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# Intuitions  **Assuming the risky asset/second stock experiences a cycle, i.e. its price moves up from \(1\) to \(p_{end}>1\) \(p_{max}>1\)  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 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.  **Assuming the risky asset/second stock moves down instead \(1>p_{end}\) \(1>p_{min}\)  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 long the risky asset on the way sown and this leads it to underperform. But symmetrically, it is long the risky asset on the way up. This leads it to outperform. This outperformance matches the initial underperformance. and the net result is zero.