Problem 20-6 Suppose you think Apple stock is going to appreciate substantially

Question

Problem 20-6 Suppose you think Apple stock is going to appreciate substantially in value in the next year. Say the stock's current price, so is $120, and a call option expiring in one year has an exercise price X of $120 and is selling at a price, C, of $5. With $12,000 to invest, you are considering three alternatives. a. Invest all $12,000 in the stock, buying 100 shares. b. Invest all $12,000 in 2,400 options (24 contracts). C. Buy 100 options (one contract) for $500, and invest the remaining $11,500 in a money market fund paying 5% in interest over 6 months (10% per year). What is your rate of retum for each alternative for the following four stock prices in one year? (Leave no cells blank be certain to enter "O" wherever required. Negative amounts should be indicated by a minus sign. Round the "Percentage return of your portfolio (Bills+100 options)" answers to 2 decimal places.) The total value of your portfolio in six months for each of the following stock prices is Price of Stock One Year from Now Stock Price All stocks (100 shares) All options (2,400 options) Bills100 options 120 $ 12,000 130 S 13,000 24,000 13,075 140 14,000 48,000 14,075 100 S 10,000 12,075 12,075 The percentage return of your portfolio in six months for each of the following stock prices is Price of Stock One Year from Now 140 Stock Price All stocks (100 shares) All options (2.400 options) Bils100 options 100 120 130 01% (100) 0.63 (17)196 81% 17 (100) 0.63

Explanation / Answer

Please find the table with answers below: (Missing Values in Bold & Italic)

Explanation: We need to find out the absolute percentage returns 6 months from now for each of the missing blanks in respective positions:

All Options

This option will only have a positive payoff when Stock Price is higher than the Exercise Price. In all other cases, the options will simply expire.

Stock Price @ 130 - This means a payoff of 130-120 = $10 for each option resulting in total payoff of $10*2400 = $24,000. Deducting the initial premium of 2400*5 = $12,000, we get an absolute profit of 24000-12000 = $12,000 which reflects a 100% return ($12,000/$12000) over the invested capital.

Stock Price @ 140 - Similarly, the payoff here is $20 for total payoff of 20*2400 = $48,000 and absolute profit = 48,000-12,000 = $36,000. Therefore, percentage return = 300% (36,000/12,000)

Bills + 100 Options

In this case, there is a fixed return on money market fund of 11,500*5% = $575 for 6 months holding in each case. Therefore, we need to see the option payoff in each case and then add this return to find the total return.

Stock Price @ 130 - Option Pay-Off is 10*100 = $1,000 and net option payoff after dedcuting premium of $5 for 100 options= 1000-500 = $500

Therefore, total return = 500 + 575 =$1075 and percentage return = 1075/12000 = 8.96%

Stock Price @ 140 - Option Pay-Off is 20*100 = $2,000 and net option payoff after dedcuting premium of $5 for 100 options= 2000-500 = $1500

Therefore, total return = 1500 + 575 =$2075 and percentage return = 2075/12000 = 17.29%

Price of Stock One Year from Now Stock Price 100 120 130 140 All Stocks (100 Shares) -17% 0% 8% 17% All Options (2400 Options) -100.0% -100.0% 100.0% 300.0% Bills + 100 Options 0.63% 0.63% 8.96% 17.29%

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