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**Assuming the risky asset experiences a cycle, i.e. its price moves up from \(1\) to \(p_{max}>1\) 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 (vis-à-vis the buy-and-hold portfolio)  on the way up and this leads it to underperform. But symmetrically, it is short the risky asset on the way down. This leads it to outperform. This outperformance matches the initial underperformance. and the net result is zero. The situation is symmetric if the stock moves down end then back to \(1\).