank mainly inervened when he dollar deviaed from is implici arges. They specify hese arges based on Funabashi s (1988) analysis of cenral bank inervenion and, alernaively, by assuming ha he arges equal he exchange rae level implied by purchasing power pariy. A similar conclusion is reached by Goodhar and Hesse (1993) based on an analysis of inra-day daa beween 9 April and 30 June A recen paper by Frenkel e al (2002) looks a he period and finds ha he Bank of Japan regularly inervened in response o deviaions of he yen/dollar rae from a shor-erm and a long-erm arge. By conras, heir resuls sugges ha he Federal Reserve inervened only occasionally o accompany he Bank of Japan s inervenion. Almekinders and Eijffinger (1996) presen evidence ha, from 1987 o 1989, he Federal Reserve inervened wih he inenion of lowering exchange rae uncerainy. Baillie and Oserberg (1997) find ha, beween 1985 and 1990, spo exchange rae volailiy Granger causes inervenion in he yen/dollar marke, while he forward premium s condiional volailiy does no. They conclude ha inervenion is moivaed by increases in spo raher han forward marke volailiy. 3. The daa We sudy he daily movemens of he yen agains he dollar beween Sepember 1993 and April 2000 (Graph 1). The beginning of he sample is dicaed by he availabiliy of opions daa needed o esimae empirical PDFs. We chose April 2000 as he end of he sample since here was no inervenion in he yen/dollar marke in he following 12 monhs. The exchange rae we used is aken a noon in London, quoed in yen per dollar. 3.1 Cenral bank inervenion In his paper, we use wo daa ses on inervenion in he yen/dollar marke. The firs se comprises official inervenion daa ha were provided by he Federal Reserve and he Japanese Minisry of 8

11 Finance. While he Federal Reserve has made official inervenion daa available in he pas, he Japanese Minisry of Finance sared o pos official inervenion daa on is websie in July The second daa source for idenifying episodes of cenral bank inervenion in he yen/dollar marke consiss of Reuers press repors. 12 These press repors reveal inervenions ha are perceived by marke paricipans and hence may oversae or undersae acual cenral bank inervenions. For example, Reuers aricles may well repor cases where marke paricipans hough a cenral bank was inervening when in fac his was no he case. Wih he new daa se on official inervenion i is now possible o gauge he accuracy of press repors on raders percepions of inervenion by he Japanese auhoriies. Previous sudies (Dominguez and Frankel (1993a), Bonser-Neal and Tanner (1996), Ramaswamy and Samiei (2000)) have used official daa for Federal Reserve inervenions and used newspaper aricles o build a daa se on inervenion conduced by he Bank of Japan. A recen paper by Frenkel e al (forhcoming) compares he Minisry of Finance daa wih repors of inervenions in he Financial Times and he Wall Sree Journal. They find ha beween January 1995 and December 1999, press repors are a relaively inaccurae indicaor of acual inervenion by he Bank of Japan. In conras o Frenkel e al s conclusion, Table 1 reveals ha Reuers repors quie accuraely mached acual inervenion in he yen/dollar marke. The probabiliy ha inervenion in he yen/dollar marke was repored and perceived by raders given ha i acually occurred was Likewise, he probabiliy ha inervenion was acually underaken given ha i was repored in Reuers aricles was A cross-check wih Bonser-Neal and Tanner s (1996) daa se for he period from January o July 1991 suggess ha he Reuers daa se used in his paper conains many more inervenion episodes han heir daa se. 13 Table 1 also repors informaion from he wo alernaive sources on inervenion sraegies ha were followed in he yen/dollar marke beween 20 Sepember 1993 and April During his period, Chang and Taylor (1998) have used Reuers repors o idenify he occurrence and iming of inervenion in he dollar/yen marke during he period 1 Ocober 1992 o 30 Sepember Bonser-Neal and Tanner (1996) show ha heir reporing of inervenion episodes is more complee han Dominguez and Frankel s (1993). 9

12 almos 90% of all inervenions were conduced unilaerally by he Bank of Japan, in a discree fashion, and on successive days. The Federal Reserve inervened only ogeher wih he Bank of Japan. This is in line wih he common observaion ha he U.S. moneary auhoriies became much less acive in foreign exchange markes in he 1990s (see eg Bonser-Neal and Tanner (1996)). Abou wo-hirds of he inervenions involved amouns of $1 billion or less. Ineresingly, while raders quie accuraely perceived he occurrence of cenral bank inervenion in he yen/dollar marke, hey ended o underesimae he magniude of inervenions. Beween mid-february 1996 and November 1997, no cenral bank inervenion ook place in he yen/dollar marke. Since November 1997, moreover, he wo cenral banks have ended o ener he yen/dollar marke less frequenly han in during he period I is herefore useful o spli he sample ino wo sub-periods, Sepember 1993 o February 1996 and November 1997 o April All economeric ess are carried ou separaely on hese wo sub-samples. 3.2 Macroeconomic news In he empirical analysis of he effec of inervenion on exchange rae expecaions, we also include a number of variables ha capure he effec of news abou macroeconomic or policy developmens ha may arrive on he same day on which inervenion is carried ou. We measure he unexpeced componen of macroeconomic news by he difference beween official daa announcemens and he resuls of opinion surveys conduced during he days preceding he announcemens by Money Marke Services and Bloomberg. We inroduce news variables for boh he Unied Saes and for Japan. For he Unied Saes, we include news abou he CPI, he PPI, indusrial producion, he unemploymen rae and he rade balance. For Japan, we include news abou Tankan surveys, reail sales and indusrial producion. In order o capure he effec of news abou changes in policy raes, for boh he Unied Saes and Japan we creaed a dummy variable ha equals one on a day on which he cenral bank announced ha i changed is policy rae and zero oherwise. 4. Esimaing and inerpreing probabiliy densiy funcions In recen years, daa from foreign exchange opion markes have been used o exrac informaion abou he enire risk-neural PDF of he underlying exchange rae (eg BIS (1996 and 1999); Malz 10

13 (1996); McCauley and Melick (1996a and 1996b)). The four momens of his disribuion he mean, variance, skewness and kurosis can be used o characerise marke expecaions of fuure exchange raes. The mean of a PDF can be inerpreed as raders average expecaion of he yen/dollar rae a a fuure dae. For a risk-neural PDF he mean is equal o he forward rae. We will use his mean in he empirical secion bu i is imporan o undersand ha here is lile difference, eiher in principle or resul, beween using his measure or he spo exchange rae. Obviously he spo and forward rae are joinly deermined and linked via covered ineres pariy. Given ha he correlaion beween he mean of he PDF (he forward rae) and he spo rae is 0.99 for levels and 0.83 for firs differences over he sample period, our resuls using he mean of he PDF can be undersood o apply o he spo exchange rae as well. The variance of a PDF can be inerpreed as providing a measure of how uncerain he marke is on a given day abou he exchange rae ha will prevail over he near fuure. The hird momen of a PDF, skewness, can be inerpreed as he weigh ha marke paricipans pu on a much higher and a much lower yen/dollar exchange rae in he near fuure wih respec o he forward rae. We define a PDF o be skewed o he lef (or negaively skewed) when, compared wih he forward rae, marke paricipans assign more weigh o a much weaker dollar raher han o a much sronger dollar agains he yen. Similarly, we define a PDF as skewed o he righ (or posiively skewed) when he marke aaches more weigh o a much sronger dollar han a much weaker dollar in he near fuure. Kurosis, he fourh momen of a PDF, measures how fa is ails are, and can be inerpreed as indicaing how likely marke paricipans hink very large exchange rae changes in eiher direcion will be in he near fuure. I is imporan o keep in mind ha he inerpreaion of he esimaed risk-neural PDFs is no as sraighforward as migh be hoped, given ha he PDFs capure marke views as o he likelihood of paricular exchange rae oucomes as well as marke preferences owards risk. Unforunaely, in he absence of srong assumpions, i is impossible o disinguish beween he wo. A simple example illusraes he problem. Suppose we observe an increase in he price of fire insurance. This increase migh reflec he marke view ha fires are now more likely; hence here is a greaer need for insurance. Alernaively, he price increase migh reflec a change in marke senimen regarding poenial exposures in he even of a fire. The probabiliy of a fire may no have increased; however, 11

14 he marke view of any loss associaed wih a fire may have increased. The observaion ha he price of insurance has increased does no allow us o deermine wheher fires are more likely, wheher exposure is perceived as larger, or some combinaion of boh. In he same way, a change in opion prices does no allow us o separae ou changes in views on fuure exchange raes from changes in poenial exposures. Boh Jackwerh (2000) and Bliss and Panigirzoglou (2002), when sudying equiy markes, decompose he risk-neural PDF ino he produc of he subjecive or acuarial densiy funcion and a risk aversion funcion. While his approach migh in principle be applied o expecaions of fuure exchange raes, we decided no o follow heir lead for several reasons. Firs, we are aemping o answer he quesion of wheher or no cenral bank inervenion has an effec on marke paricipans, and hence we have only a secondary ineres in wheher he effec is fel wih regard o expecaions, preferences owards risk or boh. Secondly, boh sudies make srong assumpions wih regard o he saionariy of he risk aversion funcion, assumpions ha are no enable for a sudy ha conemplaes changes in expecaions and preferences oward risk a a daily horizon. Finally, in he equiy marke here is a naural measure of wealh o use in recovering preferences owards risk, mainly he value of he equiy index iself. However, in he foreign exchange marke here is no naural definiion of wealh. Therefore, we make use of only he risk-neural PDFs raher han aemping he furher sep of decomposing he risk-neural PDF ino is componens. For each day from 20 Sepember 1993 o 30 April 2000, he four momens of he risk-neural PDF of he yen/dollar exchange rae were esimaed using he indicaive quoes of a marke maker in London on a-he-money implied volailiy, he risk reversal and he srangle. 14 The mauriy of he opions is consan and equal o one monh. The midpoin of he ime srangle price can be expressed as STR 75δ 25δ ( σ + σ ) ATM = 0.5 (1) 14 The risk reversal is he price difference beween wo equally ou-of-he money opions. I provides a direc measure of he skewness of he probabiliy disribuion. A srangle is a financial insrumen ha consiss of a purchase or sale of an ou-ofhe-money pu opion and call opion on he same underlying insrumen, wih he same expiraion dae. A srangle leads o profis if here is a drasic move in he price of he underlying asse. 12

15 and he risk reversal price as RR = σ σ, (2) 25δ 75δ where STR, RR and ATM denoe, respecively, he srangle price, risk reversal price and he a-he- 25δ money volailiy. σ and σ 75 represen he implied volailiies of he 25 dela call and 25 dela pu. δ 15 We use he above equaions o recover implied volailiies corresponding o he given dela values. Our approach hen follows wo seps. Firs, we use sandard Garman-Kohlhagen equaions o ranslae he hree quoes ino six opion prices (one pu and one call for every srike price) in erms of unis of yen per dollar. 16 Second, hese opion prices are used for he empirical esimaion of he PDFs. There are differen possible echniques for recovering implied risk neural densiy funcions from opion prices. 17 In our sudy we use he Hermie polynomial approach, a echnique developed by Madan and Milne (1994). We follow his approach since i gives a fairly robus esimaion of he PDF momens and has a beer convergence performance compared wih oher echniques. 18 A more deailed descripion of our empirical mehodology is presened in he annex. Figure 2 shows he imes series of esimaes of he firs wo momens of he PDF, he mean and he variance, of he yen/dollar exchange rae. As an alernaive measure of he variabiliy of exchange rae expecaions, we also compued he difference beween he 90% and he 10% quanile of he PDF, which we normalised by he median. Figure 2a shows he ime series of his variable. Since he variance of he PDF and he inerquanile range comove very closely, in he res of he paper we repor The dela of an opion is he firs derivaive of he opion price wih respec o he underlying asse. See annex or Malz (1996) and McCauley and Melick (1996a) for furher deails. These echniques can be classified in four broad caegories (Bahra (1997), Chang and Melick (1999)): I) echniques ha recover he implied densiy funcions by assuming a paricular sochasic process for he underlying asse (eg Baes (1991), Malz (1996)); II) a funcional form for he PDF is assumed wih he parameers for he funcion esimaed by minimizing he difference beween acual and prediced opion prices (eg Rubinsein (1994), Melick and Thomas (1997), Bahra (1997)); III) he probabiliy densiy funcion is implied from some parameric specificaion of he call pricing funcion or he implied volailiy smile (see eg Shimko (1993), Madan and Milne (1994), Malz (1997)); IV) non-parameric esimaion of he densiy funcion (see eg Aï-Sahalia and Lo (1998)). Applicaions of his echnique can also be found in Abken, Madan and Ramamurie (1996), Jondeau and Rockinger (2000), Couan, Jondeau and Rockinger (2001), and Mc Manus (1999). A poenial problem wih his echnique is ha esimaed probabiliies can be negaive (Jondeau and Rockinger (2001)). In our daa se, however, his problem urned ou no o be relevan. Melick (1999) demonsraes ha differen echniques for exracing risk-neural PDFs give very similar resuls for probabiliies beween he 10 h and 90 h quaniles, hence our findings are robus o he echnique used o exrac he PDF. 13

16 only resuls for he variance of he PDF. 19 Esimaes of he skewness are repored in Figure 3 ogeher wih esimaes of he mean. Figure 4 repors esimaes of he fourh momen of he PDF (he kurosis) over he period Sepember 1993 o November To explore he relaionship beween inervenion and exchange raes i is necessary o specify he iming of inervenions wih respec o he ime a which he opion daa are recorded. Given he difference of nine hours beween he Asian ime zone and GMT, if he Bank of Japan inervened in Asian markes, he inervenion will precede he recording of opion prices in London on ha day. In his case, he iming of he inervenion variables and ha of he parameers of he PDFs are se equal in he daa se. When inervenion occurred on day in New York, i is inroduced a ime +1 in he daa se because i will be known in London afer he opion daa are repored. In he few cases in which inervenion was carried ou in Europe we assume ha inervenion in European markes always preceded he recording of opion prices and herefore use he same iming convenion ha we use for inervenions conduced in Asia Inervenion and marke expecaions 5.1 Inervenion and PDFs Figure 5 illusraes wih an example how risk-neural PDFs can be used o analyse he effec of foreign exchange inervenion. The episode of concered inervenion by Japanese, German and US auhoriies on 15 Augus 1995 has been described as pushing on an open door (BIS (1996)) given he sharp appreciaion of he dollar on 15 and 16 Augus. Cenral banks purchased dollars when he US currency was appreciaing agains he background of heavy Japanese buying of US bonds and opion dealers hedging The correlaion coefficien beween he PDF variance and he inerquanile range is All he economeric resuls are robus o using he inerquanile range insead of he variance. Robusness checks show ha using a differen iming assumpion for inervenion in Europe, according o which inervenion carried ou in Europe generally followed he recording of opion prices, does no aler he empirical resuls in his paper. 14

17 Figure 5 shows ha he PDFs around Augus 1995 exhibied righ skewness, indicaing ha marke paricipans aached a higher probabiliy o a much sronger raher han a much weaker dollar one monh ahead wih respec o he forward rae. 21 Following cenral bank inervenion, he skewness increased on 16 Augus, suggesing ha he concered acion by cenral banks increased he marke bias owards a much sronger dollar. A he same ime, he variance of he PDFs rose on 16 Augus I hen declined during he following days. This can be inerpreed as indicaing ha inervenion was followed by a emporary increase in marke uncerainy. Moreover, he kurosis of he PDFs increased on he day ha cenral banks inervened, suggesing ha he concered effor o boos he already appreciaing dollar induced marke paricipans o aach more weigh o he possibiliy of furher very large changes of he yen/dollar exchange rae in eiher direcion in he following monh. Figures 6 o 11 provide some informaion on he average movemens of he mean, variance and skewness of he risk-neural PDFs around inervenion episodes over he period from Sepember 1993 o November For he five days before and five days afer inervenion, which happens a = 0, Figure 6 shows he mean of he risk-neural PDF, ie he forward rae, averaged over all dollar purchases. We repor he averages for a horizon of 10 days because mos of he empirical lieraure has suggesed ha he effec of inervenion is shor lived. The value of he mean is normalised a zero on he day preceding he inervenion, ie a = -1. The grey area gives an indicaion of he variabiliy of he changes in he momen of he PDF across all inervenions. For each day, i is calculaed as he average value of he mean plus/minus one sandard deviaion, where he sandard deviaion is compued over all inervenion episodes. Figure 7 shows he same informaion for dollar sales. The char looks very similar when we use he spo rae insead of he mean of he PDF. Figures 8 and 11 show averages of he variance, and he kurosis, respecively for all inervenion episodes, while Figures 9 and 10 show he movemen of skewness around dollar purchases and sales respecively. Purchases and sales are no separaely presened for he variance and kurosis, since he hypohesis of ineres in hese cases - wheher 21 The PDFs in Figure 5 are expressed in yen per dollar. 15

18 inervenion increases uncerainy is symmeric in boh direcions. Again, shaded areas indicae sandard deviaions around he averages of he momens. Figures 6-8 in paricular sugges he possibiliy ha inervenion may have had subsanial effecs on he momens of he expeced exchange rae, alhough he sandard deviaion shadings encompass zero in all cases. However, one should be careful in using hem o draw inferences abou he impac of inervenion for hree reasons. Firs, he figures do no conrol for simulaneiy. I could be ha inervenion responds o movemens in he momens raher han vice-versa. Second, on he day ha cenral banks inervene, oher imporan macroeconomic or policy news may arrive ha could promp marke paricipans o reac. For example, he announcemen of an unexpecedly high indusrial producion figure for Japan could induce raders o revise heir expecaions of fuure Japanese ineres raes upwards, hereby boosing he yen. Inervenion could also be carried ou on he same day on which a paricipaing cenral bank changes is moneary policy rae. The behaviour of he momens would hen reflec he effec of boh he arrival of macroeconomic or policy news and cenral bank inervenion. The simple averages repored in Figures 6 11 do no accoun for he influence of hese differen facors. The hird shorcoming of hese graphs is ha inervenion could be carried ou on several successive days. Table 1 shows ha his was indeed he case for mos of he inervenions during our sample period. As a consequence, he average values of he PDF momens on day reflec no only he effec of inervenion ha occurred on ha day, bu also he effec of cenral bank acions carried ou on previous days. In order o assess he effec of inervenion and conrol for hese hree issues, we use daily daa o esimae regression equaions ha explain each momen in erms of curren and lagged inervenion and a se of oher explanaory variables. To disinguish he effec of inervenion from he effec of news abou relevan macroeconomic variables ha may arrive on he same day, we include a se of variables ha measure he unanicipaed componen of announcemens of major macroeconomic variables. Our se of news variables includes variables for boh he Unied Saes, as in mos previous sudies on inervenion in he yen/dollar marke, and Japan. In our model of he relaionship beween inervenion and exchange rae expecaions, he momens of he PDFs are deermined by expecaions of exchange rae fundamenals. The expeced level of he 16

19 exchange rae is deermined by, among oher hings, expeced fuure price levels and fuure likely moneary policy. The expeced volailiy of exchange raes is deermined by expeced fuure goods price volailiy and uncerainy abou fuure moneary and inervenion policy and oher facors. Similar argumens apply o he skewness and he kurosis. Hence, he PDF momens change when hose expecaions change. Inervenion is a deerminan of hese expecaions as suggesed by he signalling channel. In formal erms, consider a simple inerpreaion of he exchange rae s as deermined by fundamenals Z, Z, Z,... Assuming lineariy and aking expecaions, his would imply ha he ime expecaion of he value of s = s( Z, Z, Z,...) he exchange rae a ime +i would be given by: (3) E s E Z E Z E Z i = α + β1 + i + β 2 + i + β3 + i +... (4) Similarly, and assuming for simpliciy zero covariances, he variance of he exchange rae would be given by: ( ) var s + i = β1 var( Z + i ) + β 2 var( Z + i ) + β3 var( Z + i )... (5) The expeced exchange raes and variances, as well as he expeced fundamenals, depend on informaion available a ime, which includes informaion abou inervenion a ime. As such, if cenral banks inervene a ime, his can poenially lead o a change in he expeced momen: E + 1 s + i Es + i = β1( E + 1Z + i E Z + i ) + β2( E + 1Z + i E Z + i ) + β3( E + 1Z + i E Z + i ) +... (6) The level of inervenion direcly affecs he change in expecaions of fundamenals and, hereby, he changes in expecaions. 5.2 The simulaneiy problem Regressions ha esimae he effec of cenral bank inervenion on marke condiions face a poenial simulaneiy problem. In a regression of he variance of he expeced exchange rae on an inervenion 17

20 dummy, for example, a posiive coefficien can mean eiher ha inervenion increases expeced volailiy, or ha cenral banks inervene o smooh rising exchange rae volailiy, bu are no successful. A simple example can be used o illusrae his problem. Consider he case where a cenral bank inervenes o smooh volailiy. To simplify he exposiion, we ignore here he role of oher momens of he PDF. In is simples form, we can hen wrie he following sysem of equaions: M = a + a2i + a3 1 X + ε (7) I = b + b 2M + b3 1 Y + η (8) where M measures he variance of he PDF, I capures inervenion, and X and Y represen oher facors ha influence volailiy and inervenion. ε and η are error erms. Equaion (7) is probably of greaes ineres, since i describes he effec of inervenion on he variance of he exchange rae. Equaion (8) is a reacion funcion ha describes how inervenion responds o movemens in he variance. Esimaing he effec of inervenion on he variance implies esimaing he coefficien a 2 in Equaion (7), while he effec of he variance on inervenion is capured by he coefficien b 2 in Equaion (8). This would require solving he simulaneous sysem for M and I in erms of X, Y, and ε and sandard OLS procedures are applied o esimae hese wo equaions separaely, hey will yield biased and inconsisen esimaes of a 2 and b 2 because cov( I, ε ) 0 and cov(, ) 0 M η. η. If Ideally hen, equaions like (7) and (8) would be esimaed simulaneously. In pracice however, his is no a viable alernaive because he resuls would be very sensiive o specificaion errors in eiher of he equaions in he sysem. A mehod ha has been used in he lieraure o address his simulaneiy 18

21 problem consiss in lagging he inervenion variable by one period in equaion (7) and hen esimaing ha equaion direcly wih OLS. 22 However, his mehod will misrepresen he rue effec of inervenion on marke expecaions because par of his effec may already be capured in lagged values of he dependen variable (he momen), which are inroduced among he explanaory variables. A beer alernaive is a limied informaion esimaor such as Insrumenal Variables (IV), alhough even his approach can be problemaic. As is well known, and discussed for example in Sock and Yogo (2002) and Sock and Wason (2003), weak insrumens can produce biased IV esimaors and hypohesis ess wih large disorions. An IV esimaion of equaion (7) requires an insrumen for inervenion, while an IV esimaion of equaion (8) requires an insrumen for he momen of he exchange rae. Unforunaely, he noorious difficuly in explaining daily exchange rae movemens means ha i is highly unlikely ha a good insrumen can be found for he momen of he exchange rae. Forunaely, as shown below, i is possible o obain a good insrumen for inervenion. Therefore, a specificaion like equaion (7) can be esimaed wih IV while a specificaion like equaion (8) probably should no. For equaions like (8) he safes approach is o include only lagged values of he exchange rae momens on he righ hand side o avoid he simulaneiy problem. Humpage (1999) follows a similar approach when esimaing reacion funcions, including only early morning quoes for he exchange rae on he righ hand side. Alhough no perfec, his compromise of esimaing one equaion wih IV and he oher wih only lagged values and OLS is he bes sraegy. The main quesion of ineres, he effec of inervenion on he exchange rae, is answered wih he IV esimaion, while he OLS esimaion of he reacion funcion will provide a rough descripion of he behaviour of he cenral banks. The bigges drawback o his approach is he possibiliy of omied variables bias in he OLS esimaion of he reacion funcion, since only lagged values of he exchange rae momens are included and he conemporaneous values of he exchange rae momens via an insrumen are omied. However, his bias is likely o be rivial, since he exchange rae momens show lile if any persisence and hus 22 Sudies ha followed his mehod include Dominguez (1993a), Bonser-Neal and Tanner (1996) and Murray e al. (1997). For a criique of his approach o he simulaneiy bias, see Humpage (1999). 19

22 here is no much correlaion beween he included lagged momens and he omied insrumen for he conemporaneous momens. In paricular, we esimae he following equaions ha correspond o he simple sysem of equaions (7) and (8): M j 5 5 = j a + bim i + cii i + 5 i = 1 i = 0 i = 0 d X i i + ε (9) and I 8 5 j j = a + bi Mˆ i + η (10) j = 1 i = 1 j where is he j-h momen a ime, ˆ j is he arge value (explained below) for he jh momen M M i lagged by i periods. I is he amoun of inervenion on day, X is a vecor of macroeconomic variables and ε and η are error erms. Insead of esimaing equaion (9) using OLS, we use insrumenal variables, essenially replacing inervenion wih is prediced value from he reacion funcion. Equaion (10), since i only includes lagged momens, can be esimaed wih OLS. 5.3 Esimaing a reacion funcion for he Federal Reserve and he Bank of Japan The mehod we follow o esimae reacion funcions (equaion (10)) builds on he work of Baillie and Oserberg (1997). In heir sudy of he behaviour of he Federal Reserve and he Bank of Japan, hey find ha he probabiliy of he wo cenral banks inervening is deermined by he deviaion of he exchange rae from some arge nominal exchange rae level and by he volailiy of he exchange rae. In he pos-breon Woods era, he Federal Reserve and he Bank of Japan have never officially announced a arge for he yen/dollar exchange rae. However, Funabashi (1988) argues ha hey adoped some implici arge levels for he nominal exchange raes. This is also consisen wih he findings of Io (2003). Baillie and Oserberg (1997) ake he arge levels for he nominal exchange raes from Funabashi (1988). We assume ha he Federal Reserve and he Bank of Japan inervened when he spo rae, he variance or he skewness deviaed from implici arge ranges. We also assume he likelihood of 20

23 inervenion depended on he disance from hese arges. We choose implici arges for he spo exchange rae based on press repors, which ypically emphasised he role of he spo rae as rigger for cenral bank inervenion (Table 2). 23 Equaion (10) is esimaed separaely for he Bank of Japan and he Federal Reserve. Given ha he Federal Reserve were much less acive in foreign exchange markes during he sample period and inervened only on days when he Bank of Japan was in he marke, we followed Frenkel e al (2002) and included Bank of Japan inervenion in he specificaion for he Federal Reserve s reacion funcion. We inroduced Bank of Japan inervenion a ime and - 1, since cenral banks almos always inervene in heir local markes, a fac noed by Dominguez (2003a,2003c) and confirmed by an examinaion of he Reuers repors in our daase. Therefore, U.S. auhoriies would usually know ha he Bank of Japan had inervened, since he Tokyo rading session is well ahead of he U.S. rading session. As a firs approximaion, we se he arges for he higher momens equal o heir hisoric average. In oher words, we assume ha cenral banks ended o inervene whenever he variance or skewness of marke expecaions was abnormally high or low wih respec o is hisorical average. 24 The explanaory variables ˆ j M i include he disance a ime -i of he yen/dollar spo rae from he boom of he arge range when he exchange rae is below ha limi and a variable for he case in which he exchange rae breaks hrough he op of he arge range. We also include he disance of he variance from is hisorical average when he dollar is, respecively, appreciaing or depreciaing. Furhermore, a variable is inroduced o measure he disance of skewness from is hisorical average when he yen is depreciaing and he marke is skewed owards a much weaker yen. Similarly, we use a measure of he disance from he average of skewness when he yen is srenghening and he marke is biased owards a much sronger yen. Finally, we inroduced a variable measuring he disance of kurosis from is hisorical average when he dollar was, respecively, appreciaing and depreciaing An alernaive approach used in he lieraure consiss of seing he implici arge equal o he PPP value of he dollar/yen exchange rae, as in Dominguez and Frankel (1993a). Oher sudies have se he arge rae equal o pas levels of he exchange rae, hereby assuming ha cenral banks sysemaically lean agains he wind (Almekinder and Eijffinger (1991)). The arge bounds are aken here as he hisorical mean ± 1.5 sandard deviaion. 21