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**Assuming the risky asset/second drifts 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. Assume \(p_{end} < 1\). \(1>p_{end}\).  The rebalanced portfolio is overweight (vis-à-vis the buy-and-hold portfolio) the risky asset which in the end underperforms. 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.