Scaling of impact parameters under execution-horizon rescaling

Determine how the temporary impact coefficient and the permanent impact (alpha‑decay) parameter should scale when the actual execution horizon is compressed or dilated while total traded quantity remains fixed, within the Almgren–Chriss-style impact model used in the paper. In particular, assess whether scaling the temporary impact coefficient in direct proportion to the increase in average trading rate (e.g., by a factor of ten when compressing a 20‑day program to 2 days) is correct, and characterize how the alpha‑decay parameter expands or contracts as the trading duration shortens or lengthens so that normalized implementation cost predictions remain valid across horizons.

Background

The paper normalizes both time and total quantity to unity to simplify the analysis of competitive execution and derivation of Nash equilibria. While mathematically convenient, this erases differences between practical scenarios such as executing the same total quantity over 20 days versus 2 days, which would materially change average trading rates and hence temporary impact.

The author discusses a heuristic where the temporary impact coefficient might scale proportionally with the compression of the horizon (e.g., 10x higher average rate implying 10x higher temporary impact sensitivity), but notes uncertainty about whether this scaling is correct and how permanent impact (alpha-decay) should adjust under shorter horizons, given competing effects of reduced time for information leakage versus higher trading intensity per unit time.