Assuming that you are the Financial controller of Capital AA Ltd. that operates low cost airlines services across Asian countries. You need to purchase 5 million gallons of Jet Fuel in September 2022. As you are uncertain about the Jet Fuel price per gallon on September 2022, you decided to hedge the possible Jet Fuel price increase with September 2022 Jet Fuel Futures contracts. However, Jet Fuel is not listed the futures market but the closest possible commodity is Crude Petroleum Oil Futures (CPOF). The standard deviation of monthly spot price change in Jet Fuel is $0.0656, and the standard deviation of monthly change in CPOF is $0.0899, and the correlation between the two commodities is 0.915. Each CPOF contract size is to deliver 42,000 gallons of Crude Oil. You have the current price data of Jet Fuel per gallon recorded as $1.85 and the September CPOF is trading at $1.95 per gallon.

You are required to:

1. Determine the Optimum Hedge Ratio (OHR) of hedging Jet Fuel against CPOF.
2. Determine the optimum number of September CPOF contracts to be hedged (with tailing adjusted).
3. Should you take a long or short position on CPOFs?
4. If in September 2022, the Jet Fuel spot price S_tturns out to be $2.05 per gallon and the September CPOF F_tis closed out at $2.15 per gallon, determine what is your gain or lost in CPOF and what is your net cost of purchasing the 5 million gallons of Jet Fuel in September?
5. Explain why such hedging strategy may not be a perfect hedge?