Agent-specific impact of single trades in financial markets

We present an analysis of the price impact associated with single trades effected by different financial firms. Using data from the Spanish Stock Market, we find a high degree of heterogeneity across different market members, both in the instantaneous impact functions and in the time-dependent market response to trades by individual members. This heterogeneity is statistically incompatible with the existence of market-wide universal impact dynamics that apply uniformly to all trades and suggest that, rather, market dynamics emerge from the complex interaction of different behaviors of market participants. Several possible reasons for this are discussed, along with potential extensions one may consider to increase the range of applicability of existing models of market impact.

Figure 1

Instantaneous price impact as a function of the volume (in euros) of the market order. Black circles show the result for the whole-market impact function for TEF (taking account of all data from 2001 to 2004) and can be fitted to the power law $\Delta \sim V^{\alpha }$ with $\alpha =0.25\pm 0.01$ (dashed line indicates this exponent). The remaining curves show the instantaneous price impact functions $I_i/\tilde{s}$ for four different firms. The dotted lines indicate the values of $V_0$ and ${\Delta }_0$ (see text).

Figure 2

The left-hand panel shows the exponents ${\alpha }_i$ for the different firms $i$ as a function of their market participation ratio ${\pi }_i$. The solid (red online) line is ${\alpha }_M$; the gray area indicates one standard deviation from that value, as obtained by shuffling firm codes in the database (see text for details). The dashed line is the weighted average $\overline{\alpha }$ of ${\alpha }_i$. The right-hand panel shows the relationship between the parameters ${\alpha }_i$ and $c_i$ (see text). The solid line corresponds to the prediction of $c_i{V}_0^{{\alpha }_i}={\Delta }_0$, with ${\Delta }_0=40$ basis points (bps) and $V_0=60000$ euros.

Figure 3

Individual normalized distribution of volumes per order $P_i(V/\langle V_i\rangle )$ for each agent in TEF (gray lines). Open symbols identify the agents depicted in Fig. 1, and black circles are the result for the whole market. The result of fitting the distribution of $V/\langle V_i\rangle$ from all data sets together to the functional form in $\mathcal{P}\left(x\right)=a/{(b+x)}^{\gamma }$ with $\gamma =2.95$ is shown in the inset.

Figure 4

The average impact of each trader plotted against their average traded volume for all data sets (black circles). To allow better comparison between data sets the values obtained for each trader are scaled by the average values for their stock. The dashed line is a power-law fit to the data with an exponent of $0.68\pm 0.05$. The inset demonstrates the validity of Eq. (6).

Figure 5

(a) Response function $\mathcal{R}\left(l\right)$ for the market (black line) and a set of different firms (color lines with open symbols) for TEF. Gray shaded area is one standard deviation around the average value obtained from shuffled data. Dashed line is the weighted average ${\sum }_i{\pi }_i{\mathcal{R}}_i\left(l\right)$. (b) Correlation function of sign of the orders for the market and a set of different firms. Color codes, symbols, and line types correspond to those in (a). The inset shows the fit of $C_M\left(l\right)$ (solid line) to the power law $C_M\left(l\right)\sim l^{-0.21}$ (dashed line).

Figure 6

$G_0\left(l\right)$ calculated from inverting Eq. (14) (solid line) and a fit to the form given in Eq. (15) over the first 2000 points (dashed line). Data are from TEF. The parameters of the fit are ${\Gamma }_0=3.5\pm 0.03$, $l_0=21.3\pm 0.3$, and $\beta =0.375\pm 0.001$.

Figure 7

(a) ${\kappa }_i$ as defined in the main text as a function of the area of the correlation function for the real ${\Delta }_i\left(l\right)$ (black circles) and for the reconstructed response functions using Eq. (16) (red squares). (b) The average instantaneous market impact as a function of the area of the correlation function for different firms and stocks.