Quantifying fluctuations in market liquidity: Analysis of the bid-ask spread

Quantifying the statistical features of the bid-ask spread offers the possibility of understanding some aspects of market liquidity. Using quote data for the 116 most frequently traded stocks on the New York Stock Exchange over the two-year period 1994–1995, we analyze the fluctuations of the average bid-ask spread S over a time interval Δt. We find that S is characterized by a distribution that decays as a power law P{S>x}∼x^−ζ_S, with an exponent ζ_S≈3 for all 116 stocks analyzed. Our analysis of the autocorrelation function of S shows long-range power-law correlations, ⟨S(t)S(t+τ)⟩∼τ^−μ_s, similar to those previously found for the volatility. We next examine the relationship between the bid-ask spread and the volume Q, and find that S∼ln Q; we find that a similar logarithmic relationship holds between the transaction-level bid-ask spread and the trade size. We then study the relationship between S and other indicators of market liquidity such as the frequency of trades N and the frequency of quote updates U, and find S∼ln N and S∼ln U. Lastly, we show that the bid-ask spread and the volatility are also related logarithmically.