Question

Suppose that put options on a stock with strike prices $25 and 5 month maturity costs $3. Suppose the current stock price is $24. (a) How can those securities be used to create a protective put? (b) What is the initial investment? (c) Construct a table showing how the payoff and profit varies with ST in 5 month, for the protective put you created. Whenever you need to refer to stock price on expiration date, use ST . The only notation that should show up in the table should be ST . The table should look like this: Stock Price Payoff Profit ST < 25 ST ≥ 25

Answer 1

a)

Protective Put is a strategy where, one holds the underlying security and buys a put option.

Therefore, in this case, one can Buy the stock at curren price i.e. $24 AND Buy a Put Option with strike price of $25 for a premium of $3.

b)

Initial Investment = Cost to Buy Stock + Cost to Buy a Put Option = $24 + $3 = $27

NOTE: Initial Investment and Payoff & Profit per share is calculated. Lot Size is ignored.

c)

ST	Payoff(of Option) [Higher of (25-ST) & 0]	Profit/Loss [Payoff-Premium]
17	8	5
18	7	4
19	6	3
20	5	2
21	4	1
22	3	0
23	2	-1
24	1	-2
25	0	-3
26	0	-3

Note: above Payoffs and Profits are for Option Position ONLY. If we also take the stock into consideration, the Profit will be, If ST<25 the Profit = (25-24)-3 = -2 AND If ST>=25, then Profit VARIES depending on the ST.