1. Mechanics of Futures and the hedging strategies Chapter 2&3
Geng Niu

2. Future Contracts Available on a wide range of assets Exchange traded
Specifications need to be defined:
What can be delivered,
Where it can be delivered, &
When it can be delivered
Settled daily

3. Corn futures contract in CME
On March 5 a trader in NY call a broker to buy 5,000 bushels of corn for July delivery
The broker immediately issue instructions to a trader to buy one July corn contract
Another trader in Kansa instruct a broker to sell 5,000 bushels for July delivery.
The broker then issues instructions to sell
A price would be set and the deal would be done

4. Closing Out Positions Most futures contracts do not lead to delivery
Closing out: enter into the opposite trade to the original one before the delivery
E.g. On Apr 20, the NY investor closed out his position by selling (shorting) one July corn futures.
E.g On May 25, the Kansas investor closed out his position by buying one July contract.

5. Specification of a futures contract
The asset: which asset should be delivered on maturity
The contract size: amount that has to be delivered under one contract
Delivery arrangements: place where delivery will be made
Delivery Month: when the delivery can be made
Last trading day
Price quotes: how to understand the listed prices
Price limits and position limits

6. Sample futures contracts specification
Corn futures contract traded in CME group
Corn futures contract traded in Dalian commodity exchange
Wulin Suo

7. Convergence of Futures to Spot
Time
(a)
(b)
Futures
Price
Spot Price
When the delivery period is reached, the future price = or close to the spot price for the underlying asset.
If Future price>spot price, then sell (short) a futures contract, buy the asset, and make the delivery.
If Spot Price>Future Price, then long the future contracts and wait for the delivery to be made.
What if the Future price does not equal to the Spot price?

8. Understand daily settlement
Daily settlement (mark-to-market) determinants the “ market values” of futures contracts at the end of each day.
It is used to calculate the profit or loss status of the two parties in a futures transaction every day.

9. Understand daily settlement
Suppose trade A longed 1 December Lumber futures contracts on March 1st for a price of $ 100 per contract
On March 2nd, the news said that new Lumber mills will be completed earlier than expected, indicating a Lumber supply increase.
Dec Lumber futures price decreased to $90 per contract.
Compared to people who longed Lumber futures on March 2nd , A is better off or worse off?
Or, if on March 2nd A sold 1 Dec Lumber futures and hold the two contracts together, is A better off?

10. Understand daily settlement
A is worse off:
If A waited for one more day and longed the futures on Mar 2nd, A is able to buy Lumber on Dec for $90 per contract instead of $100.
If A sold 1 Dec Lumber futures on 2nd March, and also hold the 1 contract bought on 1st March, the current cost is zero, but he will buy Lumber on Dec for 100 and sell Lumber for 90.
This futures price decrease is shown as a loss of $10 in the daily settlement for long traders.

11. Understand daily settlement
Suppose trade B longed 1 December Lumber futures contracts on March 2nd for a price of $ 90 per contract
On March 3th , the news said that more people are willing to build houses in the future.
Dec Lumber futures price increased to $110 per contract.
B is better off or worse off?
An increase in futures price is recorded as a gain for long traders.

12. Margins Risk of futures contracts: -- one party may regret
-- may not have the money to honor the agreement
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

13. Margins
An investor contacts his broker to buy two December gold futures
Current future price：1,250 per oz.
Contract size : 100 ounces.
The broker will require the investor to deposit funds in a margin account
Initial margin: the amount must be deposited at the beginning; suppose it’s $ 6000 per contract
Initial balance in the margin: 2*6000=12,000

14. Margins
Daily settlement or marking to market: margin account is adjusted a the end of each trading day to reflect market values of futures contract.
By the end of the first day, futures price dropped to 1,241
The investor has a loss of 1,800 (200*9)
New balance in the margin account: =10,200

15. Margins The investor’s broker pays the 1,800 to the exchange
The exchange passes the money on to a broker of an investor of a short position
This is because the investor with a short position gains from price decline.
Wulin Suo

16. Margins
The investor can withdraw any balance in the margin account in excess of the initial margin

17. Margins
If price keep declining (increasing), long (short) position investors may have negative balance in margin account
To avoid this, a maintenance margin is set.
If balance < maintenance margin, the investor receives a margin call: top up the margin account to the initial margin level by the end of the next day
If not, the broker closes out the position.

18. A Possible Outcome Day Trade Price ($) Settle Price ($) Daily Gain ($)
Cumul. Gain ($)
Margin Balance ($)
Margin Call ($) 1
1,250.00
12,000
1,241.00
−1,800
− 1,800
10,200 2
1,238.30
−540
−2,340
9,660
….. …… 6
1,236.20
−780
−2,760
9,240 7
1,229.90
−1,260
−4,020
7,980
4,020 8
1,230.80
180
−3,840
12,180 15
1,380
-5,400
14,400 16
1,226.90
780
−4,620
15,180

19. Margin Cash Flows When Futures Price Increases
Long Trader
Broker
Clearing House
Member
Short Trader

20. Margin Cash Flows When Futures Price Decreases
Long Trader
Broker
Clearing House
Member
Short Trader

21. Collateralization in OTC Markets
It is becoming increasingly common for transactions to be collateralized in OTC markets
Consider transactions between companies A and B
These might be governed by an ISDA Master agreement with a credit support annex (CSA)
The CSA might require A to post collateral with B equal to the value of its outstanding transactions with B when this value is positive.
If A defaults, B is entitled to take possession of the collateral
The transactions are not settled daily and interest is paid on cash collateral

22. Clearing Houses and OTC Markets
Traditionally transactions have been cleared bilaterally in OTC markets
Following the crisis, the has been a requirement for most standardized OTC derivatives transactions to be cleared centrally though clearing houses.

23. Clearing Houses and OTC Markets
An OTC transaction is negotiated between A and B to a clearing house
It is then presented to a clearing house
If the clearing house accepts the transaction, it becomes the counterparty to both A and B.
The clearing house takes on the credit risk of both A and B.
The clearing house then require margins from A and B.
Wulin Suo

24. Bilateral Clearing vs Central Clearing House

25. Crude Oil Trading on May 26, 2010
Open
High
Low
Settle
Change
Volume
Open Int
Jul 2010
70.06
71.70
69.21
71.51
2.76
6,315
388,902
Aug 2010
71.25
72.77
70.42
72.54
2.44
3,746
115,305
Dec 2010
74.00
75.34
73.17
75.23
2.19
5,055
196,033
Dec 2011
77.01
78.59
76.51
78.53
2.00
4,175
100,674
Dec 2012
78.50
80.21
80.18
1.86
1,258
70,126

26. Some Terminology
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 daily settlement process, not the closing price. Why?
Volume of trading: the number of trades that have changed hands in one day

27. Volume Total amount of purchases or sales during a trading session
Not purchases and sales together
Client A buys one contract of Jan wheat and Client B sells one contract of Jan wheat, the volume of trading between them is one.

28. Open interest
Total number of futures contracts that remain open at the end of a trading session
Include those contracts not yet liquidated by either an offsetting futures market transaction or delivery.
Client A buys one contract of Jan wheat from Client B, and neither client started with a position in Jan wheat, one futures contract will be created and open interest will increase by one.

29. Open interest For seller of a contract there must be a buyer
One new buyer and one new seller: open interest + 1
One old buyer sells to one old seller: open interest -1
One old buyer sells to one new buyer: open interest not change

30. Open interest: suppose before Jan 1 no trade had any futures positions.
Time
Trading Activities
Open Interests
Jan 1
A buys 1 futures and B sells 1 futures 1
Jan 2
C buys 5 futures and D sells 5 futures 6
Jan 3
A sells 1 futures and D buys 1 futures 5
Jan 4
E buys 5 futures from C who sells 5 futures contracts

31. Open interest
On January 1, A buys one futures contract , which leaves an open interest and also creates trading volume of 1.
On January 2, C and D create a trading volume of 5, and there are also five more options left open.

32. Open interest
On January 3, A takes an offsetting position, open interest is reduced by 1, and trading volume is 1.
On January 4, E simply replaces C, open interest does not change, and trading volume increases by 5.

33. Operation of the Clearinghouse
100 oz GOLD Contract
Time
Buyer
Seller
Contract Value
Cl. House Position
Open Longs
Open Shots
Open Interests 1 A B
$46,000
A’s Seller
B’s Buyer 2 C
$47,000
C’ Seller
A’s Buyer ? 3
$46,500
B’ Seller
C’s Buyer - 4
$48,000

34. Questions
When a new trade is completed what are the possible effects on the open interest?
Can the volume of trading in a day be greater than the open interest?
A new trade can increase or decrease the open interest, depending on whether it is a long/short position to the existing contracts
The volume of trading in a day can be greater than the open interest if lots of trades are open and closed within the same day

35. Delivery
If a futures contract is not closed out before maturity, it is usually 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

36. 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

37. Forward Contracts vs Futures Contracts
Private contract between 2 parties
Exchange traded
Non-standard contract
Standard contract
Usually 1 specified delivery date
Range of delivery dates
Settled at end of contract
Settled daily
Delivery or final cash
settlement usually occurs
Usually closed out
prior to maturity
FORWARDS
FUTURES
Some credit risk
Virtually no credit risk

38. Hedging Strategies Using Futures

39. Long & Short Hedges A long hedge: long position in futures contracts
A short hedge: short position in futures contracts
If you know you will purchase an asset in the future and want to lock in the price, which one is appropriate?
If you know you will sell an asset in the future and want to lock in the price, , which one is appropriate?
Simulated trading game cme group

40. Basis Risk
Perfect hedge: reduce all the risk arising from the price of the asset
In reality:
The asset whose price is to be hedged is not exactly the same as the asset underlying the futures contract
The exact date when the asset will be bought or sold is uncertain
The hedge may require the contract to be closed out before delivery month

41. Examples:
An airline company has to purchase jet fuel in the future. Only heating oil futures are available.
A company needs to purchase 20,000 barrels of crude oil at some time in October or November.
A US company will receive 50 million yen in July. Yen futures contracts have delivery months of March, June, September, and December

42. Basis
Basis= Spot price of asset to be hedged – Futures price of contract used
Basis Risk: The risk to a hedger arising from uncertainty about the basis at a future time
If asset to be hedged and asset underlying futures contract are the same, basis=0 at the expiration data: no basis risk
Prior to expiration, the basis can be positive or negative.

43. Basis (a) (b) Time Futures Price Spot Price
When the delivery period is reached, the future price = or close to the spot price for the underlying asset.
If Future price>spot price, then sell (short) a futures contract, buy the asset, and make the delivery.
If Spot Price>Future Price, then long the future contracts and wait for the delivery to be made.

44. Long Hedge for Purchase of an asset
Define
F1 : Futures price at time hedge is set up
F2 : Futures price at time asset is purchased
S2 : Asset price at time of purchase
b2 : Basis at time of purchase
Cost of asset S2
Gain on Futures
F2 −F1
Net amount paid
S2 − (F2 −F1) =F1 + b2

45. Short Hedge for Sale of an Asset
Define
F1 : Futures price at time hedge is set up
F2 : Futures price at time asset is sold
S2 : Asset price at time of sale
b2 : Basis at time of sale
Price of asset S2
Gain on Futures
F1 −F2
Net amount received
S2 + (F1 −F2) =F1 + b2

46. Strong or Weak Basis Basis=spot price-futures price
If the basis increase (spot price increases, or futures price decreases, or both), we say the basis has strengthened.
If the basis decreases (spot price decreases, or futures price increases, or both), we say the basis has weakened.

47. Basis Risk
Basis will have strengthened or weakened from the time the hedge is implemented to the time when the hedge is removed.
Basis also varies from one location to the next.
Hedgers are exposed to basis risk and are said to have a position in the basis.

48. Basis example: grain futures basis
When there is a shortage of grain in some area, the local spot price increases relative to the futures price: a strengthening basis
Spot price is relatively lower in places further away from areas where grain is used or exported: a weakening basis

49. Corn prices: spot and futures

50. Basis Risk
Short hedges gain from a strengthening basis. Short hedges have a long basis position.
Long hedges gain from a weakening basis. Long hedges have a short basis position.

51. Cross hedge
Expect to purchase 20,000 barrels of crude oil in the future: size of the exposure=20,000
Crude oil futures contract size: 1,000
How many contracts to long: 20,000/1,000
Size of futures position= 20,000
Hedge ratio=1

52. Cross hedge
If the asset underlying the futures contract is the same as the asset being hedged, it is easy: use a hedge ratio of 1.0
What if the two assets are different?
E.g.: air company has to purchase jet fuel, but only heating oil futures are available.
Use how many heating oil futures contracts?
In other words: how to choose the hedge ratio

53. Optimal Hedge Ratio
Proportion of the exposure that should optimally be hedged is
where
sS is the standard deviation of DS, the change in the spot price during the hedging period,
sF is the standard deviation of DF, the change in the futures price during the hedging period
r is the coefficient of correlation between DS and DF.
h* is the minimum variance hedge ratio

54. Optimal Number of Contracts
QA Size of position being hedged (units)
QF Size of one futures contract (units)
VA Value of position being hedged (=spot price time QA)
VF Value of one futures contract (=futures price times QF)
Optimal number of contracts if no tailing adjustment
Optimal number of contracts after tailing adjustment to allow or daily settlement of futures

55. Example
Airline will purchase 2 million gallons of jet fuel in one month and hedges using heating oil futures
From historical data sF =0.0313, sS =0.0263, and r= 0.928
The size of one heating oil contract is 42,000 gallons
The spot price is 1.94 and the futures price is 1.99 (both dollars per gallon)

56. h = 0.928* /0.0313=0.7777
QA= 2,000,000; QF= 42,000
VA= 2,000,000*1.94=3,880,000
VF= 42,000*1.99=83,580
Without tailing:
N= 0.777*2,000,000/42,000=37.03
With tailing:
N=0.777*3,880,000/83,580=36.10
Wulin Suo

57. Hedging Using Index Futures
To hedge the risk in a portfolio the number of contracts that should be shorted is
where VA is the value of the portfolio, b is its beta, and VF is the value of one futures contract

58. Hedging Using Index Futures
CAPM:
E(ri ) = rf + βi(E(rm ) – rf )
βi= cov(ri , rm ) / var(rm )
= [cov(ri , rm ) /( var (ri ) * var (rm ) ) ] *
var (ri )/var (rm )
= ρim * σi / σm
= h
Wulin Suo

59. Example S&P 500 futures price is 1,000
Value of Portfolio is $5 million
Beta of portfolio is 1.5
What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?

60. Changing Beta To change the beta of the portfolio from β to β*:
reduce exposure to market risk (If β> β* ):
a short position in (β- β* )* VA / VF
Increase exposure to market risk (If β< β* ): a long position in (β* - β )* VA / VF
Wulin Suo

61. Changing Beta
What position is necessary to reduce the beta of the portfolio to 0.75?
What position is necessary to increase the beta of the portfolio to 2.0?

62. Why Hedge Equity Returns
May want to be out of the market for a while. Hedging avoids the costs of selling and repurchasing the portfolio
Preserve alphas.

63. Stack and Roll
We can roll futures contracts forward to hedge future exposures
Initially we enter into futures contracts to hedge exposures up to a time horizon
Just before maturity we close them out and replace them with new contract reflect the new exposure
etc

64. Liquidity Issues
In any hedging situation there is a danger that losses will be realized on the hedge while the gains on the underlying exposure are unrealized
This can create liquidity problems
One example is Metallgesellschaft which sold long term fixed-price contracts on heating oil and gasoline and hedged using stack and roll
The price of oil fell.....