A NSW ERS TO Q UESTIONS & P ROBLEM S

Chapter 22 - Futures Strategies 22-1: A.

Buy 10 November Soybean contracts @ 431. Deposit $8,100 to margin.

B.

Basis = $4.00 - $4.11 = -11¢ This is a text book hedge. Tofu Inc - Hedge Position Hedge is set

Buy November Futures: 6 10 contracts at 431 ($215,500)

Margin:

- $8,100.

October (Hedge is lifted)

Sell November Futures: 6 10 contracts at 411 ($205,500)

Margin: Profit:

+ $8,100. - $10,000.

Buy Soybeans on the spot market at $4.00

- $200,000. NET POSITION: Effective price per bushel:

C.

-$210,000. $4.20

Basis = $5.00 - $5.08 = -8¢ Tofu Inc - Hedge Position Hedge is set

Buy November Futures: 6 10 contracts at 431 ($215,500)

Margin:

- $8,100.

October (Hedge is lifted)

Sell November Futures: 6 10 contracts at 508 ($254,000)

Margin: Profit:

+ $8,100. + $ 38,500.

Buy Soybeans on the spot market at $5.00

- $250,000. NET POSITION: Effective price per bushel:

- $211,500. 4.23

Tofu Inc. tried to lock in a price of $4.20 but the basis narrowed from - 11¢ to -8¢. This means that the spot price increased 80¢ per bushel while the futures price increased 77¢ per bushel; thus the effective price of soybeans was $4.23; 3¢ more per bushel than the original spot price of $4.20. When the basis changes over the hedge then it is no longer a perfect or textbook hedge.

O LTHETEN & W ASPI 2012

In summary: Tofu

Textbook Hedge Set

Lift

Spot Price

$4.20

Futures Price Basis

Price Change

Profit/ (Loss)

$4.00

- .20

$4.31

$4.11

- .20

- .11

- .11

.00

Net:

D.

Non-Textbook Hedge Set

Lift

Price Change

$10,000.

$4.20

$5.00

+ .80

($40,000.)

($10,000.)

$4.31

$5.08

+ .77

$38,500.

- .11

- .08

- .03

$0.

Profit/ (Loss)

($1,500) -3¢ / bushel

Basis = $1.00 - $1.11 = -11¢ Tofu Inc - Hedge Position Hedge is set

Buy November Futures: 6 10 contracts at 431 ($215,500)

Margin:

- $8,100.

October (Hedge is lifted)

Sell November Futures: 6 10 contracts at 111 ($55,500)

Margin: Profit:

+ $8,100. - $ 160,000.

Buy Soybeans on the spot market at $1.00

- $50,000. NET POSITION: Effective price per bushel:

- $210,000. 4.20

Tofu Inc. tried to lock in a price of $4.20. The basis remained unchanged at - 11¢ so this is a textbook hedge.

A NSW ERS TO Q UESTIONS & P ROBLEM S

22-2: A.

Buy 1 November soybean future contract @ 431. Deposit $810 to margin.

B. Kankakee Canning Corporation - Cross Hedge Position Hedge is set

Buy l November Futures: 6 1 contract at 431 ($21,550)

Margin:

- $810.

October (Hedge is lifted)

Sell November Futures: 6 1 contract at 411 ($20,550)

Margin: Profit:

+ $810. - $1,000.

Buy Squash on the spot market at $4.84

- $24,200. NET POSITION: Effective price per bushel:

- $25,200. $5.04

C. Kankakee Canning Corporation - Hedge Position Hedge is set

Buyl November Futures: 6 1 contract at 431 ($21,550)

Margin:

- $810.

October (Hedge is lifted)

Sell November Futures: 6 1 contract at 411 ($20,550)

Margin: Profit:

+ $810. - $1,000.

Buy Squash on the spot market at $4.85

- $24,250. NET POSITION: Effective price per bushel

- $25,250. $5.05

In this case, although the basis remained at 11¢, the price of squash is now $0.85 higher than the price of soybeans rather than $0.84 higher as in B. In the corresponding example in the book George Q. Farmer received an extra penny per bushel; in this question Kankakee Canning was required to pay an extra penny per bushel. In summary: K.C.C.

Textbook Hedge Set

Lift

Price Change

Spot Price (Squash)

$5.04

$4.84

- .20

Spot Price (Soybeans)

$4.20

$4.00

Futures Price

$4.31

$4.11

- .11

- .11

.84

.84

Basis Spot Price Spread Net:

Non-Texbook Hedge Profit/ (Loss)

Lift

Price Change

Profit/ (Loss)

$5.04

$4.85

- .19

-.20

$4.20

$4.00

- .20

- .20 ($1,000.)

$4.31

$4.11

- .20 ($1,000.)

.00

- .11

- .11

.00

.00

.84

.85

- .01

.00

$1,000.

Set

$0.

$950.

- .01 ($50.) = -$0.01/bushel

O LTHETEN & W ASPI 2012

22-3: A.

We buy 100 (3,750,000 / 37,500) September Contracts

B.

The basis narrows by 15.5¢ from 55.5¢ to 40¢ per pound.

C. Details

$$

May

Buy 100 September contracts @ 194.500 [100c * 37,500 lbs * $1.945 = $7,293,750.00]

- margin:

- $ 100,000.

August

Sell 100 September contracts @ 360.00 [100c * 37,500 lbs * $3.60 = $13,500,000]

+ margin: + profit:

+ $ 100,000. + $6,206,250.

Buy 3,750,000 lbs coffee spot @ $4.00/lb

- $ 15,000,000. Net position:

D.

- $ 8,793,750.

Nescafé pays $2.345 per pound for 3,750,000 pounds of coffee. Nescafé is enchanted to the tune of 15.5¢ per pound because when we set up the hedge the price of coffee was $2.50 per pound. The difference between the original spot price and the effective price must be equal to the change in basis. Set

Lift

Price Change

Profit/ (Loss)

Spot Price

$ 2.50

$ 4.00

+ $ 1.50

($ 5,625,000.)

Futures Price

$ 1.945

$ 3.60

+ $ 1.655

$ 6,206,250.

0.555

.40

Basis

-

.155

$ 581,250.

Nescafé's effective price per pound is the original spot price minus 15½ ¢ per pound

A NSW ERS TO Q UESTIONS & P ROBLEM S

22-4: A.

6706 * 15,000 = 100,590,000 pounds

B.

The basis is $1.10 - $1.1855 = - $ 0.0855 = - 8.55¢

C.

There is no activity (no open, high, or low) but there is a settle. Yet, despite the lack of activity each of these contracts moved down by a suspiciously even amount. We can deduce that the far contracts (September and November) made a limit move down and that the limit on the far contracts is 65¢ and that the July contract made a limit move down and that the limit on the May and July contracts is 85¢. The May contract traded but the lowest trade at $1.215 is not as low as the settle of $1.2055 So we can deduce that trading stopped at $1.215 and the contract made a limit move down as well.

D.

Set the Hedge by buying 4 March contracts @ 118.55

E.

The basis narrowed by 2.35¢, from 8.55¢ to 6.20¢ per pound.

F. Details

$$

Dec

Buy 4 March contracts @ 118.55 [4c * 15,000 lbs * $1.1855 = $71,130]

- margin:

- $ 2,000.

February

Sell 4 March contracts @ 126.20 [4c * 15,000 lbs * $1.262 = $75,720]

+ margin: + profit:

+ $ 2,000. + $4,590.

Buy 60,000 lbs FCOJ spot @ $1.20/lb

- $ 72,000. Net position:

G.

- $ 67,410.

Droste pays $1.1235 per pound for 60,000 pounds of FCOJ. Droste pays 2.35¢ per pound more than the original spot price of $1.10 per pound. This 2.35¢ difference is because the basis narrowed by 2.35¢. Droste is still happy with the hedge because, without it, they would have paid $1.20 per pound.

O LTHETEN & W ASPI 2012

M

Note that in both the hedge we set up for Droste and the hedge we set up for Nescafe in the previous question,

the basis narrowed. But Nescafe paid less than the original spot price because the basis was positive and narrowed. With Droste the basis change was negative and narrowed, so the effective price was more than the original spot price. When you are buying and the effective price goes down this is good news. Droste paid more that the original spot price because the basis was negative and narrowed. The basis change was positive so the effective price was more than the original spot price. When you are buying and the effective price goes up this is bad news. In summary: DROSTE

Set

Lift

Price Change

Spot Price

$ 1.10

$ 1.20

+ $ 0.10

Futures Price

$ 1.1855

$ 1.2620

+ $ 0.0765

Basis

- 0.0855

- 0.0620

+

0.0235

Profit/(Loss) ($ 6,000.) $ 4,509. ($ 1,410.)

Droste's effective price per pound is the original spot price + $0.0235 per pound

NESCAFE

Set

Lift

Price Change

Profit/(Loss)

Spot Price

$ 2.50

$ 4.00

+ $ 1.50

($ 5,625,000.)

Futures Price

$ 1.945

$ 3.60

+ $ 1.655

$ 6,206,250.

0.555

.40

Basis

-

.155

$ 581,250.

Nescafé's effective price per pound is the original spot price - $1.55 per pound

A NSW ERS TO Q UESTIONS & P ROBLEM S

22-5: A.

To find the price limits we need to find at which prices we can and cannot make a profit through arbitrage.

Buy futures low; sell spot high

Buy spot low; sell futures high

Buy 1 copper futures contract @ p margin:

- $600.

Sell short 10,000 lbs copper @ $3.70

+ $37,000.

Borrowing fee @ $300 per month Lend @ 5% for 12 months

- $3,600. - $32,800.

Net Investment:

0.

Futures: take delivery of copper @ p margin:

- (10,000 * p) + $600.

Sell 1 copper futures contract @ P margin: Buy 10,000 lbs copper @ $3.70 Storage @ $10 per month

- $600. - $37,000. - $120.

Borrow @ 5% for 12 months Net Investment:

+ $37,720. 0.

12 months later

Realize Loan:

principal: interest: $35,040 -10,000p = 0 p = $3.504 per pound

+ $32,800. + $1,640.

Futures: deliver copper@ P Repay loan:

margin:

+ (10,000 * P) + $600.

principal: interest:

- $37,720. - $1,886.

10,000P - $39,006 = 0 P = $3.9006 per pound

The price range for 12 month copper futures is $3.5040 to $3.9006; a range of $0.3966. Any price outside this range will be arbitraged away. The table shows the calculations for the breakeven point for each of three futures, the 12 month future, the 6 month future, the 3 month future, and the 0 month future (delivering tomorrow). The graph illustrates how the price range converges to the spot price over time.

M

Note the asymmetry of the probability curve. This asymmetry derives from the nature of moving commodities

through time. Moving forward in time is much easier (and cheaper) than moving backwards even when the borrowing and lending rates are the same.

O LTHETEN & W ASPI 2012 Buy spot low; sell futures high

12 month

Buy 10,000 lbs of copper on the spot market storage and insurance at $10 per month Sell 1 future @ P

Initial Margin

Borrow at 15% Net Investment

6 month

- $37,000.

- $37,000.

- $120.

- $60.

3 month -$37,000 - $30.

0 month - $37,000. $0.

-$600.

-$600.

-$600.

-$600.

+ $37,720

+ $37,660.

+ $37,630

+ $37,600.

0.

0.

0.

0.

At Delivery Deliver copper @ $P/lb on contract Repay loan

+ $10,000 P

+ $10,000 P

+ $10,000 P

Margin

+ $600.

+ $600.

+ $600.

+ $600.

principal interest

- $37,720. - $5,658.

- $37,660. - $2,824.50

- $37,630. - $1,411.125

- $37,600. $0.00

Breakeven Price of copper per pound (P = )

Buy futures low; sell spot high

12 month

Short 10,000 lbs of copper on the spot market borrowing fee at $300 per month Buy 1 future @ p

$4.2778

Initial Margin

Lend at 15% Net Investment

$3.9884

$3.8441

+ $10,000 P

$3.7000

6 month

3 month

0 month

+ $37,000.

+ $37,000.

+ $37,000.

- $3,600.

- $1,800.

- $900

- $0

- $600.

- $600.

- $600.

- $600.

- $32,800.

- $34,600

- $35,500

- $36,400.

+ $37,000.

0.

0.

0.

0.

- $10,000 p

- $10,000 p

- $10,000 p

+ $600.

+ $600.

+ $600.

+ $600.

principal + $32,800. interest + $4,920.

+ $34,600. + $2,595.

+ $35,500. + $1,331.25

+ $36,400. + $0.00

At Delivery Take delivery of copper@ $p on contract Margin Realize loan

- $10,000 p

Breakeven Price of copper per pound (P = )

$3.8320

$3.7795

$3.7431

$3.7000

Spread

$0.4458

$0.2089

$0.1010

$0.0000

A NSW ERS TO Q UESTIONS & P ROBLEM S

22-6: A.

Start by identifying in which market you should buy and in which you should sell. Since we aim to buy low and sell high we buy in the spot market @ $1200 and sell in the futures market @ $1280. The rest is detail.

B. Arbitrage Trade Buy 50 ounces of platinum on the spot market @ $1200

- $60,000.

storage and insurance at $5 per ounce per year Sell 1 future @ $1280. [1c * 50oz * $1280 = $64,000]

- $250. Initial Margin

-$3,000.

Borrow at 5%

+ $63,250.

Net Investment

0.

At Delivery Deliver 50 ounces platinum on contract @ $1280/oz

+ $64,000. Withdraw Margin

Repay Loan

+ $3,000.

principal interest

- $63,250. - $3,162.50

Profit:

$ 587.50

You can make a $587.50 profit on each contract by arbitraging. C.

Since you buy spot and carry it to the future this is cash and carry arbitrage.

22-7: A.

$50 ± 5% => $47.50 to $52.50

B.

At $45, May futures are below the lower bound we have just calculated so, buying low and selling high means we buy futures and sell the stock.

February

Buy 10 TI futures contracts [10 * 1000 * $45.00 = $450,000] Margin:

- $10,000.

Short Sell 10,000 shares TI @ $50 deposit to margin account under Regulation T (150% of short sale)

+ $500,000. - $750,000.

borrow at 10%

+ $260,000. 0.

C.

In this example we – theoretically at least – buy shares in the future and carry them backwards through time to sell them in the present. So this is reverse cash and carry.

O LTHETEN & W ASPI 2012

D.

If we abort the arbitrage in April rather than waiting to delivery then we make a profit of $48,500.

April

E.

Sell 10 TI futures contracts [10 * 1000 * $20.50 = $205,000] Margin: Profit:

+ $10,000. - $245,000.

Buy 10,000 shares TI to cover short position @ $20. short position margin returned:

- $200,000. + $750,000.

Repayment of loan (three months)

principal: interest:

- $260,000. - $6,500.

PROFIT:

+ $48,500.

If we go to delivery we make a profit of $41,333.33 Note that the current price of Tardis ($72 per share) appears nowhere. The arbitrage trade seeks to profit on the difference in the price in two markets; in this case on the difference between the price of Tardis shares in the stock market ($50) and the price of Tardis shares in the futures market ($45). As soon as price changes become relevant we are speculating rather than arbitraging.

May

Take delivery of 10,000 shares TI on futures contract @ $45 [10 * 1000 * $45.00 = $450,000]

margin:

- $450,000. + $10,000.

Deliver 10,000 shares to the broker TI to cover short position short position margin returned:

+ $750,000.

Repayment of loan (four months)

principal: interest:

- $260,000. - $8,666.67

PROFIT:

+ $41,333.33

F.

We would generate greater profit by aborting the arbitrage in April. The difference of $7,166.67 comes from $5,000 in basis ($20.50 - $20.00 is 50¢ per share times 10,000 shares) and $2,166.67 in interest for the month of May that we don't have to pay. Notice that if we abort the arbitrage in April our additional profits come from speculation.

G.

This type of transaction is virtually risk free because all our prices are locked in when we set up the arbitrage. Both the futures price of $45 per share and the short sell price of $50 per share were locked in February. Whether Tardis Intertemporal is now selling at 6¢ or $103.50 concerns us not in the least. The “virtually” comes from the risk that we will be required to make further margin calls to keep the position open until delivery if the price moves significantly.