Reading 29 Risk Management Applications of Option Strategies FinQuiz.com FinQuiz.com CFA Level III Item-set - Solution Study Session 15 June 2018 Copyright © 2010-2018 FinQuiz.com All rights reserved Copying, reproduction or redistribution of this material is strictly prohibited info@finquiz.com FinQuiz.com © 2018 - All rights reserved Reading 29 Risk Management Applications of Option Strategies FinQuiz.com FinQuiz Level III 2018 – Item-sets Solution Reading 29: Risk Management Applications of Option Strategies Question ID: 8852 Correct Answer: A The statement is correct Adding a short call is a covered call strategy, and adding a long put is called a protective put A covered call limits the upside potential but generates cash up front A protective put retains the upside potential at the expense of requiring the payment of cash up front Question ID: 8853 Correct Answer: A Hughes is correct If the price of the bond exceeds the exercise price, the put will expire out of money The position will be worth only the value of the underlying This is true for all prices of the bond above the exercise price so Reed is incorrect Question ID: 8854 Correct Answer: B If Reed adds a long put position to her long bond position, she will be following a protective put strategy The breakeven price for a protective put equals: S0 + p0 which in this case equals: 104.5 + 11.23 = $115.73 This means the price will have to increase by 10.75% over the life of the option for Reed to breakeven In case Reed adds a short call to the long bond position, the strategy would be a covered call The breakeven price will equal: S0 - c0 In this case it equals: 104.5 – 12.45 = $92.05 Question ID: 8855 Correct Answer: A Buying the put will result in a protective put A protective put limits the downside but has unlimited upside potential Even though the option premium reduces the gain, it does not limit the upside potential Also, a protective put limits the downside risk; the maximum possible loss equals: S0 + p0-X = 104.5+11.23-96 =$19.73 FinQuiz.com © 2018 - All rights reserved Reading 29 Risk Management Applications of Option Strategies FinQuiz.com Question ID: 8856 Correct Answer: C In this case, Reed has implemented a protective put The maximum profit for a protective put equals infinity This is because there is no upper limit to price increases, and a protective put strategy gains when the price increases Question ID: 8857 Correct Answer: C If the price falls to $93.27, the value of the position will equal: Value = St + max (0, X- St) = 93.27 + max (0, 96-93.27) = $96 The profit will equal: 96-(104.5+11.23) = -$19.7 Question ID: 8868 Correct Answer: C In case of a call option held till expiration, for an index value at expiration greater than the exercise price, both the value and the profit will move up one-for one with the index value (the only difference is that the profit will be less than the value by the amount of the premium paid) Question ID: 8869 Correct Answer: C Statement is correct The point where the profit line crosses the x-axis is the point where the profit is zero Hence, the index value at that point results in zero profit and is therefore the breakeven price Statement is also correct For a call option, the value at expiration is the maximum of zero or the index price less the exercise price: Value = max(0, St-x) Question ID: 8870 Correct Answer: A The breakeven price of a call option is the exercise price plus the option premium; the value of the underlying at expiration must exceed the exercise price by the amount of the premium to recover the cost of the premium Breakeven price: 2500+76.05 = 2,576.05 10 Question ID: 8871 Correct Answer: B If the price of the underlying is 2650 at expiration, the value will equal: Value = max (0, St – x) = max (0, 2650 – 2500) = 150 The profit will include the cost of the option: Profit = value – cost = 150 – 76.05 = 73.95 11 Question ID: 8872 Correct Answer: B The maximum profit to the seller of the option equals the premium amount which will be earned by the seller when the option expires out of money The maximum loss for the seller has no upper bound; there are chances of an infinite loss (the price can go up by any amount) FinQuiz.com © 2018 - All rights reserved Reading 29 Risk Management Applications of Option Strategies FinQuiz.com 12 Question ID: 8873 Correct Answer: C If the price is 2,010, the value and profit equal: Value = – max(0,2010 – 2500) = Profit = – 0+76.05= 76.05 If the price is 2,550, the value and profit equal: Value = – max(0,2,550 – 2,500) = – 50 Profit = – 50+76.05 = 26.05 13 Question ID: 8885 Correct Answer: B Option spread strategies in which the options differ by time to expiration are called ‘time spread’ strategies There are other strategies in which the two options differ only by exercise price These are known as money spreads 14 Question ID: 8886 Correct Answer: A Option spread strategies in which the options differ by time to expiration are usually designed to exploit differences in perceptions of volatility of the underlying (which varies over the length of the time period) 15 Question ID: 8887 Correct Answer: C A bull spread has some similarities to a covered call Both strategies involve positions in a short call, and the short call can be viewed as giving up gains beyond its exercise price Also, in a covered call, the long position in the underlying covers the short position in the call; just as in the bull spread the long position in the call with the lower exercise price covers the short position in the call with the higher exercise price 16 Question ID: 8888 Correct Answer: B If the market is expected to go up (or the price of the underlying is expected to increase), an investor should use bull spreads, which involve selling a call with a high exercise price and buying one with a low exercise price In such strategies, the maximum profit is earned if the price of the underlying increases to at least the exercise price of the written call 17 Question ID: 8889 Correct Answer: A Hamilton expects the stock to go down and wants to benefit from this decrease Both a bear call spread and a bear put spread benefit on the downside However, a bear put spread requires a cash outlay at initiation whereas in a bear call spread there is a cash inflow at initiation of the position and a profit if the calls expire worthless FinQuiz.com © 2018 - All rights reserved Reading 29 Risk Management Applications of Option Strategies FinQuiz.com 18 Question ID: 8890 Correct Answer: B Statement is incorrect Although a bear put spread and a bear call spread have similar shapes for their graphical depictions, their payoffs and initial investments differ A bear put requires an initial cash outflow whereas a bear call has a cash inflow at initiation of the position Also, the maximum profit for a bear put and a bear call differ as does the maximum loss Statement is correct 19 Question ID: 8892 Correct Answer: C Statement is incorrect It is not necessary for the exercise prices of both puts to be lower than the current price of the underlying for implementing a bear put spread Sometimes one put can be in-themoney and one can be out-of-money Statement is incorrect It is rare for both calls to be in the money in a bull call spread Usually both are out of money, but sometimes one can be in the money 20 Question ID: 8893 Correct Answer: B If the price of the underlying is $62, the profit equals: max(0,ST-X1) – max(0,ST-X2) –C1 +C2 max (0,62 – 55) – max(0,62 – 65) – 15+7 = – – 15+7 = – $1 21 Question ID: 8894 Correct Answer: A Maximum profit equals: X2 – X1 – C1 + C2 65 – 55 – 15+7 = $2 Maximum loss equals: C1 – C2 15 – = $8 22 Question ID: 8895 Correct Answer: C The breakeven price equals: X1 + C1 – C2 = 55+15 – = $63 23 Question ID: 8896 Correct Answer: C The maximum profit for a bear put spread occurs when both the puts (the long put and the short put) are in the money The breakeven price falls between the exercise prices of the two puts, so that one is in the money and the other is out of money FinQuiz.com © 2018 - All rights reserved Reading 29 Risk Management Applications of Option Strategies FinQuiz.com 24 Question ID: 8897 Correct Answer: A A bear call spread is the exact opposite (inverted image) of a bull call spread The other two options are incorrect The worst outcome for a bear put spread occurs when the underlying’s price is greater than the exercise price of the long put (and the options expire out of money) The maximum a bull call spread can gain is the difference between the exercise price of the short call and the long call less the initial cash outlay 25 Question ID: 8902 Correct Answer: B If the price of the underlying is $92 at expiration, the value and profit equal: Value= max (XH-ST) – max (0, XL-ST) = max (0, 105-92) – max (0,95-92) = 13-3 = $10 Profit = VT – V0 = 10 – 17 + 12 = $5 26 Question ID: 8903 Correct Answer: A Option A is correct For all prices above $105 (the exercise price of the long put) and below $95(the exercise price of the short put) the profit remains the same (negative in the former case and positive in the latter case) Between the exercise prices, the profit will vary 27 Question ID: 8904 Correct Answer: A Breakeven price for a bear put spread equals: XH – pH+pL In this case the breakeven price equals: 105 – 17 +12 = $100 28 Question ID: 8905 Correct Answer: C The maximum profit will equal: XH – XL – (pH – pL) = 105 – 95 – 17+12 = $5 Maximum loss equals: pH-pL = 17 – 12 = $5 29 Question ID: 8906 Correct Answer: B Statement is correct The maximum profit for both a bull call spread and bear put spread equals the difference between the exercise prices of the options less the initial outlay Statement is incorrect The breakeven prices for a bull call spread and bear put spread differ In case of a bull call, the breakeven price is the lower exercise price plus the initial outlay In case of a bear put, the breakeven price is the higher exercise price less the initial outlay FinQuiz.com © 2018 - All rights reserved Reading 29 Risk Management Applications of Option Strategies FinQuiz.com 30 Question ID: 8907 Correct Answer: A The profit if the bond’s price is $95 will equal: Max (0,105 – 95) – max(0,95 – 95) – 17+12 = 10 – – = $5 The profit if the bond’s price is $105 will equal: Max(0,105 –105) – max(0,95 – 105) –17+12 = – – 5= – $5 31 Question ID: 8909 Correct Answer: A The breakeven price equals: XL+cL-cH = 1350 + 18 – 13 = 1355 The market is currently at 1400 This means that the market must go down by: 1355/1400 – = 0.9678 – = – 3.21% 32 Question ID: 8910 Correct Answer: B The maximum loss to a bear call spread will equal: 1600 – 1350 - (18 - 13) = 1600 - 1350 - 18 + 13 = $245 33 Question ID: 8911 Correct Answer: C Palmer is correct A butterfly spread is a combination of a bull and bear spread Also, in virtually all cases in practice, the exercise prices of the options used to construct a butterfly spread are equally spaced such that: 2X2 – X1 – X3 = Where X2= the exercise price of the sold call options X1 and X3 = the exercise prices of the long call options 34 Question ID: 8912 Correct Answer: C Payne is incorrect with respect to the initial value of a butterfly spread The initial value of the position is almost always positive This is because the bull spread bought is more expensive than the bull spread sold (because the lower exercise price on the long bull spread is lower than the lower exercise price on the short bull spread) Therefore, there is almost always a cash outflow at initiation Payne is incorrect with respect to the maximum profit The maximum profit occurs when the price of the underlying is at the exercise price of the sold options (the middle exercise price) FinQuiz.com © 2018 - All rights reserved Reading 29 Risk Management Applications of Option Strategies FinQuiz.com 35 Question ID: 8913 Correct Answer: A If the price of the underlying is $22, the value will equal: If X2 ≤ ST < X3 Value = max(0, ST – X1) – 2max(0, ST – X2) + max(0, ST – X3) Profit = max(0, ST – X1) – 2max(0, ST – X2) + max(0, ST – X3) – c1 + 2c2 – c3 Max(0, 22 – 20) – 2max(0, 22 – 25) + max(0, 22 – 30) = – + = $2 Profit equals: Profit = – + (5) – = $1 36 Question ID: 8914 Correct Answer: C Maximum profit = X2 – X1 – c1 + 2c2 – c3 Maximum profit equals: 25 – 20 – + (5) – = $4 Maximum loss = c1 – 2c2 + c3 Maximum loss equals: – (5) + = $1 37 Question ID: 9014 Correct Answer: C Ford is correct The strategy is a straddle that benefits from high volatility The short butterfly spread can also be used in such cases but its gains are limited A straddle, however, can be costly to implement 38 Question ID: 9015 Correct Answer: B Value = max (0, ST – X) + max (0, X – ST) Profit = max (0, ST – X) + max (0, X – ST) – c0 – p0 If the price of the stock is $98, the value and profit will equal: Value = max(0,98 – 76) + max (0,76 – 98) = 22 + = $22 Profit = 22 – 7.5 – 5.8 = $8.7 39 Question ID: 9016 Correct Answer: B Ford is correct regarding the long butterfly spread The long butterfly spread earns its maximum profit if the price of the underlying is precisely at the exercise price of the sold options (the middle exercise price) However, in case of the strategy mentioned (straddle), the maximum loss occurs if the underlying ends up at the exercise price of the options FinQuiz.com © 2018 - All rights reserved Reading 29 Risk Management Applications of Option Strategies FinQuiz.com 40 Question ID: 9017 Correct Answer: A Breakeven = ST* = X ± (c0 + p0) The breakeven prices equal: 76 ± (7.5+5.8) = 76 ± (13.3) = $89.3, $62.7 41 Question ID: 9018 Correct Answer: C Options A and B are incorrect A straddle would be profitable around major events such as earnings announcements (because of a higher chance of the price increasing/decreasing significantly) However, if the announcement is expected then the uncertainty surrounding it may have already been reflected in options’ prices Also, a straddle is beneficial if the volatility is expected to increase (not decrease) 42 Question ID: 9019 Correct Answer: C The maximum profit and maximum loss equal: Max Profit = ∞ (because of the long call) Max Loss = 7.5+5.8 = $13.3 (if the options expire out of money the premiums will be lost) 43 Question ID: 9031 Correct Answer: B Statement is incorrect Long butterfly spreads (whether they are executed using puts or calls) are used when the expectation is that the market will be less volatile than what everyone else expects Statement is correct When a butterfly spread is executed using puts, the investor is in effect buying a bear put spread and simultaneously selling a bear put spread 44 Question ID: 9032 Correct Answer: A Value = max (0, X1 – ST) – 2max (0, X2 – ST) + max (0, X3 – ST) Profit = Value – (p1 – 2p2 + p3) If the price is $67, the value and profit will equal: Value = max(0,60 – 67) – 2max(0,70 – 67)+max(0,80 – 67) = – 6+13 = $7 Profit = $7 – 4.75 + 2(5.89) – 7.89 = $6.14 45 Question ID: 9033 Correct Answer: A The breakeven prices for the butterfly spread equal: BP = 60 + 4.75 – (5.89) + 7.89 = $60.86 BP = (70) – 60 – 4.75 + (5.89) – 7.89 = $79.14 From the starting value of $70, this represents a range of ± 13% from the starting value of the stock FinQuiz.com © 2018 - All rights reserved Reading 29 Risk Management Applications of Option Strategies FinQuiz.com 46 Question ID: 9034 Correct Answer: C If the stock price is $71, the profit will equal: max (0,60 – 71) – 2max (0,70 – 71) + max (0,80 – 71) – 4.75 + (5.89) – 7.89 = – + – 0.86 = $8.14 The initial investment is 4.75-2(5.89)+7.89= $0.86 Therefore the return equals 8.14/0.86 = 946.5% 47 Question ID: 9035 Correct Answer: A Gibson is correct Both a butterfly spread using puts and butterfly spread using calls are used if the expectation is that the market (or any underlying for that matter) will remain relatively low over the specific time horizon Both would earn their maximum profit if the price of the underlying is at the exercise price of the sold options Also, if the options are priced correctly, it does not really matter whether one uses puts or calls However, if puts were underpriced, it would be better to buy the butterfly spread using puts (and vice versa) 48 Question ID: 9036 Correct Answer: B A short butterfly spread (whether executed using calls or puts) is sometimes called a “sandwich spread” 49 Question ID: 9038 Correct Answer: C A collar is a combination of a short call and protective put position An investor buys a put to protect the underlying and then sells a call to cover the premium of the long put If the call and put premiums exactly offset each other, the position is referred to as a ‘zero cost collar’ However, there are still costs to the position even though there may be no cash paid up-front The cost takes the form of forgoing upside gains (due to the sale of the call) 50 Question ID: 9039 Correct Answer: A Statement is incorrect There is cost associated with a collar in terms of the forgone profit by capping both losses and gains Statement is correct The profit is strictly determined by the underlying and moves directly with the value of the underlying Statement is also incorrect For a zero cost collar, the breakeven price is simply the original underlying price, which in this case is $45.5 FinQuiz.com © 2018 - All rights reserved Reading 29 Risk Management Applications of Option Strategies FinQuiz.com 51 Question ID: 9040 Correct Answer: C Value = ST + max (0, X1 – ST) – max (0, ST – X2) Profit = Value – S0 If the stock’s price is $47, the value and profit equal: Value= 47 + max (0, 40 – 47) – max (0, 47 – 47.5) = 47 + – = $47 Profit = 47 – 45.5 = $1.5 52 Question ID: 9041 Correct Answer: C Profit = ST + max (0, X1 – ST) – max (0, ST – X2) – S0 If the stock’s price is at expiration the profit will equal: + max (0,40 – 0) – max (0,0 – 47.5) – 45.5 = – $5.5 If the stock price hits $100, the profit will equal: 100 + max (0,40 – 100) – max (0,100 – 47.5) – 45.5 = $2 Therefore, the profit will range from – $5.5 to $2 53 Question ID: 9042 Correct Answer: A A collar is similar to a forward contract because it requires no initial outlay other than for the underlying Unlike a forward contract though, which has a linear payoff profile, the collar payoff breaks at the two exercise prices, thus creating a range 54 Question ID: 9043 Correct Answer: C Collars are virtually the same as bull spreads The latter has a cap on the gain and a floor on the loss but does not involve actually holding the underlying Collars also have caps on gains and losses (so the payoffs are similar) 55 Question ID: 9047 Correct Answer: B The caplet payoff on April will be zero because the first caplet has no time value The actual interest payment on the loan will equal: Payment on April 1= 40,000,000 [(0.0901+0.0275)(90/360)] = $1,176,000 This will also be the effective interest payment because the caplet payoff is zero FinQuiz.com © 2018 - All rights reserved Reading 29 Risk Management Applications of Option Strategies FinQuiz.com 56 Question ID: 9048 Correct Answer: A The caplet payoff on July will be zero because the rate is below the cap strike rate The floorlet payoff will equal: 40,000,000[(0.045 – 0.035)(91/360)] = $101,111.12 The actual interest equals: 40,000,000[(0.035 + 0.0275)(91/360)] = $631,944.45 The effective interest equals: 631,944.45+101,111.12 – = $733,055.56 57 Question ID: 9049 Correct Answer: B The flooret payoff on October will be zero because the rate is above the floor strike rate The caplet payoff will equal: 40,000,000[(0.09-0.078)(92/360)] = $122,666.67 The actual interest equals: 40,000,000[(0.09+0.0275)(92/360)] = $1,201,111.12 The effective interest equals: 1,201,111.12+0 – 122,666.67 = $1,078,444.44 58 Question ID: 9050 Correct Answer: A The lowest payment the bank can expect corresponds to a rate equal to the floor strike rate plus the spread and the time period with the fewest number of days: 40,000,000[(0.045+0.0275)(90/360)] = $725,000 59 Question ID: 9051 Correct Answer: B AAA Bank is long a floor with a strike rate of 4.5% and short a cap with a strike rate of 7.8% Hence, AAA Bank can expect to receive interest within the range of: (0.045+0.0275) to (0.078+0.0275) = 7.25% to 10.55% no matter what the interest rate is, because a collar sets a fixed range for the bank FinQuiz.com © 2018 - All rights reserved Reading 29 Risk Management Applications of Option Strategies FinQuiz.com 60 Question ID: 9052 Correct Answer: A The future value of the put and call premium on January will equal: FV of put premium = 15,000 [1 + (0.0475+0.0275)(92/360)] = $15,287.5 FV of call premium = 22,000 [1 + (0.0475+0.0275)(92/360)] = $22,421.67 The effective amount loaned out equals: 40,000,000 (outflow) + 15,287.5 (outflow) - 22,421.67 (inflow) = $39,992,866 61 Question ID: 9072 Correct Answer: C Gamma hedging does not ensure hedging against volatility changes A delta hedged portfolio with a zero gamma can greatly change in value if the volatility changes 62 Question ID: 9073 Correct Answer: C Green is correct with respect to both in the money options and slightly in the money options The deltas of in the money options move towards 1.0 as expiration approaches The deltas of options that are very slightly in the money temporarily move down as expiration approaches and then eventually move up towards 1.0 63 Question ID: 9074 Correct Answer: B During their life, out of money options generally have deltas below 0.5 Hence Option B is the most appropriate choice 64 Question ID: 9075 Correct Answer: C Statement is incorrect A dealer who is long an option will benefit from increases in volatility because the option’s value will increase generating profits for the dealer Statement is incorrect Although it is true that the gamma for at the money options is the largest, options are most sensitive to the volatility when they are at the money 65 Question ID: 9076 Correct Answer: A Dealers in some cases, try to hedge vega by taking on a position in another option, using that option’s vega to offset the vega on the original option 66 Question ID: 9077 Correct Answer: C These risks need to be managed jointly Managing vega risk cannot be done independently of managing delta and gamma risk Thus, the risks associated with delta, gamma and vega need to be monitored and managed jointly FinQuiz.com © 2018 - All rights reserved .. .Reading 29 Risk Management Applications of Option Strategies FinQuiz. com FinQuiz Level III 2018 – Item- sets Solution Reading 29: Risk Management Applications... 135 5/1400 – = 0.9678 – = – 3. 21% 32 Question ID: 8910 Correct Answer: B The maximum loss to a bear call spread will equal: 1600 – 135 0 - (18 - 13) = 1600 - 135 0 - 18 + 13 = $245 33 Question ID: 8911... 40,000,000[(0.045 – 0. 035 )(91 /36 0)] = $101,111.12 The actual interest equals: 40,000,000[(0. 035 + 0.0275)(91 /36 0)] = $ 631 ,944.45 The effective interest equals: 631 ,944.45+101,111.12 – = $ 733 ,055.56 57 Question