Question

Question 2 Suppose you have identified two put options on a stock, both having the same expiry dates, but with strike prices K1 = $30 and K2 = $42, and premiums p1 = $4 and p2 = $6 respectively.

a) How would you use these puts to create a bear spread?

b) Construct a table that shows the payoff for each put option, the total payoff and profit for the bear spread.

c) Draw a diagram showing the two put payoffs, and the profits achieved with the bear spread. Make sure you include in your diagram the correct change points at the St prices along the horizontal axis, and the profits (π) associated with the bear spread along the vertical axis.

d) An investor who constructs a bear spread must have certain expectations about the future behaviour of the underlying asset’s price. Describe the investor’s expectations.

Answer 1

Solution:

(a)A bear put spread consists of one long put with a higher strike price and one short put with a lower strike price. Both puts have the same underlying stock and the same expiration date. A bear put spread is established for a net debit (or net cost) and profits as the underlying stock declines in price. Profit is limited if the stock price falls below the strike price of the short put (lower strike), and potential loss is limited if the stock price rises above the strike price of the long put (higher strike).

Note: One can only do these kind of arrangement when he is bearish on a stock.

Here in this question there are two put one is at a strike price of $42 (i.e long put) and another is at $30 strike price of $30 (i.e. short put)

So, in this case Put option(long Put) purchased at $6 this means if price goes below $42 then the buyer will receive money (i.e. difference between actual price –strike price) and sold put option (short put) at $4 this means if price goes below $30 he has to pay money(i.e. difference between actual price –strike price). If price rises above long put option strike option both the option will lapse. Loss incurred by person $2 i.e. ($6-$4) i.e. the maximum possible loss in any scenario.

(b)Here is the table to make you understand payoff and profit

Prices at Expiry of put option	Long put Payoff	Short put Payoff	Net Premium paid	Profit
43	0	0	2	-2
42	0	0	2	-2
41	1	0	2	-1
40	2	0	2	0
39	3	0	2	1
38	4	0	2	2
37	5	0	2	3
36	6	0	2	4
35	7	0	2	5
34	8	0	2	6
33	9	0	2	7
32	10	0	2	8
31	11	0	2	9
30	12	0	2	10
29	13	-1	2	10
28	14	-2	2	10
27	15	-3	2	10

(c)Following is the graph showing the two put payoffs, and the profits achieved with the bear spread. Make sure you include in your diagram the correct change points at the St prices along the horizontal axis, and the profits (π) associated with the bear spread along the vertical axis.

(d) Here investor is bearish on stock price , he expects that the stock price will fall in future from $42 but not fall below $30. So, he buyed a put option on $42 and sold a put option on $30.