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Q17. After discussing the concept of a delta-neutral portfolio, ffice:smarttags" />Washington determines that he needs to further explain the concept of delta. Washington draws the payoff diagram for an option as a function of the underlying stock price. Using this diagram, how is delta interpreted? Delta is the: ffice ffice" />
A) curvature of the option price graph.
B) level in the option price diagram.
C) slope in the option price diagram.
Correct answer is C)
Delta is the change in the option price for a given instantaneous change in the stock price. The change is equal to the slope of the option price diagram. (Study Session 17, LOS 62.e)
Q18. Washington considers a put option that has a delta of ?0.65. If the price of the underlying asset decreases by $6, then which of the following is the best estimate of the change in option price?
A) ?$6.50.
B) +$3.90.
C) ?$3.90.
Correct answer is B)
The estimated change in the price of the option is:
Change in asset price × delta = ?$6 × (?0.65) = $3.90
(Study Session 17, LOS 62.e)
Q19. Washington is trying to determine the value of a call option. When the slope of the at expiration curve is close to zero, the call option is:
A) out-of-the-money.
B) in-the-money.
C) at-the-money.
Correct answer is A)
When a call option is deep out-of-the-money, the slope of the at expiration curve is close to zero, which means the delta will be close to zero. (Study Session 17, LOS 62.e)
Q20. BIC owns 51,750 shares of Smith & Oates. The shares are currently priced at $69. A call option on Smith & Oates with a strike price of $70 is selling at $3.50, and has a delta of 0.69 What is the number of call options necessary to create a delta-neutral hedge?
A) 75,000.
B) 14,785.
C) 0.
Correct answer is A)
The number of call options necessary to delta hedge is = 51,750 / 0.69 = 75,000 options or 750 option contracts, each covering 100 shares. Since these are call options, the options should be sold short. (Study Session 17, LOS 62.e)
Q21. Which of the following statements regarding the goal of a delta-neutral portfolio is most accurate? One example of a delta-neutral portfolio is to combine a:
A) long position in a stock with a short position in call options so that the value of the portfolio does not change with changes in the value of the stock.
B) long position in a stock with a short position in a call option so that the value of the portfolio changes with changes in the value of the stock.
C) long position in a stock with a long position in call options so that the value of the portfolio does not change with changes in the value of the stock.
Correct answer is A)
A delta-neutral portfolio can be created with any of the following combinations: long stock and short calls, long stock and long puts, short stock and long calls, and short stock and short puts. (Study Session 17, LOS 62.e)
Q22. 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.
Correct answer is B)
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.
Q23. 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.
Correct answer is C)
The delta of an option is the dollar change in option price per $1 change in the price of the underlying asset.
Q24. An instantaneously riskless hedged portfolio has a delta of:
A) anything, gamma determines the instantaneous risk of a hedge portfolio.
B) 0.
C) 1.
Correct answer is B)
A riskless portfolio is delta neutral, the delta is zero.
Q25. 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) Sell 497,141 put options.
B) Buy 497,141 put options.
C) Sell 370,300 call options.
Correct answer is B)
Number of put options = (Reston Portfolio Value / Stock PriceReston) / ?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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发表于 2009-3-28 16:45
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