chapter 17 note - Chapter 17 An Introduction to Options By...

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Unformatted text preview: Chapter 17 An Introduction to Options By Dr. M. Metghalchi EQUITY OPTIONS: options on the common stock of individual company trades on many exchanges, they started on the CBOE (Chicago Board Options Exchange) in 1973. Options and futures are Derivative Security: derivative Securities’ values are derived from the value of another security. For example, the value of a call option on IBM is derived from the value of IBM stock price. The CBOE (Chicago Board Options Exchange) was the first secondary market in options. Prior to the creation of the CBOE, there were no secondary markets in puts and calls. If an investor wanted to invest in a put or call, the option had to be purchased from a dealer who did not make a market in the option. The creation of a secondary market increased the individual investor's ability to buy and sell options. Since options may be bought and sold in the secondary market, an investor who takes a position knows that the position can be readily closed. This marketability of put and call options greatly increased their popularity. Call option gives the buyer the right to purchase underlying asset at striking (or exercise) price on or before expiration date. Put option gives the buyer of the put the right to sell underlying asset at striking price on of before expiration date. Writer (seller) of call option has commitment to sell underlying asset at striking price on or before expiration date. Writer of put option has the commitment to buy underlying asset at striking price on or before expiration date. 1 Writing a covered call refers to owning the underlying stock; writing a naked call refers to not owning the underlying stock but selling the call on the stock. Buyer has right to exercise; writer has commitment to deliver. Buyer and seller have opposite price expectations. Premium is the price of the contract. Options may be: Exercised Traded in the open market Allowed to expire worthless. Profit and Loss on Call Option on IBM If you buy a call option on IBM: Exercise Price = $90; Premium = $7; If Market Price of IBM = $100 at expiration Proceeds = Stock Price - Exercise Price; Proceeds = $100 - $90 = $10. Profit = Proceeds - Premium; Profit = $10 -- $7 = $3. If Market Price of IBM = $89.25; You would not exercise. Loss = $7. Now if you buy a put Options on IBM: 2 Exercise Price = $90; Premium = $7.50; If Market Price = $90.25 at expiration, contract not exercised. If Market Price is $86 at expiration: Proceeds equal: Exercise Price - Stock Price; Proceeds = $90 -- $86 = $4. Profit = Proceeds - Premium; Profit = $4 -- $7.50 = -$2.50; (loss) Option would be exercised to offset partially the Premium Cost. For Option prices, see: www.yahoo.com American versus European Options 1. An American Option contract allows the owner to exercise the right to buy or sell the underlying asset on or before the expiration date. A European Option contract allows the owner to exercise the right to buy or sell the underlying asset on the expiration date only. In general, American Options are more valuable, due to increased flexibility. Virtually all option contracts traded in the U.S. are American option contracts. Payoff and Profit to Call Options at Expiration for Equity Options: Value of the Call Option @ Expiration: Payoff to Call Owner = St - X; If St > X. Payoff to Call Owner = 0 ; If St < X. St = Value of the stock @ expiration. X = Striking Price. Example: Call Option on IBM; X = $90 Or striking price = $90 Premium = $14. The buyer of the option will pay $14 for this right. 3 Value of option at different stock prices at expiration: Stock Price at expiration $80 $90 $100 $110 $120 Option Value Profit to option holder $10 (-$4) $20 $6 $30 $16 $0 $0 -14 -14 Bullish, Bearish Strategies of Puts & Calls Buyer of Call Option expects price of underlying stock to increase, therefore, if you buy a call on a stock, you expect the price of that stock to go up, you are bullish on that stock. Writer of Call Option expects price of underlying stock to decrease or to remain stable. Therefore, if you sell a call on a stock, you expect that the price of the stock to go down or stay the same. You are bearish on the stock. Buyer of Put Option expects price of underlying stock to decrease, therefore, if you buy a put option on a stock, you expect the stock price to go down, you are bearish on that stock. Writer of put option expects price of underlying stock to increase or to remain stable. If you sell a put option, you expect the stock price to go up or stay the same, you are bullish on that stock. Important variables that affect the value of a call option are: 1. 2. the market stock price. (with the exercise price and everything else constant) an increase (decrease) in the stock price will increase (decrease) the value of a call option. The exercise price (everything else the same). The higher the exercise price, the lower will be the value of a call option. 3. The longer the time remaining until expiration the higher the option value (all other things being equal). 4. The higher the level of interest rates, the higher is the call option's value (all other things being equal). 5. The greater the volatility of the stock price, the higher is the call option value (all other things being equal). 4 The intrinsic value of a call option is: Call option intrinsic value = max [0, S ‐ K] Where S= stock price and K= strike price. In English, the intrinsic value of a call option is the maximum of zero or the value of the stock price minus the strike price. Example, if S=60 and K=53, then the intrinsic value of a call option on this stock is: Call option intrinsic value = max [0, S ‐ K] = max [0, 60‐53] = $7 Put option intrinsic value = max [0, K - S] Example: if S= 50 and K = 55, then Intrinsic value of a put option = max [0, K - S] = max[0, 55-50] =$5 Put and call options are never less than their intrinsic values, or: Call option price ≥ max [0, S - K] Put option price ≥ max [0, K - S] Intrinsic and time value The premium or the option prices that you pay consist of the sum of two specific elements: The intrinsic value and time value. Intrinsic value The intrinsic value = if you exercise now (immediately) how much you can realize. Intrinsic value is always positive or zero. Out-of-the-money options have zero intrinsic values. (See above) Time value The time value of an option = Option price – intrinsic value. The price on this time value depends on a number of factors: time to expiration, volatility of the underlying product price, risk free interest rates and expected dividends. 5 Both warrants and calls are options to buy stock at a specified exercise price within a specified time period. Calls tend to have a short life (three, six, or nine months) while warrants (when issued) may be outstanding for many years. Only firms may issue warrants to buy their stock, and when the warrant is exercised, the firm issues new securities. Calls are created by individuals and financial institutions (e.g., pension plans). When a call option is exercised, no new stock is created. If the writer of a call option is required to supply the stock, he or she has to buy existing stock or supply from the writer's portfolio to meet the terms of the option. Option sensitivities Option Sensitivity or the ‘Greeks’: these are defined as follow: Delta: the change in the option price for a given change in the price of the underlying security. The delta is between 0 and +1 for calls and between 0 and -1 for puts. If IBM has a delta of .5, it means that if IBM stock goes up by $2, the particular option on the IBM stock will delta of .5 will go up by $1. Gamma: the change in delta for a given change in the underlying security. For example if a call option on IBM has a delta of 0.5 and a gamma of 0.05, this indicates that the new delta for IBM option will be 0.55 if the IBM price moves up by $1 and 0.45 if the IBM price moves down by $1. Theta: shows the effect of time decay on an option. As time passes, options will lose time value and the theta measures the extent of this decay. Both call and put options have a negative theta. The decay of options is nonlinear in that the rate of decay will accelerate as the option approaches the expiration date. Vega: defines the effect that a change in implied volatility has on an option’s price. Both calls and puts will have a positive vegas. (for more details see: http://www.euronext.com/fic/000/010/729/107297.pdf) 1. Protective put: You own a stock but in order to protect yourself from downside, you buy the put on the same stock that you own. Example: suppose you own the stock of IBM. Assume the IBM stock price is $83 dollars today. You are not confident about the next 12 months, and for some reasons (tax, not knowing the exact timing of sale, ect)you decide not to sell the stock. In order to sleep easy at nights, you can buy one year put option on IBM with an exercise price of $80. The 6 premium could be $8. So if you are wrong and the IBM price goes up, you loose the $8 premium but you gain on IBM stock price increase. If you are correct and IBM price goes down to $50 by next year, you loose $33 on the IBM price (83 – 50 = $33) but the value of your put option on IBM will be $30 (80-50), so your profits on the option will be $22 (30 – 8). On the whole, you have reduced your downside risk. The Protective put strategy can be applied to your portfolio. If your portfolio is very diversified, then you can by a put option on the S&P 500. If your portfolio is mostly high tech stocks, then you can buy a put option on Nasdaq 100. If your portfolio is mostly small stocks, then you can buy a put on Russel 2000 index. 2. Covered Call: You own the stock and you think there is not much upside and downside possibility for your stock, you sell the call option for your stock. Example: suppose you own the stock of IBM. Assume the IBM stock price is $83 dollars today. You are not confident about the next 12 months, and for some reasons you don’t think the stock will go MUCH lower, as a result you decide to sell the call option on your IBM. you can sell one year call option on IBM with an exercise price of $85. The premium could be $9. So if you are wrong and the IBM price goes up by next year to $105, you loose $11 on your option call (-105+85+9) but you own a stock that is worth $105 dollars. Or you could deliver the stock at expiration and receive $85 cash and you have already pocked the $9 premium, a total of $94 (versus $105 if you did not sell the call). However, If you are right and by next year IBM price is $78 dollars, then the call option that you have sold will expire with a zero value and you end up with IBM share that is worth $78 plus you have pocketed the $9 premium on the option (78+9=87). 3. Long Stradel: Buying both a call and a put option on a stock with the same exercise price and the same expiration date. Why you would do this? Because you think that the stock will move violently either up or down, you don’t know the direction of the move. Example: suppose you own the stock of IBM. Assume the IBM stock price is $83 dollars today and for some reasons (court case, new product, ext) you believe that within the next 6 months IBM stock will have a very strong move on either direction. So, you buy a call option On IBM, exercise price $85, expiration 6 months for $5 and at the same time you buy a put option on IBM, exercise price $85, expiration 6 months for $6. Your total costs on these two options will be $11. For you to break even on this long stradel strategy, the IBM stock should be $11 either above or below $85, or $96 and $74. If IBM stock price is $96 or $74 you just break even. Any price above $94 or below $74 will be your profits. If the stock price in six months ends up between $74 and $96, your strategy will be a loosing strategy. Your maximum loss will be $11 if the stock price settles at $85 in six months. 7 4. Short Stradel: Selling both a call and a put option on a stock with the same exercise price and the same expiration date. Why you would do this? Because you think that the stock will not move violently in either direction. 5. Strips: similar to stradel, however, a strip is two puts and one call on a security with the same exercise price and maturity date. 6. Straps: similar to stradel, however, a strap is two calls and one put on a security with the same exercise price and maturity date. 7. Spreads: usually a combination of calls and puts. There are many ways of spread strategies. Example of bull call spread: Assume the IBM stock price is $83. And you are mildly bullish on IBM. What can you do? One option would be simply to buy a call option on IBM. For example you may buy call IBM with exercise price 85 and maturity 1 year at $8. But since you are not VERY bullish on IBM you don’t want to spend $8. So you buy a call spread on IBM: You buy call 85 and sell call 95 both expiring in one year. This way you reduce your cost but at the same time you limit your upside potential. Your net cost could be $5 per share (assuming call 85 is $8 and call 95 is $3, you buy $8 call 85 and sell $3 call 95 for a net of $5. Your maximum profit would be $5 if IBM stock closes at 95 or higher one year from today. Your break even is $90, and below 90 you would lose and your maximum loss is $5 the net cost of the spread. You lose this $5 net cost of the spread strategy if IBM stock closes at $90 or lower in one year. Options on Stock Index: Call options exist for individual common stocks, but call options also exist on future contracts such as stock Indices (SP500, NYSE, NASDAQ, DOW), Treasury bonds, foreign exchange, and many other instruments. Most of these options on future contracts are traded on organized exchanges such as the Chicago Board Options Exchange and the Chicago Mercantile Exchange. WWW.CME.com The buyer of a call option on a stock index has the right, but not the obligation, to purchase (go long) a particular stock index contract at a specified price at any time during the life of the option. The buyer of a put option on a stock has the right to sell (go short) a particular stock index contract at a specified price. Put options can be purchased to profit from an anticipated price decrease. 8 Settlement is cash; Payoff is difference between the Striking Price and the Value of Index at settlement. Example Of option on stock index: On Friday December 15, 2006 the March S&P 500, 2007 closed at 1438.20. Below please find the March-07 option call and put prices for a few strike prices on S&P500: Call 1440 = $31.50 Call 1450 = $26.50 Call 1460 = $20.80 Put 1440 = $32.50 Put 1435 = $30.40 Put 1425 = $26.80 Put 1415 = $23.70 Exercise 1: Assume you are bullish on the stock market and buy one March call 1440 on the March S&P500. Estimate your profits and losses if S&P500 at its March expiration (Third Friday of March) closes at the following levels: a. 1495.40 b. 1452.80 c. 1438.50 SOLUTION FOR EXCERSIE 1: Option premium = cost of option = 31.50 * 250 (each point of S&P500 =$250) Option costs = 31.50* 250 = $7,875 a. if the index closes at 1495.40, then the value of option at expiration is: (1495.40 – 1440)* 250 = $13,850 Profits = 13,850 – 7,875 = $5,975 b. if the index closes at 1452.80, then the value of option at expiration is: (1452.80 – 1440)*250 = $3,200 Profits = 3,200 – 7,875 = -$4,675 (There will be a loss) c. if the index closes at 1438.50, then the value of option at expiration is zero and you would lose $7,875. Exercise 2: Assume you are bearish on the stock market and buy one March Put 1425 on the March S&P500. Estimate your profits and losses if S&P500 at its March expiration (Third Friday of March) closes at the following levels: 9 a. 1398.40 b. 1418.50 c. 1428.20 SOLUTION OF EXERCISE 2: Option cost = 26.80 * 250 = $6,700 a. if the index closes at 1398.40, then the value of option at expiration is: (1425 – 1398.40) * 250 = $6,650 Profits = 6,650 – 6,700 = -$50 (you lose 50 dollars) b. if the index closes at 1418.50, then the value of option at expiration is: (1425 – 1418.50) * 250 = $1,625 Profits = 1,625 – 6,700 = -$5,075 (This would be your loss). c. if the index closes at 1428.50, then the value of option at expiration is zero and you would lose $6,700 Options on Futures The buyer of a call option has the right, but not the obligation, to purchase (go long) a particular futures contract at a specified price at any time during the life of the option. Example: you pay a premium of $750 (Cost of put option) to purchase an April 620 gold put option. The option gives you the right to sell a 100 ounce gold futures contract for $620 an ounce. Assume that, at expiration, the April futures price has declined to $600 an ounce. The option giving you the right to sell at $620 can thus be sold or exercised at a gain of $20 an ounce. On 100 ounces (see contract specification file), that’s $2,000.After subtracting $750 cost of the option, your net profit comes to $1,250. Not including the transaction cost. Exercise 3: On Friday December 15, 2006 the March Euro, 2007 closed at 131.36. Below please find the March-07 option call and put prices for a few strike prices on Euro currency: Call 131.00 = 0.0193 Call 132.00 = 0.0146 Put 131.00 = 0.0157 Put 130.00 = 0.0116 Assume you think the Euro will violently move one way (Up or down), but you don’t know which way. So you go long one Stradel (Strike price 131.00). Estimate your profits and losses if March Euro at its March expiration (Third Friday of March) closes at the following levels: a. 136.80 10 b. c. d. e. 132.60 131.00 130.20 126.76 Solution of Exercise 3: Long Stradel, Stike price 131.00: Cost of the stradel = cost of call + cost of put As we have seen in the Future chapter, for Euro trading can occur in $.0001 per Euro increments ($12.50/contract). So each .0001 = $12.5. Therefore a price of .0193 implies a cost of (.0193/.0001) * 12.50 = $2,412.50. This could be also obtained by (125,000 * .0193 = $2,412.50) Cost of call = $2,412.5 Cost of put = 125,000 * .0157 = $1,962.50 Cost of the Stradel = 2,412.5 + 1,962.5 = $4,375 a. if the Euro closes at 138.80 at its expiration, then the call option value at the expiration is: (138.80 – 131.00)*1,250 = $9,750 Value of put will be zero. Profits = 9,750 – 4375 = $5,375 b. if the Euro closes at 132.60 at its expiration, then the call option value at the expiration is: (132.60 – 131.00)*1,250 = $2,000 Value of put will be zero. Profits = 2,000 – 4375 = -$2,375 (There will be a loss) c. if the Euro closes at 131.00 at its expiration, then the call option value at the expiration is: (131.00 – 131.00)*1,250 = $0 Value of put will also be zero. Loss = $4,375 d. if the Euro closes at 130.20 at its expiration, then the put option value at the expiration is: (131.00 – 130.20)*1,250 = $1,000 Value of call will also be zero. Loss = 4,375 – 1,000 = 3,375 e. if the Euro closes at 126.76 at its expiration, then the put option value at the expiration is: (131.00 – 126.76)*1,250 = $5,300 Value of call will also be zero. Profits = 5,300 - 4,375 = $925. 11 Exercise 4 On Friday December 15, 2006 the March Euro, 2007 closed at 131.36. Below please find the March-07 option call and put prices for a few strike prices on Euro currency: Call 131.00 = 0.0193 Call 132.00 = 0.0146 Put 131.00 = 0.0157 Put 130.00 = 0.0116 Assume you think the Euro will trade sideway over the next three months. So you go short one Stradel (Strike price 131.00). Estimate your profits and losses if March Euro at its March expiration (Third Friday of March) closes at the following levels: a. b. c. d. e. 136.80 132.60 131.00 130.20 126.76 Solution of Exercise 4: Short Stradel, Stike price 131.00: Cost of the stradel = cost of call + cost of put As we have seen in the Future chapter, for Euro trading can occur in $.0001 per Euro increments ($12.50/contract). So each .0001 = $12.5. Therefore a price of .0193 implies a cost of (.0193/.0001) * 12.50 = $2,412.50. This could be also obtained by (125,000 * .0193 = $2,412.50) Cost of call = $2,412.5 Cost of put = 125,000 * .0157 = $1,962.50 Cost of the Stradel = 2,412.5 + 1,962.5 = $4,375 Since you are a seller of the Stradel (Seller of both call and put), your account will be credited $4,375. a. if the Euro closes at 138.80 at its expiration, then the call option value at the expiration is: (138.80 – 131.00)*1,250 = $9,750 Value of put will be zero. Your Loss = 9,750 – 4375 = $5,375 b. if the Euro closes at 132.60 at its expiration, then the call option value at the expiration is: (132.60 – 131.00)*1,250 = $2,000 Value of put will be zero. Profits = 4375 -2,000 = $2,375 c. if the Euro closes at 131.00 at its expiration, then the call option value at the expiration is: 12 (131.00 – 131.00)*1,250 = $0 Value of put will also be zero. Your profits = $4,375 d. if the Euro closes at 130.20 at its expiration, then the put option value at the expiration is: (131.00 – 130.20)*1,250 = $1,000 Value of call will also be zero. Your profits = 4,375 – 1,000 = $3,375 e. if the Euro closes at 126.76 at its expiration, then the put option value at the expiration is: (131.00 – 126.76)*1,250 = $5,300 Value of call will also be zero. Your Loss = 5,300 - 4,375 = $925. Solutions to the End of Chapter Problems 6 -10: 6. a. The LEAP's intrinsic value: Price of the stock ‐ Strike price = $35 ‐ 24 = $11 b. The time premium: Price of the LEAP ‐ Intrinsic value = $15 ‐ 11 = $4 c. After two years, the LEAP sells for its intrinsic value because the option is at expiration and commands no time premium. If the price of the stock is $50, then the LEAP must sell for $26 ($50 ‐ 24). The stock's price has increased by 42.8 percent ($15/$35); the LEAP's price increased 73.3 percent ($11/$15). The larger percentage increase in the LEAP illustrates the option's potential leverage. d. The LEAP's time premium must disappear because no one would be willing to pay this premium at the option's expiration. An option only sells for its intrinsic value at its expiration. e. If the price of the stock were $22 at the LEAP's expiration, the LEAP would expire worthless, because the exercise price ($24) exceeds the market price of the stock ($22). No one would buy the option and exercise it at $24 when they could buy the stock for $22 on the open market. Thus, the percentage loss on the investment in the LEAP is 100 percent, while the percentage loss on the investment in the stock is 37.1 percent ($13/$35). (Leverage works both directions!) 7. a. An in‐the‐money option must have positive intrinsic value. The intrinsic values of the options are Call at $45: $47 ‐ 45 = $2 Call at $50: $47 ‐ 50 = nil 13 Only the call with the $45 strike price is in‐the‐money. b. The time premiums: Call at $45: $4 ‐ 2 = $2 Call at $50: $1 ‐ 0 = $1 c. Price of Intrinsic Profit the stock value of on the the call call $30 $0 ($4) 35 0 ( 4) 40 0 ( 4) 45 0 ( 4) 50 5 1 55 10 6 60 15 11 d. Price of Intrinsic Profit the stock value of on the the call call $30 $0 ($1) 35 0 ( 1) 40 0 ( 1) 45 0 ( 1) 50 0 ( 1) 55 5 4 60 10 9 14 The potential profits/losses differ. If you buy the "out of the money" call, the potential loss is less but the price of the stock must rise more for the option to have positive intrinsic and to assure that you earn a profit. e. Price of Intrinsic Profit Profit Total the stock value of on the on the profit the call stock call $30 $0 ($17) $1 ($16) 35 0 (12) 1 (11) 40 0 (7) 1 (6) 45 0 (2) 1 (1) 46 0 (1) 1 0 50 0 3 1 4 55 5 8 ( 4) 4 60 10 13 ( 9) 4 As long as the stock sells for greater than $46, the position generates a profit (before commissions). f. Price of Intrinsic Profit Profit Total the stock value of on the on the profit the call s tock call $30 $15 ($17) $4 ($13) 35 10 (12) 4 (8) 40 5 (7) 4 (3) 45 0 (2) 4 2 48 0 1 1 2 50 0 3 (1) 2 55 0 8 (6) 2 60 0 13 (11) 2 15 As long as the price of the stock remains above $42, the position yields a profit. Both (e) and (f) are covered calls, so their answers are similar. The maximum possible profit is $4 in (e) while the maximum possible profit in (f) is $2. For the maximum $2 profit to occur in (f), the price of the stock must exceed $45. For the maximum $4 profit to occur in (e) the price must exceed $50. Thus, (e) offers more potential profit, but the price of the stock must increase more to earn that profit. 8. This problem illustrated the protective put strategy. The profit‐loss profile at various price of the stock: Price Profit: of the Buying the Buying the Total stock stock at $36 put at $2 profit $30 ($6) $3 ($3) 35 (1) (2) (3) 40 4 (2) 2 a. Profit on the stock at $30, 35, and 40 is ($6), ($1), and $4, respectively. b. Net cash outflow is $36 to buy the stock and $2 to buy the put for a total outflow of $38. c. The above profit‐loss profile indicates the profits and losses to be ($3), ($3), and $2. For the position to break even, the price of the stock must rise to $38. d. The worse case scenario is a loss of $3, but there is no limit on the potential profit. e. If the price of the stock is $37, the investor gains $1 on the stock but loses $2 on the put for a net loss of $1. This illustrates that the protective put can sustain a loss even though the price of the stock rises. In this case the price increase was insufficient to offset the cost of the put. 9. Price of Profit on Intrinsic Profit Profit Total the stock 100 shares value of on the on the profit call call call T‐bill $90 ($1,000) $0 ($400) $400 $0 95 ( 500) 0 ( 400) 400 0 100 0 0 ( 400) 400 0 105 500 5 100 400 500 110 1,000 10 600 400 1,000 16 Notice that if the investor selects the T‐bill and the call instead of the stock, the investor does not sustain a loss if the price of the stock falls, and earns the same profit if the price of the stock rises. The call plus the bill is the better alternative, (This problem illustrates that options may be combined with other securities. I use this problem to set up the material covered in the next chapter on put‐call parity.) 10. This problem compares several strategies designed to profit if the price of the stock rises. a. the cash inflows/outflows: buying the stock: $86.00 outflow buying the call: $10.50 outflow the covered call: $86.00 ‐ 10.50 = $75.50 selling the put: $ 8.25 inflow b. profit/loss profile Price of Bought Bought Covered Sold the stock the stock the call call the put $110.00 $24.00 $14.50 $9.50 $8.25 100.00 14.00 4.50 9.50 8.25 95.50 9.50 .00 9.50 8.25 90.00 4.00 (5.50) 9.50 8.25 86.00 .00 (9.50) 9.50 8.25 80.00 (6.00) (10.50) 4.50 3.25 76.75 (9.25) (10.50) 1.25 .00 75.50 (10.50) (10.50) .00 (1.25) 70.00 (16.00) (10.50) (5.50) (6.75) 60.00 (26.00) (10.50) (15.50) (16.75) 17 c. Break‐even prices of the stock: buying the stock: $86.00 buying the call: $95.50 the covered call: $75.50 selling the put: $76.75 d. Three of the positions require a cash outflow, but the sale of the put produces a cash inflow. The potential profits are limited if you execute the covered call or the sale of the put, $9.50 and $8.25, respectively. The potential loss on the sale of the put is larger than on the covered call, once again by $1.25. Since the sale of the put produces a cash inflow, these funds may be invested. Earning a return on the cash inflow from the sale of the put increases the potential profit and reduces the break‐even price of the stock. If a sufficient amount is earned ($1.25 in this example), the two positions are equivalent. e. Purchasing the call has the smallest potential loss ($10.50), while the losses continue to rise as the price of the stock declines. f. Once the price of the stock falls below $75.50, all four possible positions generate losses. g. The largest potential gain occurs through the purchase of the stock, but the largest percent return occurs through the sale of the put, since there is no cash outflow. The largest percentage return among the three alternatives with a cash outflow is the purchase of the call. h. If the price of the stock declines and the put is exercised, your cost basis is the strike price minus the proceeds of the sale ($85.00 ‐ $8.25 = $76.75). If you buy the stock, hold on to it, and watch its price decline; selling the put is actually better than buying the stock. As one investment strategist said to me: "It is better to sell the put than to buy the stock. If you are wrong and the put is exercised, you bought a stock you like at a lower price." 18 ...
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