[Sarkari-Naukri] Harish Sati, question bank derivatives markets for SOA exam FM/CAS exam

question bank derivatives markets for SOA exam FM/CAS exam

Introduction on Derivatives and Risks

 

1. Which of the followings cannot mitigate credit risk?

(A) Collateralization

(B) Bank letters

(C) Haircut

(D) Hedging

(E) No answer is given in (A), (B), (C), and (D)

2. Which of the following is not associated with short sales?

(A) Collateral

(B) Haircut

(C) Credit risk

(D) Lease rate

(E) Hedging

3. Which of the followings is not the usage of derivatives?

(A) Risk management

(B) Reduce transaction cost

(C) Predict future price

(D) Speculation

(E) Arbitrage

4. Which of the followings is false?

(A) Derivatives provide an alternative to simple sale or purchase, and thus increase the

range of possibilities for an investor or a manager seeking to accomplish some goals

(B) The construction of a given financial product from other products is called financial

engineering

(C) Financial market permits diversifiable risk to be widely shared

(D) Catastrophe bonds are bonds that an issuer needs to repay if there is a specified

event causing large insurance claims

(E) Over-the-counter market is market where buyers and sellers transact with banks

and dealers rather than on an exchange

5. Which of the following are reasons to short-sell?

I. Speculation

II. Arbitrage

III. Financing

IV. Hedging

(A) I, II, III

(B) I, II, IV

(C) I, III, IV

(D) II, III, IV

(E) No answer is given in (A), (B), (C), and (D)

Answer keys

1

D

2

E

3

C

4

D

5

E

Solutions

1. Collateralization is to pledge a liability using assets. It definitely reduces the

exposure of credit risk. Bank letters is the acknowledgement letter from bank, which

gives guarantee to the creditors on the payment of the debtors. Haircut is similar to

collateralization, which is used in short sales.

Hedging mitigates the market risk but not credit risk. For example, a gold seller

hedges the gold price by purchasing a put option. That does not protect the gold

seller from the probability that the buyer is unable to pay for the gold. The answer is

(D)

.

2. The purpose of collateral and haircut is to reduce the credit risk of counterparty.

Lease rate is the rate at which the asset borrower is charged for the borrowing.

Obviously, hedging is not associated with short sales. Short selling is a speculative

activity, whereas hedging is a non-speculative trading. The answer is

(E).

3. Derivatives are risky assets; most risky assets can be used for risk management.

Derivatives can reduce transaction costs, since replicating the derivatives might

involve trading more than one asset or liability which incurs more transaction cost.

When there is mispricing, there is arbitrage opportunity. Hence, the answer is

(C).

4. The answer is

(D). The truth is just the opposite. Catastrophe bonds are loans that

need to be repaid if the specified event does not occur. It does not repay only when

the specified event happens.

5. When it is perceived that the underlying asset is falling in price in the future, the

short-seller short sells the asset. An arbitrageur may short sell to take advantage of

a mispriced product. A short-sale is also a way to borrow money. Finally, marketmakers

and traders can undertake a short-sale to offset the risk of owning the stock

or derivative on the stock. Hence, the answer is

(E).

Part 2: Forward Contracts and Options

1. Suppose that a nondividend-paying stock has a current price of $50 and the 6-month

forward price is $54. Which of the following is true?

(A) A long position on the contract is obligated to buy the stock at $50 after 6 months

(B) A long position on the contract is obligated to sell the stock at $50 after 6 months

(C) A short position on the contract has the right but not the obligation to buy the

stock at $54 after 6 months

(D) A short position on the contract is obligated to buy the stock at $54 after 6

months

(E) A short position on the contract is obligated to sell the stock at $54 after 6

months

2. Which of the followings is true concerning a nondividend-paying stock which has a current

price of $10 and a 1-year forward price of $10.50?

(A) If the spot price is $10.30, the long forward will make a profit of $0.20

(B) If the spot price is $10.30, the short forward will make a loss of $0.20

(C) If the spot price is $10.70, the long forward will make a profit $0.20

(D) If the spot price is $10.70, the short forward will make a profit of $0.70

(E) If the spot price is $10.50, the short forward will make a profit of $0.50

3. Which of the followings is false concerning a nondividend-paying stock which has a current

price of $25 and a 6-month forward price of $27?

(A) The long forward is obligated to pay $27 for a unit of stock after 6 months

(B) The short forward is obligated to sell a unit of stock at $27 after 6 months

(C) The long forward is obligated to pay $2 after 6 months

(D) The payoff of the short forward cannot be determined now

(E) The answer is not given in (A), (B), (C), and (D).

4. You are given that the ABC Stock price is traded at $45 now and the 3-month forward

price is $46.80. Which of the following is true about outright purchase of this stock and the

forward contract?

(A) If the spot price is $45 after 3 months, the profit for outright purchase and long

forward contract is the same

(B) If the spot price is $46.80 after 3 months, the profit for outright purchase and

long forward contract is the same.

(C) If the ABC Stock pays a dividend of $0.50 after 1 month and is traded at $46.80

after 3 months, purchasing the stock outright makes a profit of $2.30.

(D) If the ABC stock pays a dividend of $0.50 after 1 month and is traded at $46.80

after 3 months, the profit of long forward is $0.

(E) The answer is not given in (A), (B), (C), and (D).

 

5. The current price of the Lucky Company Stock is $50, and the 6-month forward price is

$52. What is the amount of money that needs to be lent today to mimic the profit of

outright purchase after 6 months? Assume that the annual continuously compounded risk

free rate is 5%.

(A) $50.00

(B) $50.20

(C) $50.70

(D) $51.20

(E) $52.00

6. A dealer has just entered into a short forward position. The underlying asset is currently

traded at $100 and the 1-year forward price is $105. Assuming an annual effective rate of

3%, find the number of 100 zero-coupon bonds that the dealer has to buy to hedge his

position.

(A) 0.00000

(B) 0.19417

(C) 0.98058

(D) 1.019417

(E) 2.00000

7. Which of the following is false?

(A) Entering into a long forward contract with a purchased zero-coupon bond maturing

at the expiration date of forward mimics the payoff of an outright purchase of

stock

(B) Purchasing a stock and borrowing the present value of forward price replicate a

long forward contract

(C) Entering into a short forward contract, selling a stock and buying a bond are always

making a negative profit, since there is transaction cost.

(D) Selling a stock and lending money at certain risk free rate earns the same payoff

as a short forward contract

(E) Forward contracts are the only derivative that has no credit risk involved

8. Which of the following is not the credit risk faced by a trader who purchases a call option?

(A) The risk that the option writer encounters illiquidity problems

(B) The risk that the option writer is declared bankruptcy before expiration date

(C) The risk that the option writer is not able to return the premium paid

(D) The risk that underlying stock price goes below the strike price

(E) No answer is given in (A), (B), (C), and (D)

9. Which of the following is incorrect about a call option?

(A) The buyer of has the right to walk away from purchasing the underlying asset when

the strike price is greater than the spot price

(B) A call option serves to insure the option buyer against the risk that the underlying

stock price goes beyond the strike price

(C) It is possible that a call option costs more than the underlying stock

(D) The payoff of a call option can never be negative, whereas the profit of a call

option can be negative

(E) No answer is given in (A), (B), (C), and (D)

10. Assume that the risk free rate is 3.5%. Find the 1-year 38.50-strike call option premium

if the profit of the buyer is $4.78 at spot price of $44.34 at expiration date.

(A) $1.00

(B) $1.02

(C) $1.04

(D) $1.06

(E) $1.08

Answer Keys

1

E

2

C

3

C

4

D

5

C

6

D

7

E

8

C

9

C

10

B

Solutions

1. The answer is

(E). The party who is in a short position in the forward contract is

obligated to sell the underlying asset at the forward price. The forward price in this

question is $54.

2. The profit of a long forward is max [0, S

T – F], whereas the profit of a short forward

is max [0, F- S

T]. Only (C) gives the correct answer.

3. The answer is

(C). This is wrong in both delivery settlement and cash settlement. If it

is interpreted as in delivery settlement, the long forward should pay $27 instead of

$2. If it is interpreted as in cash settlement, the payoff cannot be determined since

the spot price at expiration is not known.

4. (A) is incorrect, because the profit for outright purchase is $0, whereas the profit of

the forward contract is -$1.80. (B) is incorrect, since the profit for outright purchase

is $1.80, whereas the profit for long forward contract is $0. (C) is incorrect, because

the cash dividend is payable after 1 month. Due to time value of money, the profit for

stock outright purchase is $1.80 + $0.50e

0.1667r > $2.30, when r > 0. (D) is correct,

since the forward contract is not directly affected by dividend paid before the date

of maturity. So, the answer is

(D).

5. The answer is

(C). Remember that the payoff of a forward contract is equivalent to

purchasing a stock at expiration plus paying cash of the forward price. In order to

achieve this, the present value of the forward price needs to be lent (buy bond) so

that at expiration date, the money lent will grow to the forward price. Therefore, the

money that needs to be lent today is $52e

-0.05(0.5)= $50.7161.

6. To hedge the position of a short forward, we need to replicate a long forward

contract. This requires selling bonds (borrowing money) today so that there will be

cash outflow at the expiration date. Hence, the dealer needs to borrow the present

value of the forward price: $105/1.03 = $101.9417, which is 1.019417 unit of a 100

zero-coupon bond. The answer is

(D).

7. The answer is

(E). All derivatives involve credit risk. It is just the matter of exposure

of the risk. For example, for forward contract, the short forward faces the credit

risk that the buyer is unable to pay for the underlying asset.

8. The answer is

(C). The premium is paid when both of the parties, the seller and buyer

enter the derivative contract. It is paid at t=0. Hence, there is no credit risk

associated with the premiums.

9. The answer is

(C). The logic is not very complicated. What can a call option give? The

best that a call option can give is a unit of the underlying asset. If a call option is

more expensive than the current stock price, why would one purchase a call option?

Why would one not just purchase the underlying asset outright? Therefore, it does

not make sense if a call option is more expensive than the current asset price. More

details will be learned in exam MFE.

10. The profit of a position in a derivative always hinges on 2: The payoff of the

derivative and the premium. In this case, since the spot price is greater than the

strike price, and we are given that the profit is $4.78, it means:

4.78 =(44.34 - 38.50) - FV (C)

FV (C) = 1.06 

C = 1.06e -0.35 = 1.02354

Thus, the answer is

(B).

--
with warm regards

Harish Sati
Indira Gandhi National Open University (IGNOU)
Maidan Garhi, New Delhi-110068

(M) + 91 - 9990646343 | (E-mail) Harish.sati@gmail.com


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