Reference no: EM132389503

(a) If the annual discrete compounding risk-free rate is 10%, and the cost of carry offsets the convenience yield exactly, then the future price is equal to the spot price. Please explain. 

(b) 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 2×100=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*

If the stock price rises from 3 to 4, then

j) the future price____________________;

k) hedger makes_________________from the future, at t=1;

l)  ___________________from t=1 till t=2, _______________becomes                 _______________________________;

m) meanwhile, hedger makes a profit _______________from the stock at t=1;

n) hedger doesn't make further _____________on stock from t=1 to t=2;

o) net profit/loss is___________________;

p) stock price is_____ at t=2, hence the value of stock at t=2 is______________;

q) the value of futures is its gain and loss, hence, at t=2, its value is____________;

r) the value of the portfolio is the sum of the value of stock and the value of futures, which is___________________.

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