Question

3. You own a stock. You bought it at $29. Given the following options, develop a (a) covered call, (b) protective put and (c) collar. Be sure to describe the traded position you will take to follow each strategy. Also calculate the breakeven point for each strategy. (20 points)

Call Options			Put Options
Strike Price	Premium		Strike Price	Premium
$35.00	$0.89		$35.00	$6.69
29.00	2.74		29.00	2.57
23.00	6.60		23.00	0.46

Answer 1

(a) Covered call

We have a long position in the stock at $29 thus spending $29

We sell the call option with a strike price of $35 for $0.89. Thus we will encash $0.89.

Breakeven point is the stock price at maturity where net payoff is 0

Hence the breakeven point is $28.11

Stock price S(t)	Payoff stock (S(t) - 29)	Payoff short call strike $35	Covered call payoff
10	-19	0.89	-18.11
11	-18	0.89	-17.11
12	-17	0.89	-16.11
13	-16	0.89	-15.11
14	-15	0.89	-14.11
15	-14	0.89	-13.11
16	-13	0.89	-12.11
17	-12	0.89	-11.11
18	-11	0.89	-10.11
19	-10	0.89	-9.11
20	-9	0.89	-8.11
21	-8	0.89	-7.11
22	-7	0.89	-6.11
23	-6	0.89	-5.11
24	-5	0.89	-4.11
25	-4	0.89	-3.11
26	-3	0.89	-2.11
27	-2	0.89	-1.11
28	-1	0.89	-0.11
28.11	-0.89	0.89	0
29	0	0.89	0.89
30	1	0.89	1.89
31	2	0.89	2.89
32	3	0.89	3.89
33	4	0.89	4.89
34	5	0.89	5.89
35	6	0.89	6.89
36	7	-0.11	6.89
37	8	-1.11	6.89
38	9	-2.11	6.89
39	10	-3.11	6.89
40	11	-4.11	6.89
41	12	-5.11	6.89
42	13	-6.11	6.89
43	14	-7.11	6.89
44	15	-8.11	6.89
45	16	-9.11	6.89
46	17	-10.11	6.89
47	18	-11.11	6.89
48	19	-12.11	6.89
49	20	-13.11	6.89
50	21	-14.11	6.89

(a) Protective put

We have a long position in the stock at $29 thus spending $29

We buy the put option with a strike price of $23 for $0.46. Thus we will spend $0.46

Breakeven point is the stock price at maturity where net payoff is 0

Hence the breakeven point is $29.46

Stock price S(t)	Payoff stock (S(t) - 29)	Payoff long put strike 23	Covered call payoff
10	-19	12.54	-6.46
11	-18	11.54	-6.46
12	-17	10.54	-6.46
13	-16	9.54	-6.46
14	-15	8.54	-6.46
15	-14	7.54	-6.46
16	-13	6.54	-6.46
17	-12	5.54	-6.46
18	-11	4.54	-6.46
19	-10	3.54	-6.46
20	-9	2.54	-6.46
21	-8	1.54	-6.46
22	-7	0.54	-6.46
23	-6	-0.46	-6.46
24	-5	-0.46	-5.46
25	-4	-0.46	-4.46
26	-3	-0.46	-3.46
27	-2	-0.46	-2.46
28	-1	-0.46	-1.46
29	0	-0.46	-0.46
29.46	0.46	-0.46	8.32667E-16
30	1	-0.46	0.54
31	2	-0.46	1.54
32	3	-0.46	2.54
33	4	-0.46	3.54
34	5	-0.46	4.54
35	6	-0.46	5.54
36	7	-0.46	6.54
37	8	-0.46	7.54
38	9	-0.46	8.54
39	10	-0.46	9.54
40	11	-0.46	10.54
41	12	-0.46	11.54
42	13	-0.46	12.54
43	14	-0.46	13.54
44	15	-0.46	14.54
45	16	-0.46	15.54
46	17	-0.46	16.54
47	18	-0.46	17.54
48	19	-0.46	18.54
49	20	-0.46	19.54
50	21	-0.46	20.54

(c) Collar

The call strategy involves owing the stock

Buying a put option with strike price $23 at $0.46 (Investment of $0.46)

Selling a call option with strike price $35 for $0.89 ( Upfront cash-flow of $0.89)

Breakeven point is the stock price at maturity where net payoff is 0

Hence the breakeven point is $28.57

Stock price S(t)	Payoff stock (S(t) - 29)	Payoff long put strike 23	Payoff short call strike 35	Collar payoff
10	-19	12.54	0.89	-5.57
11	-18	11.54	0.89	-5.57
12	-17	10.54	0.89	-5.57
13	-16	9.54	0.89	-5.57
14	-15	8.54	0.89	-5.57
15	-14	7.54	0.89	-5.57
16	-13	6.54	0.89	-5.57
17	-12	5.54	0.89	-5.57
18	-11	4.54	0.89	-5.57
19	-10	3.54	0.89	-5.57
20	-9	2.54	0.89	-5.57
21	-8	1.54	0.89	-5.57
22	-7	0.54	0.89	-5.57
23	-6	-0.46	0.89	-5.57
24	-5	-0.46	0.89	-4.57
25	-4	-0.46	0.89	-3.57
26	-3	-0.46	0.89	-2.57
27	-2	-0.46	0.89	-1.57
28	-1	-0.46	0.89	-0.57
28.57	-0.43	-0.46	0.89	0
29	0	-0.46	0.89	0.43
30	1	-0.46	0.89	1.43
31	2	-0.46	0.89	2.43
32	3	-0.46	0.89	3.43
33	4	-0.46	0.89	4.43
34	5	-0.46	0.89	5.43
35	6	-0.46	0.89	6.43
36	7	-0.46	-0.11	6.43
37	8	-0.46	-1.11	6.43
38	9	-0.46	-2.11	6.43
39	10	-0.46	-3.11	6.43
40	11	-0.46	-4.11	6.43
41	12	-0.46	-5.11	6.43
42	13	-0.46	-6.11	6.43
43	14	-0.46	-7.11	6.43
44	15	-0.46	-8.11	6.43
45	16	-0.46	-9.11	6.43
46	17	-0.46	-10.11	6.43
47	18	-0.46	-11.11	6.43
48	19	-0.46	-12.11	6.43
49	20	-0.46	-13.11	6.43
50	21	-0.46	-14.11	6.43