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Quantitative Finance · Glossary

What is Effective number of venues?

Definition 11.5 Markets I: The Ecosystem and Exchange-Traded Markets · Chapter 11 — European Equity Market Structure

If venues have market shares s1,…,sns_1,\dots,s_n summing to one, the Herfindahl index is H=∑isi2H = \sum_i s_i^2 and the effective number of venues is 1/H1/H: the number of equal-sized venues that would produce the same concentration.

Effective number of venues when one venue has the share on the horizontal axis and five others split the rest equally. Six venues are “six” only when the leader is down to a sixth of the market. Data: computed by the chapter’s script.
Figure 11.2. Effective number of venues when one venue has the share on the horizontal axis and five others split the rest equally. Six venues are “six” only when the leader is down to a sixth of the market. Data: computed by the chapter’s script.

Examples

Example 11.6 (Fragmented, but how much?)

A stock trades 60% on its primary exchange, 20% on one platform and 10% on each of two others. H=0.36+0.04+0.01+0.01=0.42H = 0.36 + 0.04 + 0.01 + 0.01 = 0.42: an effective 2.4 venues, although there are four. If the primary’s share falls to 40% and the others take 20% each, H=0.28H = 0.28 and the effective number is 3.6. The measure moves mostly with the leader’s share (Figure 11.2).

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