Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs...

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Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging
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Transcript of Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs...

Page 1: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Futures Contracts

Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging

Page 2: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Derivatives

A derivative is a financial instrument whose price depends on the price of another underlying asset.

Major derivative contracts are: Futures and forward contracts, Call and put options, Swaps.

Page 3: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Futures Contracts A futures contract is an agreement to buy or sell an asset

at a certain time in the future for a predetermined price F.

F is called the futures price: the price at which you agree to transact in the future.

Both delivery and payment take place on the delivery date.

No money changes hands when the contract is entered.

The current price of any commodity is referred to as the “spot price” (S)

Page 4: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Futures Contracts

The party which agrees to buy the asset is said to have taken a “long position” in the futures contract.

The party which agrees to sell the asset is said to have taken a “short position” in the futures contract.

Taking a short position in a futures contract is not the same thing as short-selling an asset.

Page 5: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Differences Between Forward and Futures Contracts

Forwards Futures

Over-the-counter (OTC) Traded on an exchange

Not standardized Standardized

Specific delivery date Range of delivery dates

Settled at end of contract Settled daily

Contract is usually delivered Contract is usually closed out before maturity

Page 6: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Notation

S = spot price F = futures price T = date the contract expires or matures

On this date the long party delivers the asset On this date the short party pays F

0 = today t = some date after today but before T ST, FT = Spot price, Futures price at day T S0, F0 = Spot price, Futures price at day T St, Ft = Spot price, Futures price at day t

Page 7: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Profits of Forward/Futures Contracts

The payoff per unit of a forward/futures contract at the time of delivery:

Long Position: ST – F0

Short Position: F0 – ST

Futures contracts are usually closed before the contract matures What is the payoff when contract is closed?

We’ll get to this in a few slides.

Page 8: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Bank Balance Sheet Assets:

Present value: $60M Modified Duration: 9.43 YTM = 6%

Liabilities: Present value: $45M Modified Duration: 0.96 YTM=4%

Equity: Present value: $15M

Page 9: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Example:

Suppose that interest rates increase 20bp. How does that affect the equity of the bank? Value of Assets:

Value of Liabilities:

Value of Equity:

13.160*002.0*43.9 A

0864.045*002.0*96.0 L

.07)1-13.95/15 :drop (7% 05.1LA

Page 10: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Hedging Strategy:

Futures contract on a bond Profit on long position: ST – F0

Profit on short position: F0 – ST

We want a position that will pay money when rates increase ST decreases as interest rates go up So to hedge, take short position in the futures

contract.

Page 11: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Hedging

Advantage of hedging with futures contracts Can loan out to clients the kind of loans they want

Generally long term-fixed rate

Can borrow money on clients terms Generally short term-variable rate

Hedge out the interest rate risk using futures contracts.

Page 12: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Futures prices Futures are traded on an exchange

Clearinghouse reconciles trades each day and guarantees the transactions

All traders are required to establish a margin account with the clearinghouse.

Page 13: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Futures prices

Futures prices are constantly changing and are closely related to spot prices.

Example: At 10:00am on Monday, you lock in to buy “40,000

pounds of frozen pork bellies, cut and trimmed” Contract matures on October 31. Futures price is F0=$1.13 per pound. You have agreed to pay $45,200 for the 40,000

pounds of pork

Page 14: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Futures prices

Example continued At 2:00pm on Monday, a news story breaks.

“New Pope has commanded all Catholics to stop eating beef and chicken”

Futures price of pork jumps to Ft= $1.678/pound Enter a short position to sell pork at $1.678/pound

At maturity of the contract, you have locked in a profit

(1.678-1.1285)40,000 = 21,980

Page 15: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Futures prices

Example Continued: From the point of view of the clearinghouse, your

position is “closed” You are not required to deliver or take delivery of

the pork bellies. You can withdraw the present value of the profit

from your margin account as soon as your position is closed.

Page 16: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Closing the futures contract

To close a long futures position at time t<T Go short Agree to “buy” at F0, agree to “sell” at Ft

Payoff is Ft - F0

To close a short futures position at time t<T Go long Agree to “buy” at Ft, agree to “sell” at F0

Payoff is F0 – Ft

Page 17: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Short-Selling an Asset

Cash flows when you buy an asset Time 0: buy asset, pay money (negative flow) Time 1: sell asset, get money (positive flow)

Cash flows when you short-sell an asset Time 0: borrow asset, sell, get money (positive flow) Time 1: buy asset, pay-off liability (negative flow)

Page 18: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Example

You hate SPAM, so you short-sell 100 shares of Hormel. Current price/share = $10 Borrow shares, sell at market price, get $1000

One week later, price of Hormel is $8. Buy back 100 shares at $800. Return shares to party which loaned them out to you.

Profit: $200.

Page 19: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Spot and Futures Prices at Expiration

Arbitrage: Free money Suppose ST<FT

Immediately buy asset, short futures contract. At end of day: sell asset for FT

Make arbitrage profit of FT-ST

Suppose ST>FT Immediately short asset, long futures contract At end of day: buy asset for FT, close short position Make arbitrage profit of ST-FT

Page 20: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

The futures price at time 0 To determine F0 Use replicating strategy

A long futures position: Pay out cash in future (say 3 months) Get asset

Why not do following: Borrow $$ and buy asset now at current spot price Pay off loan in three months

Both strategies in three months: You hold the asset You pay out a lump sum of cash

Page 21: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

The futures price at time 0

Going long the future is identical to borrowing the money and buying the asset now if Storage costs are not high The asset pays no dividend or coupons These are good assumptions for futures contracts on

financial assets that pay no dividends

When you borrow $$ to buy the asset now you pay S0(1+rf)T for the asset rf = rate at which you can borrow money

Hence F0= S0(1+rf)T

Page 22: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Example: Arbitrage

Current price of Apache stock: $45 Assume Apache pays no dividends Futures price for Apache stock:

Delivery in three months F0=45.75 per share

rf=5%, which implies S0(1+rf)T=45(1.05)1/4 = 45.55

How can you take advantage of this arbitrage?

Page 23: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Example: Arbitrage

Take short position in futures contract Borrow $45 at risk-free rate, buy Apache

In three months: Liability has grown to 45(1.05)1/4 = 45.55 Honor short futures position, sell Apache for 45.75

(You already own it) Left with 45.75-45.55= .20 per share Free money

Page 24: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Example: Arbitrage

Current price of Apache stock: $45 Assume Apache pays no dividends Futures price for Apache stock:

Delivery in three months F0=45.25 per share

rf=5%, which implies S0(1+rf)T=45(1.05)1/4 = 45.55

How can you take advantage of this arbitrage?

Page 25: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Example: Arbitrage

Take long position in futures contract Short Apache, get $45 Deposit money in risk-free account In three months:

Money has grown to 45(1.05)1/4 = 45.55 Honor long futures position, buy Apache for 45.25 Use to close out short position Left with 45.55-45.25= 0.30 per share Free money

Page 26: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Arbitrage Example

Assume one interest rate rf = 9%. This is the rate at which you can both borrow and

lend. Zero-coupon bond:

Matures in 10 years. YTM: 9% FV=1000 Price = 1000/1.0910 = 422.41

Page 27: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Arbitrage Example

Futures contract Delivery of 1 zero-coupon bond in six months

The futures price must be

422.41(1.09)1/2 = 441.01 or else there is an “arbitrage opportunity”

Page 28: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Arbitrage Example

Suppose futures price is 450 > 441.01 Attack the arbitrage

Short the futures contract Borrow $422.41 and buy the bond.

In six months Honor short futures position – sell bond for 450 Liability has grown to 422.41 (1.09)1/2 = 441.01 Keep excess: 450.00-441.01 = 8.99

Page 29: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Arbitrage Example

Suppose futures price is 420 < 441.01 Attack the arbitrage

Long the futures contract Short the bond and loan out proceeds at risk-free rate.

Depost 422.41 in risk-free account

In six months Honor long futures position – buy bond for 420 Account has grown to 422.41 (1.09)1/2 = 441.01 Use bond to close out short bond position Keep excess: 441.01-420 = 21.01

Page 30: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Summary

If F0 > S0(1+rf)T

Now: Take a sort futures position Borrow S0, buy asset.

In future Honor short futures position, sell asset for F0

Liability has grown to S0(1+rf)T

Keep S0(1+rf)T - F0

Page 31: Futures Contracts Basics Futures prices Margin Accounts Futures and arbitrage Expected Payoffs Hedging.

Summary

If F0 < S0(1+rf)T

Now: Take a long futures position Short the asset, deposit proceeds in risk-free account.

In future Account has grown to S0(1+rf)T

Honor long futures position, buy asset for F0

Use asset to close out short position Keep S0(1+rf)T - F0