Question

3. A six-month call option is the right to buy stock at $30. Currently, the stock is selling for $32 and the call is selling for $3. You are considering buying 100 shares of the stock ($3,000) or one call option ($300).

a) If the price of the stock rises to $39 within six months, what would be the profits or losses on each position? What would be the percentage gains or losses?

b) If the price of the stock declines to $25 within six months, what would be the profits or losses on each position? What would be the percentage gains or losses?

c)If the price of the stock remained stable at $32, what would be the percentage gains or losses at the expiration of the call option?

d)If you compare purchasing the stock to purchasing the call, why do the percentage gains and losses differ?

Please show work

Answer 1

Part(a)

Calculation of profit or loss if price of the stock rises to $ 39
Price of stock now	$ 39
Exercise price	$ 30
Profit per one stock	$ 9
Total profit for 100 stock
[ 100 x 9]	$ 900
Less: Cost of premium paid
[ 100 x 3]	$ 300
NET PROFIT	$ 600

Percentage of gain / loss is calculation
Exercise price	$ 30
Total exercise price(100 x 30)	$ 3000
Add:Cost of premium (100x3)	$ 300
Total invested amount	$ 3300
Profit	$ 600
% of profit on investment(600/3300)	18.18%

Part (b)

Calculation of profit or loss if price of the stock decline to $25
Price of stock now	$ 25
Exercise price	$ 30
Since exercise price is morethan the current market price of stock investor will not exercise the call option
The ending position will be,Loss of premium paid
Cost of premium paid
[ 100 x 3]	$ 300
LOSS	$ 300
Percentage of gain / loss is calculation
Invested amount	$ 300
Total invested amount	$ 300
Loss	$ 300
% of loss on investment(300/300)	100.00%

Part(c)

Calculation of profit or loss if price of the stock remains unchanged as $ 32
Price of stock now	$ 32
Exercise price	$ 30
Profit per one stock	$ 2
Total profit for 100 stock
[ 100 x 2]	$ 200
Less: Cost of premium paid
[ 100 x 3]	$ 300
NET LOSS	$ 100
Percentage of gain / loss is calculation
Exercise price	$ 30
Total exercise price(100 x 30)	$ 3000
Add:Cost of premium (100x3)	$ 300
Total invested amount	$ 3300
LOSS	$ 200
% of Loss on investment(200/3300)	6.06%

Part (d)

Call premium is paid to get the right to buy the stock at the exercise price agreed

Purchasing the call is a cost to the investor and it is to be deducted from the profit arrived.

Call premium paid it the fixed expense and it will not change with change of stock price

Changes in the percentage of gain or loss is due the hike or down of the market price only