Question

# Consider a portfolio consisting of a long position in one stock and a short position in...

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?

We have Bought stock @20 .

Premium recieved on call option = \$3

Total Initial Outflow = 20 - 3*2 = \$14

 Stock Price (S) Call Exercised or Lapsed Payoff from Call option A = -2(S - E) Payoff from Stock (B ) Total Payoff ( C =A + B) Initial Outflow ( D ) Profit ( E = D-C) 12 Lapsed 0 12 12 14 -2 14 Lapsed 0 14 14 14 0 16 Lapsed 0 16 16 14 2 18 Lapsed 0 18 18 14 4 20 Lapsed 0 20 20 14 6 22 Exercised -4 22 18 14 4 24 Exercised -8 24 16 14 2 26 Exercised -12 26 14 14 0 28 Exercised -16 28 12 14 -2

c)

From stock price ranging from 16-24 the portfolio provides a net positive return.

d)

The Mamimum profit that can be obtained is 6 . The same is evident from the graph as well as the payoff table created.

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