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R ebalancing is an important tool for managing a portfolio. It keeps the portfolio close to the investor's desired weights and ensures that concentrations are not allowed to build up. Rebalancing can also be a source of return--the act of maintaining constant weights generates a buy-low, sell-high trading pattern that is designed to harvest extra return from the volatility of the underlying assets. Of course, there is also the risk that this type of strategy will underperform over a particular period as a result of differences in the growth rates of the assets. For example, a portfolio rebalanced to constant sector weights during the 1990s would have underperformed a buy-and-hold portfolio. By controlling the weight of technology stocks over the course of the decade, a rebalancing portfolio would have benefited less from the extraordinary performance of those stocks in 1998 and 1999. Yet over longer periods, rebalancing portfolios appear to have a higher growth rate.
In this article, we explore the theory behind the concept ofvolatility harvesting , with a focus on quantifying both the potential long-term performance advantage and the risk of underperforming in the short term. We derive a formula that decomposes the excess returns of a portfolio strategy versus the market into three terms: avolatility return , adispersion return , and adrift return . This formula is an extension of the energy-entropy decomposition of Pal and Wong [2013]. We adopt some of the naming conventions of Hallerbach [2014] to help bridge the language barrier between the mathematical and mainstream finance literatures. This approach represents a new way of thinking about the benchmark-relative risks involved with rebalancing.
Our volatility-harvesting formula is an improvement over earlier attempts to render this idea in a mathematically precise manner. First, the formula can be generalized to any portfolio strategy, whereas previous approaches were limited to only constant-weight and functionally generated portfolios. 1 Second, the formula does not require stochastic modeling assumptions: There is no need to assume that stocks follow a random walk with constant covariances. Using a discrete-time framework avoids the technicalities of stochastic calculus and allows us to calculate the components of return precisely by observing stock prices. As a result, the main ideas are easier to understand. Finally, the...