Question 1

A one year call option has a strike price of 70,expires in 3 months,and has a price of $7.34.If the risk free rate is 6%,and the current stock price is $62,what should the corresponding put be worth?

Accepted Answer

p(t)= $7.34 - $62 + $70(1 + .06)⁻¹/⁴ = $14.33

Question 2

Exhibit 20.1
Use the Information Below for the Following Problem(S)
December futures on the S&P 500 stock index trade at 250 times the index value of 1187.70. Your broker requires an initial margin of 10% percent on futures contracts. The current value of the S&P 500 stock index is 1178.
-Refer to Exhibit 20.1.How much must you deposit in a margin account if you wish to purchase one contract?

Accepted Answer

Margin = 0.10 × 250 × 1187.70 = $29,692.50

Question 3

A forward contract is similar to an option contract because they both

Accepted Answer

The answer of A forward contract is similar to an...

Question 4

Derivative securities can be used

Accepted Answer

Derivative securities can be used in all of the ways mentioned in the options A, B, and C. Investors can use derivatives to gain exposure to the underlying security, modify the risk-return profile of their portfolios, and create arbitrage opportunities by duplicating cash flows. Therefore, option D is the correct answer.

Question 5

A one year call option has a strike price of 50,expires in 6 months,and has a price of $4.74.If the risk free rate is 3%,and the current stock price is $45,what should the corresponding put be worth?

Accepted Answer

p(t)= $4.74 - $45+ $50(1 + .03)⁻¹/² = $9.0

Question 6

Exhibit 20.4
Use the Information Below for the Following Problem(S)
Rick Thompson is considering the following alternatives for investing in Davis Industries which is now selling for $44 per share:
 (1) Buy 500 shares, and
(2) Buy six month call options with mexercise price of 45 for $\$ 3.25$ premium
-Refer to Exhibit 20.4.Assuming no commissions or taxes what is the annualized percentage gain if the stock reaches $50 in four months and a call was purchased?

Accepted Answer

[(50 - 45 - 3.25)¸ 3.25] × 3 = 161.54% gain

Question 7

A buyer of the call option is speculating on the

Accepted Answer

A buyer of a call option is speculating on the direction of the price movement (expecting it to rise), the timing (before expiration), and the leverage (amplified gains with limited risk) that the option provides.

Question 8

Holding a put option and the underlying security at the same time is an example of

Accepted Answer

Holding a put option along with the underlying security is a strategy known as portfolio insurance, as it helps protect against downside risk.

Question 9

Exhibit 20.3
Use the Information Below for the Following Problem(S)
On the last day of October, Bruce Springsteen is considering the purchase of 100 shares of Olivia Corporation common stock selling at $37 1/2 per share and also considering an Olivia option.
 $\begin{array}{lcccc} 
&\quad\quad\quad\quad\quad\quad\quad\quad {\text { Calls }} &&\quad\quad\quad\quad\quad\quad\quad\quad {\text { Puts }} \
\text { Price } & \text { December } & \text { March } & \text { December } & \text { March } \
\hline 35 & 3\quad3 / 4 & 5 & 1\quad1 / 4 & 2 \
40 & 2\quad1 / 2 & 3\quad1 / 2 & 4\quad1 / 2 & 4\quad3 / 4
\end{array}$
-Refer to Exhibit 20.3.If Bruce decides to buy a March call option with an exercise price of 35,what is his dollar gain (loss)if he closes his position when the stock is selling at 43 1/2?

Accepted Answer

Bruce buys the March call option with an exercise price of 35 for $5 per share. If the stock price rises to $43.50, the intrinsic value of the option becomes $8.50 ($43.50 - $35). The gain per share is $8.50 - $5 = $3.50. For 100 shares, the total gain is $350.00.

Question 10

Exhibit 20.1
Use the Information Below for the Following Problem(S)
December futures on the S&P 500 stock index trade at 250 times the index value of 1187.70. Your broker requires an initial margin of 10% percent on futures contracts. The current value of the S&P 500 stock index is 1178.
-Refer to Exhibit 20.1.Suppose at expiration the futures contract price is 250 times the index value of 1170.Disregarding transaction costs,what is your percentage return?

Accepted Answer

Purchase December contract
250 × 1187.7 = $296,925
Sell December contract
250 × 1170 = $292,500
Loss in futures = $292,500 - $296,925 = -$4425
Rate of return = -$4425/29,692.50 = -.1490 or -14.9%

Question 11

An expiration date payoff and profit diagram for forward positions illustrates

Accepted Answer

Forward contracts are zero-sum games because the gain of one party is exactly the loss of the other party.

Question 12

Exhibit 20.2
Use the Information Below for the Following Problem(S)
A futures contract on Treasury bond futures with a December expiration date currently trade at 103:06. The face value of a Treasury bond futures contract is $100,000. Your broker requires an initial margin of 10%.
-Refer to Exhibit 20.2.If the futures contract is quoted at 105:08 at expiration calculate the percentage return.

Accepted Answer

Purchase December contract
103 6/32 percent of 100,000 = $103,187.50
Sell December contract
105 8/32 percent of $100,000 = $105,250
Gain in futures = $105,250 - $103,187.50 = $2,062.50
Rate of return = 2062.5/10318.75 = 0.1999 or 19.9%

Question 13

Exhibit 20.2
Use the Information Below for the Following Problem(S)
A futures contract on Treasury bond futures with a December expiration date currently trade at 103:06. The face value of a Treasury bond futures contract is $100,000. Your broker requires an initial margin of 10%.
-Refer to Exhibit 20.2.Calculate the current value of one contract.

Accepted Answer

Current price is 103 6/32 percent of face value of $100,000
= 1.031875 × 100,000 = $103,187.50

Question 14

Exhibit 20.1
Use the Information Below for the Following Problem(S)
December futures on the S&P 500 stock index trade at 250 times the index value of 1187.70. Your broker requires an initial margin of 10% percent on futures contracts. The current value of the S&P 500 stock index is 1178.
-Refer to Exhibit 20.1.Calculate the return on a cash investment in the S&P 500 stock index if the ending index value is 1170 over the same time period.

Accepted Answer

Return on cash investment in the index = (1170 - 1178)/1178 = -0.0068 or -0.68%

Question 15

Which of the following is consistent with put-call-spot parity?

Accepted Answer

Put-call-spot parity states that the sum of the present value of a call option and the present value of the spot price is equal to the sum of the present value of a put option and the present value of the strike price discounted at the risk-free rate. Therefore, S+P=C+X/(1+RFR) is the correct formula, as it follows this principle.

Question 16

Exhibit 20.2
Use the Information Below for the Following Problem(S)
A futures contract on Treasury bond futures with a December expiration date currently trade at 103:06. The face value of a Treasury bond futures contract is $100,000. Your broker requires an initial margin of 10%.
-Refer to Exhibit 20.2.Calculate the initial margin deposit.

Accepted Answer

Margin deposit = 0.10 × 103,187.5 = $10,318.75

Question 17

A one year call option has a strike price of 50,expires in 6 months,and has a price of $5.04.If the risk free rate is 5%,and the current stock price is $50,what should the corresponding put be worth?

Accepted Answer

p(t)= $5.04 - $50+ $50(1 + .05)⁻¹/² = $3.83

Question 18

A one year call option has a strike price of 60,expires in 6 months,and has a price of $2.5.If the risk free rate is 7%,and the current stock price is $55,what should the corresponding put be worth?

Accepted Answer

p(t)= $2.5 - $55+ $60(1 + .07)⁻¹/² = $5.50

Question 19

Exhibit 20.3
Use the Information Below for the Following Problem(S)
On the last day of October, Bruce Springsteen is considering the purchase of 100 shares of Olivia Corporation common stock selling at $37 1/2 per share and also considering an Olivia option.
 $\begin{array}{lcccc} 
&\quad\quad\quad\quad\quad\quad\quad\quad {\text { Calls }} &&\quad\quad\quad\quad\quad\quad\quad\quad {\text { Puts }} \
\text { Price } & \text { December } & \text { March } & \text { December } & \text { March } \
\hline 35 & 3\quad3 / 4 & 5 & 1\quad1 / 4 & 2 \
40 & 2\quad1 / 2 & 3\quad1 / 2 & 4\quad1 / 2 & 4\quad3 / 4
\end{array}$
-Refer to Exhibit 20.3.If Bruce buys a March put option with an exercise price of 40,what is his dollar gain (loss)if he closes his position when the stock is selling at 43 1/2?

Accepted Answer

Bruce buys a March put option with an exercise price of 40 for $4.75 per share. If the stock price rises to $43.50, the put option expires worthless, resulting in a loss of the premium paid. The total loss is 100 shares * $4.75 = $475.00.

Question 20

An advantage of a forward contract over a futures contract is that

Accepted Answer

The terms of a forward contract can be customized to fit the specific needs of the parties involved, whereas futures contracts are standardized and have limited flexibility in terms of contract size, delivery dates, and settlement procedures. This flexibility can be beneficial for parties who have unique needs or requirements that cannot be met by a standardized futures contract.

Quiz 20: An Introduction to Derivative Markets and Securities