Anticipations of Foreign Exchange Volatility and Bid-Ask Spreads

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 409

August 1991

ANTICIPATIONS OF FOREIGN EXCHANGE VOLATILITY AND BID-ASK SPREADS

Shang-Jin Wei

Note: International Finance Discussion Papers are preliminary material circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgement that the writer has had access to unpublished material) should be cleared with the author or authors.

ABSTRACT

The paper studies the effect of the market's perceived exchange rate volatility on bid-ask spreads. The anticipated volatility is extracted from currency options data. An increase in the perceived volatility is found to widen bid-ask spreads. The direction of the effect is consistent with an option model of the spread, but the magnitude is smaller. An increase in trading volume of spot exchange rates also widens the spread. The omission of the trading volume, however, does not bias the estimate of the effect of the volatility on the spreads. Although the spread-volatility relation implied by the option model of the spread is close to

linear, some form of nonlinearity can still be detected from the

data.

Anticipations of foreign exchange volatility and bid-ask spreads

Shang-Jin Wei *

Bid-ask spreads and other microstructure of foreign exchange trading are understudied. Notable exceptions are Glassman (1987), Boothe (1988), and Black(1989). They use the ex post post standard deviations in foreign exchange rates as a measure of exchange risk and find that the risk measure is positively related to the width of the bid-ask spreads. Presumably, when one talks about the effect of exchange rate risk on the transaction costs, one is thinking of the effect of the market's perception of the risk. Therefore, an important extension to be made is to examine directly the impact of the market's ex ante perceptions of exchange rate risk on the bid-ask spread.

This paper makes four main contributions. First, we derive a theoretical relationship between the spread and market's anticipated volatility. The key idea is to express the spread as a portfolio of options. Copeland and Galai (1983) also relate the spread to options. However, their model is an equilibrium one, and the spread in their model depends on, among other things, the percentage of traders who are liquidity traders. In contrast, our model links the spread with options from a different perspective. Consequently, we are able to derive a spread-volatility relation without the need to specify an equilibrium model.

Second, we are able to examine the effect of the market's ex

2

ante anticipation of exchange rate volatility on the bid-ask

spread, as opposed to the effect of the ex post exchange rate volatility that has been examined in previous papers. This measure of the market's anticipated volatility is extracted from observed option data on foreign currencies. The data used in the paper cover four major exchange rates: the British pound, German mark, Japanese yen and Swiss Franc, all in units of US dollars, from February of 1983 to February of 1990. Because we have a measure of the market's perceived risk, we can decompose ex post exchange rate volatility into anticipated and unanticipated components. Then, we can examine whether the two components have differential effects on the bid-ask spread.

Third, previous studies acknowledge the potentially important impact of trading volume on bid-ask spreads, but do not examine it directly because of a lack of data on spot market trading volume. This paper utilizes actual trading volume of the spot exchange rate for one of the currencies, and thus is able to assess explicitly the effect of trading volume on the spread-uncertainty relationship.

Fourth, the relationship between the bid-ask spread and exchange rate volatility could, in principle, be a non-linear one. Previous studies either have run linear regressions without justifying the choice of functional form, or have not dealt with possible non-linearities beyond taking some simple (and arbitrary) transformations of the variables in linear regressions. The spread-

volatility relation in our model appears to be nonlinear in its

3 general form, but the results of simulations turn out to be very close to linear. This may provide a theoretical justification for the linear functional specifications. However, nothing guarantees that the empirical relationship is indeed linear. Therefore, we also apply a nonparametric method to study the _ possible nonlinearity in the spread-volatility relationship.

The next section provides some theoretical discussion. First, it is argued that firms would be discouraged from participating in international trade or investment if the bid-ask spread widens. Then, it is shown that the spread tends to widen as the market's perceived exchange rate volatility goes up. This chain of argument implies that policies that can reduce uncertainty in the foreign exchange market can potentially increase firms' incentive to participate in international trade and investment. Section II describes the data source and the methods used in extracting the market's anticipated volatility and in computing the percentage bid-ask spreads. Section III reports the empirical findings (linear regressions) concerning the effect of anticipated volatility on the spreads. The empirical effects of unanticipated volatility and spot trading volumes are also discussed. Section IV is devoted to studying the nonlinearity in the spread-volatility relationship. In particular, the locally weighted regression technique is used to determine whether the functional relation between the spread and

volatility varies with volatility.

I. Theoretical discussions

A bid quote is the price at which customers can sell foreign currency to a specialist, whereas an ask quote is the one at which customers can buy foreign currency from a specialist. The difference between the ask and bid quotes is the spread. The bidask spread is an important part of transactions costs for international trade and investment“. As will be shown, a widening of the spread decreases the profit of a firm and thus discourages it from engaging in international trade or investment.

To illustrate this, consider a firm that uses both domestic and foreign inputs and exports all of its output to the foreign market. Let w,be the domestic price of the domestic input, p and w, be the foreign price of the output and imported input. Let E be the central rate of exchange (units of domestic currency per unit of foreign currency) and s be the bid-ask spread. E-s/2 and E+s/2 are the bid and ask prices respectively. We use n(s) = n(E, S, p,

Wy, W;) to denote the profit function of the firn. Then, we have

Lemma 1:

Lemma _1: The profit function n(s) is decreasing and convex in s.

[Proof]: Define (Y,Xy,X,) to be the profit-maximizing production plan for the exchange rate- price vector (E,S,D,Wy,W,), and (y',x,',x,') the corresponding optimal plan for (E,S',p,W,,W,). The

profit function is

5

m(S)= (E-S/2)py - (E+S/2)w,X, —WyXy-

It is easy to see that the profit function is decreasing in s. Let s' > s, then

m(S) > (E-sS'/2)py - (E+S'/2)w,x, —WyX

2 (E-s'/2)py' - (Et+s'/2)w,x,' -wyx,!' = n(s'), aS was to be shown.

The first inequality comes from the assumption that s'>s. The second inequality follows from the definition of (y',Xy',xX,') as the optimal plan for (E,S',P,Wy,W,) -

To show that n(s) is also convex ins, define s"=ts+(1-t)s', where O< t < 1. We need to show that n(s") < tn(s) + (1-t)n(s').

By definition,

t(s")= (E-s"/2)py" - (E+s"/2)w,x,"" - wyx,"

= t((E-s/2)py"-(E+s/2) WX," —WyXy" ] + (1-t) [ (E-s'/2) py"-(E+s'/2) w,px,"—-wyx,"] s tl (E-s/2)py-(E+s/2)wyx,-wygxg] + (1-t) [ (E-s'/2) py'-(Et+s'/2)w,x,'-w,x,']

= tn(s) + (1-t)n(s), as was required.

Having established the effect of the bid-ask spread on the incentive for firms to engage in international trade, we now turn to the determination of the bid-ask spread itself. There have been several qualitative reasons proposed for the determination of the spread. Part of the spread covers overhead costs (e.g. staffing and office supplies) incurred by specialists. To analyze how the

perceived exchange rate volatility can affect the bid-ask spread,

6

Black(1989) develops a simple model in which the spread is proportional to the ratio of exchange rate volatility to expected trading volume. To reach this result, it is assumed that liquidity traders' buy and sell orders have the same mean, that speculative traders' demand functions are exactly linear in the prices and that dealers are risk-neutral. These assumptions are stringent and not necessarily true.

The model in this paper relates the spread to a portfolio of options. Copeland and Galai(1983) pioneered the use of options theory in a model of bid-ask spreads. But my model and theirs link the spread with options from different perspectives.

In Copeland and Galai(1983), the offer to buy at the bid by a specialist is thought of as a put option with the strike price equal to the bid quote. Similarly, to a trader, the offer to sell at the ask is a call option with the strike price equal to the ask quote. Because the options always have positive values, and because the announcement of the bid and ask quotes are free of charge, the bid and ask quotes yields a net loss to a specialist. To derive a spread-volatility relation, Copeland and Galai need to specify an equilibrium model with heterogeneous traders. The specialist's loss from offering options (the bid and ask quotes) without charge can be compensated by the expected gains from trading with liquidity traders. In this story, assumptions on the preferences of specialists, speculators and liquidity traders are needed. The resulting spread-volatility relationship depends, among other

things, on the proportion of traders that are liquidity traders and

7 the preferences of the market participants.

This paper presents a second way of linking the spread with options. I will argue that the size of a spread is equal to the values of a call option and a put option. In contrast with the first view, the call option here has a strike price equal to the bid quote, and the put option has a strike price equal to the ask quote. In this story, the model is completed by using the options analogy alone. Because options are priced by a no-arbitrage argument, this model thus eliminates the need to specify an equilibrium model.

As in any economic model, to make the idea explicit, I have to make some audacious assumptions. First, assume that the central rate of exchange, E, is some "true" exchange rate. Information about this true rate is revealed to specialists only through trading. In other words, specialists do not have private information. Second, when a specialist announces a pair of bid and ask quotes, she is committed, for the next T minutes, to buy at the bid and sell at the ask. She can only change the quotes after some transactions®?.

To illustrate the idea, let us look at Figure 1. Anyone who might have a little bit more information a few seconds before a specialist may view a pair of bid and ask quotes as options. Consider someone who buys a foreign currency at the ask, E+0.5s. She makes a profit (in domestic currency) as E goes up, and loses money as E goes down. However, her loss has a lower bound, because

she can sell the foreign currency back to the specialist at the

8 bid, E-0.5s, as long as the bid-ask quotes have not been changed. The payoff diagram for this position resembles that of a put option.

Consider now a trader who has just sold a unit of foreign currency to a specialist at the bid, E-0.5s. Her profit increases linearly as E does down, and decreases linearly as E goes up. Her loss also has a lower bound, since she can buy back the foreign currency from the specialist at the ask, E+0.5s. This is an implicit call option).

In Figure 1, the dotted line and the solid line are the payoff diagrams of the associated call and put options, | respectively. The value of the announcement of the bid-ask quotes is equal to the call, plus the put, and minus the spread. We know that the announcement is free of charge. Therefore, the bid-ask spread must equal to the values of the call and put options.

To summarize, announcing a pair of bid and ask prices by a specialist is equivalent to selling, for the price of s, a put option with a strike price equal to the ask quote, E+s/2, and simultaneously selling a call option with a strike price equal to the bid quote, E-s/2.

In order to derive an explicit expression, more assumptions are needed. (1) I treat the spread as a (short-lived) European option. I have already assumed earlier that when a spread is announced, the specialist is committed to do transactions at theses prices for the next T minutes. Here, I assume further that T is

exogenous. (2) The effective domestic and foreign interest rates,

9 for these T minutes, are zero. (3) Other assumptions of the Black- Scholes formula are satisfied.

The assumption of an exogenous T is motivated to apply the Balck-Scholes formula. In examining the spread-volatility relation numerically, we will vary the value of T from 10 seconds to 5 minutes. They do not make a qualitative difference. The assumption on zero interest rates is not essential either, since the qualitative feature of the model is preserved with nonzero interest rates.

Let u=s/E be the percentage bid-ask spread, and o be the market anticipated exchange rate volatility over the time interval between when the bid-ask spread is announced and when it is

changed. Then, we have Lemma 2.

Lemma 2: (The option model of the spread) The relationship between the percentage spread, uw, and the anticipated volatility, o, is given by the following equation: B= {N(h,,)-(1-u/2)N(h,,) } + (N(h,,) -1-(1+u4/2) [N(h,,) -1]})}

where h,, = (-1n(1-y/2)+0.50°T]/[oT?5],

ho = (-ln(1-u/2)-0.50°T}/[oT7],

hy, = [-ln(1+u/2)+0.50°P]/[oT5],

ho = [-1n(1+y/2)-0.50°T}/[oT >], and N(.) is the cumulative distribution function of a normal random

variable.

[Proof]: Let C and P be the value of the call and put options

10 associated with the bid-ask spread. From figure 1, we see that O=C+P-s. Or, M=S/E=C/E + P/E. The terms in the first curly bracket is the Black-Scholes' value of the call option (divided by the central rate of exchange E), and the term in the second curly bracket is the Black-Scholes' value of the put option.

Lemma 2 gives at least two impressions. First, we may think that an increase in perceived volatility widens the spread. The reason is that the value of both the call and the put options are increasing functions of the volatility. However, this result is not as straightforward. The complication arises from the fact that the the percentage spread, uw, also appears on the right hand side of the equation; it is not obvious that the two are necessarily positively associated. Second, the relationship between the spread and the perceived volatility, in principle, is non-linear. In fact, no simple transformation (e.g., logarithmic transformation) is able to make the relationship linear.

Since it is difficult to express mw as an explicit function of the volatility, we turn to numerical simulations. Based on Lemma 2, for a given value of uw, the value of the volatility can be solved by the Newton-Raphson method. Appendix A records the values of volatility corresponding to different values of the percentage spreads. The range of the percentage spread is chosen so that it encompasses the actual range of the spreads observed in the data. We try four different values for the duration of the bid and ask offers: five minutes, two minutes, thirty seconds and ten seconds.

Figure 2 plots the results of the simulation. First, we note

11 that the spread is a monotonically increasing function of the volatility. In other words, the option model of the spread does imply that the spread unambiguously widens as the anticipated volatility increases. Second, perhaps more surprisingly, the relationship between the spread and the volatility is close to linear. This provides a theoretical justification for using linear regressions in the empirical sections. However, whether there is a nonlinear relationship in the data will be formally investigated

later in the paper.

II. Estimating the anticipated volatility and bid-ask spreads

The key variable that we desire to obtain is a measure of the market's ex ante estimate of one-month-ahead exchange rate volatility. It is usually difficult to obtain a measure of market expectations. However, based on observed option trading on foreign currencies, we can geta reasonably good estimate. Lyons(1989) and Wei and Frankel(1991) have also extracted such measures for purposes which are different from each other and different from the current paper.

The basic idea is the following. To price a currency option properly, market participants use some version of the Black-Scholes formula. The inputs needed for the formula are time-to-maturity of the contract, interest rates in the two countries, the current spot exchange rate and an estimate of the future volatility over the

lifetime of the option contract. The market estimate of the

12 volatility is the only variable unknown to an econometrician. All the other inputs are readily available from newspapers or the indenture of the option contracts. By solving a nonlinear function, we can obtain an estimate of the market's anticipated volatility of the exchange rate in question.

We obtain these measures of anticipated volatility for four exchange rates: British pound, German mark, Japanese yen and Swiss franc, all in units of US dollars. The estimation method and the justification for the choice of the option formula are detailed in Wei and Frankel(1991). The source of the data is described in Appendix B. Because the option contracts, by regulation, always expire on the third Wednesday of each month, we choose options that . are written on the third Wednesday of each month. The implied standard deviation (isd) from the options can be thought of as a market's anticipation of the average daily volatility over the lifetime of the contract (typically a month in this sample). The estimates of the market's anticipated volatility are plotted in Figure 3a.

The realized volatility is computed from daily exchange rates from the third Wednesday of the month to the third Wednesday of the following month. It is the sample standard deviation of the changes in logarithms of daily exchange rates. Such a measure of realized volatility is consistent with the definition of the market anticipated volatility that is used in option pricing. The unanticipated volatility is the difference between the realized

volatility (rsd) and the anticipated one of the corresponding

13. month. The realized volatility for the four currencies are plotted in Figure 3b.

The percentage bid-ask spreads for the four exchange rates are the actual bid-ask spreads as percentages of the ask quote. Alternatively, we could compute the bid-ask spreads as percentages of the middle rates; it makes little difference with respect to the empirical results in the next two sections. The data are the closing quotes in the London market on the day the options are written. Figure 4 plots the percentage bid-ask spreads. By inspecting Figure 4, we suspect that one of the observations (August 17,1988) on the spread for the dollar/pound rate may be an outlier. In the empirical testing, we will make sure that no result

is entirely driven by this single observation. III. Empirical results: Does volatility widen the spread?

IIT.A. Market anticipated volatility and bid-ask spreads

To examine the effect of anticipated volatility on percentage

bid-ask spreads, we run the following regressions: pspread,= c + b isd, + e,

where pspread is the percentage bid-ask spread, and isd is the market perceived one-month-ahead exchange rate volatility implied by the currency options data.

Table 1 reports the results of the regressions for the four

14

exchange rates. Panel A presents the results from an OLS estimation. We first note that the intercept terms for the four currencies are all positive and statistically significant. Glassman(1987) argues that the intercept gives an estimate of the cost-overhead component of the transaction cost. They include costs of office supplies, staff salaries etc., that are not directly related to risks in foreign exchange transactions. The point estimates of the intercepts are close to each other for the four currencies, ranging from 0.0318 per cent for the German mark, to 0.0559 per cent for the Swiss Franc.

Second, the slope estimates are positive for all the four currencies. They are statistically significant for the British pound and Japanese yen at the five percent level, for the German mark at the ten percent level. This indicates that increases in the perceived volatility of the exchange rates are associated with widening of the bid-ask spreads. As noted before, one of the observation on the bid-ask spread for the pound (August 17, 1988) appears to be an outlier. We redo the OLS regression for the pound omitting this observation and find that the sign and significance of the estimates are not changed, although the point estimate becomes slightly smaller. This means that the result for the pound in Panel A is not driven by that one observation. We omit the result of this regression to save space.

To take advantage of the similar structure of the regressions for the four exchange rates, we also use the seemingly unrelated

regression (SUR) technique. Since the point estimates of the slope

15

coefficient in the OLS estimation are quite close, we restrict them to be equal in the four equations. The SUR technique takes into account possible cross-equation restrictions on the parameters and covariance matrix of the error terms, and thus should yield a more efficient estimate of the slope parameter. The results are in Panel B of Table 1. Essentially, the sign and the magnitude of the point estimates are similar to those in OLS estimation. The point estimate for the coefficient associated with the market's anticipated volatility is 2.670, and is statistically different from zero at the five percent level.

Before October 1985, option contracts were only available at four maturity dates: the third Wednesdays in March, June, September and December. The monthly series of the market's anticipated volatility thus contain observations from contracts with overlapping time periods. This could cause serial correlation in the error terms of the above regressions. To make sure that this does not drive our results, we redo the SUR estimation in the subsample that excludes data from overlapping contracts. The results are in Panel C of Table 1. Again, the slope parameter for the market's anticipated volatility is positive and statistically significant at the five percent level.

We repeat the above regressions after taking a logarithmic transformation of the anticipated volatility. This serves two purposes. It indicates whether the spread-volatility relationship in table 1 is robust to small perturbations of the model

specification; and more importantly, it facilitates the

16 quantitative interpretation of the estimates. That is to say, we are able to say by how much the bid-ask spread changes in response to a one percent increase in the market's perceived volatility.

Table 2 presents the results of this exercise. Parallel to Table 1, Panels A, B and C of Table 2 are results from OLS estimation, SUR estimation with the whole sample and SUR estimation with the subsample excluding data from overlapping contracts. In the OLS estimation, the parameters associated with the market's anticipated volatility are positive for all four currencies and statistically different from zero at the five percent level for the pound and mark. In the SUR estimation, the slope parameter estimates are again positive and statistically significant. Based on the point estimates from the SUR regressions, we conclude that a one percent increase in the market's perceived exchange rate volatility widens the bid-ask spread by about 0.015-0.016 percentage points.

The positive estimates in Table-2 are good news for the option model of the spread (Lemma 2). We now go one step further to compare the magnitude of the association implied by Lemma 2 with these point estimates. The second half of Appendix A computes the theoretical response of the spread to changes in volatility. When the anticipated volatility increases by one unit, the increment of the spread varies from 69.67 percentage points, if the spread is assumed to last for five minutes, to 12.73 percentage points, if the spread lasts for 10 seconds. In comparison, the actual response

in Table 1 is between 2 to 4 percentage points. Therefore, the

17 model seems to have overpredicted the response.

Examine now the percentage response reflected in the estimation in logarithms. For a one percent increase in the volatility, the model predicts that the spread widens by about 0.084 percentage points. According to Table 2, the actual increase in the spreads is by about 0.015 to 0.016 percentage points. Again, the model has overpredicted, though the difference between the theoretical and empirical responses is much smaller. Of course, economic models should not be taken too literally. Nevertheless, it is important to bear in mind that the option model of the bid-ask spread does not capture all the aspects regarding the spread-volatility relationship.

One may worry about the impact of possible non-normal distributions of the error terms. We note first that in a large sample, the slope estimator is consistent and asymptotically normal. In a small sample, however, nothing guarantees a priori the performance of the estimator. Wei and Frankel(1991, Table 5) conduct simulation exercises to examine the effect of nonnormality on the point estimate and size of the t-test. With a sample size of 85, they have considered a wide range of non-normal distributions for the error term, the skewness parameter of the error term varying from -6.2 to 6.2, the kurtosis parameter from 3 to 113. Even with this wide range of non-normality, the point estimate of the slope parameter and the "true" size of the t-test in an OLS regression are hardly affected. This indicates that our results

here are not likely to be an artifact of non-normal error terms.

18

III. Anticipated versus unanticipated volatility

Given a measure of the market's ex ante anticipation of volatility, we can decompose the ex post exchange rate volatility into anticipated and unanticipated components. The difference between the ex post volatility and the market's anticipation is defined to be the unanticipated volatility. With this decomposition, we can examine their possibly differential effects on the bid-ask spreads. One expects that the effect of exchange rate volatility comes entirely from the anticipated component, since the specialists should choose bid-ask spreads based on their perception of exchange rate volatility in the near future. We first

run the following type of regressions:

pspread, = c + b, isd, + b, (rsd,,,-isd,) + e,

where pspread, is the percentage bid-ask spread on day t, isd, is the market's anticipation on day t of the one-month-ahead exchange rate volatility, rsd,,, the ex post volatility of the following month starting from day t. The results are in Table 3.

Panel A of Table 3 presents the results of the OLS estimation. The point estimates of the intercept terms and the slope parameters are quite close to the corresponding ones in Table 1. The parameter estimates of the unanticipated volatility are not statistically different from zero, as expected. Panels B and C are results using SUR method with the whole sample and the subsample

excluding data from overlapping contracts. The slope parameters for

19

the anticipated and unanticipated volatility are restricted to be equal across the four currencies in order to improve the efficiency of the estimation. In both panels, the parameter associated with the unanticipated volatility is not statistically different from zero at even the twenty percent level. In contrast, the parameter associated with the anticipated volatility is positive and different from zero at the five percent level.

We repeat this set of regressions with logarithmic

transformation of the right-hand-side variables:

pspread, = c + b, log(isd,) + b, [log(rsd,,,)-log(isd,)] + e,

The results are reported in Table 4. In the OLS estimation, none of the parameters for the unanticipated volatility has any effect on the bid-ask spreads at the twenty percent level. In comparison, three out of the four parameters for the anticipated volatility are positive and significantly different from zero at the ten percent level. The fourth parameter is also positive and different from zero at the twenty percent level. In both of the SUR estimations, the parameters for the unanticipated volatility are not different from zero at even the twenty percent level, while the parameters for the anticipated component are statistically greater than zero at the five percent level. Based on the SUR estimations, we conclude that a one percent increase in the anticipated volatility widens the bid-ask spread by about 0.015 to 0.016 percentage

points. Notice that the magnitude of the effect is virtually the

20 same as the estimates in Table 2.

Previous studies on the effect of volatility typically use ex post volatility as a proxy for market's anticipated volatility. Doing so would not alter point estimate of slope parameter if market's anticipated volatility is an unbiased estimate of the ex post realized volatility. Unfortunately, Wei and Frankel(1991) have shown that the unbiasedness hypothesis is rejected for the four exchange rates. Therefore, the magnitude of the effect of the market's anticipated volatility on the bid-ask spread need not be reflected by the point estimate of the parameter associated with

measures of ex post volatility.

III.c. The effect of trading volume on bid-ask spread

The literature suggests that, in theory, the trading volume of spot exchange rates has an effect on the bid-ask spread. Most suggest that the relationship should be negative in the long run(Copeland and Galai, 1983; and Black, 1989), although it could be positive in the short run(Copeland and Galai, 1983).

Due to lack of the data, few previous empirical studies have actually included the spot trading volume in their regressions. Glassman(1987, footnote 4) even suggests that "such data probably will never be available since the trading does not take place ina centralized marketplace and since banks resist revealing what they perceive to be confidential information about their business". Interestingly, spot trading volume is available for the interbank

yen/dollar trading in Tokyo. The data is obtained from Nihon Kazai

21 Shibun. This provides a chance to examine directly the impact of the spot trading volume on the spreads.

In her study, Glassman(1987) cleverly uses the volume of currency futures trading at the Chicago Mercantile Exchange as a proxy for the volume of spot currency trading. She finds that the coefficient estimate on the proxy of spot volume is generally positive. The question is how well the trading volume of the futures contracts approximates that of spot trading. As noted by Glassman herself(1987,p482), the growth rate of the futures trading was more than 200% higher than that of the spot trading during the period 1977-1983. Consequently, the movement of the two may diverge substantially from each other. Therefore the effect of spot trading volume may not be adequately reflected by estimates derived from futures trading volume.

Black (1989) uses three years of annual data on spot trading volume of seven currencies: 1980, 1983 and 1986. He then calculates the annual average of the daily spread and the annual standard deviation of daily percentage changes for these three years. With a small sample of 21 observations, the spot trading volume variable enters a regression of the spread on volatility with a negative sign and a t-statistic equal to 1.31. The sign of the volume variable is opposite to what Glassman (1987) obtained.

One may want to improve the Black's result for two reasons. First, the sample in his study is very limited. Second, the interaction among the spread, volatility and trading volume is

likely to be short-run in nature, and may not be adequately

22 reflected in annual average data.

With seven years of monthly data on the actual spot trading volume, this paper hopes to provide more insights on the issue. Table 5 presents the results of regressions for the Japanese yen, with the spot trading volume included as an additional explanatory variable. To avoid possible simultaneity problem, each regression is also run with one month lagged values of the trading volume used as the regressor.

Panel A is from the estimation with the anticipated volatility and spot trading volume in levels. The parameter estimate for the trading volume is about 0.00013 to 0.00015. It is statistically significant at the ten percent level for the whole sample with the lagged trading volume and significant at the fifteen or twenty percent levels in other instances,

Panel B reports the estimation with the anticipated volatility and trading volume in logarithms. The parameter estimates are positive and statistically different from zero at the fifteen or twenty percent levels. These results offer some support for the positive association between the spread and volatility and suggest that using futures volume as a proxy does give the qualitatively correct answer.©) Based on Panel B, a one percent increase in the trading volume leads to a widening of the spread by approximately 0.005 percentage point. This estimate of the effect of the volume appears much larger than the estimate obtained using

futures volume as a proxy for the spot volume (Glassman, 1987,

Table 1).

23 Another thing that we can learn from Table 5 relates to the effect of omitting the spot trading volume. The point estimates in Panels A and B of Table 5 are very close to the corresponding ones in Tables 1 and 2 (OLS estimation with the whole sample). This suggests that the omission of the spot volume variable does not seriously bias the point estimate of the parameter for the market's

anticipated volatility.

IV. Empirical results: Is there a nonlinear relation?

This section is devoted to investigating the possibility of nonlinearity in the relationship between the spread and anticipated volatility. The basic tool used is locally weighted regression.

Locally weighted regression (LWR) is a procedure for fitting a regression surface to data through smoothing in a moving average fashion. Suppose uw = g(x) + e, where x is a p-dimentional vector, and g is a smooth (and possibly nonlinear) function of the independent variables. e is a normally distributed disturbance term. LWR provides an estimate of g(x) at any value x*. The estimate of g at x* uses a fraction, f, of observations whose Xx; values are closest to x*. That is, a neighborhood of the independent variables is defined. Each point in the neighborhood is weighted according to its distance from x*; points close to x* have large weight, and points far from x* have small weight. A linear or a quadratic function of the independent variables is fitted to the

dependent variable using weighted least squares with these weights.

24 The resulting estimate of g(x) is taken to be the value of this fitted function at x*. Cleveland and Devlin(1988) provide a comprehensive discussion of this procedure.

If the functional relationship between the spread and the anticipated volatility depends on the size of the volatility, LWR is ideal to capture this. In choosing the fraction of data, f, to do the local fitting, one faces certain tradeoffs. As f approaches one, the estimated regression surface tends to a regular linear regression. The sampling variability is reduced, but the chance of detecting nonlinear relation is also reduced. On the other hand, as f moves away from one, the flexibility of the regression (and thus the chance of finding the nonlinearity) increases, but the influence of the sampling errors on the estimates also increases. To balance the flexibility with low sampling errors, we pick f=0.98, 0.90 and 0.85 respectively.

Figure 5 reports the smoothed scatter plots resulting from applying the LWR procedure. Each plot has the estimates of the regression surface on the vertical axis and the anticipated volatility on the horizontal axis. The four columns correspond to the four currencies, and the three rows correspond to the three values of the f. From Figure 5, we may notice two things. First, the positive association between the spread and the anticipated volatility are profound. Furthermore, for most of the data range, the relationship between the two appears to be linear. This is certainly consistent with the option model of the bid-ask spread

(Lemma 2). However, there is some systematic nonlinear pattern in

25 at least three currencies. The slope of the curves appears to be smaller in the lower tails. This becomes more obvious as we choose smaller fractions of observations to do the local fitting. Therefore, the bid-ask spreads become less elastic when the anticipated volatility is low. This feature of the data is not well

captured by the option model the bid-ask spread (Lemma 2).

V. Conclusions

This paper studies whether and how the perception of foreign exchange risk may affect the bid-ask spreads in foreign exchange market. In the theoretical section, we have argued that firms! incentive to participate in international trade is inversely related to the width of the bid-ask spread in foreign exchange. We have also derived a model of the spread-volatility relationship which is solely based on a no-arbitrage argument. Based on the model, numerical simulations indicate that an increase in the volatility widens the spread. Furthermore, the spread-volatility relationship derived from the simulations is close to linear.

The empirical part of the paper has sought to make further contributions. The key variable used in the empirical part is a measure of the market's anticipated volatility of foreign exchange. It is extracted from observable currency option trading for four major currencies from February of 1983 to February of 1990. There are three major empirical findings. First, the bid-ask spread in

foreign exchange does increase as the market's perception of the

26

volatility increases. This is consistent with the option model of the spread. Based on SUR estimations in Section III, a one percent increase in the volatility typically leads to a widening of the spread by 0.015 to 0.016 percentage points. This magnitude of the point estimate appears to be smaller than that implied by the option model of the spread. Furthermore, the ex post realized volatility in foreign exchange rates. is decomposed into unanticipated and anticipated components. The regression results show that the unanticipated component of volatility does not have any impact on bid~ask spreads.

Second, the effects of spot trading volume on the spread and on the possible bias of the volatility parameter are examined. The spot trading volume (of dollar/yen) is positively related with the bid-ask spread. The parameter for the volatility variable is unaffected by the addition or omission of the trading volume variable. This suggests that omitting the trading volume may not generate much bias in the estimation of the spread-volatility relation. These findings lend direct support to the results by Glassman(1987), who uses a proxy for the spot trading volume.

Third, the locally weighted regression technique is employed to investigate whether the relationship between the spread and the volatility is nonlinear in the data. It is found that the relationship is indeed nearly linear for most of the data range. However, nonlinearity is still there: in plots of the regression surface against the volatility terms, the slopes for smaller values

of the volatility are smaller for three currencies. Therefore, when

27

exchange rate volatility is small in the market's perception, the bid-ask spreads are much less responsive to changes in the volatility. | |

Both the option model of the bid-ask spread and the estimation of the anticipated volatility rely on the assumption that the exchange rates follow a lognormal process. Even though the model performs reasonably well in the study, it is desirable in future research to investigate the effect of deviations from the

lognormal assumption.

28

Appendix A: Simulation results based on Lemma 2.

This appendix presents some simulation results on the relationship between the percentage

bid-ask spread and the anticipated exchange rate volatility.

A1. Values of o (implied by Lemma 2) corresponding to values of p.

percentage volatility o volatility o volatility o volatility o

spread (100) (T=5 minutes) (T=2 minutes) (T=30 seconds) (T=10 seconds) 0.001 0.000014 0.000023 0.000045 0.000079 0.005 0.000072 0.000114 0.000227 0.000393 0.009 0.000129 0.000204 0.000409 0.000708 0.02 0.000291 0.000454 0.000908 0.001573 0.04 0.000581 0.000899 0.001798 0.003147 0.06 0.000871 0.001363 0.002725 0.004672 0.08 0.00116 0.001817 0.003634 0.006294 0.10 0.00145 0.002271 0.004542 0.007867 0.12 0.00172 0.002725 0.005450 0.009440 0.14 0.00201 0.003179 0.006359 0.01113 0.16 0.00230 0.003597 0.007267 0.01259 0.18 0.00259 0.004088 0.008261 0.01416 0.20 0.00287 0.004542 0.009084 0.01573

Notes:

(1) Based on Lemma 2, for a given value of yu, a value of o is computed using the Gauss-Raphson method.

(2) The volatility o is on per day basis. p is the percentage bid-ask spread.

(3) T is the time duration of the bid-ask spread. 5 minutes, 2 minutes, 30 seconds and 10 seconds correspond to T=1/288, 1/720, 1/2880 and 1/8640, respectively.

A2. The response of the spread yu (implied by Lemma 2) to changes in volatility o.

Time length (T=5 minutes) (T=2 minutes) (T= =30 seconds) (T=10 seconds) Response 69.67 44.11 22.05 12.73

Time ne length (T: 25 minutes) ] (T=2 minutes) (T= =30 seconds) c =10 seconds) Response 0.0848 0.0839 0.0846 0.0844

“29

Appendix B. Data sources

The data on four exchange rates (the British pound, German mark, Japanese yen and Swiss Franc, all in units of US dollars) are used in this paper. The sample periods for all the data are from February

of 1983 to February of 1990.

Daily spot exchange rates and the bid-ask spreads: The daily spot

exchange rates used to compute the realized standard deviations for the four currencies are the daily closing bid quotes on the London Market. The units for the four exchange rates are units of US dollar per unit of foreign currency.The monthly series of the percentage bid-ask spread is computed from the closing quotes on the thira Wednesday of each month on the London Market. The percentage spread

used in the paper is defined as 100(ask-bid)/ask. The source is

Data Resources, Inc.

Options data: The currency option data are used to extract the market's anticipated one-month-ahead exchange rate volatility. They are the closing quotes on the third Wednesday of each month on the Philadelphia Exchange. By regulation, currency options always expire on the third Wednesday of each month. The source is various issues of the Wall Street journal. The other aspects of the selection criteria of the option data are:

(1) Call options that are closest to being at the money.

(2) If possible, contracts that mature in the following month.

30

Otherwise, contracts with the next nearest maturity.

Trading volume of the spot dollar/yen rate: The trading volume of

the spot dollar/yen exchange rate is the volume of interbank transactions in Tokyo on the third Wednesday of each month. The

source is Nikkei Telecon.

31

References

Black, Stanley W., 'Transaction costs and vehicle currencies'. IM working paper, WP/89/96, November 21, 1989. Boothe, Paul, 'Exchange rate risk and the bid-ask spread: A seven

country comparison'. Economic Inquiry, July, 1988, Vol.26, 485-492.

Cleveland, Williams S. and Susan J. Devlin, ‘Locally weighted regression: An approach to regression analysis by local fitting'. Journal of the American Statistical Association, September, 1988. No.403. 596-610.

Copeland, Thomas and Dan Galai, ‘Information effects on the bid-ask spread'. Journal of Finance, December, 1983. Vol.38, No.5. .

Glassman, Debra, ‘Exchange rate risk and transactions costs:

Evidence from bid~-ask spreads'. Journal of International Money and Finance, June, 1987. 479-490.

Glosten, Lawrence, ‘Components of the bid-ask spread and the

statistical properties of transaction prices', Journal of Finance,

December ,1987. Vol.XLII, No.5. Lyons, Richard, 'Tests of the foreign exchange risk premium using the expected second moments implied by option pricing'. Journal

of International Money and Finance, March,1988. Vol.7,No.1.

Merton, Robert, 'Theory of rational option pricing', Bell Journal

of Economics and Management Science,1973. No.4. 141-183.

Wei, Shang-Jin and Jeffrey Frankel, ‘Are the forecasts of exchange

rate volatility implicit in options prices excessively variable?! University of California, Berkeley. First draft, May, 1990. Revised, June, 1991.

32

Notes

* The author is a summer intern in the Division of International Finance and a doctoral student at the University of California, Berkeley. This paper represents the views of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or other members of its staff. I have received very helpful comments from Stanley Black, Paul Boothe, Hali Edison, Jeffrey Frankel, David Gordon, Dale Henderson, Takatoshi Ito, Steven Kamin, Maurice Obstfeld, David Parsley, Kenneth Rogoff, David Romer, Andrew Rose, Richard Stern and seminar participants at the Federal Reserve Board. Sien Lee has offered cheerful

encouragement. I am responsible for any errors in the paper.

(1) Many people may think that bid-ask spreads or transaction costs in foreign exchange markets are economically unimportant. A recent study by the European Economic Commission (1990) has challenged this view. According to its estimate, the transaction costs are on the order of both 0.25-0.4% of EC's GDP per annum. The bulk of the transaction costs comes from bid-ask spreads and other fees paid to banks. There are reasons why the transaction costs for the US might

be smaller, but they are not a negligible number.

(2) In reality, a specialist certainly does not have to trade at her quoted bid and ask prices. However, refusing to trade at the quotes too often is considered bad for reputation. Therefore, quoted bid

and ask prices are usually honored by a specialist.

(3) An alternative interpretation replaces the central rate E in the above story by the actual quotes. To obtain the result on the implicit put, consider someone purchasing the foreign currency at

the ask quote. Her payoff depends on the movement of the next bid

33

quote (in stead of E). Just as in the previous story, the payoff diagram resembles that of a call option with strike price equal to the bid. Similarly, for someone selling foreign currency to the specialist, her payoff depends on the movement of the next ask quote (in stead of E). It is still a put option with the strike price equal to the ask quote. When we evaluate the value of the spread, the resulting spread-volatility relationship is exactly the same as

before. I thank David Gordon for pointing this out.

(4) We have also run the regression with the same specification as in Black(1989). The result is as follows (standard errors are in parentheses) :

psprd, = 0.0276 + 7.50 isd,/volune, + 3. 277isd,+ 0. 00017volume, (0. 0108) (22.69) (i. 979) (0. 00015) adj.R?=0.034 DW=2.35

This result is close to those in the text. In particular, the volume variable enters with a positive sign. Qualitatively similar results are obtained when one-period lagged value of the volume variable is used or a _ subsample excluding observations from overlapping contracts is used.

(5) Our result should also be interpreted with caution. The bid-ask spread in the regressions is from the London market, whereas the spot trading volume is from the Tokyo market. The inference is reliable only when the spot trading volumes in the two markets are highly positively correlated. Due to lack of the data, we do not have such a knowledge. I thank Stanley Black for pointing this out.

Table 1: Percentage spread and the anticipated volatility in levels 1983:2 - 1990:2 pspread, = c + b isd; + ©

A. OLS estimation, whole sampie (N=85)

Currency c b adj.R2 DW

BP 0.0423° 4.026° 0.04 1.85 (0.0119) (1.906)

GM 0.0318° 2.1088 0.03 1.73 (0.0072) (1.132)

JY 0.0369° 3.042° 0.03 2.27 (0.0085) (1.587)

SF 0.0559° 2.467 0.008 1.71 (0.0120) (1.882)

B. SUR estimation, whole sample (N=85)

Currency c b adj.R2 DW

BP 0.0504° 2.670° 0.051 1.86 (0.0060) (0.791)

GM 0.0283° 0.040- 1.73 (0.0052)

JY 0.0388°* 0.042 2.27 (0.0046)

SF 0.0547° 0.020 1.72 (0.0058)

C. SUR estimation, excluding data from contracts with overlapping maturities (N=64)

Currency c b adj.R@ DW

BP 0.0459" - 3.242° 0.047 1.91 (0.0075) (1.018)

GM 0.0268° 0.068 1.70 (0.0064)

JY 0.0364° 0.048 1.50 (0.0055)

SF 0.0497° 0.012 1.25 (0.0069)

meee Notes: ‘ (1) Standard errors are in parentheses. ,

(2) ° denotes that the estimate is statistically different from zero at five percent level. (3) # denotes that the estimate is statistically different from zero at ten percent level.

Table 2: Percentage spread and the anticipated volatility in logarithms

19822 - 1990:2 pspread, = c + b log(isd,) + e

A. OLS estimation, whole sample (N=85)

Currency c b adj.R2 OW

BP 0.1876° 0.02343 * 0.036 1.86 (0.0596) (0.01147)

GM 0.1184° 0.01439 * 0.037 1.73 (0.0360) (0.00703)

JY 0.1192° 0.01256 0.018 2.26 (0.0415) (0.00782)

SF 0.1564* 0.01664 0.010 1.70 (0.0625) (0.01218)

B. SUR estimation, whole sample (N=85)

Currency c b adj.R2 DW

BP 0.144° 0.0151 * 0.048 1.87 (0.024) (0.0046)

GM 0.122° 0.048 1.73 (0.024)

JY 0.133° 0.030 2.25 (0.025)

S 0.148° 0.022 1.70 (0.024)

C. SUR estimation, excluding data from contracts with overlapping maturities (N=64)

Currency — Cc b adj.R2 OW BP 0.146° 0.0158 * 0.040 1.92 | (0.028) (0.0054) _ GM 0.128° 0.077 1.71 (0.028) _ Sv 0.137" 0.036 1.50 (0.029) SF 0.150° 0.010 1.25 (0.028)

Notes: (1) Standard errors are in parentheses. @ (2) * denotes that the estimate is statistically diflerent from zero at five percent level. (3) # denotes that the estimate is statistically different from zero at ten percent level.

AN

Table 3: Differential effects of the anticipated & unanticipated volatility on the spreads 18832 - 1990-2

pspread, = ¢ + by id; + ba (rsd, 1 -isdy) + e A. OLS estimation, whole sample (N=85)

Currency c by bo adj. R° Ow

BP 0.0449° 3.763 # -1.093 0.033 1.87 (0.0126) (1.955) (1.683)

GM 0.0337" 1.847 -0.726 0.026 1.65 (0.0076) (1.172) (0.825)

JY 0.0331° 3.698 ° 0.733 0.026 2.25 (0.0098) (1.800) (0.943)

SF 0.0542" 2.694 0.319 0.003 1.71 (0.0140) (2.116) (1.328)

B. SUR estimation, whole sample (N=85)

Currency Cc by bo adj. R2 OW

BP 0.0500° 2.711° 0.0798 0.050 1.86 (0.0064) (0.841) (0.5606)

CM 0.0280" 0.038 1.74 (0.0056)

JY 0.0386" 0.044 2.26 (0.0049)

SF - 0.0543" 0.021 1.72 (0.0062)

C. SUR estimation, exclud’.1g data from contracts with overlapping maturities (N=64)

Currency c by bo adj.R2 OW

BP 0.0470° ; 2.990 * -0.384 0.051 1.92 (0.0081) (1.106) (0.656)

Gui 0.0286° 0.082 1.67 (0.0070)

JY 0.0380° 0.038 1.50 (0.0062)

SF 0.0517° 0.016 1.27 (0.0078)

Notes:

(1) Standard errors are in pare ntheses. (2) * denotes that the estimate is statistically different from zero at five percent level. (3) # denotes that the estimate is statistically different from zero at ten percent level.

37 Table 4: Differential effects of the anticipated & unanticipated volatility on the spreads 1983:2 - 1990:2 Pspread; = ¢ + by log(isd,) + bo [log(rsd;, 1 )-log(isd;)] + e,

A. OLS estimation, whole sample (N=85)

Currency c by bo adj.R2 OW

BP 0.1761° 0.0211 # -0.0045 0.026 1.87 (0.0669) (0.013) (0.0117)

GM 0.1128° 0.0133 # -0.0025 0.027 1.70 (0.0383) (0.0075) (0.0055)

JY 0.1416° 0.0169 # 0.0046 0.014 2.24 (0.0507) (0.0096) (0.0059)

SF 0.1667° 0.0187 0.0030 -0.0007 1.70 (0.0715) (0.0140) (0.0098)

B. SUR estimation, whole sample (N=85)

Currency ¢c by bo adj. R2 DW

BP 0.149° 0.0160 * 0.0014 0.046 1.86 (0.027) (0.0052) (0.0037)

GM 0.127° 0.045 1.75 (0.027)

JY 0.137° 0.033 2.25 (0.028)

SF 0.153° 0.023 1.70 (0.027)

C. SUR estimation, excluding data from contracts with overlapping maturities (N=64)

Currency c b, bo adj.R2 OW

BP 0.142° “0.0150 ° -0.0019 0.041 1.92 (0.033) (0.0063) (0.0043)

GM 0.123° ; 0.084 1.69 (0.032)

JY 0.133° 0.033 1.51 (0.033)

SF 0.146° 0.012 1.25 (0.032)

eee Notes:

(1) Standard errors are in parentheses.

(2) ° denotes that the estimate is statistically different from zero at five percent level.

(3) # denotes that the estimate is statistically different from zero at ten percent level.

Table 5: Trading volume, anticipated volatility and the spread (Japanese Yen) 19832 - 1990:2

A. OLS estimation in levels

33

pspread, = c + by ist + bp volume; + ef

or pspread, = c + by isd, ¢ by volume;.; + eo Sample c by by bg adj.R2 whole 0.0288 * 3.6444 ° 0.00013 ft 0.044 sample (0.0101) (1.6285) (0.00009) 0.0313° 3.0430# 0.000154 0.042 (0.0097) (1.6857) (0.00009) excluding 0.0348 °* 2.4447 tt 0.00013 tt 0.023 overlapping (0.0102) (1.7591) (0.00010) contracts 0.0353° 2.0710 0.00016 t 0.041 (0.0094) (1.778) (0.00010)

B. OLS estimation in logarithm pspread; = c +b log(isd;) + ba log(volume;) + & pspread; =c +b) log(isd;) + bg log(volumey.4) + &

bp b3

0.00413 Tt (0.00313)

0.00466 t (0.00310)

0.00498 tt (0.00373)

0.00501 tt (0.00367)

adj.R@

0.027 0.027 0.017

0.024

2.34

2.33

1.52

1.52

2.31

2.31

1.52

1.51 -

i

or

Sample c by

whole 0.1201 * 0.01538 #

sample (0.0413) (0.0081) 0.1052° 0.0129 +t (0.0431) (0.0081)

excluding 0.0852 # 0.00949

overlapping (0.0444) (0.0080)

contracts 0.0812° 0.00878 (0.0468) (0.0081)

Notes:

(1) Standard errors are in parentheses.

(2) *, #, t and tt denote that the estimate is statistically different from zero at five, ten, fifteen

and twenty percent levels, respectively.

y

00

T= SC mautes

PuUrconlige sprusd

ocor0 0.0025

vOasety Srrun

Figure 2:

-_-—_ ~~ ¢#

39

Exchange Rate

Implicit cait Implicit put

Figure t: Spread as a pontolio of options

T = QZ miautes T= 30 seconds T= !1o sewnds bv So 5 3 : = & 2 ° r re . 8 8 & & YY oe c-} -3 0.0 0.062 0.006 3.0 07205 20°58 roameny mn staty.i0sec

Simulation results on the spread-volatility relationship

0010

oKsa

00?

0 0 006 0010

O Cera

0002

0012

wd

Figure 3a:

40

Market's anticipated exchange rate volatility extracted

fron options data (1983:2 - 1990:2)

Peilav / Bei iis Pound

1986S 1986 1987 1988 1989 1990

1S3S 1986 1087 1988 1655 \FQ

Dollar / Japanese Yen

Dell.w / Sesss Franc

"OS °° “ar “38 "oa? >)

0006 «6001000 = 004

0002

0 006 0010

0 002

0 OCs 0010 oom

0002

0012

vOdu

Dsttar/y. Seance ' _ a J : Ss ‘ j \ : \ 1 \ ! ; 7

4|

Fi : : gure 3b: Realized exchange rate volatility (1983:2 - 1990:2)

Dotluw / Batisk Pound

rrr!

1983 1984 1948S 1986 1967 1968 1989 1990

Doar / Cermes [Wh wep?

\, JU Af

1eS3 1684 198S 1926 1667 1688 1639 GQ

am

“as "26 “car “ea “3 4

British Poul

O14

> ‘

C Cv eraAtn

002

Japor ese.

Ilr eene

Siwvess

03

02

006

42

Figure 4: Percentage bid-ask spreads in foreign exchange (1983:2 - 1990:2)

S85 1584 1S2s 1988 1987 1988 1989 199)

"és “ea 718s "106 “a7 1188 a4 -

43

Figure 5: Smoothed scatter plots by locally weighted regressions

080'0

0200

$20

0 0200 $900

4$(96 0 © | ‘PdSd)s “pSyS)8semo}

$900 9000 $$00

Ag(00.0 ° j ‘PdedAl ‘peAesemcy

s~0 9900

$200

4$(96'0

4s(e6 0

0500

yro'0 «62900 000 FtO0

=} 'Pdsdw ‘pswe)ssemo;

0200 5900

= | pdsddq ‘psida)ssemoy

0.012

0.004 0.008

0 006

0 002

0 006 0010

0 002

lowe ssUyisd. jypsod, f « 0 98)$x lowess(sfisd. stpspd,f « 0.98:S:

lowess(grnisd, gmpapd, ! ~ 0.98)$s

lowess(Dpisd. bp 530d, f = O 98)$z

0000

st00 0200 $900

A$(56 0 © | ‘Pdsdjs ‘psys)esomoy

0200 $90 0 990 0 $$00

4$(90.0%) ‘pdedAl ‘pe A)esemo

9x00 0900 900 2900 O00

4$156 0 © 1 ‘DISdwWO ‘pEwO)stemo;

$200

0.00 $200

A$(56 0 =) 'PdSdda ‘psida)ssomo,

0s00

etoo0

0.012

lowees(sS3d, sipspd, { = 0.95)$x

0.004 0.008

2 005 0010

as

C Ge

#0 ccc me ~ fen

Xen fo, eee. . re

9200 0200 900 0 AS(Se'0 = | ‘Pdedye ‘peyedesemo;

towess(yisd, jypapd, { = 0.95)$x

o.oo )8=— $800: WTD—s«dSS'O «0500

Aa(0e'0 ©) ‘PEVeAl ‘pyAevomcy.

loween(gmiad, gmpapd, | - 0.95;Su

9000 ov0'0 sto 0

Asisvo°) ‘pdedws8 ‘pepuS)esomoy

lowes 15086, Opp od, f= 0.95)$x

9200 7200 e900 ¥999

A$(se.0 ©) ‘Pdsddg ‘peda)ssemcy

0.004 0.0608 0012

bowess(siisd sipsnd f= ° *

towe sa(fyed, fyp-pd. 1 = 0 85)$z

loweasl grad. ompspd. | = 0.85)$:

fowess 90 36 Opp. 1 = 0 8S)$:

IFDP NUMBER

409

408

407

406

405

404

403

402

401

400

399

398

397

396

395

- 44 -

International Finance Discussion Papers

TITLES 1991

Anticipations of Foreign Exchange Volatility and Bid-Ask Spreads

A Re-assessment of the Relationship Between Real Exchange Rates and Real Interest Rates: 1974 - 1990

Argentina’s Experience with Parallel Exchange Markets: 1981-1990

PC-GIVE and David Hendry’s Econometric Methodolody

EMS Interest Rate Differentials and Fiscal Policy: A Model with an Empirical Application to Italy

The Statistical Discrepancy in the U.S. International Transactions Accounts:

Sources and Suggested Remedies

In Search of the Liquidity Effect

Exchange Rate Rules in Support of Disinflation Programs in Developing Countries The Adequacy of U.S. Direct Investment Data Determining Foreign Exchange Risk and Bank

Capital Requirements

Precautionary Money Balances with Aggregate Uncertainty

Using External Sustainability to Forecast the Dollar

Terms of Trade, The Trade Balance, and Stability: The Role of Savings Behavior

The Econometrics of Elasticities or the Elasticity of Econometrics: An Empirical Analysis of the Behavior of U.S. Imports

Expected and Predicted Realignments: The FF/DM Exchange Rate during the EMS

AUTHOR (s )

Shang-Jin Wei

Hali J. Edison B. Dianne Pauls

Steven B. Kamin

Neil R. Ericsson Julia Campos Hong-Anh Tran

R. Sean Craig

Lois E. Stekler

Eric M. Leeper David B. Gordon

Steven B. Kamin

Lois E. Stekler

Guy V.G. Stevens Michael P. Leahy Wilbur John Coleman II Ellen E. Meade

Charles P. Thomas

Michael Gavin

Jaime Marquez

Andrew K. Rose Lars E. 0. Svensson

Please address requests for copies to International Finance Discussion Papers, Division of International Finance, Stop 24, Board of Governors of the

Federal Reserve System, Washington, D.C.

20551.

IFDP NUMBER

394

392

391

390

388

385

384

383

382

380

379

378

- 45 -

International Finance Discussion Papers

TITLES 1991

Market Segmentation and 1992: Toward a Theory of Trade in Financial Services

1990

Post Econometric Policy Evaluation A Critique

Mercantilism as Strategic Trade Policy: The Anglo-Dutch Rivalry for the East India Trade

Free Trade at Risk? Perspective

An Historical

Why Has Trade Grown Faster Than Income?

Pricing to Market in International Trade: Evidence from Panel Data on Automobiles and Total Merchandise

Is the EMS the Perfect Fix? An Empirical

Exploration of Exchange Rate Target Zones

Estimating Pass-through: Stability

Structure and

International Capital Mobility: from Long-Term Currency Swaps

Evidence

Is National Treatment Still Viable? Policy in Theory and Practice

U.S. Three-Factor General Equilibrium Models: A Dual, Geometric Approach

Modeling the Demand for Narrow Money in the United Kingdom and the United States

The Term Structure of Interest Rates in the Onshore Markets of the United States, Germany, and Japan

Financial Structure and Economic Development

Foreign Currency Operations: Bibliography

An Annotated

The Global Economic Implications of German Unification

Computers and the Trade Deficit: The Case of the Falling Prices

AUTHOR (s)

John D. Montgomery

Beth Ingram Eric M. Leeper

Douglas A. Irwin

Douglas A. Irwin

Andrew K. Rose Joseph E. Gagnon Michael M. Knetter

Robert P. Flood Andrew K. Rose Donald J. Mathieson

William R. Melick

Helen Popper

Sydney J. Key

Douglas A. Irwin

David F. Hendry Neil R. Ericsson

Helen Popper

Ross Levine

Hali J. Edison Dale W. Henderson

Lewis S. Alexander Joseph E. Gagnon

Ellen E. Meade