# Synthetic Stock Defined and More

Hello Traders,

In my blog written on 11/19/12 titled “Are the price of the calls and put related?” I asked the question “Can X actually equal Y?”

In the options world the answer is yes... sometimes it can. I explained in the blog why this concept is so important to the pricing of call and put option contracts.

I will expand on the concepts in that blog and talk about the many synthetic or equivalent positions there are in the options market place. A quick review from the last blog defines synthetic as the following:

Definition: Syn·thet·ic (sn-thtk) - A financial instrument that is created artificially by simulating the risk and rewards of that instrument with the combined features of a collection of other assets.

In laymen's terms, a synthetic relationship is when one option trading strategy has similar risks and rewards to another entirely different strategy, making them essentially equivalent versions of each other.

**How can I tell if a position is synthetically the same?**

The easiest way to determine if two strategies are synthetic is to take a peek at the profit and loss graph (P&L) for each position and look for similar risk and rewards. To start with let’s look at the profit and loss graphs for the basic strategies in this marketplace long stock, short stock, long call, short call, long put and short put. On these generic graphs below the vertical or y-axis is the profit and loss for the strategy and the horizontal or x-axis is the stock price at expiration of the option contracts.

From looking at these basic graphs it is pretty obvious on a one off basis none of these strategies are synthetic versions of each other, so in order to create synthetic positions we will explore different combinations of these 6 basic trades.

**How can we use calls and puts to create a P&L that looks like a long stock position?**

Lets use the conditions for the marketplace that were laid out in the example in previous blog to keep things in harmony between the two.

We will assume the stock is at 80, the interest rate is 5.36%, volatility is 27.95% and expiration is 61 days away, with no dividend upcoming. Let's also assume we're using the ATM put and call in this example, with a strike price for each of 80. (Note: The interest rate is large for the current market environment, but it helps with the understanding of the concept.) All the examples in this blog will be theoretical in nature and are not meant to be recommendations or advice. In the real world the numbers may not come out as clean because of bid/ask spreads, commissions and other market forces, but the core concepts can still apply. In order to synthetically create stock using by using options, we have to buy a call and sell a put on stock with the same strike price and expiration date. An example is as follows.

Stock at 80

Buy 1 61-day 80 Call at 4.00 Commission $6.25

Sell 1 61-day 80 Put at 3.35

Net Debit 0.65

The max gain is unlimited to the upside because we are long a call and have the right to buy stock at 80 anytime over the life of an option contract.

The max loss is substantial to the downside because we are short a put and have an obligation to buy stock at 80 anytime over the life of an option contract, which just happens to be the max gain and loss potential of buying long stock outright. Unlimited upside and substantial downside if the price went to zero, but let’s examine the P&L graph of each strategy just to be sure.

The first graph shows the P&L of a long stock position (purple). The second graph shows, the P&L for a long call (blue), the P&L of a short put (green) and the P&L for the combined position (red). Compare this purple line in the first graph with the red line in the second graph, which depicts the combination of long call and short put. It's easy to see that buying the long call and selling the short put results in a very similar P&L to long stock at expiration.

Before we run away and say they're not just similar but identical, let's graph both on the same graph and see if they are any subtle differences.

When we graph each position on top of the other (long stock in purple, long call and short put in red), the point where each strategy crosses the horizontal axis is called the breakeven point at expiration. Notice the small difference in the breakeven number of these two positions (80 vs 80.65). Why? Let me explain: we have two strategies that are mostly the same as far as risk and reward are concerned, but not with regard to carry costs. For a strategy to be truly considered a synthetic alternative all aspects of the two strategies have to be considered.The combined long call and short put were executed for a net debit of 65 cents and the long stock purchased was executed for a debit of 80 dollars. The total cost for the option strategy was $0.65 x 100 or $65 and the cost to buy the stock was $80 x 100 or $8000. The bottom line is there is a lot more capital needed to buy the stock outright, which means there is an additional cost of carry that has to considered. This additional carry cost for the stock means the synthetic strategy has to have a higher breakeven point to offset it. So the 65 cent difference is not a mistake, it is there because of the additional capital needed to buy the stock outright verses placing the trade synthetically using options. (The concept of “cost to carry” was explained in detail in the previous blog post on this topic and it also covered what happens if the stock pays a dividend).

So, when is it all said and done, if we were to write a formula for a synthetic long stock position it would be the following.

Synthetic Long Stock = Long Call + Short Put + Long T-Bill

Why Long T-Bill you ask? In an attempt to make all things equal, the concept would be to take the remaining monies not needed to buy the stock and purchase a T-Bill or some other type of security that would allow you to earn the “risk free” interest rate over the life of the option contracts. When the additional interest income taken in is applied to the synthetic position at expiration the break-even in theory should be exactly the same as if you just bought the stock outright. Now we can say “in theory” each strategy is identical from a risk/reward standpoint.

If we step out of the theoretical world and into the real world, the things to think about with the synthetic position would be additional commissions costs, width of the bid/ask spreads, margin requirement for the uncovered put and the fact that there is an expiration date on option contracts. These are real world concerns that have to be considered anytime you decide to trade options.

**How many synthetic positions are there?**

Here is the shortlist for the basic option strategies, but this does not come close to covering all the possibilities. To make things simple we will not include the T-bill.

Synthetic Long Underlying = Long Call and Short Put

Synthetic Short Underlying = Short Call and Long Put

Synthetic Long Call = Long Put and Long Underlying

Synthetic Short Call = Short Put and Short Underlying

Synthetic Long Put = Long Call and Short Underlying

Synthetic Short Put = Short Call and Long Underlying

If you know one or the relationships you know them all. A little algebra goes a long way. If we assume the following variables.

U = Underlying

C = Call

P = Put

+ = Long

- = Short

A synthetic long underlying would be:

+ U = + C - P

Now using this formula, let’s find out what a synthetic long call would be:

+ U = + C - P solving for C means we move the short put to the other side of the equation and when we do that we have to change its sign so it becomes:

+ P + U = + C

Therefore, a Synthetic Long Call is a Long put and Long Underlying (a protective put) and if we look at the short list above we see that is correct. See if you can now solve the equation for the long put as a homework assignment.

Understanding the concept of synthetic positions is critical to understanding the inner workings of the options marketplace. When the Lord gives you puts, you now know it can be possible to make calls.

Regards,

TradeKing Options Guy and Senior Option Analyst

Follow Brian on Twitter or visit TradeKing on Facebook and YouTube.

Options involve risk and are not suitable for all investors. For more information, please review the Characteristics and Risks of Standard Options brochure available at www.tradeking.com/ODDbefore you begin trading options. Options investors may lose the entire amount of their investment in a relatively short period of time.

Multiple leg options strategies involve additional risks and multiple commissions, and may result in complex tax treatments. Please consult a tax professional prior to implementing these strategies.

System response and access times may vary due to market conditions, system performance and other factors.

TradeKing's Fixed Income platform is provided by Knight BondPoint, Inc. All bids (offers) submitted on the Knight BondPoint platform are limit orders and if executed will only be executed against offers (bids) on the Knight BondPoint platform. Knight BondPoint does not route orders to any other venue for the purpose of order handling and execution. The information is obtained from sources believed to be reliable; however, its accuracy or completeness is not guaranteed. Information and products are provided on a best-efforts agency basis only. Please read the full Fixed Income Terms and Conditions. Fixed-income investments are subject to various risks including changes in interest rates, credit quality, market valuations, liquidity, prepayments, early redemption, corporate events, tax ramifications and other factors.

All investments involve risk, losses may exceed the principal invested, and the past performance does not guarantee future results or returns. TradeKing provides self-directed investors with discount brokerage services, and does not make recommendations or offer investment, financial, legal or tax advice. You alone are responsible for evaluating the merits and risks associated with the use of TradeKing's systems, services or products. Content, research, tools, and stock or option symbols are for educational and illustrative purposes only and do not imply a recommendation or solicitation to buy or sell a particular security or to engage in any particular investment strategy.

## Comments

Follow commentsYou must Log In to post to this blog.Not a member? Register Now to …