Robust Structure Without Predictability: The "Compass Rose" Pattern of The Stock Market

Timothy Falcon Crack and Olivier Ledoit


Plotting daily stock returns against themselves with one day's lag reveals a striking pattern. Evenly spaced lines radiate from the origin; the thickest lines point in the major directions of the compass. This "compass rose" pattern appears in every stock. It is caused by discreteness. However, counter-examples demonstrate that the existence of exchange-imposed tick sizes (e.g. eighths) is neither necessary nor sufficient for the compass rose. The compass rose cannot be used to make abnormal profits: it is structure without predictability. Among other consequences, the compass rose may bias estimation of ARCH models, and tests for chaos.

Journal of Finance, Volume 51, Number 2, June 1996, pages 751-762

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