Discrete Stock Prices and Predictability

Crack and Ledoit (1996) discover the compass rose of stock returns, generated by discrete stock prices and additional assumptions concerning the level and variation of stock prices. They raise the question, whether this phenomenon does introduce predictable structures in stock returns. In particular, opportunities to earn abnormal profits are barely expected to arise. In this paper we investigate this point further, and prove, that the compass rose in fact introduces reversal patterns into the process of returns. Numerical simulations are conducted to illustrate this result. Moreover, observed intraday stock market data reveals predictable structure which is consistent with the analytical results.