Demystifying Rebalancing Premium and Extending Portfolio Theory in the Process

Volatility is usually considered as a synonym for risk. Mainstream financial theory states that higher portfolio volatility is translated into higher expected returns while diversification helps eliminate idiosyncratic risks. This leaves us with an apparent anomaly as low-risk (low-beta) stocks over-perform high-risk (high-beta) stocks over the long term. Is this really an anomaly? What about high conviction investing? Should we dismiss stock-picking as a futile exercise even if such an approach is used by one of the most successful investors of our times? In this paper we answer these questions and propose a framework that encompasses various investment styles and portfolio construction methodologies.Modern Portfolio Theory is a one period approach relating expected returns and volatilities as two independent variables estimated from ensemble averages. Here we focus on a multi-period setting, which is more relevant for the task of maximising investor's wealth in the long run. Contrary to previous studies based on maximising log returns, we find no contradictions with the results of modern portfolio theory. We show that Markowitz portfolios and Warren Buffett's investment style are valid special cases of optimal growth portfolios. In addition, we provide insights on rebalancing bonus, showing how and when it is possible to add value from volatility in active portfolio management. As fire can be either dangerous, if uncontrolled, or useful to run a mechanical engine if controlled, in the very same way it should be possible to put volatility to work in a controlled manner in order to produce growth