Suppose you think Apple stock is going to appreciate substantially in value in t

Question

Suppose you think Apple stock is going to appreciate substantially in value in the next year. Say the stock's current price, So, is $150, and a call option expiring in one year has an exercise price, X, of $150 and is selling at a price, C, of $6. With $15,000 to invest, you are considering three alternatives. a. Invest all $15,000 in the stock, buying 100 shares b. Invest all $15,000 in 2,500 options (25 contracts) C. Buy 100 options (one contract) for $600, and invest the remaining $14,400 in a money market fund paying 4% in interest over 6 months (8% per year). What is your rate of return 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 170 Stock Price All stocks (100 shares) All options (2,500 options) Bills100 options 130 $ 150 $ 160

Explanation / Answer

a.) Current Price, S0 = $150

Price after 1 year, S1 =$130

Call Price, C=$6

Gain in first option (100 shares) =$ (130-150)x100 =$ -2000

Return in first option = -2000/15000x100 = -13.33%

Gain in second option (25 contracts) =$ Max{(130-150),0}x2500 - 15000 =$ -15000

Return in second option = -15000/15000x100 = -100%

Gain in third option (1 contracts) =$ Max{(130-150),0}x100 - 600 + (1.08-1)x14400 =$ -600 + 1152 =$552

Return in third option = 552/15000x100 = 3.68%

b.) Current Price, S0 = $150

Price after 1 year, S1 =$150

Call Price, C=$6

Gain in first option (100 shares) =$ (150-150)x100 =$ 00

Return in first option = 00/15000x100 = 00.00%

Gain in second option (25 contracts) =$ Max{(150-150),0}x2500 - 15000 =$ -15000

Return in second option = -15000/15000x100 = -100%

Gain in third option (1 contracts) =$ Max{(150-150),0}x100 - 600 + (1.08-1)x14400 =$ -600 + 1152 =$552

Return in third option = 552/15000x100 = 3.68%

c.) Current Price, S0 = $150

Price after 1 year, S1 =$160

Call Price, C=$6

Gain in first option (100 shares) =$ (160-150)x100 =$ 1000

Return in first option = 1000/15000x100 = 6.67%

Gain in second option (25 contracts) =$ Max{(160-150),0}x2500 - 15000 =$ 10000

Return in second option = 10000/15000x100 = 66.67%

Gain in third option (1 contracts) =$ Max{(160-150),0}x100 - 600 + (1.08-1)x14400 =$ 1000 - 600 + 1152 =$1552

Return in third option = 1552/15000x100 = 10.35%

d.) Current Price, S0 = $150

Price after 1 year, S1 =$170

Call Price, C=$6

Gain in first option (100 shares) =$ (170-150)x100 =$ 2000

Return in first option = 2000/15000x100 = 13.33%

Gain in second option (25 contracts) =$ Max{(170-150),0}x2500 - 15000 =$ 35000

Return in second option = 35000/15000x100 = 233.33%

Gain in third option (1 contracts) =$ Max{(170-150),0}x100 - 600 + (1.08-1)x14400 =$ 2000 - 600 + 1152 =$2552

Return in third option = 2552/15000x100 = 17.01%

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