Suppose you think FedEx stock is going to appreciate substantially in value in t
ID: 2783337 • Letter: S
Question
Suppose you think FedEx stock is going to appreciate substantially in value in the next year. Say the stocks current price, S0, is $100, and the call option expiring in one year has an exercise price, X, of $100 and is selling at a price, C, of $10. With $10,000 to invest, you are considering three alternatives:
a. Invest all $10,000 in the stock, buying 100 shares.
b. Invest all $10,000 in 1,000 options (10 contracts).
c. Buy 100 options (one contract) for $1,000 and invest the remaining $9,000 in a money market fund paying 4% interest over 6 months (8% annually)
What is your rate of return for each alternative for four stock prices one year from now? Summarize your results in the table and diagram below.
In terms of dollar returns:
Price of Stock 1 Year from Now
$80
$100
$110
$120
a. All stocks (100 shares)
b. All options (1,000 shares)
c. Bills + 100 options
In terms of rate of return on investment, based on a $10,000 investment:
Price of Stock 1 Year from Now
$80
$100
$110
$120
a. All stocks (100 shares)
b. All options (1,000 shares)
c. Bills + 100 options
Price of Stock 1 Year from Now
$80
$100
$110
$120
a. All stocks (100 shares)
b. All options (1,000 shares)
c. Bills + 100 options
Explanation / Answer
Stock price calculation after one year and rate of returns in terms of dollar:
Price of Stock 1 Year from Now
$80
$100
$110
$120
a. All stocks (100 shares)
$80*100=$8,000
$100*100=$10,000
$110*100=$11,000
$120*100=$12,000
b. All options (1,000 shares)
$0 (option is out of money)
$0 (option is at the money)
1000* $10 = $10,000
1000* $20 = $20,000
c. Bills + 100 options
$9,000*1.08+0 = $9,720 (option is out of money)
$9,000*1.08+0 = $9,720 (option is at the money)
$9,000*1.08+ 100* $10 = $10,720
$9,000*1.08+ 100* $20 = $11,720
In terms of rate of return on investment, based on a $10,000 investment:
Price of Stock 1 Year from Now
$80
$100
$110
$120
a. All stocks (100 shares)
($8000-$10,000)/$10,000 =
-20%
($10,000-$10,000)/$10,000 =
0%
($11,000-$10,000)/$10,000 =
10%
($12,000-$10,000)/$10,000 =
20%
b. All options (1,000 shares)
($0-$10,000)/$10,000 =
-100%
($0-$10,000)/$10,000 =
-100%
($10,000-$10,000)/$10,000 =
0%
($20,000-$10,000)/$10,000 =
100%
c. Bills + 100 options
($9,720-$10,000)/$10,000 =
-2.8%
($9,720-$10,000)/$10,000 =
-2.8%
($10,720-$10,000)/$10,000 =
7.2%
($11,720-$10,000)/$10,000 =
17.2%
Explanation: For call option-
If the market price of stock is less than exercise price then call option is out of money and expire without exercise with payoff zero.
If the market price of stock is equal to exercise price then call option is at the money and expire without exercise with payoff zero.
If the market price of stock is more than exercise price then call option is in the money and get exercised with payoff = (stock price – exercise price) * number of shares
Price of Stock 1 Year from Now
$80
$100
$110
$120
a. All stocks (100 shares)
$80*100=$8,000
$100*100=$10,000
$110*100=$11,000
$120*100=$12,000
b. All options (1,000 shares)
$0 (option is out of money)
$0 (option is at the money)
1000* $10 = $10,000
1000* $20 = $20,000
c. Bills + 100 options
$9,000*1.08+0 = $9,720 (option is out of money)
$9,000*1.08+0 = $9,720 (option is at the money)
$9,000*1.08+ 100* $10 = $10,720
$9,000*1.08+ 100* $20 = $11,720
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