You are an associate at a commercial bank. One of your colleagues has sent the following email:
“Thanks again for sending Hull’s chapter on hedging with futures. As you know we do a lot of work with energy-intensive companies, so one of his examples seemed especially relevant. His cross-hedging strategy (jet fuel and heating oil) is interesting, but we were wondering what would happen in turbulent markets? For example in 2014 crude oil dropped from about USD 100 per barrel to around USD 50 per barrel. What would happen to someone using Hull’s proposed strategy over this time? Would it make sense to consider other energy futures as part of a hedging strategy (i.e. we have been wondering about including crude oil futures in addition to heating oil)?
Any thoughts you have would be greatly appreciated.”

Your colleague has limited quantitative skills and so you feel that you can best demonstrate these concepts through a clear example, based on data taken from the period she noted.
You consider what might happen over this time to someone who wanted to hedge the price risk of 500,000 gallons of jet fuel. You note that the futures data is taken from NYMEX where heating oil contracts are quoted in USD per gallon (contract size of 42,000 gallons) and crude oil is quoted in USD per barrel (contract size of 1,000 barrels).
Your assistant has downloaded spot jet fuel, crude oil futures and heating oil futures daily prices from December 31, 2012 through April 18, 2016 (see file “Daily Jet Fuel and Energy Prices – 25762 DRM – AUT 2016.xlsx”). You double check that their use of the “lookup” function in Excel was done properly so that the combined data is correctly lined up through time.
You basically have two goals. First, you want to see how hedge ratios estimated with 2013, 2014 or 2015 data differ from each other. Second, you want to note any differences between using only heating oil futures versus heating oil and crude oil futures to hedge jet fuel price changes across these different time periods. To draw your conclusions, you perform the following investigations:
i) By using the data in 2013 only, 2014 only, 2015 only and then both 2013-2014, you compute and compare the corresponding hedge ratios (thus the optimal number of futures contracts). You also consider hedging with only heating oil futures versus heating oil and crude oil futures.
ii) You assess how each of these hedge ratios performs (by comparing standard deviations of unhedged and hedged positions), when they are used to hedge the jet fuel price changes in 2015 and 2016?
iii) How do these two factors influence the valuation changes / cash flows a hedger might have received in 2015 and 2016? What are the main issues you have identified with this hedging application and what are your suggestions to deal with those?

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