1. Days 4 - 6: Hedging with futures contracts – principles
Highlights of Chapter 11 & Introduction to applied hedging projects
FIN 441
Winter 2012

2. Some 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?
What can companies do to change their natural exposures?

3. 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.

4. 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.

5. Why 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.

6. “Natural” exposure of business model
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

7. Hedging to offset “natural 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.

8. “Long” 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?

9. Fundamental issues in constructing (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.

10. Basis 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.

11. Perfect 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.

12. Perfect hedge – an example
Question 3 of Chapter 11
Sugar dealer owns 112,000 lbs. of sugar on September 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 5.50 cents/lb, then liquidates the hedge at contract expiration (i.e., delivers “owned” sugar to satisfy delivery obligation of futures contract)?

13. Cross 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!

14. A 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 cents/gallon on May 31 to hedge anticipated purchases of jet fuel.
Spot price of jet fuel on May 31 is 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?

15. Summary: How the basis affects hedge 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.

16. Hedge 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).

17. Naïve 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).

18. Minimum variance hedge ratio
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.

19. Calculating MV hedge ratio - illustration
Jet fuel spot prices and NYMEX futures prices (
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

20. Hedge 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.

21. Detailed spreadsheet example
Review 12-day airline example
Data sources:
Jet fuel spot prices and futures prices (
Chicago Mercantile Exchange (
Illustration of hedge, liquidation of hedge, daily profit on hedged transaction, changing basis, hedging outcome, hedger’s dilemma, minimum-variance hedge ratio, etc.

22. Hedging 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.

23. Diesel 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.

24. Airline 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

25. Both projects
Understanding basis relationships is essential to “good” hedging.
My discussion of history of basis relationships in oil markets – 1990s to present.

26. Exam 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.

27. Topics 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