Question

5. Suppose the current price of a stock is $35, and one associated six-month call option with a strike price of $36 currently sell for $3.5. Rachel Heyhoe-Flint, an amateur investor, feels that the price of the stock will increase and so she comes up with the following two possible strategies: (i) purchase 100 shares and (ii) buying 1,000 call options. Both strategies involve an investment of $3,500. How much the stock has to rise after six months for the option strategy to be more profitable? 6. (Synthetic Long Stock) Traders can construct a so-called "synthetic long stock” portfolio by buying a call and selling a put at the same strike price/level. (a) Draw the payoff diagram of the such a synthetic long stock portfolio. Explain why such a strategy is called “synthetic long stock”. (b) Why do people adopt this strategy instead of purchasing one share of the underlying stock? (c) Can you write down a potential cost incurred when one purchases a unit of synthetic long stock portfolio?

Answer 1

6]

Profit on shares strategy = (stock price after 6 months - current stock price) * number of shares bought.

Profit on option strategy = (stock price after 6 months - option strike price - premium) * number of options bought.

Say the stock price after 6 months is X.

Then :

(X - 36 - 3.5) * 1000 > (X - 35) * 100

1000X - 39500 > 100X - 3500

900X > 36000

X > 40

For the option strategy to be more profitable, the stock price has to be over $40.

Rise in stock price required = $40 - $35 = $5