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LOS e: Explain the delta of an option, and demonstrate how it is used in dynamic hedging. ffice ffice" />
Q1. John Fairfax is a recently retired executive from Reston Industries. Over the years he has accumulated $10 million worth of ffice:smarttags" />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) European call.
B) American put.
C) American call.
Correct answer is A)
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 62.a)
Q2. 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) $45,007.
C) $0.
Correct answer is C)
Swaps are always priced so that their value at inception is zero. (Study Session 17, LOS 63.a)
Q3. 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.
Correct answer is A)
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 62.e)
Q4. 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.
Correct answer is B)
Vega measures the sensitivity relative to changes in volatility. Theta measures sensitivity relative to changes in time to expiration. (Study Session 17, LOS 62.d)
Q5. 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.
Correct answer is C)
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 62.e)
Q6. 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 receive-fixed swap.
C) enter into a pay-fixed swap.
Correct answer is C)
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 63.d, e)
Q7. 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.
Correct answer is A)
The number of call options needed is 200,000 / 0.70 = 285,714 options or approximately 2,857 contracts.
Q8. 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.
Correct answer is C)
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.
Q9. 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.
Correct answer is B)
The call option delta is:
The put option delta is 0.25 – 1 = –0.75.
[此贴子已经被作者于2009-3-28 16:20:48编辑过] | 
发表于 2009-3-28 16:00
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