Nathan Co. wants to sell 100,000 units of commodity X in two months. Suppose that the standard deviation of the monthly changes in the price of commodity X is $4. The standard deviation of monthly changes in the futures price for a contract on commodity Y (which is similar to commodity X) is $5. The correlation between the monthly changes in the price of commodity X and the monthly changes in the futures price for the contract on commodity Y is 0.9. One futures contract is on 5,000 units of commodity Y.

(a) Explain the meaning of cross hedging. Briefly discuss when cross hedging is necessary. 

(b) Should Nathan Co. enter long or short future positions in order to hedge its exposure? Why? 

(c) What hedge ratio should be used when hedging the two-month exposure to the price of commodity X? What does this hedge ratio mean? 

(d) How many futures contracts on commodity Y should be traded? 

(e) Compute the hedge effectiveness. What does this hedge effectiveness mean?