Mastering Option Part 4

Backspread

The backspread is similar to a ratio spread, except that it has unlimited profitlong ratio spread. instead of unlimited loss on the profit and loss diagram. It is the mirror image of the ratio spread. In fact, the backspread is often called a

Call backspread

A call backspread involves the sale of a low strike price call and the purchase of a higher number of contracts at a higher price. For example, a trader may sell 10 $50 calls and buy 20 $60 calls, also known as a $50/$60 backspread.

The profit and loss diagram for a call backspread looks like this:

Assume the trader sells 10 $50 calls for $10 and buys 20 $60 calls for $3. This trade can be broken down to 10 (-1/2) spreads (please see our section on "Ratio Spreads" for more information). In other words, the trader sold one call and bought two calls, but did this ten times. For every call sold at $10, two were purchased at $3 for a total of $6. Therefore, the above trade was executed for a net credit of $4 (received $10 but paid $6). Depending upon prices and ratios used, backspreads may be entered for either debits or credits.

For any stock price below $50, the trader will keep the net credit of $4, as both calls will expire worthless. If the stock moves above $50, the trader will head into loss territory because he is short these calls. However, if the stock continues upward, the $60 calls will come to the rescue and stop the losses. The maximum loss will occur at $60 where the trader will lose ten points (the difference in strikes) less the credit of $4, for a maximum loss of $6. Because there are two $60 calls for every short $50, the trader will start to make gains above $60. In order to make up for the $6 loss, the stock must rise to $66 to reach break-even. The downside break-even can be found in two ways: One, the trader must make up the $6 loss from the low point of $60; Or, he can sustain a loss of $4 (the initial credit) above $50. Either way you choose, you will see the downside break-even is $54.

Notice that if the trader had purchased the 10 $50 calls and sold 20 $60 calls, he would have a ratio spread. Ratio spreads and backspreads are opposites. The following is a profit and loss diagram comparing the two spreads:

Why enter a call backspread?

If a trader is bullish on a stock yet fears a market turndown, then both sides of the market can be played with a backspread. The trader will capture all upside profits yet have a credit (or less of a loss if entered as a debit) if the stock should fall. Typically, novice traders will enter long straddles to play the upside and downside. However, with long straddles, the break-even points become very wide due to the fact that premiums are paid for both the call and put and must be made up. With the backspread, a trader can custom-tailor his bias in the stock and create better risk-reward ratios. The trader using a call backspread is more bullish, but fears a downturn. He will not profit as much as a long straddle trader, but does not have as much at risk either.

Backspreads are another great example of just how versatile options can be.

Put backspread

Backspreads can be used with put options too. To enter a put backspread, the trader will sell a high strike put and buy a higher number of a lower strike put. For example, a trader may sell 10 $60 puts and buy 20 $50 puts.

The profit and loss diagram for a put backspread looks like this:

Assume the trader sells the $60 puts for $10 and buys the $50 puts for $3. As above, this spread can be broken down into 10 (-1/2) spreads. This means that for every one put that was sold, two were purchased. The trader receives $10 from the sale of the $60, but pays $6 for the two $50 puts for a net credit of $4. If the stock should rise, the trader is left with a credit, as both puts will expire worthless. If the stock falls below $60, the trader heads into loss territory, as he is short these puts. If the stock continues to fall to $50, the losses stop and gains will start, as he is long two of the $50 puts for every one of the $60 puts that are short.

So for any stock price below $50, the trader starts to gain. At $50, the trader is down $10 (the difference in strikes), but received $4 from the initial trade for a net loss of $6. Because this $6 must be made up, the break-even will be $6 points below the $50 strike or $44. If the stock falls below $44, the trader will start to show profits. Where is the upside break-even? The trader will need to make up the $6 from the max loss point at $50 to the upside; equally, he can sustain a $4 loss (the initial credit) below $60. Either way of looking at it will yield an upside break-even of $56.

With puts, traders are betting more on the downside, but they fear the upside risk. A put backspread allows them to capture both possibilities while favoring the position to the downside.

Intel backspread example

Let's run through an actual example using Intel (INTC), which is currently trading around $41. The option quotes are as follows:

Dec $40 Call = Bid:$3-1/2 Ask: $3-3/4
Dec $45 Call = Bid:$1-3/8 Ask: $1-3/4

Assume a trader wants to place a $40/$45 backspread and sells the $40 call for $3-1/2 and buys 2 $45 calls for $1-3/4 each or $3-1/2 for a net debit of zero shown by:

Short 1 $40 call = -$3 1/2
long 2 $45 calls at $1 3/4 each = +$3 1/2
Net debit $0

Here is what the profit and loss diagram will look like for the above trade:

The trader will make nothing if the stock falls, and lose $5 if the stock closes at $45. If the stock is above $45, the trader will start to recover losses and eventually break even at $50. Any stock price above $50 will yield a profit. Note the break-even points of $40 and $50. If the stock closes between these two points, the trader ends up with a loss.

Remember we said the trade opposite the backspread is the ratio spread? Well, the floor trader who executes the above backspread will have the ratio spread (assuming the trades are not matched with other orders or positions). The floor trader's profit and loss diagram will look like this:

Backspreads are great tools; especially for active traders. They generally require level 2 option approval (ratio spreads require level 3). Many traders shy away from ratio and backspreads because of the initial complexity in understanding them. However, with a little work, you can quickly find the maximum gain and loss points as well as the break-evens. They are a wonderful tool for option traders, so you should take the time to understand them if you want advance to a higher level of trading!

Box Spread

There are many tools that market-makers use to hedge risks, either partially or fully. One of the most powerful tools is called a box spread. While this particular strategy is not widely used by retail investors, it is very useful in determining if your vertical spread is priced fairly.

Another important use of the box spread is for investors who place spread orders (please see our section on spreads if you are not familiar with these.) They often ask, "Do you think I can get filled at such-and-such a price?" If you understand the box spread, you will be able to immediately determine if there is any room for the market makers to work with your order.

If you are a user of spread orders, understanding box spreads will be a very helpful tool!

The box spread

A box spread is a relatively simple strategy. To enter into a long box position, all you need to do is buy the bull spread and buy the bear spread with the same strikes and all other factors the same (if you are unsure about bull and bear spreads, please see our section on "Basic Spreads.")

For example, say a stock is trading at $50. A trader could buy the Jan $50 call and sell the Jan $55 call (bull spread), and also buy the Jan $55 put and sell the Jan $50 put (bear spread.)

This trade will result in a debit for both spreads. What is interesting about this position is that it is now guaranteed to be worth $5 (the difference in strikes) at expiration (keep in mind this is a theoretical price, and in the real world of trading, the bid-ask spreads will probably make the value slightly less than $5 at expiration).

How? Think about this: No matter where the stock closes, either the $50 call or the $55 put will be in-the-money. Because these are the two long positions of the box spread, the trader who buys the box spread is guaranteed to have a position worth $5 at expiration.

Let's run through some examples if you are still not sure:

If the stock closes at $53, the long $50 call will be worth $3 and the long $55 put will be worth $2 for a total of $5. The short $55 call and short $50 put will expire worthless (if you are not sure why these prices must hold, please see our section under "Basic Option Pricing").

If the stock closes at $51, the $50 call will be worth $1, and the $55 put will be worth $4 for a total of $5. Again, the two short positions expire worthless.

What if the stock closes outside the ranges of $50 and $55?

If the stock closes at, say, $30, the $55 put will be worth $25 and both calls will expire worthless. However, the short $50 put now has value. In fact, it will be worth $20, which is an obligation because the trader is short. So the total value of the position is +$25 - $20 = $5.

You can't get around it. No matter where the stock closes, the position will be worth the difference in strikes, in this case, $5.

Question: Okay, here's one for you to try. What will be the value of the above box spread is the stock is trading for $100 at expiration? How would you show it? (Answers at the end.)

Pricing a box spread

Now that we know the mechanics of the box spread, how can we use it to help with our trading?

It is now October 31 and say you are interested in SCMR, which is currently $58-3/8, with the following quotes available for options:

	BID	ASK
Dec $55 Call	$12-7/8	$13-7/8
Dec $65 Call	$8-7/8	$9-5/8
Dec $55 Put	$8-3/4	$9-1/2
Dec $65 Put	$14-3/4	$15-3/4

Let's say you are bullish on SCMR and want to place a $55/$65 bull spread:

Buy Dec $55 Calls = $13-7/8
Sell Dec $65 Calls = $ 8-7/8
Net debit $ 5

Is this being priced fairly? Is it likely we will get filled if we put a net debit of $4-3/4?

In order to answer these questions, let's look at the other side of the box spread:

Buy Dec $65 Puts = $15-3/4
Sell Dec $55 Puts = $ 8-3/4
Net debit $ 7

Now, you will pay $5 for the bull spread and $7 for the bear spread for a total debit of $12, which is guaranteed to fall to a value of $10 at expiration! So with the current bid/ask spreads, this box is not being priced fairly. In fact, this is most often the case and the primary reason the box spread is not a popular tool for retail investors.

Let's see what the market makers are trying to do. Remember, the bid represents what they are willing to pay, and the ask what they are willing to sell. So, from the market-makers perspective, here is how the box spread looks:

Buy Dec $55 Calls = $12-7/8
Sell Dec $65 Calls = $ 9-5/8
Net debit $ 3-1/4

Buy Dec $65 Puts = $14-3/4
Sell Dec $55 Puts = $ 9-1/2
Net debit $ 5-1/4

The market makers want to complete the box spread for a total of $8 1/2 points, which is guaranteed to grow to a value of $10.

On the surface, it appears to be a pretty good deal. Let's see just how good it is.

Remember, it is October 31 and we are looking at December options, which will expire in 45 days. That actually works out to be 17.6% simple interest, or a whopping 267% annualized rate of return -- which certainly beats the guaranteed rates on T-bills.

So to answer the second question: yes there is certainly a lot of room to work with on the bull spread.

Let's go a step further. Just how much room is there? One useful method is to start with what the spread "should" cost. If the spread is guaranteed, it should earn the risk-free rate (roughly 6%). So the value of $10 guaranteed in 45 days is about $9.93, which is roughly $1.17 above the $8-3/4 price the market makers are trying to pay.

In a case like this, it is very feasible to get 1/2 point or maybe more off of this spread.

Please remember, any limit order, no matter how close to the market, is not guaranteed to fill, so, if you really need to get into or out of a trade, use caution in applying this method. This pricing method is a great tool for analyzing the potential for all traders who like to use limit orders.

Uses of the box spread

Why would a market maker enter into a box spread? The box spread is effectively a way for market makers to borrow or lend money. If a market maker sells a box spread, they are effectively borrowing money. They receive a credit and must pay back the value of the box at expiration. Similarly, if they buy a box spread, they are loaning money. They will pay money but receive a guaranteed return at expiration.

Of course, the market makers will price the boxes in their favor and either buy it below or sell it above the theoretical fair value.

For example, say a $90/$100 box is priced at $9. If the $90/$100 put spread is priced at $4, the $90/$100 call spread should be worth $5. However, the market maker may bid $4-3/4 and ask $5-1/4 for the call spread. This way, regardless of whether he buys or sells the call spread, he is either borrowing at less than (or loaning for a higher rate of) current risk-free rates by completing the box. For instance, if he buys the call spread for $4-3/4, he will buy the put spread for $4 and thus pay only $8-3/4 for a box position worth $9, and effectively loan money for higher than the risk-free rate. Likewise, if he sells the bull spread for $5-1/4, he will sell the bear spread for $4 thereby completing the box for $9-1/4. Now the market maker has sold a box worth $9 for $9-1/4 and effectively borrowed money for less than the risk-free rate.

Other views of the box spread

We said earlier that a long box spread could be viewed as a long bull spread matched with a long bear spread. There are two other ways to view boxes, and depending on your situation, one or the other may be more helpful.

One way to see it as a conversion at one strike and a reversal at another. For example, if a trader is short stock at $50, long $50 calls and short the $50 puts, he has a reversal at $50. If he subsequently buys stock at $60 with long $60 puts and short $60 calls, he has a $60 conversion.

Notice that the long and short stock positions cancel out, leaving the trader with long $50 calls and short $50 puts (synthetic long position) with long $60 puts and short $60 calls (synthetic short position).

$50 reversal $60 conversion Short 1,000 shares at $50 Long 1,000 shares at $60 Long 10 $50 calls Long 10 $60 puts Short 10 $50 puts Short 10 $60 calls The long and short stock positions cancel each other out (shown in red). The remaining positions are a synthetic long position (blue) at $50 and a synthetic short position (black) at $60. Notice the embedded bull and bear spreads (long $50 call and short $60 call, long $60 put and short $50 put).

Of course, a long position matched with a short position cancels each other. This holds true whether it's actual stock or synthetic versions. The trader who is synthetic long at $50 and synthetic short at $60 has effectively purchased stock at $50 and sold at $60. Bear in mind this is not as good as it seems, as the trader was also short stock at $50 and long at $60. The profits or losses come for the total reversal and conversion prices.

If you trade spreads, take the time to really understand box positions, as it will make all the difference in the world in your understanding of spread pricing. Once you have a handle on that, you will be able to make more knowledgeable decisions as to which limits to use with your orders.

Answers:
What will be the value of the above box spread if the stock is trading for $100 at expiration? How would you show it?

The question was referring to the $50/$55 box spread. The value of the box spread must be worth $5 -- the difference in strikes -- at expiration. To prove it, if the stock is trading at $100, the long $50 call will be worth $50 and the short $55 call (which is an obligation) will be worth $45. Both puts, the $50 and $55, will expire worthless because they are out-of-the-money. So the total value to the trader will be +$50 - $45 = $5

Synthetic Options

The name sure sounds intimidating, but synthetic options are fairly easy to understand and are truly a fascinating and useful part of options trading. Understanding synthetic positions will allow you to effectively do things many traders will tell you cannot be done, such as shorting stock on a downtick (or even when no stock is available), buying calls or selling naked puts in an IRA, buying stock for virtually no money, and a host of other imaginative strategies. Further, understanding synthetics will give you great insights into option pricing. You will understand how options are created, and why the market makers are quoting the puts and calls the way they are.

In order to understand these mysterious sounding options, you need to understand one of the most fundamental concepts of option pricing known as put-call parity.

Put-call parity

Put-call parity is a relationship showing that call and put prices are very dependent on one another, and not just arbitrarily chosen. In order to understand the put-call parity equation better, it's best to show how orders are filled on the floor of the exchange. Here's an example of how it works:

Say you want to buy 10 calls to open of the ABC $50 strike (with 1 year to expiration) at market. ABC stock is also trading at $50.

When this buy order is received on the floor, the market maker must become the seller so that the transaction can be completed. This means the market maker must be willing to be short a call. Now, while you may be totally comfortable in speculating by buying 10 calls, the market maker may not be so eager to be on the short side. The reason is this: Market makers are in the business to take 1/8th's or 1/4th's of a point on a large number of trades; they are not really too interested in holding open speculative positions over long periods of time -- especially short calls that have unlimited upside risk!

How does the market maker create a short call?

If the market maker is to be short a one-year call, his risk will be that the stock goes higher. So, in order to protect himself from this risk, he will purchase 1,000 shares. No matter how high the stock moves, he will always be able to deliver 1,000 shares of stock (represented by the 10 calls) at expiration.

However, now there is a new risk; the stock may fall. So to protect himself from this, he will buy a $50 put with one year to expiration.

Now our market maker is now long 1,000 shares of stock, long 10 $50 put options and short 10 $50 call options. Because he is short 10 calls, he can now fill your order to be long 10 calls. But what price should he charge?

Here is what's interesting about this position: The market maker is now fully hedged (protected) against any stock price movement at expiration. This means he cannot lose on the position! How? Well, the stock price can do one of three things between now and expiration of the call:It can stay the same, go up or go down. If the stock stays exactly at $50, the call and put expire worthless and the market maker's position is worth exactly $50,000, which is the amount he originally paid for the stock. If the stock closes above $50, the long put will expire worthless and the market maker will get assigned on the short call and lose the stock; however, he will be paid the $50 strike and receive exactly $50,000. Likewise, if the stock closes below $50 at expiration, the short call will expire worthless and the market maker will exercise his put and receive $50,000.

With the long stock at $50, long $50 put and short $50 call, the market maker is now guaranteed to receive $50,000 in one year. It is kind of ironic by using these speculative derivatives of puts and calls we can actually create a risk-free portfolio!

Now, if any financial asset is guaranteed to be worth a certain amount in the future, then its value today must be worth the present value discounted at the risk-free rate of interest.

PRESENT VALUE/FUTURE VALUEare "time value of money" concepts used throughout the financial industry to describe the value of assets at different points in time. The concept of time value says that a dollar today is worth more than a dollar tomorrow because the dollar today can be invested and earn interest. For example, if you deposit $100 into an account that pays 5% interest, you will have $100 (1+5%) = $105 in the future. So the future value of $100 today is $105 if interest rates are 5%. Similarly, if someone owes you $105 one year from now and interest rates are 5%, then you should be willing to accept $105/(1+5%) = $100 today. In other words, it should make no difference to you by waiting one year and receiving $105 or collecting $100 today. The reason is that you can take the $100 today, invest it at 5% for one year, and still have your $105 a year from now. So the present value of $105 one year from now is $100 (if rates are 5%). To calculate the present value, we simply take the future value of the asset and divide it by 1 + risk-free interest rate.

The market maker is guaranteed to receive $50,000 in one year regardless of the stock price. So the present value of $50,000 in one year is $50,000 / (1.05) = $47,619 today. The market maker should pay $47,619 today for these three assets -- the stock, long put and short call positions. Why? If he pays $47,619 and receives $50,000 in one year, his return on investment will be 5%, which is exactly the interest rate he should receive for a risk-free investment.

The market maker will spend $50,000 for the 1,000 shares of stock trading at $50. Let's also assume he pays $5 for the put. Now he will spend an additional $5,000 for the put for a total cash outlay of $55,000. We already figured that the fair price for this package of three assets should be worth $47,619 yet he's paying $55,000 for it.

The market maker has overpaid by $55,000 - $47,619 = $7,381, so he will need to bring in a credit for this amount. How can the market maker receive a credit of $7,381? Easy -- he will fill your order on the 10 $50 calls for roughly $7-3/8. Doing so, he will receive the necessary credit to make his -$55,000 cash outlay equal to -$47,619. Of course, the market maker will try to make an 1/8 or 1/4 point profit, so the order would probably be filled around $7-1/2.

To summarize, the market maker's initial position looks like this:

Buy 1000 shares at $50 = -$50,000
Buy 10 $50 puts at $5 = -$5,000
Sells 10 $50 calls at $7 3/8 = +$7,375
Equals -$47,625 cash outlay by market maker.

This is guaranteed to grow to a value of $50,000 in one year ($47,625 * 1.05 = $50,000) because of the full hedge provided by the 3-sided position.

This three-sided position (long stock + long put + short call) established by the market maker is called a conversion. If he does the reverse (i.e. short stock + short puts + long calls) then it is called a reversal or reverse conversion.

The put-call parity equation

We have shown that the market maker's three-sided position (conversion) is guaranteed to be worth the present value of the exercise price. Remember, he was short $50 calls and long $50 puts; the stock must either be above or below this price at expiration, resulting in a cash inflow of $50 -- the exercise price. Because he's guaranteed this strike price, the long stock + long put + short call position must be worth the present value of the exercise price. We can rewrite this using S for stock price, P for put price, C for call price, and E for exercise price as follows:

S + P - C = Present Value E

And therein lies the magic of synthetic options!

Notice the notation with the plus and minus signs. The long put position is denoted by a "+" sign and the short call is denoted by "-". This will be important to remember later.

To make things a little easier to understand, we know the present value of E (the right side of the equation) is guaranteed to grow to E so it behaves like a risk-free investment -- a T-bill (or Treasury bill, treasury note or treasury bond). We can therefore rewrite the above equation as:

S + P - C = T-bill

With some very basic algebra, we can create many interesting positions. We will take it slow with lots of examples, so hang in there!

This equation is known as put-call parity. If you know the value of a call option, you can immediately figure out the value of the put.

One small adjustment

Before we can continue with some examples, there is one note we need to make with an example. Let's say we are interested in seeing what a long stock + long put position are equal to. Using the equation, S + P - C = T-bill, how can we get the S + P (the pieces we are interested in) by themselves? Algebraically, we need to get the C to the other side of the equal sign; we need to add C to both sides. Now we have S + P = C + T-bill.

What does this mean? It means that someone holding long stock and a long put in a portfolio (the left side of the equation) will have exactly the same portfolio balance at option expiration as another person holding a call plus a T-bill (the right side of the equation).

Let's see if it holds true:

Assume we are interested in 1-year options and interest rates are 5%:

Investor A holds stock at $50 and a $50 put (left side of the equation)

Investor B holds a $50 call and a T-bill (right side of equation)

Investor B will pay $50,000/(1.05) = $47,619 for the T-bill.

At expiration:

		Portfolio A			Portfolio B
Stock price	Stock		$50 put	Total Value At Expiration	T-bill	$50 Call	Total Value At Expiration
35	35		15	50	50	0	50
40	40		10	50	50	0	50
45	45		5	50	50	0	50
50	50		0	50	50	0	50
55	55		0	55	50	5	55
60	60		0	60	50	10	60
65	65		0	65	50	15	65
70	70		0	70	50	20	70
75	75		0	75	50	25	75
80	80		0	80	50	30	80
85	85		0	85	50	35	85

Regardless of where the stock closes, investor A will be worth exactly the same as investor B; there are no differences in the two portfolios. Why does this happen? Portfolio A can never fall below $50 -- the strike of the put. However, if the stock rises, investor A will participate fully. Portfolio B must grow to a value of $50 because that is the T-bill portion and is guaranteed. Portfolio B, like A, can never have a value below $50. If the stock rises, investor B's call will start to increase in value by the same amount as the increase in stock in A's portfolio so both A and B receive all of the upside potential in the stock.

Portfolio B is said to be the synthetic equivalent of portfolio A. Also A can be said to be the synthetic equivalent of B.

So, a synthetic equivalent -- or synthetic -- is any position that has exactly the same profit and loss, at expiration, as another position using different instruments.

Now here's the one small adjustment I was referring to at the beginning of this section. By definition, synthetic positions only track the changes in portfolios and not the total value. For example, in the above example with investor A and B, the total value of B's portfolio is the same as A's. To have the synthetic equivalent, we only need to look at the changes. If B just held the $50 call option and not the T-bill, he would exactly reflect the changes in A's portfolio.

For example, if A buys the stock for $50 and it falls to $40, A can exercise the put and receive $50 -- so A starts with a value of $50 and ends with $50 and therefore has no change. Portfolio B would also reflect no change as well. The $50 call will expire with a value of zero. If the stock is trading at $60 at expiration, portfolio A will be worth $60, from $50, reflecting a change of $10. Portfolio B will also change by $10, as the $50 call will now be worth $10.

The whole point of all this is that, with the original equation S + P - C = T-bill, we can ignore the T-bill on the right hand side; it accounts for total value and not the changes in portfolio value.

Now our equation is even easier! All you need to know is:

S + P - C = ?

And you can figure out any synthetic position!

Synthetic positions

Now that you have the necessary equation, let's work through lots of examples to get the hang of synthetic options.

For starters, remember that we said the above is equal to a T-bill? Well, if you are long stock + long put + short call you are said to be holding a synthetic T-bill; the positions will behave exactly the same at expiration.

Synthetic long call
Using the equation, S + P - C = ?, we are in a position to find out. We are trying to find out the synthetic value of a long call, so we need to get a +C (remember, we are using "+" to denote a long position) on one side of the equation. If we add C to both sides and we get: S + P = C, and there's the answer; long stock and long put (left side of the equation) will behave just like a long call (right side). Therefore, if you hold long stock and a long put, you have a synthetic call position.

Let's check the profit and loss diagrams to see if we're correct:

We can easily see there is no difference between long stock + long $50 put purchased at $5 (left chart) and long $50 call purchased at $5. The person holding the long stock and long put raised the cost basis of their stock from $50 to $55, that's why their break-even point is now $55. However, they still participate in all of the upside movement of the stock. What if the stock falls? The investor is protected for all prices below $50, which is the strike of the put. The worst that can happen is for the stock to fall to zero. This investor will exercise the put and receive $50 effectively only losing on the $5 they paid for the put; therefore the maximum loss is $5.

For the call holder (right chart), they paid $5 so their maximum loss is also $5 but they too participate in all of the upside of the stock. The stock will have to be $55 at expiration in order for the call holder to break even.

It should now be apparent that call owners get downside protection as well as a put holders; the call keeps you from losing value in the stock because you are not holding the stock!

So how do you own calls in an IRA? Now you should know. Use the synthetic equivalent and buy the stock and put. Your return on investment will be much lower than the person who buys the call because of the difference in capital required to purchase the stock, but the two positions will behave the same way at expiration.

Synthetic long stock
Without looking ahead, see if you can use the equation S + P - C = ? and solve it for long stock.

Because we have +S on the left side already, let's move the C and P to the other side. To do this we need to add C and subtract P from both sides. If you did it correctly you should find that S = C - P. Now you know that a trader holding a long call and short put (right side of equation) are actually holding synthetic stock (left side).

Looking at the profit and loss diagrams for each:

We see there is no difference in the two positions. The long stock purchased at $50 (left chart) will gain and lose point-for-point to the upside as well as the downside. The same holds true for the long $50 call and short $50 put (right chart). The $50 call will gain point-for-point at expiration while the short put will become a liability (loss) point-for-point if the stock should fall.

So synthetic stock is long call plus a short put. What would synthetic short stock be? Just the opposite, long put and short calls. This is great to know for all traders involved in short selling. Now you know how it is possible to short stock without an uptick or when stock is not even available for shorting -- use synthetics and buy the put and sell the call.

How much will it cost to short synthetic stock? Theoretically you should receive a credit. This can be shown by the original equation S + P - C = Present value of E. If we rearrange so that C - P = S - Present value E we see that, if S and E are equal (in other words, at-the-money), then S - Present value E must be a positive number. In order for C - P to be positive, C must be more expensive than P. Because you are buying puts and shorting calls, you should get a slight credit. Realistically though, because of bid-ask spreads and commissions, it will probably cost you a slight debit.

Synthetic covered call
Hopefully you are getting the hang of this, but we'll do one more to be sure. What is a synthetic covered call? We know a covered call is long stock plus a short call, so it would be represented by S - C in our equation. Looking at the equation S + P - C = ?, we need to get S and -C on one side. In order to do that, we can just subtract P from both sides and get S - C = -P. A covered call position is synthetically equivalent to a short put.

As expected, the profit and loss diagrams are the same. For the covered call position (left chart), the investor buys stock at $50 and sells a $50 call for $5, effectively giving the stock a cost basis of $45, which is the break-even point. If the stock rallies, the investor will be forced to sell it for $50 regardless of how high the stock moves. The short put (right chart) is at risk for all stock prices below $50, which is offset by the $5 premium received, which gives a break-even point of $45.

How can an investor sell puts in an IRA? Using synthetics, one can buy stock and sell calls, which is exactly the same thing from a profit and loss standpoint.

It is a little ironic that most brokerage firms require level 3 option approval to short puts yet require only level 0 to enter covered call positions. Synthetically, they are exactly the same thing. If you wouldn't short a put on a particular stock, you shouldn't enter into the covered call either.

Incidentally, if you do enter a into a covered call position, you should see the benefit of entering the order as a buy-write (please see our section under "Buy-writes" for more information). Doing so gives the market maker two of the three sides necessary to complete a reversal. This gives the market maker a guaranteed trade so they are very eager to get them filled. Most of the time, you will receive a better fill than the natural at the time the trade is placed.

Practicing with synthetics

It is a good idea to practice with the synthetic relationships of any trade you are thinking of entering. Doing so will help you understand synthetics as well as give you additional insights into the way the trade will behave at expiration.

As a guide, remember that there are three pieces to the puzzle: Stock, calls and puts. The synthetic of any one of the pieces will always be some combination, either long or short, of the remaining two. For example, a synthetic call will be some combination of stock and puts. Synthetic stock will be a combination of calls and puts.

Once you become proficient with synthetics, you will certainly become a better options trader!