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* Assuming the price trajectories are smooth, the value of the continuously rebalanced portfolio is the solution of:  \[\frac{dV_{rb,u}}{V_{rb,u}}=0.5\,\frac{dp}{p},\]  and this is just:  \[V_{bh}(p)=p^{0.5},\] \[V_{rb}(p)=p^{0.5},\]  assuming standard college calculus applies.  Both value functions equal \(1\) for \(p=1\) since both portfolios are initialized with one dollar. As soon as the price deviates from one, the rebalanced portfolio has an active position versus the buy-and-hold portfolio which has the wrong sign (underweight if the price has gone up, overweight if the price has gone down).