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# Option Equivalence

Some option positions are equivalent – that means identical profit/loss profiles – to others. Others are not. A few days ago I had an inquiry from a person trading options in a restricted account (e.g. an IRA that did not allow marginable trades or short options positions):

I have an IRA in which I trade options.  I wanted to sell a put, but my broker won’t allow the sale of puts in my account.  Isn’t it true that opposite option positions are equivalent?  In other words, instead of selling a put at strike X, couldn’t I just buy the call at Strike X and get the exact same risk and/or return?”

I was quite taken aback by the question, but after digging around, I learned that many investors believe opposite option positions are equivalent.  This is not true.  Rather, equivalent option positions can be found through one simple equation:

S = C – P

Where S is the stock, C is a call at strike X and P is a put at strike X.  In other words, the following two positions are equivalent:

1. Sell 5 contracts of the March 31 100 puts on stock ABC; AND Buy 500 shares of ABC
2. Sell 5 contracts of the March 31 100 call.

This position is called a “synthetic stock” position, which can be constructed by going long a call and short a put at the same strike.

A trader can rearrange the above equation and get:

C = S + P (also known as a “married put”)

Or

P = C – S

These three differing positions should perform the same with the same returns.  Of course, in reality that is not what occurs for a variety of reasons:

A.  Commission Costs

An investor pays X commission to purchase stocks (e.g. \$7.99/trade).  The same investor pays X+ to purchase options. (Buying options is typically more expensive, although commissions vary for different products.) Buying a single side of the equation likely will reduce the cost of the trade, thereby changing the performance of the overall trade.

Any experience option trader knows that commissions eat more into gains than any other single factor (other than making horrible trades).

Every option has a bid/ask spread.  On highly traded instruments, this might be a penny or two.  On less liquid options, there may be a spread of a few dollars.  On the other hand, with stocks, the bid/ask spread is almost always smaller than the bid/ask spread on the options on the same instrument.  This means constructing a synthetic stock position will almost always cost more than simply buying the stock.

Of course, a synthetic stock position also gives an investor the opportunity for leverage, not available with just going long on a stock.  Investors are encouraged to work through the risk/reward of using leveraged through synthetic stock rather than simply buying the stock for a lower total cost.  Depending on each trader’s goals, risk tolerances, and the specific trade, leverage through synthetic options may be a better trade setup – or it may not.

C. Exiting Before Expiration

Options stop trading the Friday of their expiration at the market close.  But the underlying stocks typically continue to trade in the after-hours markets.  (This is known as expiration risk).  Because of this, on the day of expiration, option positions that are at the money or only slightly out of the money maintain a premium on the positions.  In other words, if an option position is only slightly out of the money on the day of expiration, the position won’t close for \$0.00, even though the above equation suggests that it should be able to do so.  A trader likely would have to pay (or receive depending on the position)at least a nickel to exit the position.

This slippage also results in the positions not being exactly equivalent – despite theory and math suggesting they should.

Option traders should be well aware of the basic equations with equivalences.  There are times, due to inefficiencies in option pricing from volume/demand/market maker errors, when entering an equivalent position may result in more profit.

At other times, knowing the equivalent positions will allow investors to enter into trades in restricted accounts that they may not otherwise have been able to enter.  Still in other situations, depending on an investor’s margin requirements, entering into an equivalent position may save margin interest – or free up cash to enter into more trades (e.g. leverage).

To experienced option traders, the above is blindingly obvious.  If an investor does not understand option equivalence, it might be best to take a step back and study more, trade on paper, and learn more before putting capital at risk.

Christopher Welsh is a licensed investment advisor and president of LorintineCapital, LP. He provides investment advice to clients all over the United States and around the world. Christopher has been in financial services since 2008 and is a CERTIFIED FINANCIAL PLANNER™. Working with a CFP® professional represents the highest standard of financial planning advice. Christopher has a J.D. from the SMU Dedman School of Law, a Bachelor of Science in Computer Science, and a Bachelor of Science in Economics. Christopher is a regular contributor to the Steady Options Anchor Strategy and and Lorintine CapitalBlog.

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