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Position s t x 1 x 1 s t x 2 x 2 s t buy call x 2 0 0

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Position S T < X 1 X 1 S T X 2 X 2 < S T Buy call (X 2 ) 0 0 S T – X 2 Buy put (X 1 ) X 1 – S T 0 0 Total X 1 – S T 0 S T – X 2 X 1 S T X 1 X 2 Payoff 7. Position S T < X 1 X 1 S T X 2 X 2 < S T Buy call (X 2 ) 0 0 S T – X 2 Sell call (X 1 ) 0 –(S T – X 1 ) –(S T – X 1 ) Total 0 X 1 – S T X 1 – X 2 Payoff 0 S T X 1 X 2 Payoff –(X 2 –X 1 ) 20-4
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8. a. By writing covered call options, Jones receives premium income of $30,000. If, in January, the price of the stock is less than or equal to $45, then Jones will have his stock plus the premium income. But the most he can have at that time is ($450,000 + $30,000) because the stock will be called away from him if the stock price exceeds $45. (We are ignoring here any interest earned over this short period of time on the premium income received from writing the option.) The payoff structure is: Stock price Portfolio value less than $45 10,000 times stock price + $30,000 greater than $45 $450,000 + $30,000 = $480,000 This strategy offers some extra premium income but leaves Jones subject to substantial downside risk. At an extreme, if the stock price fell to zero, Jones would be left with only $30,000. This strategy also puts a cap on the final value at $480,000, but this is more than sufficient to purchase the house. b. By buying put options with a $35 strike price, Jones will be paying $30,000 in premiums in order to insure a minimum level for the final value of his position. That minimum value is: ($35 × 10,000) – $30,000 = $320,000 This strategy allows for upside gain, but exposes Jones to the possibility of a moderate loss equal to the cost of the puts. The payoff structure is: Stock price Portfolio value less than $35 $350,000 – $30,000 = $320,000 greater than $35 10,000 times stock price – $30,000 c. The net cost of the collar is zero. The value of the portfolio will be as follows: Stock price Portfolio value less than $35 $350,000 between $35 and $45 10,000 times stock price greater than $45 $450,000 If the stock price is less than or equal to $35, then the collar preserves the $350,000 principal. If the price exceeds $45, then Jones gains up to a cap of $450,000. In between $35 and $45, his proceeds equal 10,000 times the stock price. The best strategy in this case would be (c) since it satisfies the two requirements of preserving the $350,000 in principal while offering a chance of getting $450,000. Strategy (a) should be ruled out since it leaves Jones exposed to the risk of substantial loss of principal. Our ranking would be: (1) strategy c; (2) strategy b; (3) strategy a. 20-5
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9. a. Position S T 780 S T > 780 Buy stock S T S T Buy put 780 – S T 0 Total 780 S T Position S T 840 S T > 840 Buy call 0 S T – 840 Buy T-bills 840 840 Total 840 S T Payoff S T 840 780 780 840 Bills plus calls Protective put strategy b. The bills plus call strategy has a greater payoff for some values of S T and never a lower payoff. Since its payoffs are always at least as attractive and sometimes greater, it must be more costly to purchase.
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