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?
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)
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?
Swaps are always priced so that their value at inception is zero. (Study Session 17, LOS 61.a)
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. | |
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)
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?
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)
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)
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. | |
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) | 
发表于 2011-3-25 12:05
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