(remembering that $V_0(b_i):=1$), we get

For hindsight optimization over $n$ discrete rebalancing rules $b_1<\cdot\cdot\cdot<b_n$, the time-0 cost of achieving the best $b_i$ in hindsight is $$\boxed{C_0=2-n+2\sum_{i=1}^{n-1}N(\Delta b_i\sigma\sqrt{T}/2)},$$where $\Delta b_i:=b_{i+1}-b_i$. If $\delta:=\max\limits_{1\leq i\leq n-1}\Delta b_i$, then $$\boxed{C_0\leq 2-n+2(n-1)N(\delta\sigma\sqrt{T}/2)}.$$

A perpetual option on the best of any $n$ distinct rebalancing rules in hindsight is worth $C_0=n$ dollars at time-0.

Thus, we see that the time-0 price of the general horizon-$T$ rebalancing option is independent of the interest rate, and it is increasing and concave separately in the parameters $\Delta b_i, \sigma, T$. We again observe that horizontal translations of the point set $\{b_1,...,b_n\}$ do not alter the option price. We always have the relation $1\leq C_0\leq n$; the maximum $n$ dollar price obtains if any of the parameters tends to infinity and the minimum $\$1$ price obtains if any of the parameters tends to zero.

For a $T:=25$ year planning horizon, we cherry pick five favored asset allocations $\mathbb{B}:=\{0,0.5,1,1.5,2\}$. Assuming stock market volatility of $\sigma:=0.15$ going forward, we get $C_0=\$1.59$, and the excess growth rate of the hindsight-optimized asset allocation will be exactly $\log(C_0)/T=1.87\%$. Assuming that the risk-free rate is greater than $1.87\%$, the replicating strategy is guaranteed not to lose money 