Reading 39: Risk Management Applications of Option Strateg butterfly, interpret, general, option, profit

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Session 13: Risk Management Applications of Derivatives
Reading 39: Risk Management Applications of Option Strategies
LOS a: Determine and interpret the value at expiration, profit, maximum profit, maximum loss, breakeven underlying price at expiration, and general shape of the graph for the major option strategies (bull spread, bear spread, butterfly spread, collar, straddle, box spread).

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Assume that the current price of a stock is $100. A call option on that stock with an exercise price of $97 costs $7. A call option on the stock with the same expiration and an exercise price of $103 costs $3. Using these options what is the cost of entering into a long bull spread on this stock?

A) $1.

B) $0.

C) $4.

D) $7.

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Answer and Explanation

The buyer of a bull spread buys the call with an exercise price below the current stock price and sells the call option with an exercise price above the stock price. The cost of the strategy is the difference between the cost of buying the option with the lower exercise price and selling the option with the higher exercise price which is $7 - $3 = $4 to enter into this strategy.

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Which of the following best explains put-call parity?

A) No arbitrage requires that using any three of the four instruments (stock, call, put, bond) the fourth can be synthetically replicated.

B) A stock can be replicated using any call option, put option and bond.

C) A stock can be replicated using any at the money call and put options and a bond.

D) No arbitrage requires that only the underlying stock can be synthetically replicated using at the money call and put options and a zero coupon bond with a face value equal to the strike price of the options.

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Answer and Explanation

A portfolio of the three instruments will have the identical profit and loss pattern as the fourth instrument and therefore the same value by no arbitrage. So the fourth security can be synthetically replicated using the remaining three.

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Assume that the current price of a stock is $100. A call option on that stock with an exercise price of $97 costs $7. A call option on the stock with the same expiration and an exercise price of $103 costs $3. Using these options what is the profit for a long bull spread if the stock price at expiration of the options is equal to $110?

A) $2.

B) -$2.

C) $0.

D) $6.

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Answer and Explanation

The buyer of a bull spread buys the call with an exercise price below the current stock price and sells the call option with an exercise price above the stock price. Therefore, for a stock price of $110 at expiration of the options, he gets a payoff $13 from his long position and a payoff of -$7 from his short position for a net payoff of $6. The cost of the strategy is $4. Hence the profit is equal to $2.

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Assume a stock has a value of $100. Using at the money call and put options on that stock with 0.5 years to expiration and a constant interest rate of 6 percent, what is the necessary amount that needs to be invested in a zero coupon risk-free bond in order to synthetically replicate the underlying stock. Which of the following is closest to the correct answer?

A) $97.04.

B) $98.00.

C) $100.00.

D) $103.00.

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Answer and Explanation

From put-call-parity the investment in the risk-free bond should be the present value of the exercise price of the call and the put. That is, Xe^-rt = 100^{e-(0.06)(0.5)} = 97.04.

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Assume that the current price of a stock is $100. A call option on that stock with an exercise price of $97 costs $7. A call option on the stock with the same expiration and an exercise price of $103 costs $3. Using these options what is the expiration profit of a bear call spread if the stock price is equal to $110?

A) -$6.

B) -$2.

C) $2.

D) $6.

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Answer and Explanation

The trader of a bear call spread sells the call with an exercise price below the current stock price and buys the call option with an exercise price above the stock price. Therefore, for a stock price of $110 at expiration of the options, the buyer realizes a payoff of -$13 from his short position and a positive payoff of $7 from his long position for a net payoff of -$6. The revenue of the strategy is $4. Hence the profit is equal to -$2.

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What is the expiration payoff of a long straddle, with an exercise price $100, if the underlying stock price is $125?

A) -$25.

B) $25.

C) $0.

D) $50.

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Answer and Explanation

A long straddle consists of a long call and put with the same exercise price and the same expiration, at a stock price of $125 the put will expire worthless and the call value will be $25.

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Dennis Austin works for OReilly Capital Management and manages endowments and trusts for large clients. The fund invests most of its portfolio in S& 500 stocks, keeping some cash to facilitate purchases and withdrawals. The funds performance has been quite volatile, losing over 20 percent last year but reporting gains ranging from 5 percent to 35 percent over the previous five years. OReillys clients have many needs, goals, and objectives, and Austin is called upon to design investment strategies for their clients. Austin is convinced that the best way to deliver performance is to, whenever possible, combine the funds stock portfolio with option positions on equity.

Given the following scenario:

• Performance to Date: Up 3%

• Client Objective: Stay positive

• Austin's scenario: Low stock price volatility between now and end of year.

Which is the best option strategy to meet the client's objective?

Given the following scenario:

• Performance to Date: Up 3%

• Client Objective: Stay positive

• Austin's scenario: Low stock price volatility between now and end of year.

Which is the best option strategy to meet the client's objective?

A) Bull call.

B) Protective put.

C) 2:1 Ratio Spread.

D) Long butterfly.

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Answer and Explanation

Long butterfly is the choice as this combination produces gains should stock prices not move either up or down, while not producing much in loss if prices are volatile. None of the other positions produce gains should stock prices not move much. The protective put guards against falling prices, the bull call limits losses and gains should prices move, and the 2:1 ratio spread gains should prices move up.

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Given the following scenario:

• Performance to Date: Up 16%

• Client Objective: Earn at least 15%

• Austin's scenario: Good chance of large gains or large losses between now and end of year.

Which is the best option strategy to meet the client's objective?

A) Short straddle.

B) Long butterfly.

C) Long straddle.

D) Condor.

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Answer and Explanation

Long straddle produces gains if prices move up or down, and limited losses if prices do not move. Short straddle produces significant losses if prices move significantly up or down. Long Butterfly also produces losses should prices move either up or down. The condor is similar to the long butterfly, although the gains for no movement are not as great.

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Given the following scenario:

• Performance to Date: Up 16%

• Client Objective: Earn at least 15%

• Austin's scenario: Good chance of large losses between now and end of year.

Which is the best option strategy to meet the client's objective?

A) Long put options.

B) Long call options.

C) Short call options.

D) Short put options.

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Answer and Explanation

Long put positions gain when stock prices fall and produce very limited losses if prices instead rise. Short calls also gain when stock prices fall but create losses if prices instead rise. The other two positions will not protect the portfolio should prices fall.

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A stocks value on the date of option expiration is $88.50. For a call purchased with a $2.20 premium and an exercise price of $85, what is the breakeven price?

A) $88.50.

B) $87.20.

C) $86.30.

D) $90.70.

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Answer and Explanation

The breakeven price is the exercise price plus the premium. The stocks value on the date of expiration is not necessary information for this problem.

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An investor makes the following transactions in calls on a stock: 1) buys one call with a premium of $3.50 and exercise price of $20, 2) buys one call with a premium of $1.00 and exercise price of $25, and 3) sells two calls with a premium of $2.00 each and an exercise price of $22.50. What is/are the breakeven price(s)?

A) $21 only.

B) $20.50 and $24.50.

C) $20.50, $22.50, and $24.50 only.

D) $21 and $26.

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Answer and Explanation

The transaction describes a butterfly spread. The total amount spent on purchasing the calls was $3.50 + $1.00 = $4.50 and the total amount received from the sale of the calls was $2 + $2 = $4 so the investor is - $.50 from the purchase and sale of the calls. The first exercise price on one of the calls purchased is $20 so the stock price would have to go up to $20.50 to reach the first breakeven point. At $22.50, the two written calls and the purchased call with the higher strike price will all expire worthless, while the call with the strike price of $20 will be exercised for a profit of $2.50. The total transaction will result in a profit of (+$2.50 + 4.00 - 4.50 = 2). The second breakeven price is $24.50. At this price, the two written calls will breakeven ($2 loss + $2 premium = 0 for each call), the call with the $20 strike price will be exercised for a profit of $1.00 ($4.50 gain - $3.50 premium), and the call with the $25 strike price will expire worthless, resulting in the loss of the $1.00 premium. At a price of $24.50, the total of the transactions will be zero (+$4.00 4.00 + 1.00 1.00 = 0).