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# Options Equivalent Positions

One of the interesting features about options is that there is a relationship between calls, puts, and the underlying stock. And because of that relationship, some option positions are equivalent – that means identical profit/loss profiles – to others.

Why is that important? You will discover that some option combinations – called spreads – are easier, or less costly to trade than others. Even with today’s low commissions, why spend more than you must?

The basic equation that describes an underlying and its options is: Owning one call option and selling one put option (with the same strike price and expiration date) is equivalent to owning 100 shares of stock. Thus,

S = C – P; where S = stock; C = call; P = put

If you want a simple proof that the above equation is true, consider a position that is long one call and short one put. When expiration arrives, if the call option is in the money, you exercise the call and own 100 shares. If the put option is in the money, you are assigned an exercise notice and buy 100 shares of stock. In either case, you own stock.

NOTE: If the stock is at the money when expiration arrives, you are in a quandary. You don’t know if the put owner is going to exercise and therefore, you don’t know whether to exercise the call. If you want to maintain the long stock position, the simplest way out is to buy the put, paying \$0.05, or less, and exercise the call.

Example of options equivalent positions

There is one equivalent position that you, the options rookie, should know because these are options spread trading strategies you are likely to adopt.

Take a look at a covered call position (long stock and 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 the put. Amazingly some brokers don’t allow all clients to sell naked puts, but they allow all to write covered calls. The world is not always efficient (you already knew that).

Thus, writing a covered call is equivalent to selling a naked put. This is not a big deal to anyone who is an experienced option trader, but to a newcomer to the world of options this can be an eye-opener.

The more you trade options, you more you will become aware of other equivalent positions. You may even decide to play with the equation yourself and discover others.

If you are new to the world of options, today's discussion of options equivalent positions may appear to be a bit confusing.
But if you go slowly and re-read the linked posts, you’ll understand the discussion.

If you’ve been trading options for a while and never bothered to learn about equivalent positions, this post contains information that can make your trading more efficient.

Here is summary of some recent blog posts:

• Some option positions are equivalent to others, and covered call writing is equivalent to writing naked puts.
• To significantly reduce the risk of writing naked puts, turn it into a credit spread by buying a put that is further out of the money than the put sold.
• Collars are a good, conservative strategy for any conservative investor.

Let’s take a closer look at a collar, which consists of three legs: long stock, long put, short call. ZZY is trading at \$67 per share and you want to collar that stock. To do that you may decide to write one Dec 75 call and buy one Dec 60 put.

Separating the collar into two parts:

Collar: Part One

Part Two

• Long 100 shares of ZZY
• Long 1 ZZY Dec 60 put
• Short 1 ZZY Dec 75 call

Part one is a covered call position, and we know that a covered call is equivalent to being short the put with the same strike and expiration.

The collar, part one is equivalent to:  Short 1 ZZY Dec 75 put

The collar, part two is:  Long 1 ZZY Dec 60 put

This position is a put credit spread (short a put and long a put with a lower strike price).

So what, you ask? This is proof that the collar position is equivalent to the put credit spread – but only when the put owned is the same and the put sold has the same strike and expiration date as the covered call.

If the conservative approach offered by collars appeals to you, consider selling the put credit spread instead. First, there are fewer commissions to pay, and second, the put spread is easier to trade because there are only two legs in the position, instead of three.

NOTE to more experienced traders: The collar is also equivalent to buying the bull call spread, when the strike prices and expiration date are the same as the puts that are part of the put credit spread. In other words, buying the ZZY Dec 60/75 call spread is equivalent to selling the ZZY Dec 60/75 put spread.

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