Synthetic Stock
Not only can synthetic calls and puts be derived by manipulation of put-call
parity, but synthetic positions for the other security in the equation—stock
—can be derived, as well. By isolating stock on one side of the equation,
the formula becomes
After accounting for interest and dividends, buying a call and selling a put
of the same strike and time to expiration creates the equivalent of a long
stock position. This is called a synthetic stock position, or a combo. After
accounting for the basis, the equation looks conceptually like this:
This is easy to appreciate when put-call parity is written out as it is here.
It begins to make even more sense when considering at-expiration diagrams
and the greeks.
Exhibit 6.6 illustrates a long stock position compared with a long call
combined with a short put position.
EXHIBIT 6.6 Long stock vs. long call + short put.
A quick glance at these two strategies demonstrates that they are the
same, but think about why. Consider the synthetic stock position if both
options are held until expiration. The long call gives the trader the right to
buy the stock at the strike price. The short put gives the trader the obligation