Questions and answers 283 Chapter 11 questions 1 Coca-Cola’s earnings prospects are good, but the stock market as a whole has been bearish and volatile lately. The market could rally, or it could retrace to recent lows, dragging Coca-Cola along with it. The stock price is 52.67, and the following August options are listed with 90 days until expiration: Coca-Cola at 52.67 August options with 90 days until expiration: Coca- Cola strike 45.00 47.50 50.00 52.50 55.00 57.50 60.00 Calls 4.04 2.52 1.45 0.79 0.34 Puts 0.82 1.30 2.05 2.90 4.25 (a) i) What is the cost of the August 52.50 straddle? ii) At expiration, what is the upside break-even level? iii) What is the downside break-even level? iv) What is the maximum profit? v) What is the maximum loss? vi) What is the profit/loss if the stock closes at 57.50 at expiration? (b) i) What is the cost of the long August 50–55 strangle? ii) At expiration, what is the upside break-even level? iii) What is the downside break-even level? iv) What is the maximum profit? v) What is the maximum loss? vi) What is the profit/loss if the stock closes at 47.50 at expiration? (c) Why is the 50 put priced higher than the 55 call? 2 In the UK, the outlook for Sainsbury during the next several months is for continued good, but not spectacular, trading, and you expect the shares to be stable. The implied volatility for the options is 38 per cent, down from over 50 per cent. It is November, and the January options are entering their accel- erated time decay period. Sainsbury is trading at 537.5, and the following options prices are listed: Sainsbury at 537.5 January options with 70 days until expiry: 284 Questions and answers Strike 420 460 500 550 600 650 700 Calls 34 17.5 8 3 Puts 3 8 17.5 39.5 i) What is the income from selling the January 500–600 strangle? ii) At expiry, what is the upside break-even level? iii) What is the downside break-even level? iv) What is the maximum profit? v) What is the maximum loss? Chapter 11 answers 1 (a) i) 2.52 + 2.90 = 5.42 ii) 52.50 + 5.42 = 57.92 iii) 52.50 – 5.42 = 47.08 iv) upside unlimited; downside, value of the stock v) 5.42 vi) [57.50 – 55] – 5.42 = –2.92 loss (b) i) 2.05 + 1.45 = 3.50 ii) 55 + 3.50 = 58.35 iii) 50 – 3.5 = 46.5 iv) upside unlimited; downside 50 – 3.5 = 46.5 v) 3.50 vi) 5 – 3.5 = 1.5 (c) Because of the put volatility skew. This explained in Part 4. 2 i) 17.5 + 17.5 = 35 ii) 600 + 35 = 635 iii) 500 – 35 = 465 iv) 35 v) unlimited upside, 465 on the downside. Questions and answers 285 Chapter 12 questions 1 Refer to the previous set of Sainsbury January options: Sainsbury at 537.5 January options with 70 days until expiry Strike 420.0 460.0 500.0 550.0 600.0 650.0 700.0 Calls 34.0 17.5 8.0 3.0 Puts 3.0 8.0 17.5 39.5 (a) i) What is the income from the short January 460–500–600–650 iron condor? This is an asymmetric spread. ii) At expiry, what is the upside break-even level? iii) What is the downside break-even level? iv) What is the maximum upside loss? v) What is the maximum downside loss? vi) What is the maximum profit from this spread? vii) What is the profit range? (b) i) What is the income from the short January 460–550–650 iron butterfly? This is also an asymmetric spread. ii) At expiry, what is the upside break-even level? iii) What is the downside break-even level? iv) What is the maximum upside loss? v) What is the maximum downside loss? vi) What is the maximum profit? vii) What is the profit range? 2 Given the previous set of Coca-Cola options. Coca-Cola at 90 August options with 90 days until expiration Strike 45.00 47.50 50.00 52.50 55.00 57.50 60.00 Calls 4.04 2.52 1.45 0.79 0.34 Puts 0.82 1.30 2.05 2.90 4.25 286 Questions and answers (a) i) What is the cost of the long August 45–50–55–60 iron condor? ii) At expiration, what is the upside break-even level? iii) What is the downside break-even level? iv) What is the maximum upside profit? v) What is the maximum downside profit? vi) What is the maximum loss? (b) i) What is the cost of the long August 45–52.50–60 iron butterfly? ii) At expiration, what is the upside break-even level? iii) At expiration, what is the downside break-even level? iv) What is the maximum upside profit? v) What is the maximum downside profit? vi) What is the maximum loss? Chapter 12 answers (a) i) 17.5 + 17.5 – 8 – 8 = 19 credit ii) 600 + 19 = 619 iii) 500 – 19 = 481 iv) [650 – 600] – 19 = 31 v) [500 – 460] – 19 = 21 vi) 19 vii) 619 – 481 = 138 (b) i) 34 + 39.5 – 8 – 8.5 = 57.5 credit ii) 550 + 57.5 = 607.5 iii) 550 – 57.5 = 492.5 iv) [650 – 550] – 57.5 = 42.5 v) [550 – 460] – 57.5 = 32.5 vi) 57.5 vii) 607.5 – 492.5 = 115 2 (a) i) 2.05 + 1.45 – 0.82 – 0.34 = 2.34 debit ii) 55 + 2.34 = 57.34 iii) 50 – 2.34 = 47.66 iv) [60 – 55] – 2.34 = 2.66 v) [50 – 45] – 2.34 = 2.66 vi) 2.34 Questions and answers 287 (b) i) 2.52 + 2.90 – 0.82 – 0.34 = 4.26 debit ii) 52.50 + 4.26 = 56.76 iii) 52.50 – 4.26 = 48.24 iv) [60 – 52.50] – 4.26 = 3.24 v) [52.50 – 45] – 4.26 = 3.24 vi) 4.26 288 Questions and answers Chaper 13 Questions 1 In the UK, the FTSE-100 index has been bullish since the end of October, and you expect this trend to continue through the end of the year. The December futures contract is currently at 5470. Using technical analysis, you determine that there is resistance at a former support area between 5700 and 5800. You note the following European-style December call options: December FTSE contract at 5470 December options with 40 days until expiry Strike 5625.0 5675.0 5725.0 5775.0 5825.0 5875.0 5925.0 5975.0 6025.0 Calls 159.5 137.5 117.0 97.5 81.0 68.0 57.0 46.5 35.5 (a) i) What is the cost of the long 5675–5775–5875 call butterfly? ii) At expiry, what is the maximum profit of the spread? iii) What is the lower break-even level? iv) What is the upper break-even level? v) What is the profit range? vi) What is the maximum loss? (b) i) What is the cost of the long 5625–5725–5825–5925 call condor? ii) At expiry, what is the maximum profit of the spread? iii) What is the lower break-even level? iv) What is the upper break-even level? v) What is the profit range? vi) What is the maximum loss? (c) How do you account for the greater profit range of the condor? 2 Because of budget deficit problems in Western economies the stock markets have been extremely volatile. However, bail-out packages with the IMF and the more solvent nations have finally been agreed upon. The global stock markets have sold off, and you expect them to range for the next two months. DJ Eurostoxx 50 at 2831 June puts with 57 days until expiration Strike 2700 2750 2800 2850 Puts 54.50 68.40 85.80 107.00 Questions and answers 289 (a) i) What is the price of the long June 2850–2800–2750 put butterfly? ii) At expiration, what is the maximum profit? iii) What is the upper break-even level for this butterfly? iv) What is the lower break-even level? v) What is the profit range? vi) What is the maximum loss? (b) i) Suppose you prefer to leave yourself a margin of error in your outlook. You are range bearish. What is the cost of the 2850– 2800–2700–2650 put condor? ii) At expiration, what is the maximum profit? iii) What is the upper break-even level? iv) What is the lower break-even level? v) What is the profit range? vi) What is the maximum loss? (c) Compare the advantages and disadvantages of the put butterfly to the put condor. Chapter 13 answers 1 (a) i) 137.5 + 68 – [2 × 97.5] = 10.5 ii) [5775 – 5675] – 105 = 89.5 iii) 5675 + 10.5 = 5685.5 iv) 5875 – 10.5 = 5864.5 v) 5864.5 – 5685.5 = 179 points vi) 10.5 = £105 (b) i) 159.5 + 57 – 117 – 81 = 18.5 ii) [5725 – 5625] – 18.5 = 81.5 iii) 5625 + 18.5 = 5643.5 iv) 5925 – 18.5 = 5906.5 v) 5906.5 – 5643.5 = 263 points vi) 18.5 = £185 (c) The condor has a gross profit range that is 100 points greater. The 8p extra cost reduces eight points of profit from both the lower and upper break-even levels. The net profit range of the condor is therefore 84p greater. 2 (a) i) 107 + 68.40 – (2 × 85.80) = 3.8 ii) (2850 – 2800) – 3.8 = 46.2 290 Questions and answers iii) 2850 – 3.8 = 2846.2 iv) 2750 + 3.8 = 2753.8 v) 2846.2 – 2753.8 = 92.4 points vi) 3.8 (b) i) 107 + 54.5 – 85.8 – 68.4 = 7.3 ii) (2850 – 2800) = 42.7 iii) 2850 – 7.3 = 2842.7 iv) 2650 + 7.3 = 2657.3 v) 2842.7 – 2657.3 = 185.4 points vi) 7.3 (c) The condor has a gross profit range that is 185.4 – 92.4 = 93 points greater at an additional cost of 3.5. Questions and answers 291 Chapter 14 questions 1 Your shares in Intel have performed well in the past, but now, with the pos- sibility of a global recession, Intel’s orders are down, and the stock is in a trading range. You are looking to supplement your dividend by writing one call on each 100 shares that you own. You realise that if the stock rallies above the call strike price, it will be called away from you. Intel is currently trading at 21.42, and the July 24 calls, with 46 days until expiration, are trading at 0.21. They are 12 per cent out-of-the-money. (a) What is the maximum profit from writing one July 24 call? (b) What happens if at expiration the stock closes above 24? (c) What is the break-even level? (d) What is your percentage return over the next 46 days with your stock valued at 21.42? 2 Sainsbury’s range this past year is no less than 370 to 588.5. You have held onto your shares, riding the market turbulence. Because supermarkets are cur- rently cutting prices, you forsee reduced profit margins for the near term. Sainsbury is currently trading at 537.5. With 70 days until expiration, the January 550 calls are trading at 34, and the January 600 calls are trading at 17.5. You would like to sell one of these as a covered write on 1,000 shares that you own. (a) i) What is the maximum profit from writing one January 550 call? ii) What happens if at expiry the shares closes above 550? iii) What is the break-even level? iv) What is your percentage return over the next 70 days with your shares valued at 537.5? (b) i) What is the maximum profit from writing one January 600 call? ii) What happens if at expiry the shares closes above 600? iii) What is the break-even level? iv) What is your percentage return over the next 70 days with your shares valued at 537.5? 292 Questions and answers 3 It is late November, and IBM is currently trading at 159.75. You expect IBM to remain at approximately 160 for the next month. You note the following prices for 160 calls. November 160 calls, with one day until expiration: 0.69 December 160 calls, with 29 days until expiration: 5.13 January 160 calls, with 64 days until expiration: 7.5 (a) What is the cost of the December–January 160 call calendar? (b) Barring a special dividend or takeover within the next 29 days, what is the maximum loss of your calendar spread? (c) i) Although there are 28 days between November and December expirations, and 35 days between December and January expirations, you would like to estimate the profit potential of the December–January spread. What is your estimate for the value of this spread with IBM at 160 and one day until December expiration? ii) Would you expect the December–January spread to be worth more or less than the November–December spread? Chapter 14 answers 1 (a) [24 – 21.42] + 0.21 = 2.79 (b) Your stock will be called away, or sold, but you will still have your maximum profit. (c) 21.42 – 0.21 = 21.21 (d) 0.21/21.42 = 1% 2 (a) i) [550 – 537.5] + 34 = 46.5 ii) Your shares will be called away, or sold, but you will still have your maximum profit. iii) 537.5 – 34 = 503.5 iv) 34/537.5 = 6.33% (b) i) [600 – 537.5] + 17.5 = 80 ii) Your shares will be called away, or sold, but you will still have your maximum profit. iii) 537.5 – 17.5 = 520 iv) 17.5/537.5 = 3.26% 3 (a) 7.5 – 5.13 = 2.37 [...]... at 52.67 The January options have 60 days until expiration and the December options have 30 days until expiration Is each of the following statements true or false? (a) If the implied volatility increases, then the delta and theta of the January 47.50 put will also increase (b) If the implied increases, then the gamma of the January 57.50 call will increase, and the vega will decrease (c) If the implied... January puts theoretical value 14.75 (a) What is the value of the May synthetic future, and why is it so valued? (b) To be realistic, there is probably a bid–ask market for Marks and Spencer of 350–351 and the spread is certain to increase during volatile markets In order to price the May 350 conversion, the market assumes that the shares are bought at 351 At what price must the call and put be traded... order to break even, or make a small profit on the cost of carry on the shares? Questions and answers (c) Now determine the market price of May 350 reversal Here the shares must be sold at 350 At what prices must the call and put be traded in order to break even, or make a small profit on the cash income from the shares? (d) If the prices in the options markets correspond to the current Bank of England... price above the shock is due to the cost of carry on the shock for 75 days: 350.60 + (350.60 × 0.005 × 75/365) = 0.36, traded at 0.40 (b) The synthetic must be sold at £0.40 over the ask price of the stock in order to recoup the cost of carry Bearing in mind that the options contract trades in multiples of 0.25, the synthetic must be sold at 351.50 This is possible if the call is sold at 16.00, and 14.50... call is sold at 16.00, and 14.50 is paid for the put (c) If the return on a sale of the stock is 0.50 per cent, then no more than £0.40 must be paid for the synthetic over the bid price of the stock Bearing in mind that the options contract trades in multiples of 0.25, the synthetic must be traded at 350.25 Therefore 15.25 will be paid for the call, while the put will be sold at 15.00 (d) Call market... that comprise the index Glossary Gamma The rate of change of the delta with respect to a change in the underlying Hybrid spread A spread combination that is not one of the standard spreads In -the- money (ITM) Apart from at -the- money options, calls below the underlying and puts above the underlying Intrinsic value The amount that an option is in the money, or the parity component of an in -the- money option... known as the Christmas tree Leverage The right or obligation to trade the full value of the underlying by trading only the value of the option Long To be long is to own A long futures contract owns a cash or physical asset when the contract expires A long options contract owns the right to buy, for a call, or the right to sell, for a put Long deltas Any combination of long calls, short puts and long... media mogul, and the December futures contract rallies to 5620 You know that your call position has made a profit, and while awaiting a price quote (and a possible change in the tabloid’s editorial policy), you decide to evaluate the effect of the market move on your call’s Greeks How will they be affected by the change in the December futures contract? (a) delta (b) gamma (c) vega (d) theta 5 Coca-Cola... the implied decreases, then the vega of the December 52.50 call will decrease (d) If the implied decreases, then the gamma and delta of the January 47.50 call will increase 6 Under what circumstances can an increase in the implied cause an increase in an out-of -the- money option’s gamma? 7 Suppose the S&P 500 index is at 1030, and you are long a number of 975 puts The chairman of the US Federal Reserve... unchanged (d) True Questions and answers 6 If the implied is increasing from a very low level then the gammas of the far out-of -the- money options will increase 7 If his retirement is unexpected, then the implied may increase due to uncertainty; if his retirement is expected, then the implied will most likely remain unchanged 297 298 Questions and answers Chapter 21 questions 1 Given the following set of FTSE . Questions and answers Chaper 13 Questions 1 In the UK, the FTSE-100 index has been bullish since the end of October, and you expect this trend to continue through the end of the year. The December. of the following statements true or false? (a) If the implied volatility increases, then the delta and theta of the January 47.50 put will also increase. (b) If the implied increases, then the. of the January 57.50 call will increase, and the vega will decrease. (c) If the implied decreases, then the vega of the December 52.50 call will decrease. (d) If the implied decreases, then the