A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market

Motivation(s)

In an informationally efficient market with zero trading costs, the observed market price contains all the relevant information. A price change will only occur if and only if unanticipated information is received by market participants.

In the current market, transaction costs have a strong influence on the net gains to investments and market equilibrium returns. The most accurate measure of trading costs is the monthly statement of an account. The alternative measures are subject to considerable error because of hard-to-quantify factors such as commissions, transaction size, and discounts. This issue worsens when the desired measurement is the bid-ask spread, a small region of price which brackets the underlying value of the asset.

The bid-ask spread is often of interest because it is part of the compensation package for the market maker. Furthermore, empirical studies have shown that negative serial dependence in observed price changes should be anticipated when a market maker is involved in transactions.

Proposed Solution(s)

The author uses the first-order serial covariance of price changes to infer the effective bid-ask spread. The implicit percentage spread is given by

\[s_j = 200 \sqrt{-\mathrm{Cov}_j}\]

where \(s_j\) is the spread and \(\mathrm{Cov}_j\) is the serial covariance of returns for asset \(j\).

This method assumes

  • The asset is traded in an informationally efficient market.

  • The probability distribution of observed price changes is stationary (at least for short monthly intervals).

If the markets are efficient, the covariance between successive price changes cannot be due to news, whereas the variance of observed price changes is likely to be dominated by news.

Evaluation(s)

The author proved that under an efficient market:

  • the covariance between successive price changes cannot be due to new information,

  • the implicit spread measure is independent of the observation interval, and

  • even if the spread changes in reaction to news, the serial covariance will still be \(\frac{-s^2}{4}\) where \(s^2\) is the average squared spread in the sample.

The author estimated the annual trading costs from daily and weekly returns of stocks listed on the New York and American Exchanges. The results were validated indirectly by relating the measured implicit spread to firm size. Since firm size is positively related to volume, and volume is negatively related to spread, there should exist a strong negative cross-sectional relation between measured spread and measured size.

The resulting estimates indicate a strong negative relation to firm size. However, a statistically significant difference was detected between spreads estimated from daily and weekly data, which implies informational inefficiency or very short-term nonstationarity in expected returns.

Future Direction(s)

  • In the current era where social media is everywhere, how to determine if the market informationally efficient?

Question(s)

  • Has there been any cases where the market maker abused their information to trade?

Analysis

In an efficient market, one can impose simplifying assumptions to derive a closed form measure using empirical estimates. One such example is the bid-ask: it is proven and shown empirically to be closely related to firm size.

Unfortunately, it is not obvious to what extent those assumptions hold for the real market. The author did not validate the results using real bid-ask spread data, so the method’s accuracy is questionable. Nonetheless, the theoretical insights of the proposal model is quite interesting and warrant further investigations.

References

Rol84

Richard Roll. A simple implicit measure of the effective bid-ask spread in an efficient market. The Journal of Finance, 39(4):1127–1139, 1984.