Try this on then...
I do not believe the synthetic stock performs anywhere near the same as the base stock. It might appear to on first order, but it does not. Here is why.
As I mentioned earlier, stocks on average return 10%/year. Say we are talking about a one year time frame, so we can expect our stock to earn 10%. In reality it might double or it might halve, but we expect an average over the long term of the 10%.
Your synthetic position consist of the purchased call option and the sold put option. If your option is to perform as the stock does, it must, on average return 10% over the next year. Now, this is the zero sum part that is important. Somebody out there was willing to sell you the call option, and purchase the put option. This means, that those people are willing to make an investment that will on average lose 10% a year. Of course nobody is willing to do that. This shows up as a minor adjustment in the pricing of the options to favor those individuals such that they have an equal chance of making money as you do.
This comes back to the way options are fundamentally different than stocks. Only one person has an interest in a stock; the person who owns it. For an option, there are opposing positions. For every sold call, there is a bought call. For every sold put, somebody else bought it. Both parties have an interest in the option until it expires. When you make a dollar on an option contract, somebody else just lost a dollar. If you sum all the option contracts across the country you get a value of zero. If you sum all the stocks across the country you get a value of billions.
So why do they call these things synthetic stocks then if they do not really perform like stocks? The issue is in the volatility. The "average" stock return is 10%, however the volatility is so high that it is very difficult and takes a very long time to tell if it is 10% or 0% or 20% or -40%. If the stock goes up 50%, the option contract will go up almost 50%, and if the stock goes down 50% the option contract will go down almost 50%...hence to the first order it does look like the stock.
--Alan
