Quantifying stock-price response to demand fluctuations

We empirically address the question of how stock prices respond to changes in demand. We quantify the relations between price change G over a time interval $\Delta t$ and two different measures of demand fluctuations: (a) $\Phi ,$ defined as the difference between the number of buyer-initiated and seller-initiated trades, and (b) Ω, defined as the difference in number of shares traded in buyer- and seller-initiated trades. We find that the conditional expectation functions of price change for a given Φ or Ω, $〈G{〉}_{\Phi }$ and $〈G{〉}_{\Omega }$ (“market impact function”), display concave functional forms that seem universal for all stocks. For small Ω, we find a power-law behavior $〈G{〉}_{\Omega }\sim {\Omega }^{1/8}$ with δ depending on $\Delta t$ $(\delta \approx 3$ for $\Delta t=5\mathrm{}$ min, $\delta \approx 3/2$ for $\Delta t=15\mathrm{}$ min and $\delta \approx 1$ for large $\Delta t).\mathrm{}$ We find that large price fluctuations occur when demand is very small—a fact that is reminiscent of large fluctuations that occur at critical points in spin systems, where the divergent nature of the response function leads to large fluctuations.