Question

Consider a portfolio consisting of a long position in one stock and a short position in two call options. Both the current stock price (S0) and the exercise price (K) of call options are $20. The call option costs $3.

a) Construct a table showing the payoffs and net profits for all possible price ranges.

b) Draw a diagram showing the variation of an investor’s net profit with the terminal stock price

c) For what price range does this portfolio provide a net positive return? d) What is the maximum amount of profit that can be obtained?

Answer 1

(a)

Expiry Price	Cashflow	On expiry		Net Cashflow
Stock Buy	Sell 2 Call option	Cashflow Today	Sell Stock	Call Option	Value of Call Option	Value of 2 Option	Cashflow on expiry
$          5	$ (20)	$         6	$        (14)	$5	Lapse	$               -	$           -	$             5	$          (9)
$       10	$ (20)	$         6	$        (14)	$10	Lapse	$               -	$           -	$          10	$          (4)
$       11	$ (20)	$         6	$        (14)	$11	Lapse	$               -	$           -	$          11	$          (3)
$       12	$ (20)	$         6	$        (14)	$12	Lapse	$               -	$           -	$          12	$          (2)
$       13	$ (20)	$         6	$        (14)	$13	Lapse	$               -	$           -	$          13	$          (1)
$       14	$ (20)	$         6	$        (14)	$14	Lapse	$               -	$           -	$          14	$           -
$       15	$ (20)	$         6	$        (14)	$15	Lapse	$               -	$           -	$          15	$             1
$       16	$ (20)	$         6	$        (14)	$16	Lapse	$               -	$           -	$          16	$             2
$       17	$ (20)	$         6	$        (14)	$17	Lapse	$               -	$           -	$          17	$             3
$       18	$ (20)	$         6	$        (14)	$18	Lapse	$               -	$           -	$          18	$             4
$       19	$ (20)	$         6	$        (14)	$19	Lapse	$               -	$           -	$          19	$             5
$       20	$ (20)	$         6	$        (14)	$20	Indiff.	$               -	$           -	$          20	$             6
$       21	$ (20)	$         6	$        (14)	$21	Exercise	$                1	$             2	$          19	$             5
$       22	$ (20)	$         6	$        (14)	$22	Exercise	$                2	$             4	$          18	$             4
$       23	$ (20)	$         6	$        (14)	$23	Exercise	$                3	$             6	$          17	$             3
$       24	$ (20)	$         6	$        (14)	$24	Exercise	$                4	$             8	$          16	$             2
$       25	$ (20)	$         6	$        (14)	$25	Exercise	$                5	$          10	$          15	$             1
$       26	$ (20)	$         6	$        (14)	$26	Exercise	$                6	$          12	$          14	$           -
$       27	$ (20)	$         6	$        (14)	$27	Exercise	$                7	$          14	$          13	$          (1)
$       28	$ (20)	$         6	$        (14)	$28	Exercise	$                8	$          16	$          12	$          (2)
$       29	$ (20)	$         6	$        (14)	$29	Exercise	$                9	$          18	$          11	$          (3)
$       30	$ (20)	$         6	$        (14)	$30	Exercise	$              10	$          20	$          10	$          (4)
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