(c) To make the hedge portfolio risk-free, the value of the portfolio should not vary no matter stock price rises or falls (or, equivalently, the hedge portfolio should not make profit in one state and make loss in the other, where the state means stock price rises or falls).

Hence in both cases portfolio value will be equal, that is, 200+110h^* = 400-90h^*

solving for optimal hedge ratio,

^=> h^* = (400-200)/(110+90) = 200/200 = 1

Optimal ratio is 1

(d) To make the hedge portfolio risk-free, the hedge portfolio should not make profit in one state and make loss in the other, where the state means stock price rises or falls. Please use the optimal hedge ratio solved in (c) to verify this fact