Practise Exam MCQ's

Question 1

What is the reason for undertaking a gamma hedge?

a. government regulation
b. the possibility of counterparty default
c. changes in volatility
d. large movements in the underlying
e. none of the above

Answer 1

d. large movements in the underlying

Hint: Delta hedging works only for small stock price changes. For large changes, the risk is captured by the gamma.

Question 2

A lookback call option provides the right

a. to change the stock on which the option is written
b. to buy the stock at its lowest price over the option’s life
c. to insure a stock against loss
d. to change your mind about the exercise price
e. none of the above

Answer 2

b. to buy the stock at its lowest price over the option’s life

Hint: Look-back call: Minimum price for X
Max [0, ST- Min(S0…..ST)], no regret.

Question 3

You hold a stock portfolio worth $30 million with a beta of 1.05. You would like to lower the beta to .90 using S&P 500 futures, which have a price of 460.20 and a multiplier of 500. What transaction should you do? Round off to the nearest whole contract.

a. sell 130 contracts
b. sell 9,778 contracts
c. sell 20 contracts
d. buy 50,000 contracts e. sell 50,000 contracts

Answer 3

c. sell 20 contracts

Hint: 0.9 (30000000/(460.2x500) - 1.05 (30000000/460.2x500) = -19.55 = -20 contracts, thus should sell

Question 4

What is the profit on a hedge if bonds are purchased at $150,000, two futures contracts are sold at $72,500 each, then the bonds are sold at $147,500 and the futures are repurchased at $74,000 each?

a. -$2,500
b. -$5,500
c. -$500
d. -$3,000
e. none of the above

Answer 4

b. -$5,500

Hint: -150,000+72,500x2+147,500-74,000x2=-5500

Question 5

Which of the following can explain a contango?

a. the interest rate exceeds the dividend yield
b. the cost of carry is negative
c. futures prices exceed forward prices
d. the market is at less than full carry

Answer 5

a. the interest rate exceeds the dividend yield

Hint: f (T)>S when contango; f (T)-S= theta = interest - dividend > 0

Question 6

The difference in profit from an actual put and a synthetic put is

a. X
b. ST - X
c. X -ST
d. ST + X(1 + r)^-T
e. none of the above

Answer 6

e. none of the above

Hint: The difference between a synthetic put and an actual put is whether a bond is included or not

Question 7

Which of the following statements is true about the relationship between the option price and the risk-free rate?

a. a call price is nearly linear with respect to the risk-free rate
b. a call price is highly sensitive to the risk-free rate
c. the risk-free rate affects a call but not a put
d. the risk-free rate does not affect a call price
e. none of the above

Answer 7

a. a call price is nearly linear with respect to the risk-free rate

Hint: stable and linear relationship; a big interest change only has minor impact on call price

Question 8

If the stock price is 44, the exercise price is 40, the put price is 1.54, and the Black-Scholes price using .28 as the volatility is 1.11, the implied volatility will be

a. higher than .28
b. lower than .28
c. .28
d. lower than the risk-free rate
e. none of the above

Answer 8

a. higher than .28

Hint: the higher the volatility, the higher the price; Since the actual price of $1.54 is higher than $1.11, the implied volatility is higher than .28 used in the model, cetris paribus.

Question 9

Consider a binomial world in which the current stock price of 80 can either go up by 10 percent or down by 8 percent. The risk-free rate is 4 percent. Assume a one-period world. What would be the call’s price if the stock goes up?

a. 3.60
b. 8.00
c. 5.71
d. 4.39
e. none of the above

Answer 9

b. 8.00

Hint: When the stock price moves up to be 80(1+0.1)=88, the call’s value will be Max(0, 88-80)=8.

Question 10

In a two-period binomial world, a mispriced call will lead to an arbitrage profit if

a. the proper hedge ratio is maintained over the two periods
b. the hedge portfolio is terminated after one period
c. the option goes from over- to underpriced or vice versa
d. the option remains mispriced over both periods
e. none of the above

Answer 10

a. the proper hedge ratio is maintained over the two periods

Hint: The theoretical call price is calculated through hedge ratio. An arbitrage profit would occur when h is maintained while call is mispriced.
If call is underpriced: Long call and short stock, maintaining the correct hedge ratio – essentially borrowing at less than risk free rate;
If call is overpriced: Short call and long stock with the correct hedge ratio – essentially lending at more than risk free rate.

Question 11

When puts are priced with the binomial model, which of the following is true?

a. the puts must be American
b. the puts cannot be properly hedged
c. the puts will violate put-call parity
d. the hedge ratio is one throughout the tree
e. none of the above

Answer 11

e. none of the above

Question 12

Interest rate parity is essentially the same as

a. the cross-rate relationship
b. the cost of carry relationship
c. the Garman-Kohlhagen model
d. all of the above
e. none of the above

Answer 12

b. the cost of carry relationship

Hint: The relationship between spot and forward / futures prices of a currency. Same as cost of carry model in other forward and futures markets.

Question 13

What happens to the basis through the contract’s life?

a. it initially decreases, then increases (toward one)
b. it initially increases, then decreases (toward zero)
c. it remains relatively steady
d. it moves toward zero
e. none of the above

Answer 13

d. it moves toward zero

Hint: bT=ST-fT = 0

Question 14

Find the price of a European call option on a futures if the put option is priced at 4.45, the futures is at 115.65, the exercise price is 115, the time to expiration is 65 days and the discrete risk-free interest rate is 8.75 percent

a. $110.55
b. $4.45
c. $3.81
d. $5.09
e. none of the above

Answer 14

d. $5.09

Hint: P + S = C + PV(X)
P + f0(T) (1+r)^-T = C+X(1+r)^-T
C= 4.45 + [115.65-115] (1+8.75%)^(-65/365)= $5.09036

Question 15

Determine the value of a European foreign currency put if the call is at $0.05, the spot rate is $0.5702, the exercise price is $0.59, the domestic interest rate is 5.75 percent, the foreign interest rate is 4.95 percent and the options expire in 45 days.

a. $0.069
b. $0.031
c. $0.050
d. $0.517
e. none of the above

Answer 15

a. $0.069

Hint: P + S0 e^(-ρT) = C + X e^(-rT)
P = 0.05 + 0.59 e^(-0.057545/365) -0.5702 e^(-0.049545/365)= 0.069

Question 16

Which of the following statements about the value of a call option at expiration is FALSE?

A. The short position in the same call option can result in a loss if the stock price exceeds the exercise price.
B. The value of the long position equals zero or the stock price minus the exercise price, whichever is higher.
C. The value of the long position equals zero or the exercise price minus the stock price, whichever is higher.
D. The short position in the same call option has a zero value for all stock prices equal to or less than the exercise price.

Answer 16

C. The value of the long position equals zero or the exercise price minus the stock price, whichever is higher.

This statement is incorrect because for a call option, the payoff is zero or the stock price minus the exercise price, not the exercise price minus the stock price.

Question 17

Which of the following statements about “short selling” is TRUE?

A. A short position may be hedged by writing call options.
B. A short position may be hedged by purchasing call options.
C. Short sellers may be subject to margin calls if the stock price increases.
D. Stocks that pay large dividends should be sold short before the ex-dividend date and
bought afterward to take advantage of the large price decline in a short time period.

Answer 17

C. Short sellers may be subject to margin calls if the stock price increases.

Short sellers are exposed to potential losses if the stock price increases, which can trigger margin calls to maintain the required margin balance.

Question 18

The current price of an asset is 75. A three-month, at-the-money American call option on the asset has a current value of 5. At what value of the asset will a covered call writer break even at expiration?

A. 70.
B. 75.
C. 80.
D. 85.

Answer 18

A. 70.

Breakeven price = Current asset price - Call premium received = 75−5=70

For a covered call writer to break even, the stock price at expiration must cover the cost basis minus the call premium received. Here, the asset price of 70 is the breakeven point.

Question 19

A silver futures contract requires the seller to deliver 5,000 Troy ounces of silver. An investor sells one July silver futures contract at a price of $8 per ounce, posting a $2,025 initial margin. If the required maintenance margin is $1,500, the price per ounce at which the investor would first receive a maintenance margin call is closest to:

A. $5.92.
B. $7.89.
C. $8.11.
D. $10.80.

Answer 19

C. $8.11.

Maintenance price per ounce = Initial price + (Initial margin−Maintenance margin)/Contract size
= 8+[(2025−1500)/5000]=8.118

A maintenance margin call is triggered if losses reduce the margin below the required level. The price level causing this margin call can be calculated using the initial and maintenance margins.

Question 20

Which of the following statements about an American call is not true?

A. Its time value decreases as expiration approaches
B. Its maximum value is the stock price
C. It can be exercised prior to expiration
D. It pays dividends
E. none of the above

Answer 20

D. It pays dividends

An American call option on a non-dividend-paying stock does not pay dividends directly to its holder.

Question 21

When puts are priced with the binomial model, which of the following is true?

A. the puts must be American
B. the puts cannot be properly hedged
C. the puts will violate put-call parity
D. the hedge ratio is one throughout the tree
E. none of the above

Answer 21

E. none of the above

None of the given options are correct; American and European puts can both be priced with the binomial model without these restrictions.

Question 22

When the number of time periods in a binomial model is large, what happens to the binomial probability of an up move?

A. it approaches 1.0
B. it approaches zero
C. it fluctuates without pattern
D. it converges to 0.5
E. none of the above

Answer 22

D. it converges to 0.5

As the number of periods in the binomial model increases, the probability of an up move converges to 0.5 due to the Central Limit Theorem.

Question 23

What would be the spot price if a stock index futures price were $75, the risk-free rate were 10 percent, the dividend yield 3 percent, and the futures expires in three months?

A. $73.70
B. $77.48
C. $72.60
D. $76.32
E. none of the above

Answer 23

A. $73.70

Spot price = Futures price / e^(risk-free rate−dividend yield)×time
= 75/e^[(0.10−0.03)×(3/12)] = 73.70

The spot price can be derived from the futures price, risk-free rate, dividend yield, and time to expiration using a discounting formula.

Question 24

Find the profit if the investor buys a July futures at 75, sells an October futures at 78 and then reverses the July futures at 72 and the October futures at 77.
A. -3
B. -2
C. 2
D. 1
E. none of the above

Answer 24

B. -2

Profit = (October sell price - October buy price) + (July sell price - July buy price)
= (78−77)+(72−75)=−2

The profit is calculated based on the initial buy and sell prices, minus the final reversal prices, yielding a net loss of -2.

Question 25

Find the price of an American call option on a futures if the current spot price is 30, the exercise price is 25, the futures price is 33.70, the risk-free interest rate is 6 percent, the spot asset can go up by 10 percent or down by 8 percent per period and the call expires in two periods, which is also when the futures expires.

A. 9.98
B. 8.70
C. 7.73
D. 8.22
E. none of the above

Answer 25

B. 8.70

Using a binomial pricing model and given information, the calculated value of the American call option on the futures is closest to 8.70. Use a two-period binomial model calculation: Option price ≈ 8.70 (based on up and down probabilities and given factors).

Question 26

A firm that has a sum of money denominated in a foreign currency that plans to later convert it to dollars could hedge by which of the following methods.

A. a call on the foreign currency
B. a long futures or forward on the foreign currency
C. a short put on the foreign currency futures
D. alloftheabove
E. none of the above

Answer 26

E. none of the above

Hedging foreign currency risk typically involves long or short futures and forwards rather than the specified options, making “none of the above” correct.

Question 27

What is the lower bound of a European call on a futures contract where f0 is the futures price and X is the exercise price?

A. the difference between f0 and X
B. zero
C. the present value of the difference between f0 and X
D. the ratio of f0 to X
E. none of the above

Answer 27

E. none of the above

The lower bound for a European call on a futures contract is typically the present value of f0-X; none of the provided answers are correct.

Question 28

When referring to futures markets, a short hedge is one in which

A. the margin requirement is waived
B. the hedger is short futures
C. the hedger is short in the spot market
D. the futures price is lower than the spot price
E. none of the above

Answer 28

B. the hedger is short futures

A short hedge in futures markets involves selling futures contracts to offset potential losses in an underlying asset.

Question 29

Ignoring transaction costs, which of the following statements about the value of the put option at expiration is TRUE?

A. The value of the short position in the put is $4 if the stock price is $76.
B. The value of the long position in the put is –$4 if the stock price is $76.
C. The long put has value when the stock price is below the $80 exercise price.
D. The value of the short position in the put is zero for stock prices equalling or
exceeding $76.

refer to graph for context

Answer 29

C. The long put has value when the stock price is below the $80 exercise price.

(Long Put Value Below Exercise Price)

A long put has value at expiration when the stock price is below the exercise price ($80), as the payoff is calculated as max(0,X−S), where X=80 and S<80