Finance 300Financial Markets

Lecture 24

© Professor J. Petry, Fall 2002

http://www.cba.uiuc.edu/broker/fin300/fin300pp.htm

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Housekeeping• Bond project is due on Thursday. • All groups should run their analysis by the TAs

prior to turning it in to make sure you are giving them what you want. They are there to help with this project. Please make use of them.

• UISES: Invest wisely.– We are ahead!!!

Team Rate of Return (as of 11/18)Petry 3.11%Finnerty 2.86%Oltheten 1.64%Waspi 1.37%Sinow 0.52%

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(Similar to) Things To Do: IX-3• George Q. Farmer expects to harvest 50,000 bushels of

soybeans in October, but there are no October futures in soybeans. Tofu, Inc wishes to buy 50,000 bushels of soybeans in October, but faces the same problem.

• The current spot price for soybeans is $6.20 and the price for November soybeans is 631. Initial margin is $1,125 per contract.

A) Construct a hedge strategy for George and for Tofu Inc.B) In October the spot price for soybeans is $6.00 and the November futures price is 611. What is the basis on November soybeans? How do George and Tofu Inc. make out? How would George and Tofu made out had they not hedged?C) In October the spot price for soybeans is $7.00 and the November futures price is 714. Now how do George and Tofu make out? Why is this different than in Part B?

Chapter IX – Futures

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IX-3 A & B: (Similar question to TTD, different numbers)George Q. Farmer - Hedge Positionhedge is set Sell Nov 98 Futures

10 contracts at 631 (=$315,500) Margin:Oct 1998 Buy Nov 98 Futureshedge is lifted 10 contracts at 611 (=$305,500) Profit:

Margin:Sell Soybeans on spot market at 6.00

Net Position:George Q. Farmer - No Hedge PositionOct 1998 Sell Soybeans on the spot market at 6.00

Net Position:

Tofu, Inc - Hedge Positionhedge is set Buy Nov 98 Futures

10 contracts at 631 (=$315,500) Margin:Oct 1998 Sell Nov 98 Futureshedge is lifted 10 contracts at 611 (=$305,500) Profit:

Margin:Buy Soybeans on the spot market at 6.00

Net Position:Tofu, Inc - No Hedge PositionOct 1998 Buy Soybeans on the spot market at 6.00

Net Position:

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IX-3 C: (Similar to TTD, but different numbers)George Q. Farmer - Hedge Positionhedge is set

Margin:Oct 1998hedge is lifted Profit:

Margin:

Net Position:George Q. Farmer - No Hedge PositionOct 1998

Net Position:

Tofu, Inc - Hedge Positionhedge is set

Margin:Oct 1998hedge is lifted Profit:

Margin:

Net Position:Tofu, Inc - No Hedge PositionOct 1998

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Things To Do: IX-3• Tofu Inc plans to buy 50,000 bushels of soybeans in October.

Tofu Inc would like to hedge its price risk exposure on soybeans but there are no October futures in soybeans.

• The current spot price for soybeans is $4.20 and the price for November soybeans is 431. Initial margin is $810 and maintenance is $600 per contract.

A) Construct a hedge strategy for Tofu Inc.B) In October the spot price for soybeans is $4.00 and the November futures price is 411. What is the basis on November soybeans? What is the net position and effective price per bushel for Tofu, Inc?C) In October the spot price for soybeans is $5.00 and the November futures price is 508. What is the basis? What is the net position and effective price per bushel for Tofu Inc? Why is there a difference between this situation and the one in part B?

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TTD: IX-3 (part B)Tofu, Inc - Hedge Positionhedge is set

Margin:Oct 1998hedge is lifted Profit:

Margin:

Net Position:Effective price per bushel:

Tofu, Inc - No Hedge PositionOct 1998

TTD: IX-3 (part C)Tofu, Inc - Hedge Positionhedge is set

Margin:Oct 1998hedge is lifted Profit:

Margin:

Net Position:Effective price per bushel:

Tofu, Inc - No Hedge PositionOct 1998

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Determination of Futures Prices• Futures prices are based on the following theorem:

Spot-futures parity theorem (a.k.a. cost of carry relationship): Describes the theoretically correct spread between spot and futures prices.

It states that the futures price reflects the spot price of the underlying asset plus the carrying charges (cost of borrowing, storage, insurance, etc) necessary to carry the underlying asset forward to delivery.

Violation of the parity relationship gives rise to arbitrage opportunities

• A risk-free profit requiring no initial investment. Arbitrage often involves the simultaneous purchase and sale of essentially the same asset.

Chapter IX – Futures

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Determination of Futures Prices• Ranges for futures prices can be established by calculating the points at

which arbitrage profits become possible. Futures prices will not remain at these levels, as market participants quickly buy up these opportunities until prices adjust them away.

• For arbitrage profits to be possible: • Example: Suppose in January 1998 the spot price of gold is $370 and

the January 1999 gold futures are trading at $400. The risk free rate of interest is 5%, storage & insurance cost $.10 per ounce, per month. CBT gold futures trade in contracts of 100 ounces, with an initial margin requirement of $1,800.– Abitrage opportunities exist in each of the following slides. – In the first, we use the assumptions from above, and go long in the spot market

and short in the futures market. When we sell in the future, the price must be high enough to pay carry costs, and still leave risk-free profit. P future >= Pspot + [cost of carry]

– In the second, we change the futures price from 400 to 360, and go short the spot market and long the futures market. Now for arbitrage profits to exist P future+[carry]<=Pspot. The futures price must be low enough to make a profit when we buy the gold.

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Arbitrage Profit Opportunities in Futures MarketsJanuary 1998 Cash Flow Per Ounce

Buy 100 troy ounces of gold on the spot market -37,000 -370Storage and insurance -120 -1.2Sell 1 Jan 99 gold futures contract at $400 Initial margin -1800Borrow at 5% for 12 months -38920Initial Investment 0

January 1999Deliver gold at futures price of $400 40,000 400Withdraw Margin 1,800Pay off debt principle -38,920 interest -1,946 -19.46

Profit 934 9.34

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Arbitrage Profit Opportunities in Futures Markets

January 1998 Cash Flow Per OunceShort 100 troy ounces of gold on the spot market 37,000 370 Borrowing Fee -2,000 -20Buy 1 Jan 99 gold futures contract at $360 Initial margin -1800Invest at 5% for 12 months -33200Initial Investment 0

January 1999Take delivery gold at futures price of $360 -36,000 -360Withdraw Margin 1,800Cash in investments principle 33,200 interest 1,660 16.60

Profit 660 6.60

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Things To Do: IX-8• The gold futures contract is defined as 100 ounces and the initial

margin is $600 per contract. The spot price of gold is $370/oz. Gold storage and insurance is 0.10 per ounce per month. Your broker will lend you gold for $3 per ounce per month. You may borrow or lend at 5% per annum.

A) What is the price range for 12 month gold futures (at what prices do the arbitrage opportunities disappear) if the interest rate at which you can borrow or lend is 5%?B) What is the expected price range for 12 month gold futures if the interest rate increases to 15%?C) What is the expected price range for 6 month gold futures if the interest rate increases to 15%?D) What is the expected price range for 3 month gold futures if the interest rate increases to 15%?E) What is the expected price range for gold futures if the interest rate is 15% and the delivery date is tomorrow.

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Financial Futures• Financial Futures are futures contracts where the underlying asset

itself is a financial instrument. These instruments are commonly referred to as derivates, as they derive their value from the value of an underlying asset.

• Futures on fixed income securities such as treasuries are referred to as interest rate futures.

• Short Hedge: the sale of a financial futures contract to hedge against an increase in interest rates (a decrease in the price of the asset)

• Long Hedge: the purchase of a financial futures contract to hedge against a decrease in interest rates (an increase in the price of the asset).

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Power of Leverage in Futures MarketsLong term interest rates at 8%, expected to decline to 7% w/in 6 monthsStrategy A: buy $1mn 20 year 8% T-Bonds on the run at 100.00March Buy 20 yr 8% bonds at 100 -1,000,000 -1,000,000September If the interest rates are: 7% 9%

coupon ($1,000,000*0.08*.5) 40,000 40,000sell 19.5 yr 8% T-bond at 7% (110:18) 1,105,625sell 19.5 yr 8% T-bond at 9% (90:28) 908,750Profit 145,625 51,250Rate of Return (semi-annual) 14.56% -5.13%

Strategy B: buy 400 Sept T-Bond futures at 89.00*March Buy 400 Sept T-Bond futures at 89.00 -1,000,000 -1,000,000September If interest rates are: 7% 9%

Sell 400 Sept T-Bond futures at 98:16 3,800,000margin returned 1,000,000Sell 400 Sept T-Bond futures at 81:08 -3,100,000margin returned 1,000,000Profit 3,800,000 -3,100,000

380% -310%*T-bond futures contract for $100,000. Assum margin of $2500 per contract.

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Miscellaneous• There are a number of closely related concepts and

examples in this chapter that we did not directly discuss. You are responsible for this information, and problems, with the one exception being Things To Do: IX -12 relating to portfolio volatility. You will be notified of any other omissions on web-board.