11. If you anticipate that the price of a stock will rise, you could (1) buy the
ID: 2755419 • Letter: 1
Question
11. If you anticipate that the price of a stock will rise, you could (1) buy the stock, (2) buy a call, (3) sell a covered call, or (4) sell a put. All four positions may generate profits if the price of the stock rises, but the cash inflows or outflows, the amount of any gains, and the potential losses differ for each position. Currently, the price of a stock is $86; four-month calls and puts with a strike price of $85 are trading for $10.50 and $8.25, respectively.
a) What are the cash inflows or outflows associated with each of the four positions?
b) Construct a profit/loss profile for each position at the following prices of the stock.
Profit / Loss
price of stock
bought the stock
cover call
Bought the call
Sold the put
$110.00
$100.00
$95.50
$90.00
$86.00
$80.00
$76.75
$75.50
$70.00
$65.00
As this profile illustrates, each strategy produces a gain but the amounts and potential losses differ.
c) What are the prices of the stock that generate breakeven for each position?
d) Compare the cash inflows/outflows, profits, and potential loss from the covered call and sale of the put. Which is better if you are able to invest any cash inflows and earn $1.25?
e) Which strategy has the smallest potential dollar loss?
f) What price of the stock produces a loss on all four positions?
g) Which position generates the highest possible gain in dollar and in percentage terms?
h) Suppose the price of the stock declines, and the put is exercised (i.e., you have to buy the stock). Since the option is exercised, what is your cost basis of the stock? Compare this cost basis to your initially buying the stock instead of selling the put.
price of stock
bought the stock
cover call
Bought the call
Sold the put
$110.00
$100.00
$95.50
$90.00
$86.00
$80.00
$76.75
$75.50
$70.00
$65.00
Explanation / Answer
a & b Price of stock bought the stock (CMP-$85) cover call Workings Bought the call Workings Sold the put Workings $110.00 $25.00 ($14.50) $10.5 - (CMP-$85) $14.50 (CMP - $85)-$10.50 8.25 Buyer will not excercise the option, hence premium of $8.25 will be the gain $100.00 $15.00 ($4.50) $10.5 - (CMP-$85) $4.50 (CMP - $85)-$10.50 8.25 $95.50 $10.50 $0.00 $10.5 - (CMP-$85) $0.00 (CMP - $85)-$10.50 8.25 $90.00 $5.00 $5.50 $10.5 - (CMP-$85) ($5.50) (CMP - $85)-$10.50 8.25 $86.00 $1.00 $9.50 $10.5 - (CMP-$85) -9.5 (CMP - $85)-$10.50 8.25 $80.00 ($5.00) 10.5 Buyer will not excercise the option, hence premium of $12.50 will be the gain -10.5 Premium loss $3.25 8.25-($85-CMP) $76.75 ($8.25) 10.5 -10.5 Premium loss $0.00 8.25-($85-CMP) $75.50 ($9.50) 10.5 -10.5 Premium loss ($1.25) 8.25-($85-CMP) $70.00 ($15.00) 10.5 -10.5 Premium loss ($6.75) 8.25-($85-CMP) $65.00 ($20.00) 10.5 -10.5 Premium loss ($11.75) 8.25-($85-CMP) c) BEP Price of stock ($) 86.00 75.5 Call premium-(CMP-86) 96.5 Premium - (CMP -86) 77.75 d) Which is better if you are able to invest any cash inflows and earn $1.25? Price of stock bought the stock (CMP-$85) cover call Workings Sold the put Workings Net profit /(loss) $110.00 $25.00 ($14.50) $10.5 - (CMP-$85) 8.25 Buyer will not excercise the option, hence premium of $8.25 will be the gain ($22.75) $100.00 $15.00 ($4.50) $10.5 - (CMP-$85) 8.25 ($12.75) $95.50 $10.50 $0.00 $10.5 - (CMP-$85) 8.25 ($8.25) $90.00 $5.00 $5.50 $10.5 - (CMP-$85) 8.25 ($2.75) $86.00 $1.00 $9.50 $10.5 - (CMP-$85) 8.25 $1.25 $80.00 ($5.00) 10.5 Buyer will not excercise the option, hence premium of $12.50 will be the gain 3.25 8.25-($85-CMP) $7.25 $76.75 ($8.25) 10.5 0 8.25-($85-CMP) $10.50 $75.50 ($9.50) 10.5 -1.25 8.25-($85-CMP) $11.75 $70.00 ($15.00) 10.5 -6.75 8.25-($85-CMP) $17.25 $65.00 ($20.00) 10.5 -11.75 8.25-($85-CMP) $22.25 Best strategy to cover a call & write a put option at the present premium to earn a profit
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