标题: Derivatives【 Reading 37】习题精选 [打印本页]
作者: clearlycanadian 时间: 2012-4-2 14:26 标题: [2012 L3] Derivatives【Session15- Reading 37】习题精选
An investor believes that a stock they own will continue to oscillate in price and may trend downward in price. The best course of action for them to take would be to: A)
| enter into both a covered call and protective put strategy. |
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B)
| sell call options on the stock. |
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C)
| buy put options on the stock. |
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With a stock that is oscillating in price in which it is not trending upward, a covered call strategy is appropriate in which the investor owns the underlying asset and sells call options to enhance income. This strategy will work as long as the stock price does not go above the call strike price. In a downward trending market in which the investor believes the stock price will decrease, a protective put is appropriate in which they purchase a put on the underlying stock.
作者: clearlycanadian 时间: 2012-4-2 14:26
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?
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 = 100e-(0.06)(0.5) = 97.04.
作者: clearlycanadian 时间: 2012-4-2 14:27
A stock’s 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?
The breakeven price is the exercise price plus the premium. The stock’s value on the date of expiration is not necessary information for this problem.
作者: clearlycanadian 时间: 2012-4-2 14:27
What is the expiration payoff of a long straddle, with an exercise price $100, if the underlying stock price is $125?
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.
作者: clearlycanadian 时间: 2012-4-2 14:27
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?
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.
作者: clearlycanadian 时间: 2012-4-2 14:28
An investor purchases a stock for $38 and a put for $0.50 with a strike price of $35. The investor sells a call for $0.50 with a strike price of $40. What is the maximum profit and loss for this position? A)
| infinite profit and maximum loss = -$4.00. |
|
B)
| maximum profit = $2.00 and maximum loss = -$3.00. |
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C)
| maximum profit = $3.00 and maximum loss = -$4.00. |
|
The option position described is a zero cost collar. It is zero cost because the premium paid for the protective put is offset by the premium received for writing a covered call. The collar will put a band around the prospective returns by limiting the upside and downside of position. The upside will be limited by the strike price on the covered call ($40), while the downside will be limited by the strike price of the put ($35).
Maximum profit = $40 - $38 = $2
Maximum loss = $35 - $38 = -$3
作者: clearlycanadian 时间: 2012-4-2 14:28
The buyer of a straddle on a stock is most likely to benefit: A)
| if the volatility of the underlying asset’s price decreases. |
|
B)
| under all conditions because the straddle is guaranteed a risk-free rate of return. |
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C)
| if the volatility of the underlying asset’s price increases. |
|
The buyer of the straddle purchases both a call and a put. This position will benefit from large swings of the price of the underlying stock in either direction. If the position expires worthless, which occurs when the stock price stays flat, the investor will lose 100% of the investment. The payoff diagram is:
作者: clearlycanadian 时间: 2012-4-2 14:28
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?
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.
作者: optiix 时间: 2012-4-2 14:30
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)?
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).
作者: optiix 时间: 2012-4-2 14:30
Dennis Austin works for O’Reilly Capital Management and manages endowments and trusts for large clients.
The fund invests most of its portfolio in S&P 500 stocks, keeping some cash to facilitate purchases and withdrawals.
The fund’s 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.
O’Reilly’s 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 fund’s 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?
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.
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?
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.
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?
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.
作者: optiix 时间: 2012-4-2 14:31
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?
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.
作者: optiix 时间: 2012-4-2 14:31
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)
| 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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C)
| A stock can be replicated using any call option, put option and bond. |
|
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.
作者: optiix 时间: 2012-4-2 14:31
In 30 days, a firm wishes to borrow $15 million for 90 days. The borrowing rate is LIBOR plus 250 basis points. The current LIBOR is 3.8%. The firm buys an interest-rate call that matures in 30 days with a notional principal of $15 million, 90 days in underlying, and a strike rate of 4%. The call premium is $4,000. What is the maximum effective annual rate the firm can anticipate paying?
First we compute the implied net amount to be borrowed after the cost of the call:
$ 14,995,979 = $15,000,000 − $4,000 × (1 + (0.038 + 0.025) × (30 / 360))
The most the firm will expect to pay is the rate associated with the strike rate: 4% plus the 250 basis-point spread equals 6.5%. This gives the nominal cost of the loan:
$243,750 = $15,000,000 × 0.065 (90 / 360)
The highest effective annual rate is:
0.0687 = ($15,243,750 / $14,995,979)(365/90) − 1
作者: optiix 时间: 2012-4-2 14:32
In 90 days, a firm wishes to borrow $10 million for 180 days. The borrowing rate is LIBOR plus 200 basis points. The current LIBOR is 4%. The firm buys an interest-rate call that matures in 90 days with a notional principal of $10 million, 180 days in underlying, and a strike rate of 4.1%. The call premium is $9,000. What is the effective annual rate of the loan if at expiration LIBOR = 4%?
The call option is out-of-the-money. The implied net amount to be borrowed after the cost of the call is: $9,990,865 =$10,000,000 - $9,000 × (1 + (0.04+0.02) × (90/360))
For LIBOR = 0.04 at expiration, the dollar cost is:
$300,000 = $10,000,000 × 0.06 × (180/360)
The effective annual rate is:
0.0637 = ($10,300,000 / $9,990,865)(365/180) - 1
作者: optiix 时间: 2012-4-2 14:32
In 60 days, a bank plans to lend $10 million for 180 days. The lending rate is LIBOR plus 200 basis points. The current LIBOR is 4.5%. The bank buys an interest-rate put that matures in 60 days with a notional principal of $10 million, days in underlying of 180 days, and a strike rate of 4.3%. The put premium is $4,000. What is the effective annual rate of the loan if at expiration LIBOR = 4.1%?
The effective amount the bank parts with or “lends” at time of the loan is: $10,004,043 = $10,000,000 + $4,000 × (1 + (0.045 + 0.02) × (60/360))
If LIBOR at maturity equals 4.1%, the payoff of the put would be:
payoff = ($10,000,000) × [max(0, 0.043 – 0.041) × (180/360)
payoff = $10,000
The dollar interest earned is:
$305,000=$10,000,000 × (0.041 + 0.02) × (180/360), and
EAR = [($10,000,000 + $10,000 +$305,000) / ($10,004,043)](365/180) - 1
EAR = 0.0640 or 6.40%
作者: optiix 时间: 2012-4-2 14:32
A firm purchases a collar with floor rate of 3% and a cap rate of 4.4%. The cap and floor have quarterly settlement and a notional principal of $10 million. The maximum outflow and inflow the buyer can expect on a given settlement is (assume equal settlement periods): A)
| $110,000 and maximum inflow = $140,000. |
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B)
| $75,000 and maximum inflow = $140,000. |
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C)
| $75,000 and maximum inflow = infinite. |
|
Given the possible answers, this must be a collar consisting of a short floor and long cap. The firm’s maximum outflow would occur from the floor when the reference rate is zero: $10,000,000 × (0.03 − 0) / 4 = $75,000. Although interest rates cannot go to infinity, there is no upper limit on what the owner can expect from the cap. Thus “infinite” is the best answer.
作者: optiix 时间: 2012-4-2 14:33
Which of the following is equivalent to a pay-fixed interest rate swap? A)
| Buying a cap and selling a floor. |
|
B)
| Buying a cap and selling an interest rate collar. |
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C)
| Selling a cap and buying a floor. |
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A pay-fixed interest rate swap has the same payoffs as a long position in the corresponding interest rate collar (with the strike rate equal to the swap fixed rate).
作者: optiix 时间: 2012-4-2 14:33
A firm purchases a one-year cap with a strike rate of 4%, a notional principal of $3 million, and semiannual settlement. The reference rate at the initiation of the cap is 5%, falls to 4.5% at the next settlement and then to 4% one year after the cap’s initiation. The total payoffs (without discounting) over the maturity of the swap would be:
Since the number of days is not given for each period, approximate it with 182 in the first period and 183 in the second period. Remember that payments are made in arrears.
First payoff = $ 15,167 = $3,000,000 × max(0, 0.05 – 0.04) × (182/360).
Second payoff = $7,625 = $3,000,000 × max(0, 0.045 – 0.04) × (183/360)
Total = $22,792 = $7,625 + $ 15,167
作者: optiix 时间: 2012-4-2 14:34
A manager would delta hedge a position to: A)
| earn extra “dividend” income on a given position. |
|
B)
| earn the risk-free rate. |
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C)
| place a floor on the position while leaving the potential for upside risk. |
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A delta hedged position should earn the risk-free rate. The position does not earn a “dividend” although it should increase in value gradually (at the risk-free rate). The upside potential is limited to the risk-free rate. The manager would have to constantly monitor and adjust the position to achieve the goal.
作者: optiix 时间: 2012-4-2 14:34
A short position in naked calls on an asset can be delta hedged by: A)
| shorting the underlying asset. |
|
|
C)
| buying the underlying asset. |
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Delta hedging a naked call can be accomplished by owning the underlying asset in an amount that will make the value of the short-call/long-asset portfolio immune to changes in the price of the underlying asset.
作者: optiix 时间: 2012-4-2 14:34
An option dealer is delta hedging a short call position on a stock. As the stock price increases, in order to maintain the hedge, the dealer would most likely have to: |
B)
| sell some the shares of the stock. |
|
C)
| buy more shares of the stock. |
|
As the value of the underlying increases, the delta of a call option increases. This means more of the underlying asset is needed to hedge the position.
作者: optiix 时间: 2012-4-2 14:35
In delta-hedging a call position, which of the following pairs of conditions would lead to the gamma effect being the most important? The call is: A)
| at-the-money and has a long time until expiration. |
|
B)
| out-of-the-money and near expiration. |
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C)
| at-the-money and near expiration. |
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Gamma refers to the change in value of the delta given the change in value of the underlying stock. Gamma will be most important when the call option being hedged is either at the money or near expiration.
作者: optiix 时间: 2012-4-2 14:35
In delta-hedging, gamma would be important if the price of the underlying asset: A)
| had a large move upward only. |
|
|
C)
| had a large move upward or downward. |
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Gamma refers to the change in value of delta given the change in value of the underlying stock. Typically, larger swings in the price of an asset will cause larger changes in delta, thus impacting the delta hedge. This means that the larger the move in the underlying asset in either direction, the more important is the second-order gamma effect.
作者: optiix 时间: 2012-4-2 14:35
All of the following are conditions that make the second-order gamma effect more important to a manager delta-hedging an option EXCEPT when the: |
B)
| option is at-the-money. |
|
C)
| option is near expiration. |
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All of these conditions make the gamma effect more important except the delta being near zero. If the delta is near zero or one then the option delta will move more slowly towards zero or one and cause less of an affect on gamma.
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