Topic 6-Futures BUFN740

Forwards, Futures and Swaps(BKM 22, 23)

BUFN 740: Capital MarketsTopic 6

BUFN 740: Capital Markets Topic 6 1

A forward contract is an agreement today to buy or sell an asset on a fixed future date for a fixed price.

--The fixed future date is called the maturity date. --The fixed price is called delivery price. The delivery price is to be paid at maturity. Example: On Mar 31, a farmer and a miller could enter into a forward contract: On June 30, the miller will buy 5,000 bushels of wheat from the farmer at the price of 600 cents per bushel. The contract is an over-the-counter agreement between two

companies. The delivery price is chosen so that the initial value of the

contract is zero. No money changes hands when the contract is initiated.

Forwards Contract

2BUFN 740: Capital Markets Topic 6

A futures contract is an agreement to buy or sell an asset for a certain price at a certain time.

Similar to a forward contract

– The delivery price is chosen such that the value of the contract

is zero

-- No money changes hands at initiation Special features of a futures contract

– Standardized contracts create liquidity– Exchange mitigates credit risk– Settled daily by marking to market

Futures Contract


Types of Futures Contracts Futures contracts fall into two categories: commodities and

financials.

--The commodities: e.g., wheat, soy bean, cattle, gold, electricity.

--The financials: e.g., futures on Treasury Bill, British Pound, S&P 500.

Example: Corn futures on CBOT

--Trading unit: 5,000 bu

--Deliverable grades: No. 2 Yellow at par and substitutions at

differentials established by the exchange

--Price quote: cents and quarter-cents/bu

http://www.cmegroup.com/trading/agricultural/grain-and-oilseed/corn_contract_specifications.html




Basics of Futures Contracts

The party who agreed to buy in a futures contract is said to have a long position. The party who agreed to sell is said to have a short position.

Open interest is the number of contracts outstanding. The futures contract is a zero-sum game, which means gains and

losses net out to zero. Profit to long = spot price at maturity (PT) - original futures price

(F0)

Profit to short = original futures price - spot price at maturity Example: Mark buys 10 gold futures at $350/oz with maturity in 250

days (contract size 100 oz). Suppose the gold futures price goes down $0.1 every day for 250 days. Will Mark lose or gain?


Figure 22.2 Profits to Buyers and Sellers of a Futures Contract

Profit is zero when the ultimate spot price, PT equals the initial futures price, F0 .

Profit rises or falls one-for-one with changes in the final spot price.


How Clearinghouse Works

The exchange acts as a clearing house and counterparty to both sides of the trade.

The net position of the clearing house is zero. Example: George buys 2 December corn futures contracts from

Susan at the futures price 2820 cents/bu. At 11am on June 10.

--When will George have an incentive to default?

--Immediately after the initiation, clearinghouse becomes the

seller to George and the buyer to Susan at the same futures price.

-- Susan and George no longer face credit risk from counterparty.


Margin and Marking to Market Initial Margin – cash or near-cash securities deposited by an investor

with his or her broker (5%-15% of the total value of the contract) Marking to Market - each day the profits or losses from the new

futures price are paid over or subtracted from the account Maintenance Margin - an established value below which the trader

receives a margin call Example: An investor takes a short position in one December Coffee

futures contracts at noon on June 3

--Contract size is 37,500 lb and futures price is $1.60/lb

--Initial margin is $6,000/contract (10% of the contract value)

--Maintenance margin is $4,000/contract

How far could the price rise before the investor gets a margin call?


A Coffee Futures Example (Cont.)


How to Close a Futures

How to close a futures?

--Enter into an offsetting trade Long position, then short to close Short position, then long to close

--Most futures contracts are closed out before maturity. Only 1-3% of contracts result in actual delivery of the underlying commodity.

Example: Suppose Kathy bought 10 December gold futures at $290/0z on January 2. The contract size is 100 oz. At 11:30am on March 25, the futures price is $295/oz and she decides to close. So she sells 10 December gold futures at the market price $295/oz. The settlement price (the price just before the final bell each day) on March 25 is $296.50/oz. The settlement price on March 24 was $294/oz.


What will happen then?

At the settlement time on March 25, the 10 long contracts margin account will get credited (296.50-294)×100×10=$2,500.

The 10 short contracts margin account will get debited

(296.50-295)×100×10=$1,500.

In the net, she gained $1,000 at the settlement on March 25.

Now the 10 long contracts and short contracts are identical and thus offset each other.


Hedging and SpeculationSpeculators

Seek to profit from price movement– short - believe price will fall– long - believe price will rise

Example: If you believe that crude oil prices would increase, then you can purchase crude oil futures. Why not buy the underlying asset directly?

Seek protection from price movement

– long hedge - protecting against a rise in purchase price

– short hedge - protecting against a fall in selling price Example: An oil distributor needs to sell oil in a few months and

faces the risk that price might fall. The firm can sell oil futures.


Hedgers

Example 22.5 Hedging with Oil Futures An oil distributor plans to sell 100,000 barrels of oil in February

and wishes to hedge against a possible decline in oil prices. Each contract calls for delivery of 1,000 barrels. It would sell 100

contracts. The current futures price is $71.86.


Oil Price in February, PT

$69.86 $71.86 $73.86

Revenue from oil sale: 100,000×PT

$6,986,000 $7,186,000 $7,386,000

+ Profit on futures: 100,000×(F0-PT)

200,000 0 -200,000

Total $7,186,000 $7,186,000 $7,186,000

The variation in the price of the oil is precisely offset by the profits or losses on the futures position.

Example of a Long Hedge Suppose miller Mary will have to buy 5,000 bushels wheat from

the spot market on December 1. The December futures is quoted at $2.75 per bu.

Buy 1 Dec. futures (the size of wheat futures contract is 5,000 bu.) If the Dec. 1 spot price is $2.80 per bu., then Mary buys at $2.80

per bu. from the spot market. Mary gains about $0.05 per bu. from the futures contract. The net

cost is $2.75 per bu. If, on the other hand, the Dec. 1 spot price is $2.60 per bu., then

Mary buys at $2.60 per bu. She loses about $0.15 per bu. from the futures contract. The net cost is again $2.75.

Good hedging does not always improve the ex post outcome, but it always decreases the fluctuation in the possible outcome.


Hedging Example: Section 22.4 Investor holds $1000 in a mutual fund indexed to the S&P 500. A futures contract with delivery in one year is available for $1,010. The investor hedges by selling one futures contract .

0 0

0

1,010 1,0001%

1,000

F S

S


Value of ST 990 1,010 1,030

Payoff on Short(1,010 - ST)

20 0 -20

Total 1,010 1,010 1,010

Futures Pricing

Spot-Futures Parity Theorem With a perfect hedge, the payoff of the asset-plus-futures is certain

-- there is no risk. A perfect hedge should earn the riskless rate of return. This can be used to develop the futures pricing relationship.


0 00 0 0 0

0

(1 ), , (1 )Tf f f

F Sr F S r forT periods F S r

S

If spot-futures parity is not observed, then arbitrage is possible. If the futures price is too high, short the futures and acquire the

stock by borrowing the money at the risk free rate. If the futures price is too low, go long futures, short the stock

and invest the proceeds at the risk free rate.

Futures Pricing (Cont.)


Futures Pricing (Cont.)


To get one share of the stock, we have two ways:

(1) borrow to buy one share of the stock now and keep it to T

(2) buy one future contract

Let’s compare the cash flow of these two strategies:

Futures Market Arbitrage Suppose the risk-free rate is 0.5% , the futures price should be

$1000×1.005=$1005. The actual futures prices is $1010. The spot-futures parity is violated. An arbitrage

opportunity exists! Buy low sell high-- sell overpriced futures and buy the stock using borrowed

money.

The Cash Flow of Cash and Carry


Strategy Initial Cash Flow Cash Flow in 1 year

Borrow $1000 +1,000 -1,000×1.005=-$1,005

Buy stock for $1000 -1,000 ST

Sell the futures 0 $1,010- ST

Total 0 $5

Futures Market Arbitrage (Cont’d) What if the actual futures price is $980. The spot-futures parity is

violated. An arbitrage opportunity exists! Buy low sell high-- buy underpriced futures

--sell the stock and lend the proceed

The Cash Flow of Reverse Cash and Carry


Strategy Initial Cash Flow Cash Flow in 1 year

Buy the futures 0 -980+ ST

Short sale stock 1,000 -ST

Lend -1,000 $1,005

Total 0 $25

Relationship between Forward and Futures Prices

In the previous example, we assume for convenience that the entire profit to the futures contract accrues on the delivery date.

The parity theorems apply strictly to forward pricing because contract proceeds are realized only on delivery.

When interest rate is uncorrelated with the price of the underlying asset, forward and futures prices are the same.

Even if interest rate IS correlated with the price of the underlying asset, forward and futures prices are still very close.

In real data, generally, the difference between forward price and futures price is indeed insignificant and thus will be ignored throughout this course.


Swaps


A swap is an exchange of periodic cash flows between two parties. The cash flows may vary in terms of currency denomination, interest rate basis and/or other financial features.

Examples:

1. Interest Rate Swap - exchange of fixed-rate interest payments for floating-rate interest payments

2. Currency Swap - exchange of one stream of cash flows denominated in one currency for another stream of cash flows denominated in another currency.

Plain Vanilla Interest Rate Swap


A plain vanilla interest rate swap is a widely used interest rate swap. Party B agrees to pay party A cash flows equal to interest at a fixed interest

rate on a notional principal for a number of years. At the same time, party A agrees to pay party B cash flows equal to interest at a floating interest rate on the same notional principal for the same number of years.

The notional principal does not change hand. The cash flows are in the same currencies.

It involves two companies that have different comparative advantages in the

debt market: one company may be relatively more competitive in the fixed-rate market, while the other may be relatively more competitive in the floating-rate markets.

Example Suppose BUD wants to borrow $100 million at a floating rate for 5 years and IBM wants to borrow $100 million at a fixed rate for 5 years. Costs

of funds are as the following

The central question in the analysis of a swap is: can both companies be better off by contracting a swap agreement? Even though the rates IBM can borrow at in both markets are higher than those for BUD, IBM's disadvantage (the difference in rates) is smaller

in the floating rate market. So we say that IBM has a comparative advantage in borrowing at floating rates and BUD has a comparative advantage in borrowing at fixed

rates.


Total Gains From Swap Assume interest is paid semiannually. If a swap market does not exist, then BUD has to borrow at

LIBOR and IBM has to borrow at 12%. The total amount of each interest payment BUD and IBM have to pay is 100(LIBOR +12%)/2 m.

Now if BUD and IBM enter into a swap contract and let BUD borrow at fixed rate of 10% and IBM borrow at LIBOR + 0.5%, The total amount of each interest payment BUD and IBM have to pay is only 100(LIBOR +10.5%)/2 m.

The difference for each payment is 100(LIBOR +12%)/2 -100(LIBOR +10.5%)/2=$0.75million.


Mechanics of Swap

Step 1: BUD and IBM sign a swap contract which specifies that every 6 months, BUD pays IBM 100 × LIBOR/2 million and IBM pays BUD 100 × 11%/2=$5.5 million. Only the net payment change hands.

Step 2: BUD borrows $100m for 5 years, paying 10% annually. IBM borrows $100m for 5 years, paying LIBOR+0.5% annually.

The net cost of fund for BUD is LIBOR-1% each year (1% better). The net cost of fund for IBM is 11.5% each year (0.5% better).


Topic 6-Futures BUFN740

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