Exchange Market Physical or virtual location where buyers and sellers meet in order to trade securities or commodities.

Exchange Market

• Physical or virtual location where buyers and sellers meet in order to trade securities or commodities

Exchange Market

• Anonymous trading

• Risks are assumed by the clearing corporation

Exchange Market

• Types of available products– Futures contracts

• Financial futures contracts– Interest rates– Currencies– Indexes

• Commodities– Agricultural products– Metals– Livestock, etc.

Exchange Market

Broker

Clearing Corporation

RISK

Exchange Market Broker

Margin Margin

CLIENT A CLIENT B

Futures Contract

• A futures contract is an agreement that obliges the buyer to take delivery of a specific quantity of an underlying asset, at a specific date, and at a price established at the time of the transaction.

• Conversely, the seller is obliged to deliver a specific quantity of an underlying asset, at a specific date, and at a price established at the time of the transaction.

Futures Contract

• The value of a futures contract is zero when initiated– Delivery price identical to the forward price– The contract develops value as the forward

price change– Zero-sum game

• What is lost by one is gained by the other

• No initial payment– Performance bond required

The Payoff of a Forward Contract

• The payoff of a long positionPt – D

• The payoff of a short positionD – Pt

where…Pt = Price of the underlying asset at the maturity of

the contract

D = Delivery price

The Payoff of a Forward Contract

• Futures contracts have a linear profit and loss profile

• Zero-sum game– What is lost by one is gained by the other

The Payoff of a Forward Contract

Profit and loss for a long position

Profit

Loss

+

-

Price

Profit and loss for a short position

Profit

Loss

+

-

Price

Futures Contract

• Example– Suppose we are in June and a coffee

producer wants to sell his September harvest at the current market price of $2 per pound. At this price, the producer would realize a return of 25%.

Futures Contract

• Example– A futures contract expiring in September will be

sold at a price of $2.

– The producer is committing himself to deliver the coffee at a price of $2 per pound in September. He is obliged to do so even if the price of coffee rises.

– However, he is protected against a drop in the price since the buyer is obliged to purchase the coffee at a price of $2.

Futures Contract

In September : $3/lb In September : $1/lb

• The producer is obliged to sell coffee at $2/lb

• Opportunity cost of $1/lb

• The counterparty realizes a profit of $1/lb

• The producer sells coffee at $2/lb

• Profit of $1/lb• The counterparty incurs

a loss of $1/lb

Contract Specifications

• Contract size and value

• Minimum price fluctuations

• Daily price limits

• Delivery month

• Trading hours

• Delivery location

Settlement

• Delivery by an offsetting transaction– Taking an opposite position to the initial position

• Settlement by delivery– The short position holder initiate the delivery

process at any time after the first notice day• Cash settlement

– The long and the short must pay or receive a payment in cash instead of having to accept or to make delivery of the merchandise

Specifications

Specifications

Specifications

Margin Requirements and Marking to Market

• Margin– Good faith deposit or performance bond– Determined by the exchange or clearinghouse as a

fixed amount per contract or as a percentage of the total contract value (3% to 10% of the contract value)

• Initial margin– The required deposit at the contract inception– Adjustments are being made at the end of every days

(daily settlement, mark to market)• Maintenance margin

– The amount that must be maintained in the account at all time

Margin Requirements and Marking to Market

• Margin call– A margin call is issued when the account falls under

the maintenance margin level. The account must then be immediately brought back to the initial margin level.

Margin Requirements and Marking to Market

• Example– Long position on 1 Coffee futures– Size : 37,500 pounds– Initial margin : $2,500 per contract– Maintenance margin : $2,000 per contract

Margin Requirements and Marking to Market

Day Futures Price(Cents per

Pound)

Daily $ Gain/Loss

Cumulative $

Gain/Loss

Margin Account Balance

Required Deposit

(Surplus)

Aug. 15 49.45 $2,500.00

Aug. 16 48.95 ($187.50) ($187.50) $2,312.50

Aug. 17 49.25 $112.50 ($75.00) $2,425.00

Aug. 18 48.65 ($225.00) ($300.00) $2,200.00

Aug. 19 48.50 ($56.25) ($356.25) $2,143.75

Aug. 20 48.25 ($93.75) ($450.00) $2,050.00

Aug. 21 48.00 ($93.75) ($543.75) $1,956.25 $543.75

Aug. 21 Deposit $543.75 $2,500.00

Aug. 22 48.45 $168.75 ($375.00) $2,668.75 ($168.75)

Aug. 23 48.75 $112.50 ($262.50) $2,781.25 ($281.25)

Pricing of Futures/Forwards

Cost of Carry Model

• Price of a futures contract– Priced so that the investor is indifferent about:

• buying the asset immediately and paying the carrying costs associated with holding the asset until the delivery date, or

• buying a futures contract

– Carrying costs• Financing, storage, and insurance.

• Futures price– The price of a futures is established by

determining the arbitrage free price (the indifference price).

• Two possible choices– Buy the asset immediately and keep it until needed

» Loss of interest rate income» Storage fees

– Buy a futures contract in order to buy the asset» Interest rate income» No storage fees

• What do you do?

Cost of Carry Model

Basis

• Basis– The spread between the

spot and the futures price

• Contango (Normal)– The futures price is higher

than the spot price

• Backwardation (Inversion)– The futures price is lower

than the spot price

Basis

• Contango (Normal)– The basis is widening when

futures prices increase faster or decline slower than the spot price.

– The basis is narrowing when futures prices decline faster or rise slower than the spot price.

• Backwardation– The basis is widening when

futures prices decline faster or rise slower than the spot price.

– The basis is narrowing when futures prices rise faster or decline slower than the spot price.

Normal Market

• A normal market is characterized by adequate supplies of the underlying asset through all delivery months. Prices reflect all or at least some of the carrying costs.

Cash and Carry Arbitrage

• Arbitrage– According to the law of one price in finance,

two assets generating the same cash flows should sell for the same price.

– Arbitrage consist of taking advantage of price discrepancies between two or more assets generating the same cash flows.

Cash and Carry Arbitrage

• Example– Asset XYZ– Spot (cash) price = $100– Futures price expiring in one year = $110– Storage costs per year = $8– Fair or theoretical value of the futures = $108

Cash and Carry Arbitrage

• Example– $108 is the indifference price. Since the

futures price is $110 than there is an arbitrage opportunity.

– Purchase of the undervalued asset (in the cash market) and sale of the overvalued asset (the futures contract).

Cash and Carry Arbitrage

• Arbitrage

Today:Cash

flow

1. Borrow $100 + $100

2. Purchase the asset at the spot price - $100

3. Sell a futures at $110 $0

Total cash flow $0

One year later:

1. Deliver the asset and receive the payment + $110

2. Repay loan and storage costs ($100 + $8) - $108

Total cash flow + $2

Reverse Cash and Carry Arbitrage

• Example– Asset XYZ– Spot (cash) price = $100– Futures price expiring in one year = $105– Storage costs per year = $8– Fair or theoretical value of the futures = $108

Reverse Cash and Carry Arbitrage

• Example– $108 is the indifference price. Since the

futures price is $105 than there is an arbitrage opportunity.

– Purchase of the undervalued asset (the futures contract) and sale of the overvalued asset (in the cash market).

Reverse Cash and Carry Arbitrage

• Arbitrage

Today:Cash

flow

1. Sell the asset at the spot price - $100

2. Invest $100 + $100

3. Buy a futures at $105 $0

Total cash flow $0

One year later:

1. Accept delivery of the asset and make the payment - $105

2. Collect proceeds (principal + storage costs) from investment ($100 + $8)

+ $108

Total cash flow + $3

Conditions Which Facilitate Arbitrage

• Ease of short selling

• A large supply of the underlying asset

• High storability

• Non-seasonal production and/or consumption

Conditions Which Facilitate Arbitrage

• Arbitrage can easily be performed with financial futures

• Arbitrage is more difficult to execute on commodities.– When shortages occur, market participants

places a higher value on the benefits of owning the physical commodity.

– The spot price will be values at a higher price then the futures price (backwardation or inverted market)

Inverted Markets

• An inverted market typically results from a shortage of the underlying asset in the cash market. The spot price increases above the futures price. Futures prices for the nearest delivery months are also above the deferred month prices.

The Relationship Between Forward Prices and Spot Prices

• The futures price of an asset providing no income is always higher than the spot price• The futures price of an asset providing a known income could be lower than the spot

price

Types of operations

• Hedging with futures contracts

• Speculation with futures contracts

• Arbitrage with futures contracts

Hedging with futures contracts

• Hedging is an operation that aims to reduce or eliminate risk

• Short hedge and long hedge

• Perfect and imperfect hedge

• Basis risk

• The optimal hedge ratio

Long Hedge

• A long hedge aims to protect against rising prices between the present and the time when the asset is needed.

• Example of a perfect hedge– You want to buy 1000 troy ounces of gold in 3 months– Actual price = $350 per ounce

• Storage fees = $10 per ounce per month, which implies that the fair futures price should be equal to $380 per troy ounce

• Buy 10 gold futures contracts on the New York Mercantile Exchange (COMEX division) at $380 per troy ounce

– Spot price at expiry = $400 per ounce– Futures price at expiry = $400 per ounce

Long Hedge

• Example of a perfect hedge

Today: Cashflow

1. Initial cash in the account ($350 x 1000 ounces) - $350,000

2. Invest $350,000 + $350,000

3. Long 10 futures contracts at $380 $0

Total cash flow $0

Three months later:

1. Accept delivery of 1000 troy ounces of gold and make the payment

- $380,000

2. Collect proceeds (principal + storage costs) from investment [$350 + (3 x $10)] x 1000 ounces + $380,000

Perfect hedge $0

Perfect Hedge

• Conditions for a perfect hedge1. The holding period matches the expiration

date of the futures contract

2. The asset being hedged matches the asset underlying the futures contract

• When these conditions are not met, the hedger is exposed to a basis risk

Imperfect Hedge

• Basis– The spread between the spot and the

futures price– At expiry, the basis is worthless– Prior to expiry, the basis can fluctuate

unexpectedly

Imperfect Hedge

• Example of an imperfect hedge– You want to buy 1000 troy ounces of gold in 3 months– Actual price = $350 per ounce

• Storage fees = $10 per ounce per month, which implies that the fair futures price should be equal to $380 per troy ounce

• Buy 10 gold futures contracts on the New York Mercantile Exchange (COMEX division) at $380 per troy ounce

– You must close the position one month prior to expiry– Spot price in two months = $400 per ounce– Futures price in two months = $400 per ounce

Imperfect Hedge

• Example of an imperfect hedgeToday: Cash flow

1. Initial cash in the account ($350 x 1000 ounces) - $350,000

2. Invest $350,000 + $350,000

3. Long 10 futures contracts at $380 $0

Total cash flow $0

Two months later:

1. Proceeds from the sale of 10 futures contracts at $400 [($400 - $380) x 10 ] x 1000 ounces + $20,000$

2. Purchase of 1000 troy ounces of gold in the cash market at $400 per ounce - $400,000

3. Collect proceeds (principal + storage costs) from investment [$350 + (2 x $10)] x 1000 ounces + $370,000

Imperfect hedge - $10,000

Optimal Hedge Ratio

• The basis risk is usually linked to the interest rate fluctuations (changes in the cost of financing)

• Commodities including agricultural and energy based assets entail higher basis risk then other products.– In case of shortage, holding the physical commodities

is more valuable then holding the futures contract.– The spot or cash price will be worth much more than

the futures contract (inverted or backwardation market).

Optimal Hedge Ratio

• There is a high basis risk when one of the following conditions is not met:– A large supply of the underlying asset– Storability of the underlying asset– Non-seasonal production and/or consumption– Ease of short selling

Optimal Hedge Ratio

• When the basis risk is not high, a hedge ratio of 1 is appropriate

• If there is not maturity or asset match, the hedge ratio needs to be adjusted to reflect the historical or expected price correlation between the futures contract and the asset.

Optimal Hedge Ratio

• A hedge where the futures contract uses an underlying asset similar but not the same as the physical asset being hedged is called a cross-hedge.– The hedge ratio might be different than 1.– The correlation between the assets and their

respective volatility have to be taken into account.

Optimal Hedge Ratio

• The optimal hedge ratio (H)

H = Corr(PF) (SDP / SDF)where:

SDP = standard deviation of changes in the spot price (P),

SDF = standard deviation of changes in the futures price (F),

Corr(PF) = coefficient of correlation between changes in CP and F.

Optimal Hedge Ratio

• ExampleA portfolio manager wants to reduce, by $10 M, for three months, the market risk of her portfolio composed of shares of American companies.The three-month standard deviation of the portfolio is 0.25, and the three-month standard deviation of the S&P/TSX 60 index is 0.20. The correlation between the portfolio and the index is 0.88.

Optimal Hedge Ratio

• Example:SDP = 0.25 SDF = 0.20 Corr(PF) = 0.88

H = Corr(PF) (SDP / SDF)H = 0.88 (0.25 / 0.20) = 1.10

The size of the futures on the S&P/TSX 60 index is $200 times the index level. If the index is valued at 500 then each contract has a value of $100,000 ($200 x 500). In order to hedge the portfolio manager must sell:

1.10 x ($10 M / $100,000) = 110 contractsIf she is not taking into account the volatility or the correlation then she has to sell only 100 contracts ($10 M/$100,000).

Speculation with futures contracts

• The futures market is particularly attractive to speculators for the following reasons:– Ease of entry and exit– Variety of opportunities– Leverage– Excitement