Wester Energy Inc. plans to buy $10$ million barrels of crude oil next month and decides to hedge their position using crude oil futures.

From historical data we know that $\backslash$sigma F $=0\mathrm{.}0422,\backslash$sigma S $=0\mathrm{.}0415,$ and $\backslash$rho $=0\mathrm{.}923.$

Find out the Optimal Hedge Ratio.

If the size of one futures contract of Oil is $1,000$ barrel then find out the optimal number of contracts assuming no daily settlement

The spot price is $$43\mathrm{.}74$ per barrel and the futures price is $$53\mathrm{.}99$ per barrel. Find out the optimal number of contracts after tailing.