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«Volume Title: The Microstructure of Foreign Exchange Markets Volume Author/Editor: Jeffrey A. Frankel, Giampaolo Galli, Alberto Giovannini, editors ...»

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17). For this model to be a full explanation of the relation between spreads and volume, he presumably requires that the informed also trade more heavily at close.

2.2.3 Bollerslev and Domowitz (1993) Bollerslev and Domowitz (1993) examine the same data as in this paper, namely, continuously recorded quotes on the deutsche mark/dollar exchange rate in the interbank foreign exchange market. They document quote arrivals and bid-ask spreads over the trading day, across geographic locations, and across trading participants. The analytic focus is on two main areas: first (which is most relevant for this paper), an evaluation of the predictions of the asymmetric information models of Admati and Pfleiderer (1988) and Subrahmanyam (1989) and, second, time-series modeling of means and conditional variances.

Bollerslev and Domowitz conclude that their evidence "is encouraging with respect to the ability to validate and discriminate between theoretical models of trading activity using intraday information on foreign exchange trading" (1993, 1439). They suggest that periodic nondiscretionary liquidity trading around open and close will intensify the results of Admati and Pfleiderer, while round-the-clock trading will weaken them, and conclude that the U-shaped patterns of trading activity from open through close, well documented for the

14. The model of Admati and Pfleiderer (1988) and Subrahmanyam (1989, 1991) assumes sequential batch auctions rather than the continuous auctions associated with bids and asks on the NYSE. However, Admati and Pfleiderer regard their results as applying to the volume behavior on the NYSE, and Subrahmanyam (1989) explicitly equates the costs in Admati and Pfleiderer (which are the same as in his model) with bid-ask spreads. We follow this approach. Further, as Grossman and Miller (1988,628) point out, transactions costs should be measured by the difference between the price paid now and the price expected to be paid by waiting; but, if the average spread falls after opening and rises at close, one would expect a priori that a given liquidity trader would expect higher transactions costs in such periods.

57 Bid-Ask Spreads in Foreign Exchange Markets NYSE and addressed by Admati and Pfleiderer (1988), is apparent only in the European markets (p. 1426, n. 8).

Bollerslev and Domowitz also find that, for traders who restrict their trading to regional markets within well-defined openings and closings (as opposed to international firms with traders in multiple regional markets), the activity pattern (quote volume) "typically shows a U-shape, as does the distribution of their own spreads over the course of the day" (1993, 1428). Since these traders "operate more like the stock market traders usually modeled in much of the theoretical literature, with behavior influenced by openings and closings" (p. 1429), Bollerslev and Domowitz interpret this evidence as confirming the model of Admati and Pfleiderer (1988), although they note that the "daily patterns of the spread and market activity suggest risk-averse behavior on the part of these traders" (p. 1439). This modification is tied to "Subrahmanyam's (1989) extension of the Admati and Pfleiderer model to include risk-averse behavior [that] predicts that more trading by informed risk-averse participants brings about higher costs" (p. 1426, n. 9).

2.2.4 Foreign Exchange Quote Data and Standard Information Models We conclude that the asymmetric information models of Admati and Pfleiderer and Subrahmanyam are not consistent with the foreign exchange data on spreads and volatility, for two reasons. First, close examination of Subrahmanyam's extension of the Admati-Pfleiderer model shows that, although he can account for high spreads at times of high informed trading, the cost is that he loses the major result of the Admati-Pfleiderer model, namely, the concentrated trading equilibrium relied on by Admati and Pfleiderer to account for simultaneous high volume and high volatility. Second, the results from section 2.1 above show that volatilities (and spreads) across markets that trade simultaneously do not show the congruence implied by either the AdmatiPfleiderer or the Subrahmanyam models.

On the first point, note that Subrahmanyam's model implies that discretionary liquidity traders who can time their trades will avoid the high-cost, highvolume periods that he links to high levels of informed trading. However, this breaks the concentration of trading relied on in Admati and Pfleiderer's equilibrium. This in turn makes it difficult to explain the observed high volume in terms of discretionary liquidity traders and informed traders, since the former will avoid the high-cost open and close and the number of informed traders must be "sufficiently small" (Subrahmanyam 1989, p. 18) for the result to go through. Further, were the increased volume due to a very large increase in the number of informed traders (sufficient both to offset the departure of discretionary liquidity traders and to account for the total increase in volume), one wonders who takes the other side of their trades, especially since they receive correlated signals in this model.

Presumably, the burden falls, once again, on the luckless nondiscretionary liquidity traders, who in these models have zero elasticity of demand and must 58 David A. Hsieh and Allan W. Kleidon trade at these times regardless of price or cost. That is, the empirical results on spreads and volume—which the Admati-Pfleiderer and Subrahmanyam models attempt to explain—imply that within those models there must be an increase in nondiscretionary liquidity trading at open and close sufficient to offset the departure of discretionary traders in the face of higher transactions costs. Admati and Pfleiderer (1988, 34) conjecture that the orders of nondiscretionary traders may cluster around open and close because of market closure;





however, this is not part of their formal model, and they rely on such periodic demand as simply a timing catalyst for their endogenous clustering that requires low trading costs at open and close to attract discretionary traders.

The second problem with these asymmetric information models relates to the cross-market results from section 2.1 above. These results show that the observed behavior in spreads and variances cannot be explained within standard information models. It is true that, looking at the two markets individually, the variance results appear similar to those from the NYSE used to motivate the asymmetric information model of Admati and Pfleiderer. At first blush, then, these results may appear to provide confirmation of the conclusion that activity at the open and close of trading in foreign exchange markets is heavily influenced by concentrations of informed traders at those times, resulting in high variances.

The results obtained from looking at London and New York separately are highly misleading, however, in terms of evidence concerning any tracks left in the data by privately informed traders. Recall that these quotes appear directly on the Reuters' screens of traders in all locations. Assume that the high variance (and high spread) at close of trade in London is indeed caused by an unusually high concentration of informed traders at that time, which in turn causes rapid changes in quotes and, consequently, high variance. Traders in New York observe directly and simultaneously these London quote revisions that are ostensibly caused by the incorporation of previously private information. Since the commodity is the same whether the quotes are posted in London or New York, it must be the case that the incorporation of new information into the London quotes must virtually simultaneously show up in New York quotes, resulting in simultaneous high variance in New York quotes.

The results in table 2.3 and figure 2.5 above clearly refute this implication.

Note that the New York opening—which is ostensibly replete with private information, causing the New York variance of returns to rise dramatically— causes scarcely a ripple on the London market! Similarly, the London market closes with dramatic local effects in terms of variance but with no effect on New York. Similarly, table 2.1 and figure 2.6 above show an apparent lack of integration across these two markets with respect to spreads.

2.3 Evaluation of Results We regard the results from section 2.2 as striking evidence that, whatever is causing the patterns in variances and spreads at the open and close of trading 59 Bid-Ask Spreads in Foreign Exchange Markets in the foreign exchange market, it is not the incorporation of previously private information through the heavy trading of informed traders at the open and close of trading in London and New York. This is particularly evident from the comparison of volatility patterns across London and New York in figure 2.5 and table 2.3 above.

We consider two main alternative explanations for these results. First, we consider a broader class of information models that has recently been proposed to explain related forms of apparent excess volatility in stock prices, namely, models that relax the assumption in standard information models that traders have perfect knowledge about the preferences and beliefs of other traders in the market. These new models, based on imperfect information aggregation and subsequent learning by market participants, can be linked to experimental results in the behavioral literature and have proved successful in accounting for such difficult phenomena as the crash of October 1987. The second explanation that we consider, which is particularly relevant for behavior at the close of a market, returns to inventory models such as Garman (1976).

2.3.1 Models of Imperfect Information Aggregation: The Open of Trade Our results at the open of New York and the close of London trading show that no new information is reaching the international foreign exchange market as a whole since there is an absence of unusual volatility in quotes generated by traders in London when New York opens and, conversely, at London close.

One way to view these results is that quotes generated by traders in the volatile market show excess volatility relative to that implied by standard information models.

Others have noted the difficulty in explaining foreign exchange data in terms of standard information models. For example, Frankel and Froot (1990) emphasize heterogeneity of expectations across traders in foreign exchange markets and suggest three possible implications of the high trading volume in these markets for price movements: (1) greater depth means more efficient processing of fundamental information; (2) there is no relation between trading volume and prices since the market is "already perfectly efficient"; and (3) there may be "excessive volatility" caused by trading based on "noise" rather than "news" (p. 182). Frankel and Rose (1994) explore the third possibility in some detail, with emphasis on the possibility of "endogenous speculative bubbles" in foreign exchange markets.

The special nature of our cross-market data implies a high hurdle for potential explanations since such an explanation must account for both the systematic behavior within markets and the lack of congruence across markets around open and close. Thus, for example, if the explanation is to be "noise" rather than "news," it appears that London is not affected by noise when New York opens with high volatility; but at London close, the roles are reversed, with London displaying high volatility but New York now immune from any noise affecting London. This appears to be more complicated than is implied by the noise-trading models cited in Frankel and Rose (1994) or by models of learnDavid A. Hsieh and Allan W. Kleidon ing currently applied to foreign exchange markets such as Lewis (1989a, 1989b).

One recent approach that shows promise in this context focuses on imperfect, although rational, information aggregation.15 There are two extreme views on price formation. One assumes that all private information is instantly aggregated and revealed to market participants through prices. The other assumes that price changes are capricious and irrational. One attempt to find a middle ground assumes that prices are formed as some average of these two types of behavior, an approach similar to the noise-trading models cited in Frankel and Rose (1994, 37). The approach of imperfect information aggregation also supplies a middle ground between the extremes, but in a very different way.

It is well known from behavioral laboratory experiments that, under certain conditions, asset prices can be readily generated that display systematic deviations from those predicted by fully revealing rational expectations models.

These deviations display both apparent excess volatility and the characteristics often associated with speculative bubbles. The conditions needed to generate these phenomena in experimental laboratories are revealing: market participants must lack common knowledge about other traders' preferences or beliefs, or there must be insufficient traded instruments to theoretically allow traders to invert from prices to infer information. Significantly, if traders have common knowledge about preferences and beliefs, then the consistent result is that prices quickly converge to the fully revealing rational expectations equilibrium if there are sufficient traded assets given the sources of information uncertainty and if the traders have trading experience in the market.16 While standard information models typically assume common information among market participants about traders' preferences and beliefs, we regard this assumption as unrealistic in many settings, including the foreign exchange market. When traders first begin trading at the open of their local market, a commonly described issue is that they need to get the "feel" of the market at that time.17 The most important elements of this "feel" are the participants in the market at that point in time and what their trading behavior has been in the immediately prior trading period.

Clearly, current prices are not sufficient statistics for these items. Traders attempt to obtain this information by contacting traders who have been trading for some time; for example, New York traders will have contacts in London (not necessarily in the same bank) whom they will call to obtain a sense of the current market. Our interpretation of this phenomenon is consistent with the importance of knowledge about the preferences and beliefs of other traders to allow information aggregation across traders. In the more limited view of an



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