Here is a quote from an investment website about an investment strategy using options:

One strategy investors are applying to the XYZ options is using synthetic stock. A synthetic stock is created when an investor simultaneously purchases a call option and sells a put option on the same stock. The end result is that the synthetic stock has the same value, in terms of capital gain potential, as the underlying stock itself. Provided the premiums on the options are the same, they cancel each other out so the transaction fees are a wash. (as cited in McDonald, 2013, question 3.19)

Suppose, to be concrete that the premium on the call you buy is the same as the premium on the put you sell, and both have the same strikes and times to expiration.

a. What can you say about the strike price?

b. What term best describes the position you have created? What is the shape of the profit diagram?

c. Suppose the options have a bid-ask spread. If you are creating a synthetic purchased stock and the net premium is zero inclusive of the bid-ask spread, where will the strike price be relative to the forward price?

d.If you create a synthetic short stock with zero premium inclusive of the bid-ask spread, where will the strike price be relative to the forward price?

e. Do you consider the transaction fees to really be a wash? Why or why not?