Days 4 - 6: Hedging with futures Days 4 - 6: Hedging with futures contracts – principlescontracts – principles

Highlights of Chapter 11 & Introduction Highlights of Chapter 11 & Introduction to applied hedging projectsto applied hedging projects

FIN 441FIN 441Winter 2012Winter 2012

Some basic conceptsSome basic concepts

• What is “hedging”?• What is “price risk”?

– Examples

• What are some basic rationales as to why companies should consider hedging?

• What is a firm’s “natural exposure” to a price risk?– Examples

• What can companies do to change their natural exposures?

What is price risk?What is price risk?

• Quite simply, “price risk” refers to the uncertainty associated with movements in the price of an asset.– Stock market investors face “price risk” associated with volatility

in the stock market and individual stocks.– Banks and bond market investors are highly concerned about

“price risk” of money (i.e., volatility of interest rates).– Multinational companies, importers, and exporters face “price

risk” associated with changing currency rates.– Commodity sellers and users face “price risk” because of

uncertainty about future price levels at which they can sell and buy raw materials such as gold, oil, electricity, wheat, etc.

What is a “hedge”?What is a “hedge”?

• Glossary definition: “A transaction in which an investor seeks to protect (the price risk of) a position or anticipated position in the spot market by using an opposite position in derivatives.”

• Page 12: “Derivative market participants seeking to reduce their risk are called hedgers.”

• Would a hedge be the opposite of speculation?• Some good quotes about hedging.

Why should firms hedge? IntroWhy should firms hedge? Intro

• Organizations should hedge if hedging “adds value” beyond what could be achieved by “owners” hedging risks.

• Is “reducing risk” the same as “adding value?” Why or why not?– Two primary motives of risk reduction that add

value• Tax advantages.• Reducing expected costs of distress.

““Natural” exposure of business Natural” exposure of business modelmodel

• An organization (or investor) is “exposed” to price risk if the realization of a price change causes “losses.”

• Natural exposure refers to the “price direction” (“long” vs. “short”) in which the organization earns gains on the source of price risk.

• Examples:– Wheat farmer loses money if wheat prices go down between time of

planting and harvest.

• Natural exposure: “long” wheat

– Stock investor loses money if price of stock goes down between time of buying and time of selling.

• Natural exposure: “long” stock

– Airline loses money if jet fuel prices go up between time of customer ticket purchase and date of flight.

• Natural exposure: “short” jet fuel

Hedging to offset “natural Hedging to offset “natural exposure”exposure”

• If a farmer’s natural exposure to the price risk of wheat is “long,” what can she do to change the exposure?– Sell appropriate number of futures contracts on

wheat.

• Hedging to offset “long” stock market exposure.– Sell appropriate number of futures contracts on a

stock index (or on a single stock).

• Hedging to offset “short” jet fuel exposure– Buy appropriate number of futures contracts on oil.

““Long” vs. “short” hedgesLong” vs. “short” hedges

• The first two examples (wheat and stock) on the prior slide highlight short hedges.

• The third example (jet fuel) on the prior slide highlights a long (or anticipatory) hedge.

• What hedges (long or short) would be appropriate in each of the 3 situations in Question 6 of Chapter 11?

Fundamental issues in constructing Fundamental issues in constructing (and liquidating) a simple hedge(and liquidating) a simple hedge

• Understand “basis” between spot and futures.– Behavior of basis for “perfect hedge” (see Question 3

of Chapter 11).– Cross hedge.

• Choice of futures contract (including expiration date).

• Setting the hedge ratio (i.e., how many futures contracts to buy or sell).– Understanding the “units” for futures contracts.– Minimum variance hedge ratio.

• Covariance, volatility, and correlation.

Basis and profits on hedgingBasis and profits on hedging• Framework: 2 dates: t=1 (initiation date) and t=2

(liquidation date).• Definition: Basis (b) = spot price – futures price• Define: S1 = spot price at initiation of hedge, S2 =

spot price at liquidation of hedge, F1 = futures price at initiation of hedge, and F2 = futures price at liquidation of hedge.

• Profit on long hedge = (F2 – F1) + (S1 – S2) = (S1 – F1) – (S2 – F2) = b1 – b2 = basis at hedge initiation date – basis at hedge liquidation date.

• Profit on short hedge = (F1 – F2) + (S2 – S1) = (S2 – F2) – (S1 – F1) = b2 – b1 = basis at hedge liquidation date – basis at hedge initiation date.

Perfect hedgePerfect hedge• Definition: Perfect hedge = a hedge in which

the price changes of the hedging instrument are perfectly correlated with price changes of the spot price.– Zero basis risk.

• A slightly different definition of a perfect hedge: a hedge in which the underlying asset of the hedging instrument is EXACTLY the same as the spot asset.– This is the scenario discussed in the book on pages

358 – 359.– In such a case, basis MUST be zero at the expiration

of the futures contract.

Perfect hedge – an examplePerfect hedge – an example

• Question 3 of Chapter 11• Sugar dealer owns 112,000 lbs. of sugar on September

26 @ 4.79 cents/lb.• January sugar futures contract price is 5.50 cents/lb. on

Sep 26.• What accounts for the difference between futures price

and spot price?• What is the profit if dealer sells one January sugar

futures contract @ 5.50 cents/lb, then liquidates the hedge at contract expiration (i.e., delivers “owned” sugar to satisfy delivery obligation of futures contract)?

Cross hedgeCross hedge

• Definition: Basis risk = uncertainty in the future basis.

• Definition: Cross hedge = a hedge in which basis risk is NOT zero, most likely because there is some difference between the asset underlying the hedging instrument and the spot asset being hedged.– This type of situation is much more common AND

interesting to the student and practitioner of hedging with derivatives!

– In a cross-hedge, the basis does not converge to zero (or any particular value) as expiration of the futures contract approaches!

A simple cross hedge exampleA simple cross hedge example

• At end of May, airline wants to “lock in” a price for jet fuel for first 12 days of June.

• Anticipated consumption = 33,768,000 gallons• No jet fuel futures contract available!• Cross hedge by using heating oil futures contract.• Buy 804 July HO futures @ 77.50 cents/gallon on May 31 to hedge

anticipated purchases of jet fuel.• Spot price of jet fuel on May 31 is 79.10 cents/gallon.• Liquidates portion of hedge (i.e., sells some HO futures) each day

as jet fuel is purchased (at prevailing spot price).• Locked-in price = Futures price at initiation of hedge + average

basis over duration of hedge.– Why does this result occur?

Summary: How the basis affects Summary: How the basis affects hedge outcomeshedge outcomes

• A hedging transaction’s profit is determined by 2 outcomes:– Profit/(Loss) on the spot transaction (often in “opportunity” terms)– Profit/(Loss) on the futures transaction (always a cash outcome)

• NOTE: as a hedger, it is often easier to focus too much attention on this particular outcome…RESIST!

– These combined outcomes reflect changes in the basis during the hedge.

• In general,– A short hedge “locks in” a selling price: Known futures price +

unknown basis at hedge liquidation (unless “perfect hedge”)– Short hedge generates positive profits from increasing basis during the

hedge.• For a perfect hedge, a “contango” market will result in increasing basis.

– A long hedge “locks in” a purchase price: Known futures price + unknown basis at hedge liquidation (unless “perfect hedge”).

– Long hedge generate positive profits from decreasing basis during the hedge.

• Backwardation would create this type of condition.

Hedge ratiosHedge ratios

• “Naive” hedge ratio• Minimum variance hedge ratio

– See equation in grey box on page 366.– Hedge ratio also reflects the “beta” of a regression of the

changes in spot price on changes in futures prices.– Difficulties in estimating!

• Hedging effectiveness coefficient– See equation on page 369.– Can estimate before AND after hedge outcomes.– Reflects correlation between spot and futures price changes.– NOTE WELL: correlation less than 100% reflects basis risk (i.e.,

lower correlation implies greater basis risk).

Naïve hedge ratioNaïve hedge ratio

• Merely refers to a situation in which a hedger buys or sells an amount of futures contract exactly equal to the exposure (i.e., hedge ratio = 1).

• Naïve hedge ratio would be appropriate for “perfect hedge” (but this situation rarely exists).

Minimum variance hedge ratioMinimum variance hedge ratio

f

SfSfN

,

*

The equation solves for the number of futures contracts that minimizes the variance (i.e., standard deviation) of profits from the hedge transaction.

The inputs to the equation are 1) the correlation coefficient between changes in the spot price and changes in the futures price, 2) the standard deviation (or volatility) of changes in the spot price, and 3) the standard deviation of changes in the futures price.

If the assets are measured with the same scale, the equation provides a proportion.

Calculating MV hedge ratio - Calculating MV hedge ratio - illustrationillustration

• Jet fuel spot prices and NYMEX futures prices (www.eia.doe.gov)

• MV hedge ratio is estimated from historical data, BUT – There is no “guidance” as to the “correct” time frame

over which to estimate.– The estimated hedge ratio may vary considerably

based on time frame chosen.• Can also estimate using regression (“h” is the hedge

ratio):

– ΔSt = a + h* (Δft) + εt

Hedge effectivenessHedge effectiveness

• Equation for hedge effectiveness (e*) on page 369 equals “correlation-squared.”

• The hedge ratio and hedge effectiveness metrics can be calculated AGAIN using the data from the hedging horizon time frame to contrast against the “historically estimated” hedge ratio.

• Accounting measures of hedge effectiveness.

Detailed spreadsheet exampleDetailed spreadsheet example• Review 12-day airline example• Data sources:

– Jet fuel spot prices and futures prices (www.eia.doe.gov)

– Chicago Mercantile Exchange (www.cmegroup.com)

• Illustration of hedge, liquidation of hedge, daily profit on hedged transaction, changing basis, hedging outcome, hedger’s dilemma, minimum-variance hedge ratio, etc.

Hedging Project IntroductionHedging Project Introduction

• Two projects• Project #1: Diesel fuel supplier marketing a

fixed-price offer• Project #2: Airline liquidation of crude oil futures

contracts• Work on these from now – end of quarter• Both projects are due on Tuesday, March 13.

Diesel fuel projectDiesel fuel project

• Compute a fixed-price diesel fuel customer

• Apply basic principle of “price lock”: fixed price = known futures price + unknown basis

• Essence of project: data analysis of basis.

Airline jet fuel hedging projectAirline jet fuel hedging project

• Easy part of project:– Liquidate the hedge your boss implemented.– Keep records (design a spreadsheet tracking futures

prices, spot prices, profits (losses) on futures liquidation, etc.).

• Data analysis part of project:– Measurement of correlation– Basis risk– Calculation of minimum variance hedge ratios– Other issues

Both projectsBoth projects

• Understanding basis relationships is essential to “good” hedging.

• My discussion of history of basis relationships in oil markets – 1990s to present.

Exam on Monday, 1/26Exam on Monday, 1/26• Approximately 40% on “hedging with

futures” (i.e., Chapter 11 + material from class discussion).

• Approximately 25-30% on Chapter 9 material (and class discussion).

• Approximately 20% on Chapters 2 & 8 (and class discussion).

• 10-15% or less on introductory material.

Topics to cover in Week 4Topics to cover in Week 4

• Begin option valuation.– Principles of option valuation (Chapter 3)– Basic binomial model of option valuation

(Chapter 4)

• Option Valuation component continues through Weeks 5 & 6 of quarter