PROBLEM SET 1 – FUTURES AND OPTIONS FIN 436
1. You have opened a futures account with a cash deposit of $10,000.00. You decide to sell 8
October contracts of bean meal at 305.4. Contract specs are as follows:
CONTRACT
UNIT
100 TONS
QUOTE
UNITS
US$ AND
CENTS/TON
TIC SIZE
CONTRACT MOS.
0.10/TON =
$10.00
Jan, Mar, May, Jul,
Sep, Oct, Dec
INITIAL
MARGIN
$1,122/
CONTRACT
MAINT
MARGIN
$1,020/
CONTRACT
If soybean meal drops $.10, what is the equity of the account when marked-to-market?
2. You are day-trading the S&P E-Mini contract with $5,750.00 of equity in your account. Contract
specs are as follows:
CONTRACT
UNIT
$50 x S&P
500 INDEX
QUOTE
UNITS
US$ AND
CENTS/TIC
TIC SIZE
CONTRACT MOS.
0.25 INDEX
PTS =
$12.50
Mar, Jun, Sep, Dec
INITIAL
MARGIN
$907.50/
CONTRACT
(DAY-TRADE)
MAINT
MARGIN
$825/
CONTRACT
(DAYTRADE)
Based on your new sophisticated algorithm, there is an 85% chance that the S & P will fall over
the next half hour, so you go all in by selling 6 June contracts. The market rises 5 tics, and then
plunges 50 tics when you flatten your position (buy to close them all). What was your gross profit
or loss for the day?
3. After the trade in Problem 2, you decide to buy October Copper futures (HGV-). Contract specs
are as follows:
CONTRACT
UNIT
25,000 lbs
QUOTE
UNITS
US$ &
CENTS/ib
TIC SIZE
CONTRACT MOS.
$.0005/lb =
$12.50
3 NEAREST MOS. +
Feb, Apr, Aug, Oct
INITIAL
MARGIN
$5,800/
CONTRACT
MAINT
MARGIN
$5,500/
CONTRACT
a. How many contracts can you (safely) buy?
b. If HGV then declines $0.0455 per pound, what is the market-to-market equity in the
account?
4. You are a trading associate at a major bank. Your supervisor assigns you with an assignment to
hedge against increases in future interest rates the bank’s inventory of two-year notes. You have
these alternatives:
I. Sell the necessary (optimal) amount of 2-year treasury futures, longest delivery date.
II. Sell the necessary (optimal) amount of 2-year treasury futures, shortest delivery date.
III. Buy necessary (optimal) amount of 2-year treasury futures puts, longest delivery date.
IV. Buy necessary (optimal) amount of 2-year treasury futures puts, shortest delivery date.
V. Buy necessary (optimal) amount of 2-year treasury futures calls, shortest delivery date.
What do you do?
a.
b.
c.
d.
Either I. or III.
Either I., III., or V.
Either I., II., III., or IV.
Only V.
5. Silver futures and spot silver have a correlation factor of 0.97. If the standard deviation for the
futures contract is 2.98 and the standard deviation for the spot is 1.87, what is the optimum
hedge ratio?
6. Based on the results in Problem 5, what is the optimum number of SIL contracts to hedge 5,220
troy ounces of silver held in inventory? (Each mini-futures contract represents 1000 troy ounces
– SIL is the symbol for Silver Micro-contracts).
7. You are the CFO of an airline and you are concerned that jet fuel prices will increase. You know
that there are no futures for jet fuel, but there are futures for gasoline. So, you call decide to check
the spot price of jet fuel and gasoline. Changes in their relative prices are as follows:
Mo 1
Mo 2
Mo 3
Mo 4
Mo 5
Mo 6
Mo 7
Mo  Gas Futures 2.0%
3.0%
-4.0%
0.0%
3.5%
-3.0%
-2.5%
2.0%
3.5%
-5.0%
1.0%
2.6%
-2.0%
-1.0%
Mo  Jet Fuel
If you are trying to hedge 1,000,000 gallons of jet fuel, how many gasoline contracts do you need
to buy to adequately hedge your position? (Each futures contract represents 42,000 gallons of
gasoline).
8. What is a cross-hedge?
a. It is a trade between similar commodities, different delivery dates, intended to hedge against
a detrimental change in price.
b. It is a trade between two uncorrelated commodities.
c. It is a trade between a commodity and a closely price-correlated non-traded commodity,
intended to hedge against a detrimental change in price.
d. I don’t know, and don’t care.
9. Your futures account had equity of $20,000.00 at the start. Given the following positions, what
is the account's CURRENT equity balance? (Refer to the contract specifications in the chart
following).
POSITIONS
QTY
Cost Basis
Price Now
Sep Wheat
Dec Gold
Dec Cocoa
Cash
TOTAL
5
1
2
-
CONTRACT
UNIT
QUOTE
UNITS
TIC SIZE
Wheat
5,000 bu
¢/bushel
$0.01
572'0
$1,554.70
$2,526.00
?
Equity
559'2
$1,666.50
$2,756.00
$
Gold
1,000 troy oz $1.00/troy oz
$0.10
Cocoa
10 m tons
$1.00
$ / ton
MOS.
Mar, May, Jul,
Sep, Dec
Feb-Apr, Jun,
Aug, Dec
Mar, May, Jul,
Sep, Dec
?
INITIAL
MGN
MAINT
MGN
$1,375
$1,250
$5,500
$5,000
$2,090
$1,900
10. Note the following contract specifications:
QUOTE
UNITS
CONTRACT
UNIT
Corn (C)
5000 bu 1/4c/bushel
WTI Crude Oil (CL)
1000
bls
$ and c
/barrel
TIC SIZE
.25c =
$12.50
.01/bl =
$10.00
MOS.
INITIAL
MGN
MAINT
MGN
H,K,N,U,Z
$2,750
$2,300
All Mos.
$7,250
$6,280
Assuming you were long 2 contracts of each of these commodities, how much would the total
account value decline if EACH position DECLINED 2.5% (round price to the nearest tic)?
11. You are working for a home builder, and want to hedge against increases in lumber prices. You
estimate that you will need 2,687,500 board feet of 2"x4"x84" stud lumber to complete their tract.
Doing some research, you find that contract specs for the closest commodity is for Random Length
Lumber:
CONTRACT
UNIT
QUOTE
UNITS
TIC SIZE
MOS.
INITIAL
MGN
MAINT
MGN
R L Lumber
110,000 bd ft
$/1K bd ft
$0.10 /bd ft= $11
Jan, Mar,
May, Jul,
Sep, Nov
$2,475
$2,225
Further research has shown that the correlation between spot 2 X 4 lumber and Random Length
Lumber is .9275. Meanwhile, the variance of price for 2 X 4 lumber is only .246, while the variance
of random length lumber is .378. Given this information, what is the hedge ratio? (Round to the
nearest thousandth).
12. You still work for a home builder. Now that you have calculated the hedge ratio (see Problem
11), based on the information in Problem 11, what is the optimal number of contracts you need
to hedge your future orders of stud lumber? (Round to the nearest contract - no fractional
contracts!).