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If you are confident that you understand the benefits of rebalancing, read this post to test your intuition. Confronting these intuitions is, I believe, the only way to really understand the rebalancing problem.  As in a previous post, I assume there are two stocks. The first stock is taken as the numeraire so that its price is constant. The second stock is quoted in terms of the first one, with and its relative  price is  \(p\). Alternatively, one can see this as a universe with cash (paying zero interest rate) and a risky asset with price \(p\). I assume the price is initialized at \(1\). I consider two policies. The first one continuously rebalances so that the weight of the portfolio on the risky asset is \(50\%\). The second one starts with a weight of \(50\%\) on the risky asset but never rebalances. Both strategies are funded with one dollar at inception. I then look at the relative pay-off \(R\) of the two strategies, i.e. long the rebalanced portfolio, short the buy-and-hold portfolio.  # Price cycles  **Assuming the risky asset/second stock experiences a cycle, i.e. its price movessmoothly  from \(1\) to \(p_{max}\) and then back to \(1\). What is the relative return \(R\)?** **Proposed answer and intuition**: Both portfolios make the same return. Indeed, the rebalanced strategy is short the risky asset on the way up and this leads it to underperform. But symmetrically, it is long the risky asset on the way down. This leads it to outperform. This outperformance matches the initial underperformance. and the net result is zero.  # Price divergence  **Assuming the risky asset/second driftssmoothly  away from \(1\) to end at \(p_{end} \neq 1\). What is the relative return \(R\)?** **Proposed answer and intuition**: Assume \(p_{end} > 1\). The rebalanced portfolio is underweight (vis-à-vis the buy-and-hold portfolio) the risky asset which in the end outperforms. Thus the rebalanced portfolio underperforms along such trajectories.    # Tentative conclusion  If the intuition above is correct, the pay-off of the relative strategy is always negative.  # Advanced analytical question  What is the pay-off of the buy-and-hold portfolio? What is the pay-off of the rebalanced portfolio?