Reading 62: Option Markets and Contracts-LOS e 习题精选 dynamic, recently, executive, face, 2011

1215

Session 17: Derivative Investments: Options, Swaps, and Interest Rate and Credit Derivatives
Reading 62: Option Markets and Contracts

LOS e: Explain the delta of an option, and demonstrate how it is used in dynamic hedging.

 

 

John Fairfax is a recently retired executive from Reston Industries. Over the years he has accumulated $10 million worth of Reston stock and another $2 million in a cash savings account. He hires Richard Potter, CFA, a financial adviser from Stan Morgan, LLC, to help him develop investment strategies. Potter suggests a number of interesting investment strategies for Fairfax's portfolio. Many of the strategies include the use of various equity derivatives. Potter's first recommendation includes the use of a total return equity swap. Potter outlines the characteristics of the swap in Table 1. In addition to the equity swap, Potter explains to Fairfax that there are numerous options available for him to obtain almost any risk return profile he might need. Potter suggests that Fairfax consider options on both Reston stock and the S& 500. Potter collects the information needed to evaluate options for each security. These results are presented in Table 2.

Table 1: Specification of Equity Swap> >

Term	3 years
Notional principal	$10 million
Settlement frequency	Annual, commencing at end of year 1
Fairfax pays to broker	Total return on Reston Industries stock
Broker pays to Fairfax	Total return on S& 500 Stock Index

Table 2: Option Characteristics> >

>>	Reston	S& 500
Stock price	$50.00	$1,400.00
Strike price	$50.00	$1,400.00
Interest rate	6.00%	6.00%
Dividend yield	0.00%	0.00%
Time to expiration (years)	0.5	0.5
Volatility	40.00%	17.00%
Beta Coefficient	1.23	1
Correlation	0.4> >	>>

Potter presents Fairfax with the prices of various options as shown in Table 3. Table 3 details standard European calls and put options. Potter presents the option sensitivities in Tables 4 and 5.

Table 3: Regular and Options (Option Values)

	Reston	S& 500
European call	$6.31	$6.31
European put	$4.83	$4.83
American call	$6.28	$6.28
American put	$4.96	$4.96

Table 4: Reston Stock Option Sensitivities

	Delta
European call	0.5977
European put	?0.4023
American call	0.5973
American put	?0.4258

Table 5: S& 500 Option Sensitivities

	Delta
European call	0.622
European put	?0.378
American call	0.621
American put	?0.441

 

Given the information regarding the various Reston stock options, which option will increase the most relative to an increase in the underlying Reston stock price?

A) American put.

B) American call.

C) European call.

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Using its delta in Table 4, if the Reston stock increases by a dollar the European call on the stock will increase by 0.5977. (Study Session 17, LOS 60.a)

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Fairfax is very interested in the total return swap and asks Potter how much it would cost to enter into this transaction. Which of the following is the cost of the swap at inception?

A) $340,885.

B) $0.

C) $45,007.

---

 

Swaps are always priced so that their value at inception is zero. (Study Session 17, LOS 61.a)

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Fairfax would like to consider neutralizing his Reston equity position from changes in the stock price of Reston. Using the information in Table 4 how many standard Reston European options would have to be either bought or sold in order to create a delta neutral portfolio?

A) Sell 334,616 call options.

B) Sell 334,616 put options.

C) Buy 300,703 put options.

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Number of call options = (Reston Portfolio Value / Stock PriceReston)(1 / Deltacall).
Number of call options = ($10,000,000 / $50.00/sh)(1 / 0.5977) = 334,616. (Study Session 17, LOS 60.e)

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Fairfax remembers Potter explaining something about how options are not like futures and swaps because their risk-return profiles are non-linear. Which of the following option sensitivity measures does Fairfax need to consider to completely hedge his equity position in Reston from changes in the price of Reston stock?

A) Delta and Vega.

B) Delta and Gamma.

C) Gamma and Theta.

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Vega measures the sensitivity relative to changes in volatility. Theta measures sensitivity relative to changes in time to expiration. (Study Session 17, LOS 60.d)

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Fairfax has heard people talking about "making a portfolio delta neutral." What does it mean to make a portfolio delta neutral? The portfolio:

A) is insensitive to volatility changes in the returns on the underlying equity.

B) is insensitive to interest rate changes.

C) is insensitive to stock price changes.

---

 

The delta of the option portfolio is the change in value of the portfolio if the stock price changes. A delta neutral option portfolio has a delta of zero. (Study Session 17, LOS 60.e)

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After discussing the various equity swap options with Fairfax, Potter checks his e-mail and reads a message from Clark Ali, a client of Potter and the treasurer of a firm that issued floating rate debt denominated in euros at London Interbank Offered Rate (LIBOR) + 125 basis points. Now Ali is concerned that LIBOR will rise in the future and wants to convert this into synthetic fixed rate debt. Potter recommends that Ali:

A) take a short position in Eurodollar futures.

B) enter into a pay-fixed swap.

C) enter into a receive-fixed swap.

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The floating-rate debt will be effectively converted into fixed rate debt if he entered into a pay-fixed swap. A short position in Eurodollar futures would create a hedge, but in the wrong currency. (Study Session 17, LOS 61.d, e)

1215

As a portfolio manager for the Herron Investments, an analyst is interested in establishing a dynamic hedge for one of his clients, Lou Gier. Gier has 200,000 shares of a stock that he believes could take a dive in the near future. Suppose that a call option with an exercise price of $100 and a maturity of 90 days has a price of $7. Also assume that the current stock price is $95 and the risk free rate is 5%.

Assuming that the delta value of call option is 0.70, how many call option contracts would be needed to create a delta neutral hedge?

A) 2,857 contracts.

B) 2,000 contracts.

C) 285,714 contracts.

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The number of call options needed is 200,000 / 0.70 = 285,714 options or approximately 2,857 contracts. Since Gier is long the stock, he should short the calls.

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When a delta neutral hedge has been established using call options, which of the following statements is most correct? As the price of the underlying stock:

A) changes, no changes are needed in the number of call options purchased.

B) increases, some option contracts would need to be sold in order to retain the delta neutral position.

C) increases, some option contracts would need to be repurchased in order to retain the delta neutral position.

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As the stock price increases, the delta of the call option increases as well, requiring fewer option contracts to hedge against the underlying stock price movements. Therefore, some options contracts would need to be repurchased in order to maintain the hedge.

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1215

The price of a June call option with an exercise price of $50 falls by $0.50 when the underlying stock price falls by $2.00. The delta of a June put option with an exercise price of $50 is closest to:

A) –0.25.

B) –0.75.

C) 0.25.

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The call option delta is:

The put option delta is 0.25 – 1 = –0.75.

1215

In order to form a dynamic hedge using stock and calls with a delta of 0.2, an investor could buy 10,000 shares of stock and:

A) write 2,000 calls.

B) write 50,000 calls.

C) buy 50,000 calls.

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Each call will increase in price by $0.20 for each $1 increase in the stock price. The hedge ratio is –1/delta or –5. A short position of 50,000 calls will offset the risk of 10,000 shares of stock over the next instant.

1215

The delta of an option is equal to the:

A) dollar change in the stock price divided by the dollar change in the option price.

B) percentage change in option price divided by the percentage change in the asset price.

C) dollar change in the option price divided by the dollar change in the stock price.

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The delta of an option is the dollar change in option price per $1 change in the price of the underlying asset.

1215

An instantaneously riskless hedged portfolio has a delta of:

A) 0.

B) anything, gamma determines the instantaneous risk of a hedge portfolio.

C) 1.

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A riskless portfolio is delta neutral, the delta is zero.

1215

John Williamson is a recently retired executive from Reston Industries. Over the years he has accumulated $10 million worth of Reston stock and another $2 million in a cash savings account. He hires Frank Potter, CFA, a financial adviser from Star Financial, LLC, to help him with his investment strategies. Potter has a number of interesting investment strategies for Williamson's portfolio. Many of the strategies include the use of various equity derivatives.

Potter's first recommendation includes the use of a total return equity swap. Potter outlines the characteristics of the swap in Table 1. In addition to the equity swap, Potter explains to Williamson that there are numerous options available for him to obtain almost any risk return profile he might need. Potter suggest that Williamson consider options on both Reston stock and the S& 500. Potter collects the information needed to evaluate options for each security. These results are presented in Table 2.

Table 1: Specification of Equity Swap

Term	3 years
Notional principal	$10 million
Settlement frequency	Annual, commencing at end of year 1
Fairfax pays to broker	Total return on Reston Industries stock
Broker pays to Fairfax	Total return on S& 500 Stock Index

Table 2: Option Characteristics

	Reston	S& 500
Stock price	$50.00	$1,400.00
Strike price	$50.00	$1,400.00
Interest rate	6.00%	6.00%
Dividend yield	0.00%	0.00%
Time to expiration (years)	0.5	0.5
Volatility	40.00%	17.00%
Beta Coefficient	1.23	1
Correlation	0.4

Table 3: Regular and Exotic Options (Option Values)

	Reston	S& 500
European call	$6.31	$6.31
European put	$4.83	$4.83
American call	$6.28	$6.28
American put	$4.96	$4.96

Table 4: Reston Stock Option Sensitivities

	Delta
European call	0.5977
European put	-0.4023
American call	0.5973
American put	-0.4258

Table 5: S& 500 Option Sensitivities

	Delta
European call	0.622
European put	-0.378
American call	0.621
American put	-0.441

Williamson would like to consider neutralizing his Reston equity position from changes in the stock price of Reston. Using the information in Tables 3 and 4 how many standard Reston European options would have to be bought/sold in order to create a delta neutral portfolio?

A) Buy 497,141 put options.

B) Sell 497,141 put options.

C) Sell 370,300 call options.

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Number of put options = (Reston Portfolio Value / Stock Price_Reston) / ?DeltaPut

Number of put options = ($10,000,000 / $50.00) / ?0.4023 = ?497,141 meaning buy 497,141 put options.

Selling put options does not deliver any downside protection, but it aggravates the losses when the stock decreases in value.

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Williamson is very interested in the total return swap. He asks Potter how much it would cost to enter into this transaction. Which of the following is the cost of the swap at inception?

A) $340,885.

B) $45,007.

C) $0.

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Swaps are priced so that their value at inception is zero.

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Williamson likes the characteristics of the swap arrangement in Table 1 but would like to consider the options in Table 3 before making an investment decision. Given Williamson's current situation which of the following option trades makes the most sense in the short-term (all options are on Reston stock)?

A) Buy at the money put options.

B) Buy out of the money call options.

C) Sell at the money call options.

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Buying at the money put options greatly reduces Williamson's downside risk. Selling call options yields an option premium to the seller but does not deliver any downside protection and limits the upside potential of the portfolio.