Volatility and Arbitrage
E. Robert Fernholz, Ph.D., Ioannis Karatzas, Ph.D. and Johannes Ruf, Ph.D.
August 23, 2016
At least since Fernholz (2002), it has been known that volatility in a stock market can generate arbitrage, or at least relative arbitrage between a specific portfolio and the market portfolio. However, the questions of exactly what level of volatility is required, and how long it might take, for this arbitrage to be realized, have never been fully answered. Here we hope to shed some light on these questions and come to an understanding about what might represent adequate volatility, and over which time-frame relative arbitrage might be achieved.