$6.$ Derive the expression for the Optimal Hedge Ratio using spot and futures

returns and the following steps

a$.$ Define the variables Q$\_$A$,$ Q$\_$F$,$ h$,$ N$,$ Delta$\_$S and Delta$\_$F

b$.$ Create a portfolio of the underlying asset and the futures contract

c$.$ Calculate the price changes of this portfolio in terms of the price

changes of the two assets

d$.$ Calculate the variance of the prices changes of this portfolio, and

express it in terms of the variance of the price changes of the

individual assets

e$.$ Express the price changes using price returns and modify the

portfolio variance formula accordingly

f$.$ Take the derivative of the variance of the portfolio with respect to

the hedge ratio, set it equal to zero, and solve for the optimal hedge

ratio

g$.$ Using the optimal hedge ratio, derive the optimal number of

contracts