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ARE 495: Introduction to Commodity Futures Markets

Lecture 19: Devising a Real-World Hedging Strategy: Optimal Hedge Ratio

(Part 2)

Nick

Piggott & Wally Thurman

NCSU Agricultural & Resource Economics

March

21, 2016

11.45 am – 1.00pm

Kilgore 125, NCSU

Slide2Review

WSJ: “Airlines Retreat on Fuel Hedging” 3/21/2016

Devising

a hedging strategy

Real-world and real-time

problems using real data

The goal here is to teach you skills using standard software packages such as Excel to make more informed risk management strategies and decisions

A hedger faces two critical decisions:

What kind of futures to use

Which contract month of that futures to

use

The hedger in making these choices will be wanting to

maximize hedging effectiveness

, this means choosing a futures contract with prices that

are highly correlated with the underlying cash commodity.

Slide3Our “Real World” Assignment

You have just been hired by Qantas Airlines to manage their procurement and risk management of jet fuel prices for their new route between DFW and SYD.

Jet fuel is a product from crude oil and does not have a futures contract so what contract should we use to

cross-hedge

the price risk exposure?

Last lecture &

Hwk

#7 where we found heating oil to be most highly correlated to jet fuel.

What is the optimal futures position to assume or alternatively the

optimal hedge ratio

?

Today’s Lecture

Slide4Some important details

“Qantas relies on a long-range A380 (seats 484 passengers weighs 1.2 million pounds) for the service, which feeds into the Texas hub of One World partner American Airlines to shuttle passengers to destinations in the eastern half of the US. According to Airbus, the extended range A380 has a range of 8,200 nautical miles. This route definitely pushes the envelope at SYD to DFW being 7,451 nautical miles and will take nearly 58,200 gallons of jet fuel to power the aircraft across the Pacific Ocean.”With fuel mileage of (7,453/58,200)=0.128 nautical miles per gallon “Qantas Flight 7 will depart Sydney six times a week (everyday except Tues)”WEEKLY FUEL USEAGE: 58,200 gallons ×6 ×2 = 698,400 gallons per week3/11/2014=Jet Fuel was $2.912 per gallon so $2.034 million per week in Jet Fuel expenses or $105.8 million annually for this one route SYD-DFWInterestingly, currently their most profitable flight

Slide5Slide6

Which Futures Contract Should We Use to Cross-Hedge?

The futures contract that is most strongly correlated?Table 1 reveals there is a relationship between jet fuel prices and all three futures prices, the relationship between jet fuel prices is more correlated with heating oil than the other two. Thus heating oil futures are the best choice with which to cross-hedge jet fuel prices.

HWK#7

Slide7Next Decision is the Optimal Futures Position to Assume or the Optimal Hedge Ratio

How many heating oil contracts will result in the maximum possible reduction in the variability of the total hedged position

?

THE HEDGER WISHES TO

MINIMIZE RISK

: TAKE A FUTURES POSITION THAT RESULTS IN THE MAXIMIMUM REDUCTION IN THE VARIABILITY OF THE TOTAL HEDGED POSITION.

Slide8Some Definitions & Algebra

Hedge ratio (HR)where Qf is the quantity (or units) of the commodity represented by the futures position and Qc is the quantity (or units) of the commodity being hedged.In our example we need to hedge 698,400 gallons of jet fuel per week using heating oil futures. There are 42,000 gallons in 1 heating oil (HO) contract.

Slide9Some Definitions & Algebra…

The HR that minimizes risk is defined as:where is the quantity (or units) of futures that minimize risk.

Slide10Change in Value of Hedged Position

Consider the followingwhere

Slide11Change in Value of Hedged Position…

Important properties of the hedge: are assumed to be constant for the life of the hedge. If we set the change in the value of the hedged position to zero (making variability equal to zero),

Slide12Risk Minimizing Quantity of Futures

We have shown that So it follows thatThis result can be used to determine the quantity (or units) of the futures position with which to hedge

Slide13Change in Value of Hedged Position…

One last detail important detail to deal with where is the number of contracts that minimizes risk, and is the quantity (or units) of the commodity represented by each futures contract for .in our example for heating oil (HO) there are =42,000 gallons per contract and we know we need gallons of jet fuel per weekThusSince we know Qc and Qfc the challenge is to estimate HR*:

Slide14The Naïve Method

Table 1 provides daily jet fuel prices (col 2) and heating oil (Col 3) for the last month of 2012.Col 6 showsNote the value of varies daily its average value is 0.75, implying a hedge ratio HR*= 0.75.The minimum-variance hedge would be to buy (or be long) a position of 12 heating oil contracts.

Slide15Regression Method

Another method used to estimate the minimum-variance hedge ratio is regression analysis. Specifically regression methods provide the best linear unbiased estimate (BLUE).Regression involves estimating the following equation for the time series of price changes:where

Slide16Regression Method…

The summary output provides a regression of the changes in daily jet fuel prices and heating oil prices for the last month of 2012.Note the value of b provides the estimate of HR*, implying a hedge ratio 0.857.The minimum-variance hedge would be to buy (or be long) a position of 14 heating oil contracts.

Slide17HWK #8: Calculate Optimal Hedge Ratio (Due 3/23/2016 at start of class)

Using the dataset provided on class website (

http://www4.ncsu.edu/~wthurman/are495/

) in file “Jet_Fuel_Hw7.xlsx” and using the sheet “dataset”:

Estimate the optimal hedge ratio (

HR*

) over the period 2013

(1/2/2013-12/31/2013) using

the naïve method and calculate the

optimal number of heating oil contracts

that should be purchased (taking a long position) to hedge one week of jet fuel for Qantas flight SYD-DFW which

requires

698,400 gallons

Repeat the same calculation in (1) but instead using regression analysis. There are many sites and videos to show how to

do regression

in excel just by using the Excel help or google. For example:

How to add in data analysis

https://

www.youtube.com/watch?v=nfv1z2ko6jk

http://www.excel-easy.com/data-analysis/analysis-toolpak.html

How to do a regression

https://www.youtube.com/watch?v=TkiB1xBnjn4

http://www.excel-easy.com/examples/regression.html

Slide18HWK #8: Calculate Optimal Hedge Ratio…

That is, estimate the optimal hedge ratio (HR*) over the period 2013 (1/2/2013-12/31/2013) using regression analysis calculate the optimal number of heating oil contracts that should be purchased (taking a long position) to hedge one week of jet fuel for Qantas flight SYD-DFW which requires 698,400 gallonsFor (1/2/2013-12/31/2013) regress:

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