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Long Position Derivative Securities

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These are some self help textbook problems i came across .I would like to understand

1 . The common stock of Sophia Enterprises serves as the underlying asset for the following
derivative securities: (1) forward contracts, (2) European-style call options, and (3) European-
style put options.
a. Assuming that all Sophia derivatives expire at the same date in the future, complete a
table similar to the following for each of the following contract positions:
(1) A long position in a forward with a contract price of $50
(2) A long position in a call option with an exercise price of $50 and a front-end pre-
mium expense of $5.20
Expiration Date Sophia Stock price
Expiration Date Derivative Payoff
Initial Derivative Premium Net Profit
25
30
35
40
45
50
55
60
65
70
75

(3) A short position in a call option with an exercise price of $50 and a front-end
premium receipt of $5.20
In calculating net profit, ignore the time differential between the initial derivative expense or receipt and the terminal payoff.
b. Graph the net profit for each of the three derivative positions, using net profit on the
vertical axis and Sophia's expiration date stock price on the horizontal axis. Label the
breakeven (i.e., zero profit) point(s) on each graph.
c. Briefly describe the belief about the expiration date price of Sophia stock that an investor using each of these three positions implicitly holds.

2. Refer once again to the derivative securities using Sophia common stock as an underlying
Asset discussed in Problem 1.
a. Assuming that all Sophia derivatives expire at the same date in the future, complete a
Table similar to the following for each of the following contract positions:
(1) A short position in a forward with a contract price of $50
(2) A long position in a put option with an exercise price of $50 and a front-end premium expense of $3.23
(3) A short position in a put option with an exercise price of $50 and a front-end premium receipt of $3.23
Expiration Date Sophia Stock price
Expiration Date Derivative Payoff
Initial Derivative Premium Net Profit
25
30
35
40
45
50
55
60
65
70
75

In calculating net profit, ignore the time differential between the initial derivative expense or receipt and the terminal payoff.
b. Graph the net profit for each of the three derivative positions, using net profit on the
Vertical axis and Sophia's expiration date stock price on the horizontal axis. Label the
Breakeven (i.e., zero profit) point(s) on each graph.
c. Briefly describe the belief about the expiration date price of Sophia stock that an investor using each of these three positions implicitly holds

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Answer:
1) We have,
(a) Contract price $50:
(i) Long position in a forward with a contract price of $50.
Expiration Date Sophia Stock Price (S) Long Forward (K=$50) Payoff=S-$50 Initial long forward premium Net Profit
25 ($25) $0 ($25)
30 ($20) $0 ($20)
35 ($15) $0 ($15)
40 ($10) $0 ($10)
45 ($5) $0 ($5)
50 $0 $0 $0
55 $5 $0 $5
60 $10 $0 $10
65 $15 $0 $15
70 $20 $0 $20
75 $25 $0 $25

(ii) Long position in call option with exercise price of $50 and a front end premium expense of $5.20
Expiration Date Sophia Stock Price (S) Long Call (K=$50) Payoff=Max (0,S-$50) Initial long Call premium Net Profit
25 $0 $5.20 ($5.20)
30 $0 $5.20 ($5.20)
35 $0 $5.20 ($5.20)
40 $0 $5.20 ($5.20)
45 $0 $5.20 ($5.20)
50 $0 $5.20 ($5.20)
55 $5 $5.20 ($0.20)
60 $10 $5.20 $4.80
65 $15 $5.20 $9.80
70 $20 $5.20 $14.80
75 $25 $5.20 $19.80

(iii) Short position in a call option with an exercise price of $50 and a front-end premium receipt of $5.20
Expiration Date Sophia Stock Price (S) Short Call (K=$50) Payoff=-max(0,S-$50) Initial Short Call premium Net ...

Solution Summary

Long position derivative securities are examined.

$2.19