We have a simple BS-market of one risky asset $S_{t}$, a bond $B_{t}$ and a digital option $X$ on the risky asset with value process $V(t,S_{t})$. I was able to derive $V(t,S_{t})$ using risk-neutral valuation. Now, I am supposed to set up a replicating strategy for this option, i.e. find a self-financing trading strategy $\phi(t)=(\phi(t)^{B},\phi(t)^{S})$ such that for all $t$: $$\phi(t)^{B} B_{t} + \phi(t)^{S} S_{t} = V(t,S_{t})$$
The book says that I should delta hedge the option. Now I am wondering why I couldn´t just construct the replicating strategy as $\phi(t)^{S}=\frac{V(t,S_{t})}{S_{t}}$ and choose $\phi(t)^{B}$ such that the strategy is self-financing? Why is delta-hedging necessary?