Question

Three put options on a stock have the same expiration date and strike prices of $50, $60, and $70. The market prices are $3, $5, and $9, respectively. Harry buys the $50 put, buys the $70 put and sells two of the $60 puts. Harry's strategy potentially makes money (i.e. positive profit) in which of the following price ranges?

		$40 to $50
		$70 to $80
		$85 to $95
		$55 to $65

Answer 1

Note : This stratefy will make profit in range (52-68) but since there is no option of 52-68, we will have to find an option which is within the range of (52-68), therefore correct answer is 55-65.

Please refer to the solution below for details

Strike	Position	Qty	Premium	Cash Flow
50	Buy	1	3	-3
60	Sell	2	5	10
70	Buy	1	9	-9
			Net Outflow	-2

Net Outflow form this strategy is $2

Since the outflow on the strategy is 2

Lower Range below which we will incurr loss is (50+2) = 52

Upper Range above which we will incurr loss is (70-2) = 68

Therefore range in which we will earn profit = 52-68

Therefore correct answer is 55-65 (which is a subset of range 52-68)

same can be calculated by calculatiing payoff and profit from all the strikes as shown below

Stock Price	Payoff from Buying one 50 Strike Put	Payoff from Selling two 60 Strike Put	Payoff from one 70 Strike Put	Total Payoff	Premium Paid	Profit
40	10	-40	30	0	2	-2
41	9	-38	29	0	2	-2
42	8	-36	28	0	2	-2
43	7	-34	27	0	2	-2
44	6	-32	26	0	2	-2
45	5	-30	25	0	2	-2
46	4	-28	24	0	2	-2
47	3	-26	23	0	2	-2
48	2	-24	22	0	2	-2
49	1	-22	21	0	2	-2
50	0	-20	20	0	2	-2
51	0	-18	19	1	2	-1
52	0	-16	18	2	2	0
53	0	-14	17	3	2	1
54	0	-12	16	4	2	2
55	0	-10	15	5	2	3
56	0	-8	14	6	2	4
57	0	-6	13	7	2	5
58	0	-4	12	8	2	6
59	0	-2	11	9	2	7
60	0	0	10	10	2	8
61	0	0	9	9	2	7
62	0	0	8	8	2	6
63	0	0	7	7	2	5
64	0	0	6	6	2	4
65	0	0	5	5	2	3
66	0	0	4	4	2	2
67	0	0	3	3	2	1
68	0	0	2	2	2	0
69	0	0	1	1	2	-1
70	0	0	0	0	2	-2
71	0	0	0	0	2	-2
72	0	0	0	0	2	-2
73	0	0	0	0	2	-2
74	0	0	0	0	2	-2
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