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Inferring the Components of the Bid-Ask Spread: Theory and Empirical Tests

Hans Stoll

JF March 1989

Executive Summary:

This paper examines the components of the Bid-Ask Spread . The three main components are modeled as adverse information costs, order processing costs, and inventory costs. Empirically adverse information costs and order processing costs appear to be more important than inventory costs.

Quoted Bid-Ask Spread = difference of ask-bid

Realized Bid-Ask Spread = average difference of Bid and Ask at different times

This fairly long paper looks at the three cost components and tries to determine which is(are) influencing the spread through both modeling and empirical research.

Market maker sets spread to cover three costs:

1. Order processing costs-(See Demsetz 1968 and Tinic 1972)
2. Inventory holding costs-(See Stoll 1978, Ho and Stoll 1981 , and Amihud and Mendelson 1980)
3. Adverse information costs-(See Copeland and Galai, Easley and Ohara, and Seyhun 1986)

Previous "empirical studies have shown that the quoted spread is related to characteristics of securities such as the volume of trading, the stock price, the number of market makers, the risk of the security, and other factors. However, these results are roughly consistent with several theories…and do not give much insight into the evolution of the spread over time or the relative importance of the cost components of the quoted spread."

• If the main component of the Bid-Ask Spread is order processing costs and if no new information is made available, then the Bid-Ask Spread will straddle the "true price" such that the bid will be slightly below true price and the ask will be slightly above.
• If the main cost of inventory holding cost then the spread will move as a function of the inventory that the market maker is holding. (I.e. if the dealer is holding stock, the Bid-Ask Spread will be lowered below the true price so that the dealer can lower inventory.)
• If adverse information costs are driving the Bid-Ask Spread, then the shift in spread will look the same as if it is inventory holding costs, but the reason for the shift in spread will be adverse information costs not inventory holding costs. (I.e. if you buy from an insider, it suggests the price will be falling so you lower your prices to reflect this new information.)

These can be tested by looking at changes the spread following transactions. "Under a pure order processing view…,prices simply move between the bid and the ask, and the price reversal is equal to the spread." Under the pure adverse information view…, the spread is determined by the probability that traders with adverse information will trade with the dealer….the price reversal is only half of the spread." Under this theory the Bid-Ask Spread is set such that the probability of a reversing trade is 50%. "Under the pure inventory holding cost view of the spread the price reversal is half the magnitude of the spread. However, the equilibrium price does not change on the basis of the trades" but rather to modify the probability of a transaction in one way or the other so that the probability of a reversal is greater than 50%.

Data: Approximately 800 stocks with NASDAQ data for October-December 1984. Two covariances are estimated based first on closing prices and then on intraday prices.

Two serial covariances are examined based on intraday as well as closing values.

Empirical findings:

All tests showed there was a negative covariance on intraday transactions. (ie price likely to go back and forth).

There is some support for the inventory holding cost model in that there appears to be a greater than 50% chance of reversal, but this in the author's words is "very weak" support.

Using conditional expectations, a realized spread is derived

2(probability of reversal-d )= realized spread

where d is from

(1-d )Spread = the size of the reversal conditioned on a reversal

Empirically the probability of a reversal is 55% and d is 26.5% so the average realized spread is thus .57S, which allows the decomposition of the spread. This is done and the author finds:

Order Costs = .47S

Adverse Information Costs = .43S

Holding Costs = .10S

The author later finds support for view that the more market makers the lower the spread, but this is problematic in that it is highly correlated with other variables (example size, volume) and the influence is quite small.

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