Options Trading: Understanding Put-Call Parity
If I had a nickel for every time someone told me they love covered calls for their conservative income generation, but would never sell a naked put because that’s too risky, I could retire from trading.
The fact is a covered call is exactly the same, in terms of both risk and reward, of selling a naked put. They are what is called equivalent positions.
There is a relationship between calls, puts, and the underlying stock. Because of that relationship, there is more than one way to build any option position, and that translates into positions with identical profit/loss profiles, even though the positions look very different.
Knowing what positions are equivalent will not only help you understand some basic concepts but can also translate into greater profits. This is because some positions might have different capital or margin requirements, lower transaction costs, or simply allow you to choose the more liquid strike.
The basic equation is often referred to as put-call parity. For our purposes, the effect of interest rates is ignored. Put-call parity describes the relationship between calls, puts, and the underlying asset.
Owning one call option and selling one put option on the same underlying asset (with the same strike price and expiration date) is equivalent to owning 100 shares of stock. Thus,
S = C – P
Where S = 100 shares of stock; C = one call option ; P = one put option
Note that for positions to be equivalent, they need to have the same strike prices and expirations.
Consider a position with one long call and one short put. When expiration arrives, if the call option is in the money, you will exercise the call and own 100 shares. If the put option is in the money, your account will be assigned 100 shares and you must buy 100 shares. In either case, you own stock.
There is one equivalent position that every option trader, even someone who is very new to the game, should know. These represent popular strategies and you are likely to adopt one (or both).
Take a look at a covered call position (long stock; short one call), or S – C.
From the equation above, S – C = – P.
In other words, if you own stock and sell one call option (covered call writing) then your position is equivalent to being short one put option with the same strike and expiration. That position is naked short puts. Is that an eye-opener for you? Don’t feel bad about this because few rookie option traders learn about equivalent positions. For some courses, this is considered to be an advanced topic.
Did you know some brokers do not allow their inexperienced clients to sell naked puts, but they do allow the same investors to write covered calls? When you write a covered call, you already own (and paid for) stock. When you write a naked put, you may have to buy the stock later. As long as the broker knows that you can afford to buy the stock, it should make no difference which of these positions you own.
Writing a covered call is equivalent to selling a naked put. This is not a big deal to experienced options traders. Now it should be no big deal to you either.
Selling puts involves paying one commission; the covered call requires paying two. All things being equal, you should prefer selling the put option for doing a buy-write (buy stock and write calls) transaction. NOTE: IF you already own stock, then trading expenses are identical and writing calls is the more convenient choice.
We can drill down into other equivalents, such as a debit call spread with a credit put spread or a collar and a credit put spread, in later articles.
But for now, it’s enough to understand that what might seem like different positions are really exactly the same.
Note: This article originally appeared at Option Sensei.
Category: Options Trading
