CFALEVEL III PRACTICE SOLUTIONS (LOS # 28) Question - #92609 Your answer: B was incorrect The correct answer was A) 0.0637 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) - This question tested from Session 15, Reading 28, LOS c Question - #91698 Your answer: B was incorrect The correct answer was C) had a large move upward or downward 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 This question tested from Session 15, Reading 28, LOS f Question - #92358 Your answer: B was correct! 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 This question tested from Session 15, Reading 28, LOS b Question - #93027 Your answer: B was incorrect The correct answer was C) earn the risk-free rate 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 This question tested from Session 15, Reading 28, LOS e Question - #92744 Your answer: B was incorrect The correct answer was C) -$2 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 This question tested from Session 15, Reading 28, LOS b Question - #91625 Your answer: B was incorrect The correct answer was 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 This question tested from Session 15, Reading 28, LOS e Question - #92538 Your answer: B was correct! 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 basispoint 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) − This question tested from Session 15, Reading 28, LOS c Question - #92676 Your answer: B was incorrect The correct answer was C) $25 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 This question tested from Session 15, Reading 28, LOS b Question - #92914 Your answer: B was incorrect The correct answer was A) $97.04 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 This question tested from Session 15, Reading 28, LOS b Question 10 - #92926 Part 1) Your answer: B was correct! 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 This question tested from Session 15, Reading 28, LOS b Part 2) Your answer: B was incorrect The correct answer was C) Prices to increase or decrease substantially An investor would purchase a straddle when they expect a large movement in the price of a stock, but are unsure of the direction This question tested from Session 15, Reading 28, LOS b Part 3) Your answer: B was incorrect The correct answer was C) $0.00 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 This question tested from Session 15, Reading 28, LOS b Part 4) Your answer: B was correct! 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 This question tested from Session 15, Reading 28, LOS b Question 11 - #92910 Your answer: B was incorrect The correct answer was A) No arbitrage requires that using any three of the four instruments (stock, call, put, bond) the fourth can be synthetically replicated 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 This question tested from Session 15, Reading 28, LOS b Question 12 - #92852 Your answer: B was incorrect The correct answer was C) $2 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 This question tested from Session 15, Reading 28, LOS b Question 13 - #92415 Your answer: B was correct! 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) This question tested from Session 15, Reading 28, LOS b Question 14 - #93134 Your answer: B was incorrect The correct answer was A) maximum profit = $2.00 and maximum loss = -$3.00 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 This question tested from Session 15, Reading 28, LOS b Question 15 - #92150 Your answer: B was incorrect The correct answer was A) $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) / = $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 This question tested from Session 15, Reading 28, LOS d Question 16 - #93111 Your answer: B was incorrect The correct answer was C) 0.0640 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% This question tested from Session 15, Reading 28, LOS c Question 17 - #92847 Part 1) Your answer: B was incorrect The correct answer was C) Long butterfly 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 This question tested from Session 15, Reading 28, LOS b Part 2) C) Short straddle Your answer: B was correct! 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 This question tested from Session 15, Reading 28, LOS b Part 3) Your answer: B was incorrect The correct answer was A) Long put options 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 This question tested from Session 15, Reading 28, LOS b Question 18 - #92288 Your answer: B was correct! 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) This question tested from Session 15, Reading 28, LOS d Question 19 - #92248 Your answer: B was incorrect The correct answer was C) Buying a cap and selling a floor 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) This question tested from Session 15, Reading 28, LOS d Question 20 - #93141 Your answer: B was correct! 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: This question tested from Session 15, Reading 28, LOS b Question 21 - #92662 Your answer: B was incorrect The correct answer was C) $87.20 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 This question tested from Session 15, Reading 28, LOS b Question 22 - #91692 Your answer: B was incorrect The correct answer was C) at-the-money and near expiration 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 This question tested from Session 15, Reading 28, LOS f Question 23 - #93054 Your answer: B was incorrect The correct answer was A) delta is near zero 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 This question tested from Session 15, Reading 28, LOS f ... 23 - # 930 54 Your answer: B was incorrect The correct answer was A) delta is near zero All of these conditions make the gamma effect more important except the delta being near zero If the delta... B was correct! 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... selling a floor 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) This question tested