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 [...]... 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 underlying Margin Cash or liquid security deposited by holders... Purchase boxes in the FTSE to lend, sell boxes to borrow (c) 997 = (572.5 – 81) – (35.5 + ?) ? = 997 – 572.5 + 81 + 35.5 (d) ? = 541 2 (a) 350 + 15.75 – 14.75 = 351 The £0.40 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... value See Time premium Fence See Combo Future A contract to buy or sell a physical asset at a specified price at a specified future date This asset can be a commodity, bond or stock In the case of a stock index, the contract is for a cash value of all the stocks 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... Federal Reserve bank, who is liked by the financial markets, announces that he is to retire when his term expires What may happen to the implied volatility of your put options? 295 296 Questions and answers Chapter 15 answers 1 (a) decrease (b) increase (c) decrease (d) increase 2 (a) practically unchanged (b) increase (c) decrease (d) increase 3 (a) Purchase puts on a stock index and/or eurodollars (b)... (b) i) ATM puts provide more coverage per option ii) ATM puts respond more to market movement iii) ATM puts are more sensitive to an increase or decrease in the implied iv) OTM puts cost less in time decay (c) i) ii) No difference Near-term has greater gamma, it responds more to market movement iii) Not-so-near is more sensitive to change in the implied iv) Near-term costs more in daily time decay (d)... partnership with an Italian 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... futures or options contracts Multiplier Part of a contract specification: the cash amount by which a futures or options value is multiplied Naked A short option not spread with a long option or underlying One by two A long one by two call spread is a long call plus two short calls at a higher strike A long one by two put spread is a long put plus two short puts at a lower strike Out-of-the-money (OTM)... long put butterfly is a long one by two put spread plus a long put at a third, lower strike Again, all strikes are equidistant For shorts of these spreads, reverse the long/short positions Calendar spread A long calendar spread is a long option plus a short option that is closer to expiration Both options have the same strike 304 Glossary Call A call option is the right to buy the underlying asset at... rate of change of an option with respect to a change in the underlying Delta neutral Any combination of options and an underlying position whose delta sum is practically zero Delta/price ratio The percent that an option’s value changes with respect to a change in the underlying Diagonal spread A long diagonal is a long option plus a short option that is closer to expiration and further out-of-the-money... gamma (c) vega (d) theta 3 (a) If the manager of your pension fund wants to hedge a portfolio of stocks and Treasury Bills against a possible interest rate increase during the next two weeks, which options position or positions might he employ? (b) In terms of the Greeks, compare the advantages and disadvantages that he might consider by employing out-of-, or at-the-money options i) delta ii) gamma iii) . 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. 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. S&P 500 index is at 103 0, and you are long a number of 975 puts. The chairman of the US Federal Reserve bank, who is liked by the financial markets, announces that he is to retire when his term