# Equivalent Positions - The Long and Short End of It

## A Turning Point in your Education

​​Puts and calls are obviously different option types. However, there is a mathematical relationship between calls and puts -- when the put and call expire at the same time, have the same strike price, and are on the same underlying asset.

Because of that relationship, there is more than one way to build any option position -- and that means that there are equivalent positions (i.e., positions with identical profit/loss profiles) -- even though the positions appear to be very different.

Although you can survive by avoiding the small amount of homework involved in understanding this concept, it does mean that you will occasionally be leaving money off the table for no good reason. Isn't that why you are trading? To make money? Beyond that, it makes sense for you to prefer to understand how options work -- rather than hoping that you are following logical advice from another trader.

Traders own positions with an expectation of earning a profit when the markets behave. If you can own a different position that results in the same profit (or loss), but which requires paying less in commissions, wouldn't that be preferable?

Infrequently you may discover that the markets are temporarily inefficient (it won't last long) and that one of the equivalent positions is available at a slightly better (perhaps \$0.05) price than its equivalent. If you spot that difference, you can own the position with that \$0.05 discount.

### The Basic Equation

It is often referred to as put-call parity. For the purpose of introducing this topic, 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

### Simple Proof

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, and you must buy 100 shares. In either case, you own stock.

NOTE: If the stock is exactly at the money when expiration arrives, you are in a quandary. You don’t know whether the put owner will exercise and therefore, you do not know what to do with your call. The best solution is to buy the put to cancel any obligations. It should not cost more than \$0.05. Next, if you do want to own stock, exercise the call option. If not, allow the call to expire ​worthless. By covering the short put, you are in control.

### First Example of an Equivalent Position

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.

### Amazing fact

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.

### Takeaway

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 to 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.

IMPORTANT: Repeated for emphasis.

Two positions are equivalent IF AND ONLY IF the options have the same underlying, strike and expiration.

Long 100 IBM and short one IBM Nov 200 call is equivalent to being short one IBM Nov 200 put.

As you continue to trade options, you will encounter other equivalent positions