2.1.1. Spread Benchmarks

We use three spread benchmarks—the quoted spread (*QS*), the effective spread (*ES*), and the realized spread (*RS*). For easier comparison across different countries, we measure the spread as the percentage of the quote midpoint for all the three spread measures. As discussed in detail below, the three spread measures distinctly represent the different aspects of transaction costs.

The quoted spread at time *t* is calculated as follows, as the difference between the ask quote and the bid quote at time *t*, divided by the average of the two quotes.

$$QS\_{l} = (a\_{l} - b\_{l}) / m\_{i\prime}$$

where *at* and *bt* are the posted ask price and bid price, respectively at time *t*, and *mt* is the quote midpoint, or the mean of *at* and *bt*.

The quoted spread measures the pre-trade transaction costs. Even when the quoted spread provides important information about transaction costs, it is not necessarily translated into actual transaction costs. For example, in a quote driven market, where market makers intervene in the trading process, transactions are frequently made within the bid and ask price. Even in an order driven market where most trades take place either at the ask or bid price, traders who are wary of transaction costs will avoid trading on a wide bid-ask spread, waiting until the spread narrows sufficiently. This implies that the transaction costs that investors actually bear could be different from the quoted spread.

Thus, the actual transaction costs that are borne by investors are measured better using the effective spread. The effective spread is defined as the absolute value of the difference between the transaction price and the midpoint of the quotes prevailing at the time of the transaction, divided by the midpoint quote. The round-trip effective spread conditional on a trade that takes place at time *t* is:

$$ES\_t = 2D\_t(p\_t - m\_t)/m\_{tr}$$

where *pt* is the transaction price at time *t*, and *Dt* is an indicator variable that equals one for customer buy orders, and negative one for customer sell orders.

Our third spread benchmark is the realized spread. The realized spread matches the price of a trade with its post-trade true value. More specifically, it is the effective spread net of the price impact of a trade. We calculate the percentage realized spread as:

$$RS\_t = 2D\_t(p\_t - m\_{t+\tau})/m\_{t\prime}$$

where *mt*+*τ* is the midpoint of the bid and ask quotes recorded *τ* minutes after transaction time *t*. *τ* is between 5 and 15 min after the trade. The quote midpoint serves as a proxy for the true economic value of the stock after the trade. This spread measure can be interpreted as compensation to the liquidity providers. In other words, it is the price that the liquidity consumers pay to liquidity providers for their immediacy of consumption.
