Discussions on put call parity can quickly lose readers in a sea of mathematical formulas and complex concepts. Let’s sidestep that quagmire altogether and instead focus on the practical application of the principle. After all, financial theories are virtually useless if they can’t be used to generate better returns or at least improve decision making.
Put call parity defines the relationship between the value of a call option and a put option with the same strike price, expiration date, and, of course, underlying security. So, per the principle, the price of the Dec $150 call and Dec $150 put on Apple Inc. (NASDAQ:AAPL) are related in a mathematically quantifiable way.
The reason put call parity matters to stock option traders is it can often help you create synthetic or equivalent positions to enhance returns or reduce capital requirements. Without getting drowned in the details a simple formula that conveys the gist of put call parity is: call = put + stock.
In other words, a long call option is the theoretical equivalent of owning 100 shares of stock and owning a long put of the same class.
Let’s use an old Apple example from several months ago that I’ve shown numerous students:
Apple Example
Using Apple, which was trading for $120.92, we could say the Dec $120 call is equivalent to owning 100 shares of AAPL stock plus a long Dec $120 put. And just so there’s no confusion, by “equivalent” we mean both positions generate the same profit or loss at every possible price at expiration.
Take note of the risk graph of both positions below. Do they look identical? That’s because they are!
Knowing that a married put (i.e. long stock + long put) is identical to a long call option should tell you that the married put is a second rate strategy. Why would you tie up all that capital to buy 100 shares of stock plus buy a put option when you could create the same position synthetically, at a pittance of the cost I might add, by simply buying a call option? The answer is you wouldn’t, at least, provided you understood put call parity.
Twitter Example
Here’s another one regarding covered calls and short puts. If you we modify the put call parity formula by subtracting the put and call from both sides we get:
(-)put = stock – call
Or, in other words, a short put equals a covered call (long stock, short call). Remember, that’s if we’re using the same strike and month for the call and put.
Again, going back several months, buying Twitter Inc (NYSE:TWTR) at $28.50 and selling the Dec $29 covered call is the synthetic equivalent of selling the Dec $29 put option. A risk graph of both positions illustrates similar payouts at expiration.
But here’s the kicker. Instead of having to tie up a mountain of capital to buy the stock you can simply short the put which requires a much smaller margin requirement. That boosts your return on investment immensely. It’s not hard to find short puts that generate a 10% return when the corresponding covered call only delivers a 3% return.
If you already own stock and the capital is already tied up then, by all means, sell covered calls. On the other hand, if you haven’t purchased the stock yet, why bother? Simply sell a put with the same strike price and expiration month of the covered call you were going to sell and you’ll get the same outcome at a much lower cost. It’s a win-win.
Further synthetic relationships can be uncovered by playing around with the put call parity formula. I suspect the most telling takeaways, however, are the synthetic positions highlighted previously. Keep these in mind next time you’re considering a married put or covered call play.
