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Derivatives Test Bank by Dr. J. A. Schnabel (Questions & Answers)

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Course
E-commerce (DERIVATIVES)

Institution
Humber College ( )

Questions from Chapter 1 to Chapter 15 - The quiz and final exam questions will be similar are style the questions found in this Test Bank. Explanation of numbering system: The first one or two digits before the period refer to the textbook chapter to which the question pertains. The digits afte...

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a trader buys 100
a trader enters into a one year short forward contract to sell an asset for 60 when the spot price is 58 the spot price in one year proves to be 63 what is the trader’s profit

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Derivatives Test Bank Dr. J. A. Schnabel Page 1 of 36

Explanation of numbering system: The first one or two digits before the period refer to
the textbook chapter to which the question pertains. The digits after the period refer to
the number of the Test Bank question pertaining to the designated chapter. Thus, “3.1”
refers to the first question pertaining to Chapter 3.

The quiz and final exam questions will be similar are style the questions found in this
Test Bank.

Note that the default assumption in this course is that interest rates and dividend yields
are assumed to be quoted on a per annum and continuously compounded basis.

Chapter 1: Introduction

1.1. A trader enters into a one-year short forward contract to sell an asset for $60 when
the spot price is $58. The spot price in one year proves to be $63. What is the trader’s
profit?

Loss of $3

1.2. A trader buys 100 European call options with a strike price of $20 and a time to
maturity of one year. Each option involves one unit of the underlying asset. The cost of
each option or option premium is $2. The price of the underlying asset proves to be $25
in one year. What is the trader’s profit?

Profit of $300

1.3. A trader sells 100 European put options with a strike price of $50 and a time to
maturity of six months. Each option involves one unit of the underlying asset. The price
received for each option is $4. The price of the underlying asset is $41 in six months.
What is the trader’s profit?

Loss of $500

1.4. The price of a stock is $36 and the price of a 3-month call option on the stock with a
strike price of $36 is $3.60. Suppose a trader has $3,600 to invest and is trying to choose
between buying 1,000 options and 100 shares of stock. How high does the stock price
have to rise for an investment in options to be as profitable as an investment in the stock?

$40 Note that we are trying to solve the following equation for P, the stock price:
(P-36)100 = (P-36)1000 -3,600

1.5. A one year call option on a stock with a strike price of $30 costs $3. A one year put
option on the stock with a strike price of $30 costs $4. A trader buys two call options and
one put option.
A.) What is the breakeven stock price, above which the trader makes a profit?
B.) What is the breakeven stock price below which the trader makes a profit?

,Derivatives Test Bank Dr. J. A. Schnabel Page 2 of 36

A.) $35 since 2=10/x’ where x’ is the amount by which the breakeven price exceeds
$30, the strike price. Note that x = 30 + x’.
B.) $20 since 1=10/y’ where y’ is the amount by which the breakeven price falls short
of $30, the strike price. Note that y = 30 – y’.

$30

y x

Chapter 2: Mechanics of Futures Markets

2.1. A company enters into a short futures contract that involves 50,000 pounds of cotton
for 70 cents per pound. The initial margin is $4,000 and the maintenance margin is
$3,000. What is the futures price above which there will be a margin call?

$0.72 since we are trying to solve the equation: ($.70-P) 50,000 = - $(4,000-3,000)

2.2. A company enters into a long futures contract involving 1,000 barrels of oil for $20
per barrel. The initial margin is $6,000 and the maintenance margin is $4,000. What oil
futures price will allow $2,000 to be withdrawn from the margin account?

$22 since we are trying to solve the equation: 1000(P-20) = $2,000

Note that an amount can be withdrawn from the margin account when P, the settlement
price on the day of the transaction of the oil futures contract, exceeds $20.

2.3. On the floor of a futures exchange one futures contract is traded where both the long
and short parties are closing out existing positions. What is the resultant change in the
open interest?

Open interest drops by one.

,Derivatives Test Bank Dr. J. A. Schnabel Page 3 of 36

2.4. You sell 3 December gold futures when the futures price is $410 per ounce. Each
contract is on 100 ounces of gold and the initial margin per contract is $2,000. The
maintenance margin per contract is $1,500. During the next 7 days the futures price rises
steadily to $412 per ounce. What is the balance of your margin account at the end of the
7 days?

$5,400 since the total initial margin of 3X$2,000 is reduced by 3X$(412-410)X100=$600

2.5. A hedger takes a long position in an oil futures contract on November 1, 2009 to
hedge an exposure on March 1, 2010. Each contract is on 1,000 barrels of oil. The initial
futures price is $20. On December 31, 2009 the futures price is $21 and on March 1,
2010 it is $24. The contract is closed out on March 1, 2010. What gain is recognized in
the accounting year January 1 to December 31, 2010?

$4,000 = 1000 X $(24-20)

2.6. Answer 2.5 this time assuming that the trader in question is a speculator rather than a
hedger.

$3,000 = 1000 X ($24-21)

2.7. A speculator enters into two short cotton futures contracts, when the futures price is
$1.20 per pound. The contract entails the delivery of 50,000 pounds of cotton. The
initial margin is $7,000 per contract and the maintenance margin is $5,250 per contract.
The settlement price on the day of the transaction is $1.50 per pound. Assume that all
days are trading days.

Notes:
1.) If there is a margin call on a certain day, the deadline for depositing the variation
margin (which is the additional margin that should be deposited into the margin account
due to a margin call) is the trading day after the day of the margin call. The assumption
made in this course is that the variation margin is deposited at the deadline date, i.e. the
trading day after the day of the margin call.
2.) Margin calls are established at the settlement price, i.e. margin calls are established at
the end of the trading day.

A.) How much must the speculator deposit into his margin account on the day of the
transaction?

Initial margin = 2 x $7,000 = $14,000

B.) What is the amount of the margin call, if any, that is declared on the day of the
transaction?

, Derivatives Test Bank Dr. J. A. Schnabel Page 4 of 36

Automatic credit to MAB (margin account balance) due to adverse move in the futures
price, i.e., transaction price of 1.20 is less than the settlement price of 1.50, = 2 x 50,000
x (1.20 – 1.50) = -$30,000. A negative credit is a debit, i.e., the MAB is reduced by
$30,000.

The initial margin that is deposited of $14,000 is reduced by $30,000, resulting in a MAB
of -$16,000. As the latter is below the maintenance margin of $5,250 x 2 or $10,500, an
additional deposit of $30,000 is required to bring the MAB back to the initial margin.
The margin call thus equals $30,000.

C.) How much must the speculator deposit into his margin account, i.e. what is the
variation margin, on the day after the transaction?

The margin call or variation margin of $30,000, calculated in B.), must be deposited.
Note that margin calls or variation margins must be deposited on or before the trading
day after the day of the margin call.

2.8. On a certain day a speculator enters into 10 long soybean futures contracts, when the
futures price is $10.20 per bushel. The contract involves 5,000 bushels of soybean. The
initial margin is $4,000 per contract and the maintenance margin is $3,000 per contract.
The settlement price on that day is $10.05 per bushel. How much must the speculator
deposit into his margin account on day 1?

Note: Quiz and exam questions will broach what transpires on only one trading day.

Initial margin = $4,000 x 10 = $40,000
Maintenance margin = $3,000 x 10 = $30,000
Automatic credit = 10 x 5,000 (10.05 – 10.20) = -7,500
Margin account balance = 40,000 – 7,500 = 32,500 which exceeds maintenance margin
of 30,000. Thus, there is no variation margin required, i.e. there will be no margin call.
Deposit for day 1 = $40,000

2.9. List and explain briefly the possible effects of a single futures transaction on open
interest.

Open interest rises by 1 if both long and short positions are opening transactions.

Open interest does not change if one of the long or short positions is an opening
transactions whereas the other position is a closing transaction.

Open interest drops by 1 if both long and short positions are closing transactions.

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