Synthetic Positions
While a long put position is bearish, a short put position is bullish–it gains if the underlying rises (albeit by the maximum amount of the premium of the put) and loses if the underlying declines.
Suppose you are short a 50 put and also long a 50 call. This is not a hedge–a hedge consist of a long position and an offsetting short position, but these are both bullish positions. You might imagine that they are identical, but of course they are not. They are merely similar and they work together in an interesting way.
The short put position has a limited gain on the upside but, just like a long position in the underlying itself, has unlimited loss on the downside. Conversely, your long call position has limited downside loss but, like a long position in the underlying itself, has unlimited gain on the upside.
Both long call and short put positions exhibit the same characteristics as a long position in the underlying, just in different price regions. On the upside your combination position behaves like a long position in the underlying in that it has unlimited gain from the long call. On the downside your combination position also behaves like a long position in the underlying in that it has unlimited loss from the short put.
In fact, if neither option is exercised before expiration (if, for example, they are European options) this position is identical in behavior to a long position in the underlying. To see this, note that if the underlying is above $50 at expiration, the put will expire worthless and you will exercise your long call, purchasing the underlying for $50. If the underlying is below $50 at expiration, the owner to whom you sold the put will exercise it and force you to purchase the underlying at $50. So in either case, you will purchase the underlying for $50 at expiration.
This position is called a “synthetic long.” It is equivalent to purchasing the underlying for $50, except for interest foregone on the funds used to make the call purchase and interest earned on the proceeds from your put sale. Notice that I have made no mention of the price of the underlying. Whatever that price is, if you purchase the 50 call and sell the 50 put, you are essentially purchasing the underlying for $50.
(What if the underlying is currently selling for $60? Does this trick not allow you to purchase the underlying for $10 less than its market price? To check your understanding of this situation, conduct your own analysis. I will complete the explanation in the next commentary.)
The opposite position, short the 50 call and long the 50 put, is seen by a similar analysis to be equivalent to a short position in the underlying (or by simply noting that it is the inverse of a position equivalent to a long position in the underlying). It is equivalent to selling the underlying short for $50 and is called a “synthetic short.”
While a correct analysis of the puzzle in parentheses above will persuade you that a synthetic long cannot create a benefit not offered to you by the market itself, a synthetic short actually can offer a benefit not offered by the market, due to rules implemented by the exchanges. In particular, stock exchange rules state that a stock cannot be shorted except on an “up tick”–if you wish to sell a stock short, you must wait until the price advances by at least one tick. But you can take a synthetic short position anytime, even on a down tick, and you will have created a position that is equivalent to the short position that the exchanges will not allow you to take.