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*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 risky asset price  moves down end then back to \(1\). **Assuming the risky asset drifts away from \(1\) to end at \(p_{end} > 1\). What is the relative return \(R\)?**