TABLE 5.14 Average spreads.

Geometric average of the relative spread for each day of the week (including weekends) for the USD against DEM, JPY, CHF, and GBP and XAU (gold) against USD; for the period from January I, 1987, to December 31, 1993. The relative spread figures have to be multiplied by 1( 4.

Miiller and Sgier (1992) analyze in detail the statistical behavior of the quoted spread. Here we shall present their main conclusions. First, it is important to remember that all the statistical analyses are dominated by one property of quoted FX spreads, which is the discontinuity of quoted values (see Section 5.2.2). This data set contains price quotes rather than traded prices. The banks that issue these price quotes are facing the following constraints:

Granularity: FX prices are usually quoted with five digits-that is, 1.6755 (USD-DEM) or 105.21 (USD-JPY). The lowest digit sets the granularity and thus the unit basis points.

Quoted spreads are wider than traded spreads as they include "safety margins" on both sides of the real spread negotiated in simultaneous real transactions. These margins allow the FX dealers, when called by a customer during the lifetime of the quote, to make a fine adjustment of the bid and ask prices within the range given by the wide quoted spread. They can thus react to the most recent market developments.

FX dealers often have biased intentions: while one of the prices, bid or ask, is carefully chosen to attract a deal in the desired direction, the other price is made unattractive by increasing the spread.

Because quoted spreads are wider than traded spreads, they do not need the high precision required in the direct negotiation with the customer on the phone. Hence, there is a tendency to publish formal, "even" values of quoted spreads as discussed in Section 5.2.2.

The strong preference for a few formal spread values, mainly 5 and 10 basis points, clearly affects every statistical analysis.

The results are shown in the middle histograms of Figure 5.12 and in Table 5.14. The general behavior of spreads is opposite to those of volatility and tick frequency. Spreads are high when activity is low, as already noticed by

0.0000 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 -9.0 -8.0 -7.0 -6.0 -5.0

Relative Spread Log(Relative Spread)

FIGURE 5.15 Cumulative distributions of relative spreads (left) and logarithm of the relative spread (right) shown against the Gaussian probability on the y-axis. The distribution is computed from a time series of linearly interpolated spread sampled every 10 min for USD-DEM. The sample runs from March 1, 1986, to March 1, 1991.

Glassman (1987). FX spreads on Saturdays and Sundays can have double and more the size of those on weekdays and, as in Table 5.12, Sundays differ slightly less from working days than Saturdays. Sunday in GMT also covers the early morning of Monday in East Asian time zones. Unlike the volatilities, the average FX spreads exhibit a clear weekend effect in the sense that the Friday figures are higher, though still much lower than those of Saturday and Sunday. The spreads of gold vary less strongly, but they have double the size of the FX spreads on working days. The FX rate with the smallest spreads, USD-DEM, was the most traded one according to all the BIS studies (until it was replaced by EUR-USD in 1999). The histograms in Figure 5.12 have intraday patterns that are less distinct than those of volatility, but still characteristic. We analyze their correlations with both the volatilities and the numbers of quoted ticks. All the correlation coefficients on the second line of Table 5.13 and most of them on the third line are negative, as one would expect. The FX rates have different spread patterns. For USD-CHF, for instance, there is a general spread increase during the European afternoon when the center of market activity shifts from Europe to America, while the USD-JPY spreads decrease on average at the same daytime. This indicates that American traders are less interested in Swiss Francs and more in Japanese Yens than other traders. Hartmann (1998) uses the spreads to study the role of the German Mark and the Japanese Yen as "vehicle currencies," as compared to the USD.

An analysis of the empirical cumulative distribution function of the relative spread s is shown in the left graph of Figure 5.15 for USD-DEM and for In s in the

right graph of Figure 5.15. The resulting cumulative distribution functions have the following properties:

1. They are not Gaussian, but convex (s strongly, Ins slightly), indicating a positive skewness and leptokurticity (of the tail on the positive side).

2. They look like a staircase with smooth corners. For the nominal spread in basis point, saom, we would expect a staircase with sharp corners, the vertical parts of the staircase function indicating the preferred "even" values such as 10 basis points. Although s is a relative spread .«nom/Pbid), where the bid price fluctuates over the 5-year sample, and although we use linear interpolation in the time series construction (see Section 3.2.1), the preferred even" 5r)om values are still visible.