Financial Engineering 5

References: Villalobos, Luenberger, Faerber

Lecture 15

Introduction to Futures

Lecture Topics • Introduction • Introduction to Futures • Introduction to Exchanges • Standardized contracts • Announcements • Assignments

Futures Contracts • A futures contract is a type of derivative instrument, or financial

contract, in which two parties agree to transact a set of financial instruments or physical commodities for future delivery at a particular price.

• If you buy a futures contract, you are basically agreeing to buy something, for a set price, that a seller has not yet produced.

• A future contract is a standardized version of the forward contract for trade in the Futures markets.

• The Future price of the underlying commodity is set in such a way that the current value of the contract is zero.

• As the life of the contracts elapse multiple delivery prices are eliminated by revising contracts as the price environment changes.

• Future – Forward equivalence: Suppose that the interest rates are known to follow expectations dynamics.

– Then the theoretical futures and forward prices of corresponding contracts are identical.

– See the proof in Luenberger.

Futures Contracts • Derivative instrument. • Two parties agree to transact a set of financial instruments or

physical commodities for the future at a specific price. – Futures contracts are almost always closed prior to the

settlement date. • High standardization:

– Quantity, quality, and time. • Futures are traded in the futures markets, where as physical

commodities are traded in cash markets. • The price of futures and the price of the underlying commodity

converge as the maturity date approaches. • Buyers and sellers use futures to hedge risk while speculators

assume it in efforts to make a profit. • Why use a Futures market rather than establish a Forward

contract?

Futures Contracts Basically, the Futures markets make it possible for those who want to manage price risk (hedgers), and to transfer that risk to those who are willing to accept it (speculators) who want to make a profit.

Futures Contracts Forward Contracts Default Risk: Borne by Clearinghouse Borne by Counter-Parties What to Trade: Standardized (identified) Negotiable (anything?) The Forward/Futures Price Agreed on at time of trade, then

Marked-to-Market Agreed on at time of trade. Payment at contract cancelation.

Where to Trade: Standardized Negotiable When to Trade: Standardized Negotiable How Much to Trade: Standardized Negotiable What Type to Trade: Standardized Negotiable Margin (deposit) Required Collateral is negotiable

Trading Futures • You need an initial deposit. • The quantities are set by the exchange. • Initial (3-5%) and maintenance (typically 75% of initial) margins. • You can trade a futures contract that has a value of more of

$20,000 with a little more than $1,000; high leverage! • Gains and loses are calculated daily. • Accounts are credited or debited. • Soybeans futures:

– Contract size: 5,000 bushels (60lb per bushel) – Quality: No. 2 yellow at par (no premium or discount based

on quality) – Contract Months: Mar, May, Jul, Aug, Sep, Jan.

• Note, bushels of typical grains has a weight conversion such as 32lb of oats per bushel; corn is 8 dry gallons per bushel)

Example

• Day 1: A buyer buys a contract for 5,000 bushels of soybean at $5.50 ($27,500 total value) and a seller sells one at $5.50.

– Each person deposits a 4.18% initial margin of $1,150; the maintenance margin is $850.

• Day 2: Soybeans rise $0.10 to $5.60. – The buyer’s account balance increases by $500 ($0.10 * 5000) while the

seller’s decreases by the same amount. – The seller’s account triggers a margin call.

Buyer Seller Margin Account Settlement Margin Account

Day Deposits Call Balance Price ($/bu) Deposits Call Balance 1 1,150.00$ 1,150.00$ 5.50$ 1,150.00$ 1,150.00$ 2 1,650.00$ 5.60$ 650.00$

500.00$ 500.00$ 1,150.00$

3 1,150.00$ 5.50$ 1,650.00$ 4 900.00$ 5.45$ 1,900.00$ 5 650.00$ 5.40$ 2,150.00$

500.00$ 500.00$ 1,150.00$

Deposits 1,650.00$ 1,650.00$ Final Bal 1,150.00$ 2,150.00$

Total (500.00)$ 500.00$

Example

• On day 5, the buyer would buy 5000 bushels of soybeans in the cash market for $5.40 * 5000 = $27,000.

• The buyer's total expenditure is $27,000 + $500 = $27,500. • The seller would sell 5000 bushels of soybeans in the cash market for $27,000. • The seller's total revenue would be $27,000 + $500 = $27,500. • For a speculator (seller) the return would be 5.75% compounded daily as

opposed to 0.35% compounded daily.

Buyer Seller Margin Account Settlement Margin Account

Day Deposits Call Balance Price ($/bu) Deposits Call Balance 1 1,150.00$ 1,150.00$ 5.50$ 1,150.00$ 1,150.00$ 2 1,650.00$ 5.60$ 650.00$

500.00$ 500.00$ 1,150.00$

3 1,150.00$ 5.50$ 1,650.00$ 4 900.00$ 5.45$ 1,900.00$ 5 650.00$ 5.40$ 2,150.00$

500.00$ 500.00$ 1,150.00$

Deposits 1,650.00$ 1,650.00$ Final Bal 1,150.00$ 2,150.00$

Total (500.00)$ 500.00$

Futures Contracts • Go to: http://www.cmegroup.com • Get information on contract specifications of: • Corn • Wheat • Lean Hogs • Light Sweet Crude Oil Futures • Get familiar with terminology, trading information and margin

requirements. – http://www.cmegroup.com/wrappedpages/clearing/pbrates/perform

ancebond.html • Go to the Education link on the CME Group home page, select Tools &

Analytics, select the Agricultural Hedging Simulations Demonstration and follow the lesson on how to use the simulator.

• Try the simulator to manage risks, either from the buyer or seller’s perspective.

• Check out the other education materials including the Getting Started series of lectures.

Marking to Market Example • On August 17, 2010, an investor wants to sell a 10 gold futures

contract for delivery in September 2010.

• The investor sells the 10 contracts at 11:00am, when the futures price is $310/oz.

• The initial margin requirement is $1000.

• One contract covers 100 oz of gold.

• The settlement price at the close on August 17 is $312.10/oz.

Marking to Market Example

• Profit up to August 26 = -$1,280.00

Date Gold Price Cash Flow Beginning Equity

Margin Call

Ending Equity

17-Aug $ 310.0 $ 1,000.0 17-Aug (end) $ 312.1 $ (210.0) $ 790.0 $ - $ 790.0

18-Aug $ 313.9 $ (180.0) $ 610.0 $ 390.0 $ 1,000.0 19-Aug $ 313.3 $ 60.0 $ 1,060.0 $ - $ 1,060.0 20-Aug $ 316.8 $ (350.0) $ 710.0 $ - $ 710.0 21-Aug $ 315.7 $ 110.0 $ 820.0 $ - $ 820.0 22-Aug $ 315.5 $ 20.0 $ 840.0 $ - $ 840.0 23-Aug $ 314.1 $ 140.0 $ 980.0 $ - $ 980.0 24-Aug $ 319.2 $ (510.0) $ 470.0 $ 530.0 $ 1,000.0 25-Aug $ 321.3 $ (210.0) $ 790.0 $ - $ 790.0 26-Aug $ 322.8 $ (150.0) $ 640.0 $ 360.0 $ 1,000.0

Additional Concepts • The value of a futures contract is such that in general it does

not allow arbitrage.

• Thus this implies that Ft = S0 + Ct-0, Where Ft is the futures price of the commodity at time t, S0 is the spot price at time 0, and Ct-0 is the carrying cost.

• This implies certain relationship among the futures prices of the same contract: Ft1 < Ft2 < Ft3 < Ftn , where t1 < t2 < t3 < tn.

• This is assuming that the interest rates remain the same and that the carrying costs are non-decreasing on t.

Corn Futures Daily Settlements 10/18/2016

Month Open High Low Last Change Settle EstimatedVolume Prior Day

Open Interest

DEC 16 354'2 357'4 351'4 354'0 -'2 353'6 130,050 676,813

MAR 17 363'6 367'2 361'2 361'6 -'4 363'4 31,809 301,865

MAY 17 370'4 373'4 368'2 365'4 -'4 370'2 12,802 69,098

JLY 17 377'0 380'0 374'6 376'2 -'4 376'4 9,619 128,956

SEP 17 383'6 386'4 381'4 383'0 UNCH 383'2 3,247 44,105

DEC 17 390'6 394'0 389'2 391'0 UNCH 391'0 6,324 80,757

MAR 18 399'4 402'4 398'4 399'6B UNCH 399'6 585 5,481

MAY 18 405'6 406'2 405'6 406'0A UNCH 404'6 11 1,076

JLY 18 407'6 410'2 407'2 408'0B +'4 408'0 52 1,488

SEP 18 404'4 410'0 404'4 410'0 +1'2 405'2 7 569

DEC 18 404'4 410'0 404'2 406'4 +1'4 406'4 149 5,046

JLY 19 - - - - +1'4 422'4 0 57

DEC 19 - - - - +1'4 413'0 0 136

Total 194,655 1,315,447

• Notice the interesting dynamics of the futures prices.

• What may be the reason for this pattern?

Weekly information obtained on October 18, 2016 for Corn Futures contract to expire on December 2016, (settles on the business day prior to December 15).

Example of Trading Data

Corn Futures CME Group Contract Contract Unit 5,000 bushels (~ 127 Metric Tons) Price Quotation Cents per bushel Trading Hours Sunday – Friday, 7:00 p.m. – 7:45 a.m. CT and

Monday – Friday, 8:30 a.m. – 1:20 p.m. CT Minimum Price Fluctuation 1/4 of one cent per bushel ($12.50 per contract) Product Code CME Globex: ZC; CME ClearPort: C; Clearing: C; TAS: ZCT Listed Contracts March (H), May (K), July (N), September (U) & December (Z) Settlement Method Deliverable Termination Of Trading The business day prior to the 15th calendar day of the contract month. Trade At Marker Or Trade At Settlement Rules

Trading at settlement is available for first 3 listed futures contracts, nearby new-crop December contract (if not part of the first 3 outrights), first to second month calendar spread, second to third month calendar spread, and nearest Jul-Dec spread when available (when July is listed); and are subject to the existing TAS rules. The Last Trade Date for CBOT Grain and Oilseed TAS products will be the First Position Day (FPD) of the front-month contract (FPD is the second to last business day in the month prior to the nearby contract month). Trading in all CBOT Grain TAS products will be 19:00-07:45 and 08:30-13:15 Chicago time. All resting TAS orders at 07:45 will remain in the book for the 08:30 opening, unless cancelled. TAS products will trade a total of four ticks above and below the settlement price in ticks of the corresponding futures contract (0.0025), off of a "Base Price" of 0 to create a differential (plus or minus 4 ticks) versus settlement in the underlying product on a 1 to 1 basis. A trade done at the Base Price of 0 will correspond to a "traditional" TAS trade which will clear exactly at the final settlement price of the day.

Settlement Procedures Corn Settlement Procedures Position Limits CBOT Position Limits Exchange Rulebook CBOT 10 Price Limit Or Circuit Price Limits Vendor Codes Quote Vendor Symbols Listing Last Delivery Date Second business day following the last trading day of the delivery month. Grade And Quality #2 Yellow at contract Price, #1 Yellow at a 1.5 cent/bushel premium #3 Yellow at

a 1.5 cent/bushel discount

Illinois North Central No. 2 Yellow Corn Spot Price - USDA

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Some of the Exchanges • Chicago Mercantile Exchange (CME) Group • Intercontinental Exchange (ICE Futures Europe) • NYSE Euronext • Sydney Futures Exchange • Tokyo Stock Exchange • Tokyo Commodity Exchange • London Metal Exchange • Intercontinental Exchange (ICE Futures U.S.) - formerly New

York Board of Trade • New York Mercantile Exchange CME • Dubai Mercantile Exchange • Korea Exchange - KRX • Singapore Exchange - SGX

Organization of the Futures Exchanges

Board of Governors

Regulatory Agency

Gov't Legislation

Sellers Hedgers

Commercials Speculators

Clearinghouse

Buyers Hedgers

Commercials Speculators

Futures Exchange

• Futures trading is almost all electronic today.

• The old “shouting” pits are being closed.

CBOT

Types of Trade Orders • Market Order: An order in which the customer states the

quantity and a given delivery month the customer wishes to buy or sell.

– The customer does not specify the price but simply wants it placed as soon as possible at the best possible price.

• Limit Order: Contains a price limitation and can be executed only at the price specified or at a better price.

• Stop order: Also stop-loss order. One that is brought to the status of a market order when a given price level is reached.

• Open Order: An order which is not automatically cancelled at the end of the trading day.

– Will remain in trade deck until filled or canceled.

• Similar to ordering stocks.

How do we use Futures Contracts? • In our next lectures we will discuss the use of Futures and

other financial instruments for risk management.

Assignments • Luenberger 2nd edition Chapter 12 problems 12.1, 12.3, 12.7,

12.13. • Luenberger 1st edition Chapter 10 problems 10.1, 10.3, 10.7,

10.11.

• Log into the CME Group home page at – http://www.cmegroup.com/

• Go to the Education link on the CME Group home page, select Tools & Analytics, select the Agricultural Hedging Simulations Demonstration and follow the lesson on how to use the simulator.

• Try the simulator to manage risks, either from the buyer or seller’s perspective.

• Check out the other education materials including the Getting Started series of lectures.