# Synthetic position

Hi all - I came over the following question in Qbank:

To create a synthetic short position in a stock, an investor can buy:

A) a call option on the stock and sell a put option on the stock.

B) both a call option on the stock and a put option on the stock.

C) a put option on the stock and sell a call option on the stock.

The correct answer is C) - however it looks like for me that C) is the long synthetic position on the stock not the short one.

Thanks many times,

Anush

Short position in stock- gain when stock goes down, if stock moves up, loss

Long put- gain if.stock goes down

Short call- loss if stock moves up.

Combine both and u have position equivalent to short position in stock.

Draw a payoff graph with a long put and short call with the same strike price.

For synthetics, effectively use the Put Call Parity (Stock + Put = Call) and rearrange that formula to work it out. So a short position (I.e. a negative in the Put call parity formula) on the stock becomes Put - Call = - Stock

dazman,

Is the Xert used anywhere? If yes, in what type of situations?

Don’t get confused, look at it in a logical way

You want to replicate a short position, when you say a synthetic short position.

So , a short position gives you profits from a down move and losses from the stock moving up.

So, if someone had to replicate it, in a way that he profits from down move and loses from up moves. So,

He would buy a put option (he profits from a down move) and sell a call option (he loses when stock goes up).

So the cash flows from the above would be equivalent to a short position in a stock

hi guys, thanks many times, I guess I was writing the put call parity not correctly

It’s not explicitly referenced anywhere, but if you play through the synthetic long and short positions that’s a great way to easily remember it. Just ignore PV(X) for synthetics as you ignore the fact you need cash when the options expire.

This is what I normally do as well - I physically write down c + x = p + s, and proceed to physically crossing out PV(X). The rest is just simple algebra (in our case here, we want -s). c - p = s, -s = p - c.