Question

13. Which one of the following choices is the same synthetic position as short stock, long call? M a. Short put M b. Long call M c. Short call M d. Long put

Answer 1

So your Mc. Short call Md. Long put is the same as Short Stock & your Ma. Short put Mb. Long call is the same as Long Stock. Non of it is same as Long Call.

To clarify there are six basic synthetic positions:

1. Synthetic Long Stock = Long Call + Short Put

2. Synthetic Short Stock = Short Call + Long Put

3. Synthetic Long Call = Long Stock + Long Put

4. Synthetic Short Call = Short Stock + Short Put

5. Synthetic Short Put = Short Call + Long Stock

6. Synthetic Long Put = Long Call + Short Stock

They can be thought of as a 'synthetic triangle' of CALL, PUT, and STOCK. A combination of two elements in the synthetic triangle creates a synthetic position of the third element.

This synthetic triangular relationship is governed by the principle of Put Call Parity (requires the extrinsic values (aka time value) of call and put options to be in equilibrium so as to prevent arbitrage).

In order for the synthetic triangle relationship to work, all options used together must be of the same expiration, strike and represent the same amount of shares used in combination.

All combinations of synthetics can be created by the following formula:

S + P - C = 0

Stock + Put – Call = 0

If you want to find out the synthetic equivalent to a long put, just isolate that +P position:

S + P – C = 0

If that long put is paired with other assets so that it has no risk, then the other assets must be equal to a short put. This immediately shows that long stock (+S) plus a (-C) short call must be equal to a short put (-P).

S - C = - P

It turns out that no matter which asset you pick, the other two are the synthetic opposite and fully hedge the risk. It should make sense, then, that we could also pick any two assets and know that the third will fully hedge those two.