Lecture 2 Derivative Market

Derivative MarketFuturesForwardsOptions

What is in todays lecture?

Principles of Heeding with Future

Some Examples

Basis Risk

Minimum Hedge Ratio

Some Excercises

Lecture 3

BASIC PRINCIPLES OF HEDGING Using futures markets to hedge a risk, the objective is to take a position that neutralizes the riskThe key to hedging with future contracts is to take an opposite position to what a firm/individual already has or is expected to have Long HedgeShort Hedge

Short HedgesA short hedge is a hedge that involves a short position in futures contracts.A short hedge is appropriate when the hedger already owns an asset and expects to sell it at some time in the future.A short hedge can also be used when an asset is not owned right now but will be owned at some time in the future

Producers or those who anticipates to receive inventory should use short-hedge to reduce the risk of their outputAn Example of HedgingAn oil company may hold large inventories of petroleum to be processed into heating oil. The firm can sustain heavy inventory losses if oil price decline, how the firm can hedge its position.

SolutionThe firm could sell futures contracts in heating oil in order to lock in the sales price. Again the firm will use short hedgeWhat is future contract on heating oil is not available?

Examples of Hedging with future/forward contractsOn April 1, Glaxosmith Chemical agreed to sell petrochemicals to the Pakistan government in the future. The delivery dates and prices have been determined. Because oil is a basic ingredient of the production process, Glaxosmith Chemical will need to have large quantities of oil on hand. Moreover, if prices of oil increase, the firm cannot pass on the additional cost to the government, how to hedge?

An example of long hedge The firm can buy futures contracts with expiration months corresponding to the dates the firm needs inventory.The futures contract locks in the purchase priceThis strategy is called a long hedge where the firm purchases a futures contract to reduce risk.In general, a firm institutes a long hedge when it is committed to a fixed sales price

Real Life Example of long-hedgeA group of students opened a small meat market called Whats Your Beef near the University of Pennsylvania in the late 1970s. this was a time of volatile consumer prices, especially food prices. Knowing that their fellow students were particularly budget-conscious, the owners vowed to keep food prices constant, regardless of price movements in either direction. They accomplished this by purchasing futures contracts in various agricultural commodities.

BASIS RISKIn practice, hedging is often not quite straightforward due to the following reasons:1.The asset whose price is to be hedged may not be exactly the same as the asset underlying the futures contract.The hedger may be uncertain as to the exact date when the asset will be bought or sold.The hedge may require the futures contract to be closed out well before its expiration date.These problems give rise to what is termed basis risk.

The BasisThe basis in a hedging situation is as follows:Basis = Spot price of asset to be hedged - Futures price of contract usedIf the asset to be hedged and the asset underlying the futures contract are the same, the basis should be zero at the expiration of the futures contract. Prior to expiration, the basis may be positive or negative

Some terms related to basisWhen the spot price increases by more than the futures price, the basis increases. This is referred to as a strengthening of the basis. When the futures price increases by more than the spot price, the basis declines. This is referred to as a weakening of the basis

An Examplea company knows that it will need to purchase 20,000 barrels of crude oil at some time in October or November. Oil futures contracts are currently traded for delivery every month and the contract size is 1,000 barrels. The company therefore decides to use the December contract for hedging and takes a long position in 20 December contracts. The futures price on June 8 is $68.00 per barrel. The company finds that it is ready to purchase the crude oil on November 10. It therefore closes out its futures contract on that date. The spot price and futures price on November 10 are $70.00 per barrel and $69.10 per barrel.1. Can you find the gain on future contract?2. What is the BASIS when the contract is closed out?3. What is the final effective price paid by the company for the oil purchased on November 10?

solution1. Can you find the gain on future contract?Gain = 69.1 68 = 1.12. What is the BASIS when the contract is closed out? Basis = 70 69.1 = 0.93. What is the final effective price paid by the company for the oil purchased on November 10?Effective Price = Initial future price + Basis => 68.00+0.9=68.9

What to do to reduce basis risk?One key factor affecting basis risk is the choice of the futures contract to be used for hedging. This choice has two components:The choice of the asset underlying the futures contractThe choice of the delivery month

1. The choice of the assetIf the asset being hedged exactly matches an asset underlying a futures contract, the first choice is generally fairly easy. In other circumstances, it is necessary to carry out a careful analysis to determine which of the available futures contracts has futures prices that are most closely correlated with the price of the asset being hedged.

2. The choice of the delivery monthGenerally, basis risk increases as the difference between the hedge expiration and the delivery month increasesA good rule of thumb is therefore to choose a delivery month that is as close as possible to, but later than, the expiration of the hedge. Sometime, a contract with a later delivery month is chosen, can you imagine why?Might be the hedger has to take the delivery in cases, which can be expensive

CROSS HEDGINGIf there is no futures contract on the asset being hedged, use a cross hedge, Cross hedge occurs when the asset underlying the future contract is different from the asset whose price is being hedgedThe changes in the prices of the two asset should be as highly correlated as possibleThe delivery month should be the same as, or just after, the date the hedge will be lifted.

Minimum variance hedge ratioThe hedge ratio is the ratio of the size of the position taken in futures contracts to the size of the exposure.When the asset underlying the futures contract is the same as the asset being hedged; it is natural to use a hedge ratio of 1.0. When cross hedging is used, setting the hedge ratio equal to 1.0 is not always optimal. The optimal hedge ratio is determined by the factors outlined in the next slide

The Risk Minimizing Hedge RatioConsider the following: DVH = (DS)(QS) (DF)NFQF, where:DVH = the value of the hedged portfolio QS = the quantity of the spot/cash position being hedgedQF = the number of units of the underlying asset in one futures contract used to hedgeNF = the number of futures contractsDS = change in the spot price of the goodDF = change in the futures price

If DVH = 0, then (DS)(QS) = (DF)NFQF, and the risk-minimizing number of futures contracts to trade, NF*, is

The fractional term, DS/ DF, is the Hedge Ratio.

Example Using the Hedge RatioSuppose you are long 1000 oz. of gold (in the cash market).

There are 100 oz. of gold per futures contract.

For every $1.00 change in the futures price, the cash market changes by $0.90 You want to engage in a risk minimizing hedge.

What position should you take in the futures market?

How many contracts should you use?

Example: SolutionBecause you are long in the cash market, using a risk minimizing hedge means that you should take a short position in the futures market. Concerning the number of contracts:

Mathematics of Hedge Ratio

NoteIt is really important to note here that we are assuming that the relationship between the changes in the spot price and changes in the futures price will remain the same (i.e., at 0.90 to 1.00) over the time period we are hedging.

Hedge Ratio: Example 2

Running the following regression equation results in an estimate of the hedge ratio: DS = a + b DF + e Then, b = DS/DF, is an estimate of the hedge ratio.Suppose you have a long position of 410,000 gallons of heating oil.You are concerned heating oil prices are going to ___ (rise or fall?), and you want to protect your inventory value. Therefore, you ___ (buy or sell?) heating oil futures).

Example 2, Cont.There are 42,000 gallons of heating oil in one futures contract.

You estimate the following regression equation: DS = 0.0177 + 0.9837 DF R2 = 0.80

Example 2, Cont.

So, sell either 9 or 10 contracts for a risk-minimizing hedge.

Rolling the hedge forwardSometimes the expiration date of the hedge is later than the delivery dates of all the futures contracts that can be used.The hedger must then roll the hedge forward by closing out one futures contract and taking the same position in a futures contract with a later delivery date. Hedges can be rolled forward many times. But that would give rise to basis risk

Risk hedging in financial contractsNadeem Raza owns a mortgage-banking company. On Feb 1 he made a commitment to loan a total of Rs. 1 million to various homeowners on April 1. The loans are 20-year mortgages carrying a 12-percent coupon. Like many mortgage bankers, he has no intention of paying the Rs.1 million out of his own pocket. Rather, he intends to sell the mortgages to an insurance company. He will reach an insurance company March 30 to sell the mortgage to. Though Mr. Raza will earn profitable fees on the loan, he bears interest-rate risk. He loses money if interest rates rise. What would you suggest to him for hedging this risk?

Solution: Use short-hedgeTo hedge this risk, he sells 2-months Treasury-bond futures contracts.With rise in interest rates, the price of mortgage as well as T-bonds will fallHis loss on mortgage is offset by the profit on short-hedge of t-bonsBut this is not a perfect hedge, why?

Example 2Masood is another mortgage banker. His firm uses advance commitments, where he promises to deliver loans to a financial institution before he promises with borrowers. On March 1, his firm agreed to sell mortgages to State Insurance Co. The agreement specifies that he must turn over 12-percent coupon mortgages with a face value of Rs. 1 million to State by May 1. As of March 1, Masood had not signed up any borrowers. Over the next two months, he will seek out individuals who want mortgages beginning May 1. If interest rates fall before he signs up a borrower, the borrower will demand a premium on a 12-percent coupon loan. That is, the borrower will receive more than par on May 1. Because Masood receives par from the insurance company, he must make up the difference. How to hedge?

Solution: use long hedgeBecause he loses in the cash market when interest rates fall, he should buys futures contracts to reduce the risk.When interest rates fall, the value of his futures contracts increases. The gain in the futures market offsets the loss in the cash market. Conversely, he gains in the cash markets when interest rates rise. The value of his futures contracts decreases when interest rates rise, offsetting his gain.This is called a long hedge

ExcercisesSuppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a 3-month contract? What does it mean?

Example.2The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound) 1.2. The standard deviation of monthly changes in the futures price of live cattl for the closest contract is 1.4. The correlation between the futures price changes and the spot price changes is 0.7. It is now October 15. A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15. The producer wants to use the December live cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle. What strategy should the beef producer follow?

Solution to cattle exampleThe optimal hedge ratio is = .7*1.2/1.4 = .6The beef producer requires a long position in 200000x.6=120000 lbs of cattle. The beef producers thus requires a long position in December contracts, closing out the position on November 15.

Example 3A corn farmer argues "I do not use futures contracts for hedging. My real risk is not the price of corn. It is that my whole crop gets wiped out by the weather." Discuss his view point?Should the farmer estimate his or her expected production of corn and hedge and to try to lock in a price for expected production?

Discussion on the farmers viewIf weather creates significant uncertainty about volume of the crops, then future contracts are not appropriateFuture contracts plus the weather can create further problems for him as the prices are expected to rise in weather is bad

An airline executive has argued: "There is no point in our using oil futures. There is just as much chance that the price of oil in the future will be less than the futures price as there is that it will be greater than this price." Discuss the executive's viewpoint.

What he is saying might be true, but the firm is not in the business of speculating on the oil prices and making profit from rising/falling oil prices, it would be a lot better if the company executives focus on the main business.