How can two trades have the same risk and reward when they look so very different?

That's the frequent response when investors first learn that every option position is equivalent to a different option position. For clarification, "equivalent" refers to the fact that the positions will earn/lose the same amount at any price (when expiration arrives) for the underlying stock. It does not mean the positions are "identical."

Of all the ideas that a rookie options trader encounters, the idea of equivalence is a real eye-opener. Those who grasp the significance of this concept have an increased chance of succeeding as a trader. (For a background reading, see our Options Basics Tutorial.)

Different but Equal
Let's begin with an example, and then we'll discuss why equivalent positions exist and how you can use them to your advantage. And it is an advantage. Sometimes you discover that there's an extra $5 or $10 to be earned by making the equivalent trade. At other times, the equivalent saves money on commissions.


There are two commonly used trading strategies that are equivalent to each other. But you would never know it by the way stock brokers handle these positions. I'm referring to writing covered calls and selling naked puts. (For more, read Understanding Option Pricing.)

These two positions are equivalent:

  1. Buy 300 shares of QZZ
    Sell 3 QZZ Aug 40 calls
  2. Sell 3 QZZ Aug 40 puts
What happens when expiration arrives for each of these positions?

Buying the Covered Call:


  • If QZZ is above 40, the call owner exercises the options, your shares are sold at $40 per share, and you have no remaining position.
  • If QZZ is below 40, the options expire worthless and you own 300 shares
Selling the Naked Puts:


  • If QZZ is above 40, the puts expire worthless and you have no remaining position.
  • If QZZ is below 40, the put owner exercises the options and you are obligated to purchase 300 shares at $40 per share. You own 300 shares.
Trade Conclusion
After expiration, your position is identical. For those who are concerned with details (and option traders must be concerned) the question arises as to what happens when the stock's final trade at expiration is 40. The answer is that you have two choices:


  1. Do Nothing
    You can do nothing and wait to see whether the option owner allows the calls to expire worthless or decides to exercise. This places the decision in the hands of someone else.
  2. Repurchase the Options
    Before the market closes for trading on expiration Friday, you can repurchase the options you sold. Once you do that, you can no longer be assigned an exercise notice. The goal is to buy those options for as little as possible, and I suggest bidding 5 cents for those options. You may want to be more aggressive and raise the bid to 10 cents, but that should not be necessary if the stock is truly trading at the strike price as the closing bell rings.
If you do buy back the options sold earlier, you may write new options expiring in a later month. This is a common practice, but it's a separate trade decision.

The positions are equivalent after expiration. But does that show that the profit/loss is always equivalent? No, it doesn't. But the truth is that options are almost always efficiently priced. When priced inefficiently, professional arbitrageurs arrive on the scene and trade to take the "free money" offered. This is not a trading idea for you. Instead, it's a reassurance that you will not find options mispriced too often. The available profit from these arbitrage opportunities is very limited, but the "arbs" are willing to take the time and effort to frequently earn those few pennies per share. (Read Arbitrage Squeezes Profit From Market Inefficiency.)

Proof
To determine if one position is equivalent to another, all you need to know is this simple equation:


S = C – P
This equation defines the relationship between stocks (S), calls (C) and puts (P). Being long 100 shares of stock is equivalent to owning one call option and selling one put option when those options are on the same underlying and the options have the same strike price and expiration date.

The equation can be rearranged to solve for C or P as follows:




C = S + P
P = C - S
This gives us two more equivalent positions:


  1. A call option is equivalent to a long stock plus a long put (this is often called a married put).
  2. A put option is equivalent to a long call plus a short stock.
From the last equation, if we change the signs of each attribute, we get:

-P = S – C, or a short put equals a covered call
As long as you are cash-secured, meaning you have enough cash in your account to buy the shares if you are assigned an exercise notice, there are two very practical reasons for selling a naked put:

  1. Reduced Commissions
    The naked put is a single trade. The covered call requires that you buy stock and sell a call. That's two trades.
  2. Exiting the Trade Prior to Expiration
    Sometimes the spread turns into a quick winner when the stock rallies way above the strike price. It's often easy to close the position and take your profit easily when you sold the put. All you must do is buy that put at a very low price, such as 5 cents. With the covered call, buy the deep-in-the-money call options. Those usually have a very wide market and there is almost no chance to buy that call at a good price (and then quickly sell the stock). Thus, the strategic edge belongs to the put seller, not the covered call writer.
  3. Other Equivalent Positions
    These positions are equivalent only when the options have the same strike price and expiration date.Selling a put spread is equivalent to buying a call spread, so:
    • If QZZ is above 40, the call owner exercises the options, your shares are sold at $40 per share, and you have no remaining position.
    • If QZZ is below 40, the options expire worthless and you own 300 shares
    Selling a call spread is equivalent to buying a put spread, so:

    • If QZZ is above 40, the puts expire worthless and you have no remaining position.
    • If QZZ is below 40, the put owner exercises the options and you are obligated to purchase 300 shares at $40 per share. You own 300 shares.
    Selling put spread is equivalent to a buying collar. so:

    • Sell ZXQ Oct 50/60 Put Spread = Buy ZYQ Oct 50/60 Call Spread
    To convert a call into a put, just sell stock (because C - S = P)
    To convert a put into a call, just buy stock (because P + S = C)


The Bottom Line
There are other equivalent positions. In fact, by using the basic equation (S = C – P) you can find an equivalent for any position. From a practical perspective, the more complex the equivalent position, the less easily it can be traded. The idea behind understanding that some positions are equivalent to others is that it may help your trading become more efficient. As you gain experience, you will find it takes very little effort to recognize when an equivalent is beneficial. It just takes a little practice thinking in terms of equivalents. (To learn more, check out our Option Spreads Tutorial.)



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