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5 THE TRADITIONAL BROKERS: WHAT ARE THEIR CHANCES IN THE FOREX? 209 the broker could still be useful as a provider of information for those periods. The broker has superior information because he observes a large part of the total order flow and is particularly attentive to all news that may influence the market. This ability works like an anticipated observation of the realisation of V. Nevertheless, the broker may err. There is noise in the anticipated observation of the realisation of V. On one hand, the broker does not observe the complete order flow in the market. On the other hand, it may not interpret correctly the consequences of a piece of news. Therefore, it may happen that the broker signals a V when the true value turns out to be V, or vice versa. If the broker is mistaken, whoever follows its advice loses. The probability that the broker is mistaken is ρ. 3 The cost of trading through the broker is c. 4 c must be less than V E( V) and less than EV ( ) V. When a dealer decides whether to use the broker s services, he must take into account the possibility of meeting and trading with another dealer that has received the same information, next period. γ is the probability that the dealer he will be trying to trade with next time has also used the broker s services. Dealers trade only for speculative reasons. They must be convinced they are going to profit from the trade. They are not forced to trade by any liquidity motive. Consequently, when the dealers value the currency in the same way, no transaction takes place. The expected value of the profit made with a transaction when a dealer uses the broker s services is: ( ) ( π ) 0.5 ( 1 ρ) γ ( ) 0.5 ( 1 ρ) ( 1 γ) ( ) E B = c + V E V c + ( ) ( ) ( ) ( ) 0.5 ργ c ρ 1 γ V + E V c + ( c) ( ) ( V E( V) c) 0.5 ργ ρ 1 γ + ( ρ) γ ( c) + ( ρ) ( γ) ( V + E( V) c) (1) 3 In an efficient market, the broker would have a probability of being mistaken of 0.5, since there is no such thing as superior information, and V may take two values with equal probability. In that case, the services of the brokers would not be informationally valuable. 4 c is the broker s receipt. As pointed out by the referee, this model discusses only the

6 210 JOURNAL OF APPLIED ECONOMICS Note that for simplicity we only include the second period trade (with another dealer) and the first period cost of trading through the broker. The expected value of the first period trade is not included because it is not affected by the acquisition of information. The expected value of the profit made with a transaction when a dealer does not use the broker s services is: ( ) ( ) ( ) Zeros are left in the expression to stress that the number of possible outcomes is the same in the two situations: using or not using the broker s services. In the second case, four of those outcomes are zero. Also, and as before, the expected value of the first period trade is not included because it is not affected by the acquisition of information. We now have that: ( π ) ( π ) E B > E N ( ) ( ( )) E π N = ρ γ V + E V ρ γ V E V + ( EV ( ) V) ( ) ( V EV ( )) ργ ρ γ + 0 c+ ( 0.5 ρ) ( 1 γ) ( V V) > γ ( V V) ( ρ 0.5) ( ) ρ < 0.5 c/ V V (3) It is profitable for the dealer to use the broker s services if and only if the probability of receiving a wrong signal is less than 0.5 c/ ( V V), which is obviously less than 0.5. The credibility of the broker must be larger the larger the value it charges for its services, proportionally to the potential profits. Particularly, when the broker is never mistaken, the condition for trading through the broker is c< 0.5 ( V V), which is equivalent to demanding that the broker does not charge more for its services than the dealer may expect to profit from the hinted transaction. (2) demand for brokerage services. In some other financial markets, depending on the value of c, the broker could use the superior information to its own profit. However, in the foreign exchange market this complexity does not arise, since no dual trading is allowed.

7 THE TRADITIONAL BROKERS: WHAT ARE THEIR CHANCES IN THE FOREX? 211 If the condition for deciding to use the broker s services is verified for all dealers at the same time, then no one profits from the information for no one is willing to trade. 5 To avoid this problem we may assume that dealers are heterogeneous. For instance, the parameter ρ may be a subjective one, varying from dealer to dealer, depending on the history of the results they have obtained with previous information received from the broker. Alternatively, we may add dealers that trade for liquidity motives. We could introduce new features that would make the framework closer to reality. For instance, we could endogenize the broker s credibility. However, the simple expression (3) we arrived at is enough to show our point. That expression indicates that the larger the price dispersion, ( V V), the larger the probability of a client deciding to use the broker s services with the purpose of obtaining superior information. This is the main implication of the analysis. The intuition is plain. ( V V) is a simple form of expressing the volatility of the security price, since it is the amount of its possible variation. The larger the possible variation of the exchange rate, the larger the incentive to use the broker s services because the larger the potential gain obtained with the information received from the broker. Therefore, we should expect that if a dealer attaches great importance to the broker s ability to transmit information, he will increase his use of the broker s services when volatility is higher. B. The Econometric Model The structure presented in Section II.A suggests that we search for a relation 5 This resembles the situation present in Grossman and Stiglitz (1980): their paper also analyses the conditions for demanding information when it costs c and there is some probability of the information being wrong. The price of a risky asset is a result of supply and demand. The demand for the risky asset depends on the information obtained about the return of the risky asset and on the price. The supply is a random variable. Grossman and Stiglitz conclude that if the variance of supply is small, the equilibrium price reveals most of the information acquired by those who decided to pay for it. Therefore, the observation of the equilibrium price is almost equivalent to the observation of the information and it is not very interesting to pay for this. In an efficient market, where the price reveals all the information, there is no possible equilibrium, because if the price has all the information, no one is interested in paying for it; but if no one acquires the information, it cannot be incorporated in the price. Several ways of overcoming this problem are possible.

8 212 JOURNAL OF APPLIED ECONOMICS between the use of the traditional broker s services and the level of volatility. The hypothesis we want to test is: There is a significant positive relation between the use of the traditional broker s services and exchange rate variability. If this hypothesis is confirmed, then we will conclude that the traditional broker is highly valued as an information provider having, therefore, a large probability of survival. Otherwise, we will conclude that the traditional broker is not much valued as an information provider, and as that is its main advantage compared to the electronic broker, its probability of survival will be reduced. Since we want to investigate how a qualitative variable responds to another variable, and the qualitative variable takes only two values one if the transaction was made through the broker and zero otherwise the probit is the appropriate econometric model. In estimating the model, we considered the possibility that the volatility acts on the dealer s decision with some lag. We assumed that if there is any influence, it should have been noted after three periods. We use transaction time: each period corresponds to one transaction. Although we want to focus on the relationship between the traditional broker s services and the level of volatility, the introduction of two other variables in the set of explanatory variables improves the general quality of the model. The two mentioned variables are the transaction value and a dummy variable indicating whether the transaction was a dealer s sale or a dealer s purchase. The inclusion of the days of the week was also tried but did not improve the quality of the model. The empirical findings are similar to the ones with only current and lagged values of exchange rate variability as explanatory variables. The estimated model is the following: broker t = 1 0 * if br > 0 t * if br 0 t (4) br = α + α P + α P + α P + α P + αν + α ty + ε (5) * t 0 1 t 2 t 1 3 t 2 4 t t broker is a dummy variable that takes the value one when the current transaction is made through the traditional broker, and which is zero * otherwise. br in the talent variable. P t t is the absolute value of the price

9 THE TRADITIONAL BROKERS: WHAT ARE THEIR CHANCES IN THE FOREX? 213 variation between the previous and the current periods. P refers to the Deutsche mark-portuguese escudo foreign exchange rate.ν is the current transaction value. ty is the dummy variable that expresses the type of the previous transaction. It is 1 when the transaction is a purchase from our dealer s point of view and it is -1 when the transaction is a sale from our dealer s point of view. ε t is assumed to have a normal distribution with zero mean. If the hypothesis stated above is correct, we should find some of the α i (i=1,...,4) statistically significant and positive. To test the relationship, we used a database with the transactions of one of the most important dealers/ banks in the Portuguese foreign exchange market. The database is presented in Appendix 2. III. The Results The estimation results, presented in Table 1, show a weak relationship between volatility and the decision to use a traditional broker s services. The absolute price variation of the last two transactions seems to have little importance in the choice of the counterpart. Although α 3 is highly significant, its sign is negative, which is against what we expected to find in case volatility induced a demand for the traditional broker s services in the short term. The high significance of α 5 is in line with the statistics shown in Table 5 of the Appendix 2. These statistics reveal that the average value of transactions made through the electronic broker is about three times larger than the average value of transactions made through the traditional broker. The Kullback-Leibler R 2 does not give evidence of a good fit of the model, either. It is, however, the best model that we could test given the available data that relates the use of the traditional broker s services and exchange rate variability. The scoren statistics test the null hypothesis of no serial correlation of order n and show no evidence of serial autocorrelation at either of the considered lags. The likelihood ratio test1 compares the loglikelihood of the presented model with the one of a model with only a constant term. The null hypothesis is that all coefficients, except for the constant term, are zero. The introduction of the variables significantly improves the model. The likelihood ratio test2 tests the null hypothesis of homoscedasticity against

10 214 JOURNAL OF APPLIED ECONOMICS Table 1. Estimation Results Parameter Estimated value t-statistic P-value α α α α α α E α Log-likelihood Kullback-Leibler R scorel score score score Likelihood ratio test Likelihood ratio test Normality test Note: The test scoren tests the existence of autocorrelation of order n, mainly as a result of 2 the omission of lags in the endogenous variable. They have χ1 distributions. The likelihood 2 ratio test 1 tests H0: α 1 = α 2 = α 3 = α 4 = α 5 = α 6 = 0. It has a χ6 distribution. The likelihood ratio test 2 tests the null of homoscedasticity against heteroscedasticity where the variance is a function of the current absolute variation of the price, of the absolute variation of the price lagged one period and of the dummy variable indicating the type of transaction. It has 2 a χ3 distribution. The normality test is a LM test for probits that tests the normality of the residuals. It has a χ distribution. More details can be found in Murphy (1994). 2 2 heteroscedasticity where the variance is a function of several of the explanatory variables of the model. It does not signal heteroscedasticity. A test for normality of the residuals was introduced. It is a LM test for probits. The null hypothesis of normality is not rejected.

13 THE TRADITIONAL BROKERS: WHAT ARE THEIR CHANCES IN THE FOREX? 217 Appendix 2. The Transactions Database Our transactions database was provided by the most important dealer acting in the Portuguese foreign exchange market. The data set consists of 416 observations of the following variables: operation type (purchase or sale), transaction price (Portuguese escudo/deutsche mark exchange rate), transaction volume in PTE and in DEM, type of counterpart (traditional broker, electronic broker, dealer or customer), transaction day of occurrence. The data were collected between 2 January 1998 and 30 March Some statistics are presented in order to characterize the dealer. Table 2 gives information about transactions volume. During the sample period, this dealer had, in the spot market, a total transactions volume of 1,569,076,331 DEM. That corresponds to 160,639,560,000 PTE. The average quantity dealt was 3,771,818 DEM. The median transaction was 2,000,000 DEM. The largest transaction was 102,400,000 DEM, and it occurred on 13 February This large transaction was a dealer s purchase made through an electronic broker. The smallest transactions were 1,361 DEM. There were two such transactions: two sales from clients to the dealer, both on 17 February Table 2. Transactions Volume Transactions volume (DEM) Total volume 1,569,076,331 Average volume 3,771,818 Median volume 2,000,000 Maximum volume 102,400,000 Minimum volume 1,361 Standard deviation 7,079,685 Table 3 shows that there were more sales from the dealer than purchases, though the correspondent volumes were quite similar, which means that the average purchase quantity was larger than the average sale quantity.

14 218 JOURNAL OF APPLIED ECONOMICS Table 3. Number and Value of Total Transactions Dealer s purchases Dealer s sales Number of transactions 181 (43.5%) 235 (56.5%) Total value (DEM) 802,048,340 (51%) 767,027,991 (49%) Average value (DEM) 4,431,206 3,263,949 Average value (PTE) 453,682, ,140,410 As may be confirmed in Table 4, during the sample period, the maximum number of transactions made by this dealer was 37, on 28 January On two days there were no transactions: on 9 January and on 21 January. Taking into account the two days without transactions, the daily average number of transactions was 7. The daily median was 6 transactions. Table 4. Number of Daily Transactions Average (taking into account the two days without transactions) 7.05 Median 6 Maximum 37 Minimum 0 Standard deviation 6.54 As reported in Table 5, this dealer clearly prefers to trade through the electronic broker. He uses the electronic broker in 77 % of all his transactions. This corresponds to 92% of the value of transactions. The average value of the transactions made through the Dealing is considerably superior to the average value of the transactions made otherwise.

16 220 JOURNAL OF APPLIED ECONOMICS Hartmann, P., Manna, M., and A. Manzanares (2001), The Microstructure of the Euro Money Market, Working Paper 80, European Central Bank. Madhavan, A. (1996), Security Prices and Market Transparency, Journal of Financial Intermediation 5: McCloskey, D. and A. Klamer (1995), One Quarter of GDP is Persuasion, American Economic Review 85: Murphy, A. (1994), A Simple Artificial Regression Based Lagrange Multiplier Test of Normality in the Probit Model, WP 94/22, Department of Economics, University College Dublin.

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