Learning Objectives


By completing this case you will:


– Learn to work with futures and spot data

– Estimate hedge ratios

– Compute hedged and unhedged valuation changes with historical data

– Back-test and discuss possible hedging strategies

– Consider how hedge ratio estimates can be employed in dynamic settings

– Communicate complex analysis to a non-technical audience


Learning Activities


By completing this case you will:


– Estimate and/or compute hedge ratios

– Compute cash flows to hedging strategies using energy futures contracts

– Comment on the consequences of changing market conditions on

possible hedging strategies

– Write a brief report for a non-technical audience




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



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:

  1. 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.

  1. 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






/ 2


Submission Details


Please submit both your team’s report and the spreadsheet you used for

your quantitative analysis. Both documents will be reviewed in

assessing your work. However, please write your report so that the

reader does not have to refer to the spreadsheet to understand your key



Please submit your team’s written report through the designated



assignment box ‘Finance 5’ located in the Student Lounge, Level 5 of

Building 8 by Friday 27 May at 17h00. You must attach the assignment

cover page to this submission.


Your submission cannot be more than 4 pages in total (including cover

sheet) with at least one inch margins and double-spaced 12 point type.

Please submit the spreadsheet you used for your quantitative analysis

by using the “Assignment” feature on UTSOnline by the due date.

The file name of this spreadsheet

should include your team surnames / number.


You are welcome to discuss your basic approach with current DRM

students but all the analysis must be from your team.


Please note that the assignment box will be removed and the UTSOnline

will not accept submissions after the due date and time. 


Please be sure to cite the work of others where appropriate.


The quality of your writing is as important as the technical accuracy of

your report.


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