002 hedging with futures

SKOOL COMPUTER EDUCATION

The DerivativesHEDGING WITH FUTURES



TYPES OF TRADERS

• Hedgers– Mainly interested in protecting themselves against

adverse price changes– want to avoid risk

• Speculators– Hope to make money in the markets by betting on the

direction of prices– “accept” risk

• Arbitrageurs– Arbitrage involves locking into riskless profit by

simultaneously entering into transactions in two or more markets


HEDGING EXAMPLES

• A US company will pay £10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contract

• An investor owns 1,000 Microsoft shares currently worth $73 per share. A two-month put with a strike price of $63 costs $2.50. The investor decides to hedge by buying 10 contracts


ARBITRAGE EXAMPLE

• A stock price is quoted as £100 in London and $172 in New York

• The current exchange rate is 1.7500


1. GOLD: AN ARBITRAGE OPPORTUNITY?

• Suppose that:– The spot price of gold is US$390– The quoted 1-year futures price of gold is

US$425– The 1-year US$ interest rate is 5% per annum

• Is there an arbitrage opportunity?


2. GOLD: ANOTHER ARBITRAGE OPPORTUNITY?

• Suppose that:– The spot price of gold is US$390– The quoted 1-year futures price of gold is

US$390– The 1-year US$ interest rate is 5% per annum

• Is there an arbitrage opportunity?


THE FUTURES PRICE OF GOLD

If the spot price of gold is S & the futures price is for a contract deliverable in T years is F, then

F = S (1+r )T

where r is the 1-year (domestic currency) risk-free rate of interest.In our examples, S=390, T=1, and r=0.05 so that

F = 390(1+0.05) = 409.50


INTRODUCTION

• Futures markets have a reputation for being incredibly risky.

• It plays a beneficial role in society by allowing the transference of risk and providing information about the future direction of prices on many commodities and financial instruments.

• A futures contract is an agreement between two parties for a delivery of an asset in the future and freely traded in the exchange.

• There must be strict guidelines specifying the nature of these agreements.

• One of the most important responsibilities of the exchange is to set these guidelines


FUTURES CONTRACTS

• Available on a wide range of underlying• Exchange traded• Specifications need to be defined:

– What can be delivered,– Where it can be delivered, & – When it can be delivered

• Settled daily


THE ELEMENTS OF STANDARDIZATION OF FUTURES CONTRACTS

• The Asset

• The Contract Size

• Delivery Arrangement

• Price

• Trading hours


IMM 3-MONTH EURODOLLAR FUTURES CONTRACT EXAMPLE OF FUTURES CONTRACT STANDARDIZED TERMS

Trading Unit: Eurodollar time deposit having a principal of $1 million with a 3-month maturity

Daily Price Limit: No limit

Contract Months March, June, September, December; Serial Months, Spot Month

Trading Hours: 7:20 a.m. – 2:00 p.m. (Chicago time), Mon. – Fri, except on the last trading day of an expiration contract, when trading closes at 9:30 a.m. (3:30 p.m. London time). The contract also trades on the Globex system

Last trading day: The second London bank business day immediately preceding the third Wednesday of the contract month

Delivery: Cash settled


HENRY HUB NATURE GAS FUTURES EXAMPLE OF FUTURES CONTRACT STANDARDIZED TERMS

Trading Unit: 10,000 million British Thermal Units (MMBtu)

Price Quotation: Dollars and cents per MMBtu

Daily Price Limit: $1.50 per MMBtu ($15,000 per contract) for first 2 months. Initial back month limits of $0.15 per MMBtu rise to $0.3 per MMBtu if the previous day’s settlement price in any back month is at $0.15 limit

Contract Months 36 consecutive months commencing with the next calendar month

Trading Hours: 10:00 a.m. – 3:10 p.m. (NY time), Mon. – Fri, for any open outcry session. After-hours trading is conducted via NYMEX ACCESS electronic trading system from 4:00 – 7:00 p.m., Monday through Thursday

Last trading day: Three business days prior to the first calendar month day of the delivery month

Delivery Sabine Pipe Line Co.’s Henry Hub in LA. Seller is responsible for movement of gas through the Hub; the buyer from the Hub. Hub fee paid by the seller.

Delivery Period: No earlier than the first calendar day of the delivery month and must be completed no later than the last calendar day of the delivery month.

Quality Specifications Pipeline specifications in effect at the time of deliver


THE ASSET

• The exchange specifies bounds of quality that is accepted.


CONTRACT SIZE

• The amount of the asset delivered under one contract.


DELIVERY ARRANGEMENTS

• Futures are quoted using the delivery month, therefore the exchange usually sets a sub period of this month as the delivery period. The short party will choose the exact date.


PRICE QUOTES

• The way that the futures prices are quoted.

• For example the T-Note futures are quoted as dollars and 32s of a dollar.

• This will also define the minimum price movements, the tick, in this case $1/32.


LIMIT UP/DOWN

• When the price of the future reaches the limit, trading stops.

• These are imposed in order to prevent speculative attacks in the futures markets.

• However, when the price of the underlying declines rapidly, these limits become artificial barriers and distort the market efficiency.


POSITION LIMITS

• The maximum number of contracts that the agent is allowed to hold.

• These include the total number of contracts that can be held and the maximum number of contracts expiring in any particular month.

• These help not only preventing speculative attacks in the futures market, they help preventing attacks in the market of the underlying asset as well.


MARGINS

• A margin is cash or marketable securities deposited by an investor with his or her broker

• The balance in the margin account is adjusted to reflect daily settlement

• Margins minimize the possibility of a loss through a default on a contract


MARGINS

• When the two counterparts engage into a futures contract, there are risks concerning the ability of the party with the long position to pay on the delivery day.

• On the other hand, there is a risk that a party with a short position can be found, which will not be able to honor the delivery.

• Margins are set in order to minimize the risks of default.


MARGINS

• Both parties are required to keep a margin account. • The balance of the margin is adjusted on a daily

basis, in order to reflect the futures price movements.

• If the investor has a long position and the price declines, the broker will draw that money from the margin account.

• The broker will pass this money to the exchange, which in turn will pass it to the broker dealing with the short position in order to increase the margin account of the counterpart with the short position.


MARGINS

• The investor has the right to withdraw any amount of many which exceeds the margin.

• In the previous example, the party with the short position can do so.

• If the futures price continues to decline, there is the possibility that the margin will become negative.


CLEARNING HOUSE

• The” exchange'' above is in fact the exchange clearinghouse which acts as a middleman in futures transactions, and has a number of members.

• If a broker is not a member, she has to channel her transactions through a member and of course keep a margin account there.

• Even clearinghouse members are required to keep a margin account, which is called the clearing margin, but not maintenance accounts.

• Usually clearing is done on a net margining basis:• Every clearinghouse member first offsets the short and

long positions they deal with against each other, and then calculate their clearing margin.


EXAMPLE OF A FUTURES TRADE

• An investor takes a long position in 2 December gold futures contracts on June 5– contract size is 100 oz.– futures price is US$400– margin requirement is US$2,000/contract

(US$4,000 in total)– maintenance margin is US$1,500/contract

(US$3,000 in total)


DAILY MARK-TO-MARKET EXAMPLE

Date Settlemt. Price

Settlemt. Price ($)

Mark-to-Market

Other Entries

Account Balance

11/ 7 $2.980 29,800 -700.00 1,875 1,175

11/ 10 3.145 31,450 1,650 700 3,525

11/ 11 3.170 31,700 250 3,775

11/ 12 3.223 32,230 530 4,305

11/ 13 3.000 30,000 -2,230 2,075

11/ 14 2.970 (open)

29,700 -300 -1,775 0.00


A POSSIBLE OUTCOME

Daily Cumulative Margin

Futures Gain Gain Account Margin

Price (Loss) (Loss) Balance Call

Day (US$) (US$) (US$) (US$) (US$)

400.00 4,000

5-Jun 397.00 (600) (600) 3,400 0. . . . . .. . . . . .. . . . . .

13-Jun 393.30 (420) (1,340) 2,660 1,340 . . . . . .. . . . .. . . . . .

19-Jun 387.00 (1,140) (2,600) 2,740 1,260 . . . . . .. . . . . .. . . . . .

26-Jun 392.30 260 (1,540) 5,060 0

+

= 4,000

3,000

+

= 4,000

<


OTHER KEY POINTS ABOUT FUTURES

• They are settled daily• Closing out a futures position involves entering

into an offsetting trade• Most contracts are closed out before maturity


DELIVERY

• If a contract is not closed out before maturity, it usually is settled by delivering the assets underlying the contract.

• When there are alternatives about what is delivered, where it is delivered, and when it is delivered, the party with the short position chooses.

• A few contracts (for example, those on stock indices and Eurodollars) are settled in cash


SOME TERMINOLOGY FOR FUTURES: NEWSPAPER QUOTES

• Open interest: the total number of contracts outstanding – equal to number of long positions or number

of short positions• Settlement price: the price just before the final

bell each day – used for the marking-to-market process

• Volume of trading: the number of trades in one day


FUTURES-SPOT CONVERGENCE

• As the delivery approaches, the futures price will eventually converge to the spot price of the underlying asset.

• Two alternative ways of doing so are presented in figure


FUTURES-SPOT CONVERGENCE

• For instance, if the futures were above the spot price, one could exploit the following arbitrage opportunity

• Short a futures• Buy the asset• Deliver

• As arbitrageurs exploit this opportunity, the price of the futures will decline and the price of the underlying asset will rise.

• This pattern will continue until the futures and the spot price become equal.

• The futures price can approach the spot price either from below or above.


HEDGING WITH FUTURES

• If a company knows that it has to sell a particular asset at a particular time in the future, it can hedge by taking a short position, therefore locking in the price of delivery. This is called a short hedge.

• Similarly, a company that knows that it will need an asset in the future can take a long hedge, thus locking in the price of purchase.

• It is very important to note that hedging does not necessarily improve the financial outcome, it just reduces the uncertainty.


BASIS RISK

• Basis is the difference between spot & futures• Basis risk arises because of the uncertainty

about the basis when the hedge is closed out• The basis is defined as

b(t)=S(t)-F(t,T)

• Where S (t )is the spot price of the underlying asset and F(t,T)is the price of the futures contract that has been utilized.

• If the asset to be hedged is the same as the one underlying the futures, then the basis on expiration is equal to zero.

• If the delivery date is not the same as the one that the futures matures, then the basis will signify the ``losses'' or ``gains'' of the hedge than are not known when the hedge is constructed.


LONG HEDGE

• Suppose that

F1 : Initial Futures Price

F2 : Final Futures Price

S2 : Final Asset Price• You hedge the future purchase of an asset by

entering into a long futures contract• Cost of Asset=S2 – (F2 – F1) = F1 + Basis


SHORT HEDGE

• Suppose that

F1 : Initial Futures Price

F2 : Final Futures Price

S2 : Final Asset Price• You hedge the future sale of an asset by entering

into a short futures contract• Price Realized=S2+ (F1 – F2) = F1 + Basis


BASIS RISK: DIFFERENT MATURITIES

• Today, the gold price is S(t). • Say that one has to deliver gold at time (τ)• basis today is b(t ) = S (t ) - F (t,T ) < 0• The basis on the delivery date will be



• At time (τ) the company will close the futures contract by taking a long position and at the same time sell the gold at the current price.

• The marking-the market procedure will leave the company with a loss of F (t ,T ) - F (t,T )

• Since the futures was sold at time and bought at time (τ) ; while by selling the asset the income is S (t ).



• The basis risk arises from uncertainty about the future interest rates and uncertainty about the future yields of the underlying asset.

• For investments that are difficult or costly to store, the basis risk might increase substantially.

• The delivery month that is as close as possible -but not earlier than, the date when the hedge matures.


BASIS RISK: DIFFERENT ASSETS

• Price of Gold S.• Price of Silver Ś• Denote• One has to deliver gold at time , one has to deliver

gold at time ,


BASIS RISK: DIFFERENT ASSETS

there would only be basis due to the maturity differences. This makes clear thatwhen there is no futures contract on the asset being hedged; one has to choose thefutures that has the highest correlation with the underlying asset.


OPTIMAL HEDGE RATIO

•

• Hedge ratio is the ratio of the size of the futures position to the size of the exposure

• Have assumed this to be one.• If the objective of a hedger is to minimize risk,

the optimal hedge ratio can be found by regressing the change in the spot price against the change in the futures price.

• Number of contracts

contract) futures one of (size

hedged) beingposition of (size*ratio) hedge (opt. = contracts futures of No.


OPTIMAL HEDGE RATIO

•

Proportion of the exposure that should optimally be hedged is

where S is the standard deviation of S, the change in the

spot price during the hedging period, F is the standard deviation of F, the change in the futures price during the hedging period is the coefficient of correlation between S and F.

F

S


ROLLING THE HEDGE

•

• We can use a series of futures contracts to increase the life of a hedge

• Each time we switch from 1 futures contract to another we incur a type of basis risk.

• What the optimal instrument is in two cases where the hedge is not a perfect one


ROLLING THE HEDGE

•

• If the asset being hedged is different that the one underlying the futures contract, then one has to choose the futures contract that has the highest possible correlation with the asset to be hedged;

• If there is no futures contract on the asset to be hedged that expires on the maturity date of the hedge, then one has to choose the futures that expires as close as possible -but not earlier than, the date when the hedge matures.


ROLLING THE HEDGE Another Possibility

•

• Suppose that the hedge matures in a very distant point in time and all futures contracts available at the moment expire before that time.

• The hedger must then roll the hedge forward. • This is done in the following fashion:



•

• One wants to deliver some asset at time , where the futures contracts mature at times τ1, τ2 τ3

• The hedger initially at time τ shorts the available futures F1 .



•

002 hedging with futures

Economy & Finance

delivery month

futures price isfor

year futures price of

futures prices

price quotes

strike price

stock price

spot month contract