Assume hedger takes hedge ratio as h*, i.e, if the risk exposure is a long position of 100 units of spot commodity, to hedge the risk, hedger will short 100h* futures underlying on that commodity. Please answer the questions in the right panel in analogy to the left panel, by filling the blanks in j) -r) below

*left panel*

If the stock price falls from 3 to 2, then

a)the future price falls from 3 to 2;

b)hedger makes profit (3-2)100h*=100h* from the future, at t=1;

c)by investing the profit from t=1 till t=2, 100h* dollars profit becomes (1+0.1)100h*=110 h*;

d)meanwhile, hedger makes a loss of 100(2-3)= -100 from the stock at t=1;

e)hedger doesn't make further loss on stock from t=1 to t=2;

f)net profit/loss is [110h*-100] dollars;

g)stock price is 2 at t=2, hence the value of stock at t=2 is 2100=200;

h)the value of futures is its gain and loss, hence, at t=2,its value is 110h*;

i)the value of the portfolio is the sum of the value of stock and the value of futures, which is [200+110h*].

*right panel*

the future price__rises from 3 to 4__________________;

b)hedger makes_loss =(3-4)*100h* = 100h*___from the future, at t=1;

c)__Margin Call_______from t=1 till t=2, _____100h* loss__________becomes___(-1+0.1)X100h* = -90 loss___________________________;

d)meanwhile, hedger makes a profit ___=100X(4-3) = 100____________from the stock at t=1;

e)hedger doesn't make further ___profit__________on stock from t=1 to t=2;

f)net profit/loss is____100h*-90_______________;

g)stock price is__4___ at t=2, hence the value of stock at t=2 is__4X100 = 400____________;

h)the value of futures is its gain and loss, hence, at t=2,its value is___-90_________;

i)the value of the portfolio is the sum of the value of stock and the value of futures, which is___400-90h*________________.

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). Please based on the above fact, solve the optimal hedge ratio h*.

How do we use the information above to find it?