Schweser QBank 2017 derivatives 03 risk management applications of option strategies

Risk Management Applications of Option Strategies Test ID: 7428297 Question #1 of 30 Question ID: 466565 Which of the following is equivalent to a pay-fixed interest rate swap? ᅚ A) Buying a cap and selling a floor ᅞ B) Buying a cap and selling an interest rate collar ᅞ C) Selling a cap and buying a floor Explanation 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) Question #2 of 30 Question ID: 466561 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%? ᅞ A) 0.0619 ᅚ B) 0.0640 ᅞ C) 0.0648 Explanation 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) - EAR = 0.0640 or 6.40% Question #3 of 30 Question ID: 466549 Which of the following best explains put-call parity? ᅚ A) No arbitrage requires that using any three of the four instruments (stock, call, put, bond) the fourth can be synthetically replicated ᅞ 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 ᅞ C) A stock can be replicated using any call option, put option and bond Explanation 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 Questions #4-6 of 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 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 Question #4 of 30 Question ID: 466556 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? ᅚ A) Protective put ᅞ B) Bull call ᅞ C) Long butterfly Explanation The client wants to stay positive on the stock and a protective put will retain the stock upside with limited down side risk In addition volatility is low which will make option prices low Both of the other strategies will compromise stock upside potential and involve selling options to reduce initial investment cost Lowering initial investment was not a specific goal and it makes little sense to so while option prices are low Question #5 of 30 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 Question ID: 466557 Which is the best option strategy to meet the client's objective? ᅞ A) Long butterfly ᅚ B) Long straddle ᅞ C) Short straddle Explanation Long straddle produces gains if prices move up or down, and limited losses if prices 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 Question #6 of 30 Question ID: 466558 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? ᅞ A) Long call options ᅞ B) Short call options ᅚ C) Long put options Explanation 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 Question #7 of 30 Question ID: 466570 In delta-hedging, gamma would be important if the price of the underlying asset: ᅞ A) remained constant ᅚ B) had a large move upward or downward ᅞ C) had a large move upward only Explanation 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 Question #8 of 30 Question ID: 466544 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? ᅚ A) maximum profit = $2.00 and maximum loss = -$3.00 ᅞ B) infinite profit and maximum loss = -$4.00 ᅞ C) maximum profit = $3.00 and maximum loss = -$4.00 Explanation 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 Question #9 of 30 Question ID: 466569 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: ᅚ A) at-the-money and near expiration ᅞ B) out-of-the-money and near expiration ᅞ C) at-the-money and has a long time until expiration Explanation 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 Question #10 of 30 Question ID: 466542 What is the expiration payoff of a long straddle, with an exercise price $100, if the underlying stock price is $125? ᅞ A) $0 ᅚ B) $25 ᅞ C) -$25 Explanation 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 Question #11 of 30 Question ID: 466540 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: ᅞ A) sell call options on the stock ᅚ B) enter into both a covered call and protective put strategy ᅞ C) buy put options on the stock Explanation 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 Question #12 of 30 Question ID: 466547 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)? ᅚ A) $20.50 and $24.50 ᅞ B) $21 only ᅞ C) $21 and $26 Explanation 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 = 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) Question #13 of 30 Question ID: 466543 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? ᅚ A) -$2 ᅞ B) $2 ᅞ C) -$6 Explanation 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 Question #14 of 30 Question ID: 466548 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? ᅚ A) $2 ᅞ B) -$2 ᅞ C) $6 Explanation 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 Question #15 of 30 Question ID: 466562 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 cap would be: ᅞ A) $7,583 ᅞ B) $25,500 ᅚ C) $22,792 Explanation 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 Question #16 of 30 Question ID: 466571 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: ᅚ A) delta is near zero ᅞ B) option is at-the-money ᅞ C) option is near expiration Explanation 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 Question #17 of 30 Question ID: 466560 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%? ᅞ A) 0.0619 ᅞ B) 0.0787 ᅚ C) 0.0637 Explanation 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) - Questions #18-21 of 30 Linda Morgan is in a training program at a large investment bank Currently, she is spending three months at her firm's Derivatives Trading desk One of the traders, Jason Gover, CFA, asks her to compare different option trading strategies Gover would like Morgan to pay particular attention to strategy costs and their potential payoffs Morgan is not very comfortable with option models and must first investigate how to properly price European and American style equity options Gover has given her software that provides a variety of analytical information Morgan has decided to begin her analysis using two different scenarios to evaluate option behavior Her scenarios are illustrated in Exhibits and Note that all of the rates and yields are on a continuous compounding basis Exhibit Stock Price (S) $100 Call Strike Price (X) $100 Price Exhibit $5.51 Stock Price (S) $100 Put Strike Price (X) $100 Price $5.68 Gover instructs Morgan to consider using a straddle in which a at-the-money call and put option would be purchased Assume all other variables remain identical Question #18 of 30 Question ID: 466551 Jason explains to Linda that the volatility of returns of the underlying stock has the most influence over the price of an option Following his explanation he queries Linda on how exactly does volatility affect option values If the volatility were to increase would the price of the option change? ᅚ A) Yes, the option price will increase ᅞ B) Yes, the option price will decrease ᅞ C) It depends whether the option is a call option or a put option Explanation Since an option has an asymmetric payoff, higher volatility always increases an option price since the chance of a high payoff from the option is increased without significantly increasing the downside risk Question #19 of 30 Question ID: 466552 After computing the maximum loss of the straddle Linda wonders why an investor would want to set up a straddle Under what circumstances would an investor want to purchase a straddle? When the investor expects: ᅚ A) Prices to increase or decrease substantially ᅞ B) Prices to increase ᅞ C) Prices to stay close to the exercise price of the options Explanation An investor would purchase a straddle when they expect a large movement in the price of a stock, but are unsure of the direction Question #20 of 30 Question ID: 466553 Linda returns her attention to the straddle using the information in Exhibits and She computes the minimum payoff of the straddle at expiration Which of the following is closest to Linda's answer? ᅚ A) $0.00 ᅞ B) -$11.31 ᅞ C) -$4.42 Explanation Since a long straddle consists of a long position in a call and a put option, the owner of these options has a right but not an obligation to exercise so the option payoff can never be negative Therefore, the worst payoff resulting from this strategy is zero Do not confuse the maximum loss with the payoff at expiration Question #21 of 30 Question ID: 466554 Linda now wants to compute the breakeven points for the straddle using the options and underlying stock in Exhibits and Which of the following are the closest to the breakeven points for the straddle? ᅚ A) $88.81, $111.19 ᅞ B) $95.58, $104.42 ᅞ C) $93.11, $106.89 Explanation This is the exercise price plus/minus the maximum loss Since the total cost of the straddle is $11.19, the breakeven points are $100 +/- 11.19 Question #22 of 30 Question ID: 466568 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: ᅞ A) buy T-bills ᅞ B) sell some the shares of the stock ᅚ C) buy more shares of the stock Explanation 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 Question #23 of 30 Question ID: 466564 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): ᅞ A) $75,000 and maximum inflow = $140,000 ᅞ B) $110,000 and maximum inflow = $140,000 ᅚ C) $75,000 and maximum inflow = infinite Explanation 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) / = $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 Question #24 of 30 Question ID: 466566 A manager would delta hedge a position to: ᅚ A) earn the risk-free rate ᅞ B) place a floor on the position while leaving the potential for upside risk ᅞ C) earn extra "dividend" income on a given position Explanation 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 Question #25 of 30 Question ID: 466563 Suppose that a 1-year cap has a cap rate of percent and a notional amount of $500 million The frequency of settlement is quarterly, and the reference rate is 3-month LIBOR The contract begins on January and the settlements are on April 1, July 1, October 1, and the following January Given the indicated LIBOR rates on those dates in the table below, what is the maximum payoff and on what date did it occur on? (The days in each settlement period have been provided.) Date Dt Payoff Jan 6.15% - Apr 6.15% 90 ? July 6.15% 91 ? Oct 6.10% 92 ? Jan 6.10% 92 ? ᅞ A) $187,500 on April ᅚ B) $191,666 on Oct ᅞ C) $189,583 on July Explanation Remember that payments are made in arrears payoff on April 1= $187,500 = $500,000,000 × max(0, 0.0615 - 0.06) × (90/360) payoff on July = $189,583 = $500,000,000 × max(0, 0.0615 - 0.06) × (91/360) payoff on Oct = $191,666 = $500,000,000 × max(0, 0.0615 - 0.06) × (92/360) Question #26 of 30 Question ID: 466559 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? ᅞ A) 0.0671 ᅞ B) 0.0603 ᅚ C) 0.0687 Explanation 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) − Question #27 of 30 Question ID: 466541 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? ᅞ A) $88.50 ᅚ B) $87.20 ᅞ C) $86.30 Explanation 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 Question #28 of 30 Question ID: 466545 The buyer of a straddle on a stock is most likely to benefit: ᅚ A) if the volatility of the underlying asset's price increases ᅞ B) if the volatility of the underlying asset's price decreases ᅞ C) under all conditions because the straddle is guaranteed a risk-free rate of return Explanation 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: Question #29 of 30 Question ID: 466546 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? ᅞ A) $1 ᅞ B) $0 ᅚ C) $4 Explanation 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 Question #30 of 30 Question ID: 466567 A short position in naked calls on an asset can be delta hedged by: ᅞ A) shorting the underlying asset ᅚ B) buying the underlying asset ᅞ C) buying the put Explanation 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  ... 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 Question #14 of 30 Question ID: 466548 Assume... 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... 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