Consider a stock S whose initial price is S0 = 55. A call option with expiration date T and strike price 50 has initial price 7.50, and a put option with expiration date T and strike price 60 has initial price 4. You create a portfolio Π by selling short 100 shares of S and using the proceeds to by 500 of the call options described above, and a number of the put options described above in order to make the initial value Π0 of your portfolio equal to zero.
(i) How many of the put options do you buy?
(ii) For what values of ST is the value of the portfolio equal to zero at time T? For what values of ST is the value of the portfolio positive at time T? For what values of ST is the value of the portfolio negative at time T?