The hedge ratio and the riskless portfolio

In short

• Sell one call and buy h units of the underlying: $V_0 = hS_0 - c_0$.
• At the end, $V_1^u = hS_1^u - c_1^u$ and $V_1^d = hS_1^d - c_1^d$. Choose h so the two are equal.
• The hedge ratio is $h^* = \dfrac{c_1^u - c_1^d}{S_1^u - S_1^d}$: the change in option value divided by the change in the underlying.
• For a sold call, h* is positive: buy h* units of the underlying per call (or sell 1/h* calls per unit).
• For a put, h* is negative: the hedge is to buy the put and buy the underlying (or sell both).