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Oct

31

Understanding the Difference Between Price and Value When Trading Stock Options

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Price and Value

In order to understand the difference between price and value, let’s take a look at a real-world example. In Figure 6-8, you’ll see an eBay auction for one million Iraqi dinars:

Figure 6-8

At the time of this auction, there were many similar auctions for this currency because of the radical changes taking place in Iraq. The country was getting lots of U.S. support to help its new government get under way. They also have the second-largest oil reserves in the world, so there is tremendous potential for their currency to rise against the dollar. If you buy a large block of its currency, you’d only need a small movement in the currency against the dollar and you could make a lot of money; at least, that’s the investment story the sellers of Iraqi currency are touting on eBay. Figure 6-8 shows this opportunity could have been yours for the low, low price of only $990.

We know the price is $990 but that really tells us nothing. Any asset can be priced too high no matter how good the story is that comes with it. The rarest works of art and most precious gems can be a horrible investment if too much is paid for them. As investors, we cannot just look at the $990 price tag on this eBay auction and think it is a good deal because of a good story. We need to somehow compare the price to the value.

That’s easy to figure out since there is an open market for currency. All we need to do is look at the exchange rate for Iraqi dinars and convert them to U.S. dollars. At the time of this auction (May 27, 2005), the exchange rate for U.S. dollars per Iraqi dinar was .00068, which means that one million Iraqi dinars were worth 1,000,000 * .00068 = $680. Now we have a benchmark for value since we know what the crowd is willing to pay. However, this auction dealer wants $990 for something that is worth $680 in the open market. Not only is this not a good deal but there’s a more insidious side to the trade than just being overpriced. If you pay $990 for the block of money and its value rises, you could still lose. For example, if the block of money rises from $680 to $900, it certainly went up substantially in value but you still lost money since you paid $990. This is exactly what happened with our AGIX $20 call. The price of the underlying stock rose, but our option was overpriced. The moral of the story is that if the price you pay is greater than the value, you can end up with a loss even if your directional outlook is correct. The legendary investor Warren Buffett said it beautifully: “Price is what you pay. Value is what you get.”

The price of an option is in no way related to its value.

Option Prices and Point Spreads

One of the best ways to understand option trading is to realize they can be viewed as a directional bet on the underlying stock. (This is not to say we are using options to bet on stocks. Instead, it’s a framework to help us understand what went wrong with the AGIX $20 call.) As with any bet, you put up some money in hopes of making a particular reward. There is some probability of winning along with a probability of losing. The amount you’re willing to wager on a bet can be thought of as the price of the bet. But, as we will show shortly, some prices reflect a good deal while others do not.

In order to better understand how some prices can be too high, imagine that it is 2004 and you are betting on the Super Bowl between the New England Patriots and Philadelphia Eagles. You do your homework and find that all of the analysts are predicting that New England will win. To the unwary, it sounds like betting is too easy; all you have to do is bet big on New England and you’ll make money. Unfortunately, you find that everybody wants to bet on New England and you cannot find anybody to take the other side of the bet. How can you entice someone to take the other side? There are several ways but one of the easiest is to offer a point spread. While nobody may be willing to bet on the Eagles in actual points (or “even up”), people will take the bet if you create a point spread. For instance, if you offer a seven-point spread on New England then anybody betting on that team must subtract seven points from the Patriots’ score before comparing it to the Eagles’ score in order to determine who wins the bet. If the Patriots win 21-14, there is exactly a seven-point spread and no money is won or lost. A bigger spread results in a win for the person betting on the Patriots while a smaller spread results in a win for the one betting on the Eagles.

If nobody accepts the bet with a seven-point spread, you can always increase it until you find a “buyer.” At some point, people will think the bet is fair and take the other side. Figure 6-9 shows the spreads at the Stardust and Mirage Casinos and you can see they were offering a seven-point spread, which is designated by the -7 under each of their names:

Figure 6-9

The spread acts as a way to even up the bet. It’s the way in which markets are created; otherwise everybody would bet on the favored team and there would be nobody left to take the other side of the bet. The spread is increased until we find an equal number of buyers and sellers. If the spread is too big, bettors will realize that they are better off betting against their team even though they think they will win. It’s only when the spread is just right that we end up with an equal amount of buyers and sellers on either side of the bet.

Figure 6-9 shows the final score was 24-21 in favor of New England. This means anybody who predicted New England would win betted correctly, but they still lost the bet. In other words, New England won but not by a big enough margin to win the bet.

Now let’s see how this football analogy relates to the options market. At the time the AGIX quotes were taken there were numerous articles about upcoming experiments for one of its drugs to reduce the amount of fatty plaque that causes clogged arteries. If the experiment is positive, the stock’s price could jump significantly.

Now think about this. If everybody believes that AGIX will rise, then everybody would want to buy call options (just as if everybody thinks the Patriots will win then everybody wants to bet on them). And if everybody wants to buy calls then there is a problem. Who is going to sell those calls? The answer is that nobody will. That is, nobody will sell them unless you offer a point spread on the “bet.” And that’s exactly what has happened with the AGIX $20 call.

Figure 6-6 showed that the $20 call was asking $4.80. In essence, anybody buying this call is really betting that the stock’s price will be above $20 + $4.80 = $24.80 by expiration since that’s the breakeven point on the option. The $4.80 time premium of the option acts in the same way a point-spread does for a football bet. It’s only because of this $4.80 “point-spread” that a market between buyers and sellers could be created. If the time premium was higher than $4.80, then the point spread would be too big and we’d have too many people wanting to sell the bet and the price would fall. If the premium is less than $4.80, then the point-spread is too small and traders would believe the $20 call is a good deal. We’ll end up with too many people wanting to buy the call and the price will rise. A price of exactly $4.80 is what is required to balance the number of buyers and sellers at that point in time.

Notice that, at expiration, if the stock rises from $18.81 to $24.80 or less, any trader who paid $4.80 for the $20 call loses the bet – even though the stock’s price rose. This is exactly what happened to those who bet on the Patriots with a seven-point spread. Even though they were betting on the correct team, they still lost the bet since they did not win by a big enough spread. And this is exactly what happened to the traders who bought the $20 call on September 16 and tried to sell it six days later. Although traders buying the call were correct on the direction, they accepted too big of a point-spread on the bet. In short, the price of the call was much higher than the value.

To be continued…..

Oct

31

When To use a Jellyroll Options Trading Strategy

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When To use a Jellyroll

Options Universtiy goes into detail about complex spreads in its comprehensive Options Mastery course. One of the strategies covered is the complex strategy called the “Jellyroll”. And indeed, it is sweet. This strategy employs the use of calendar spreads-also known as time spreads. When postioned properly, Jellyrolls are going to help option traders choose between whether it is best to use the call spread on or to use the put spread.

The best way to digest a jellyroll is to eat one. So, let’s look at an example used in the Options University Mastery course. Let’s say we want to buy the June-July $65 time spread. The stock is trading at $65. So, we buy the July $65 call and we’re selling the June $65 call. The reason we did that was when we looked at the interest and dividend, we said the call spread must be trading higher than the put spread by the amount of interest minus a dividend but there is none in this case so there is no dividend.

When we saw there was a difference of interest of 10 cents, we knew the call spread should be trading at the same amount as the put spread except for that 10 cents. It should be trading higher by 10 cents so that means the put spread should be 10 cents lower but the put spread was trading at the same price.

As we let time on the front month erode the extrinsic value and widen the spread, we will have accumulated some gains. Volatility for the stock is increasing and we know that if the stock moves in either direction away from the strike we are going to lose money. There is no sense in staying in this thing. We have our profit and we want to get out. We look at the put spread and see that it is still priced the same as our call spread and we know that it should be 10 cents lower because of the interest in the call spread. Because selling the call spread is the same thing as selling the put spread and the put spread is trading effectively higher than the call spread, its best to get out of our long call spread by selling the put spread. What? Now the jellyroll is getting messy

You see, we actually would have two contra synthetic positions: short call, long put, that equals what? Short stock. Also, w are long call, short put which equals what? Long stock. So, in affect, we are short and long stock. Now here’s the value of a jellyroll: it is an arbitrage play on the difference between the interest rates of the two months. If the stock closes below the strike, our short call will be worthless, we’ll be long a put that’s now in-the-money, If this happens, we

exercise our put creating a short stock postion. Come expiration, we will be short real stock, long a call and short a put; we are in a reversal!

While we’re in this arbitrage, we’re going to be collecting short interest in our position. Come July expiration, our synthetic long stock position in our reversal will become real long stock and cancel out with the short stock. At July expiration, we’ll have nothing more. In other words, when we come out of that position in June we will be collecting interest for the month of July.

In summary, If you’re a buyer, you want to get in the cheaper spread. Likewise, if you’re a seller, you want to sell the more expensive spread and the jelly roll helps us compare the cost of both of those spreads together..

For more on all things stock options, go to www.optionsuniversity.com

Oct

30

Volatility, the Most Important Variable in the Model When Trading Stock Options

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The only variable we’re not sure of is volatility and that’s why it’s the most important variable in the model. If it’s an unknown variable, then how did we look up volatility numbers for Google and McDonald’s earlier? When we looked those numbers up they were historic numbers; they had already occurred in the past. When the Black-Scholes Model asks for volatility, it really needs to know the future volatility of the stock and not the historic volatility.

To understand why, go back to our two-price stock model where the stock could move up or down $5. If this is how the stock has behaved in the past then we would value the $50 call at $2.50. However, suppose we have reason to believe the stock will now move up or down $10 in the future. Now the $50 call is worth $5 and not $2.50. It’s the future volatility of the stock that determines the price of an option and, unfortunately, that is something we will not know until expiration.

In order to truly know the value of an option we must know the future volatility of the underlying stock. And that is something that can never be known for sure until expiration.

Using the Black-Scholes Model

Let’s take a look at how to use a Black-Scholes Model. There are many available online, but one of the best can be found at the CBOEs website www.cboe.com:

Figure 6-5: The Black-Scholes Option Pricing Model (Calculator)

Figure 6-5

Let’s assume we are looking at a stock trading for $50. We’d simply type “50” in the “Price” field on the left side of the calculator. If we wish to evaluate a $50 strike, we’d type 50 into the “Strike” field. We’ll also assume that there are 365 days to expiration and that interest rates are 2%, which we type into their respective fields. Last, we’re going to assume that the future volatility of the stock will be 17.62% over the course of the year (you’ll find out why this specific number was chosen shortly). What is the $50 call worth under these assumptions? All you have to do is click the “calculate” button in the middle of the screen and the call and put prices show up on the right by the “Option Value” field (circled).

It’s showing us the call should be $3.99 and the put should be worth $3. The reason 17.62% was chosen as the volatility is because that’s the volatility that makes the put worth exactly $3, which fits an example we worked by hand in Chapter Five. If you recall in that chapter, we were trying to figure out what a market maker should charge for a one-year, $50 call with the stock at $50. We also assumed he paid $3 for the put and interest rates were 2%. From put-call parity, we calculated that the market maker should charge $3.98 for the call, and the Black-Scholes Model in Figure 6-2 is coming up with $3.99. So we’re off by a penny, but that is due to differences in the interest compounding assumptions and number of days assumed in a year.

Although the Black-Scholes Model makes use of some very complex mathematics, the essence behind the calculations is similar to what we worked through when trying to figure out how much the market maker should charge for a call option.

Why do you suppose the call in Figure 6-5 is roughly $1 higher than the put? Hopefully you remember from put-call parity that it’s due to the cost-of-carry on the stock. If interest rates are 2%, it will cost $50 * .02 = $1 in lost interest to buy and hold the stock for one year. In other words, if you pay $50 for stock and hold it for a year, you could have had $51 at the end of the year if you had left the money in a risk-free account instead. So there is a $1 cost of carry on a $50 stock over a year if interest rates are 2%. That’s why the call is priced $1 higher than the put. The Black-Scholes Model is a complex form of put-call parity with volatility as the key ingredient.

Why You Need to Understand Volatility

This chapter is by no means meant to be a comprehensive lesson on volatility. However, most beginning option books do not even mention it, and that’s a huge disservice to new traders and investors. If you don’t understand the role of volatility, you can end up with unpleasant surprises as we will now demonstrate.

Many option traders believe option trading is a relatively easy task and that you buy calls when you think the stock is going up and buy puts when you think it’s going to fall. After all, that’s all that’s needed to trade stocks. When most traders make the switch to options, they apply this same directional procedure to the options market. However, this approach ignores the time value of calls and puts in terms of volatility and unexpected, almost paradoxical, losses can occur as the following real-life example shows.

On September 16, 2004, Atherogenix (AGIX) was trading for $18.81 as shown by the quotes in Figure 6-6. At the time, there was tremendous bullish news on the stock regarding a new heart medication. Most option traders who were bullish might have been tempted to buy the $20 call since it was the next-highest strike from the (then) current stock price. Figure 6-6 shows the $20 call (circled) would cost $4.80, or $480 per contract.

Figure 6-6: AGIX Option Quotes

Figure 6-6

On September 22, just six days later, the stock had risen significantly from $18.81 to $21.18, which is a 12.5% gain in a short time. It certainly sounds like it should have left the trader with a nice profit on the leveraged $20 call, but Figure 6-7 shows that is not what happened. The $20 call was bidding only $4.70, which left the trader with a 10-cent loss for being correct on the direction of the stock!

Figure 6-7: AGIX Option Quotes (Six Days Later)

Figure 6-7

Direction Versus Speed

What happened? How did this call option lose money even though the stock’s price went up? Loosely speaking, the reason is because options are two-dimensional assets. That is, option traders must not only guess the direction of the stock correctly but they must also guess how quickly the stock’s price will get there – the speed.

Stock traders, on the other hand, only need to correctly guess the direction; they are dealing with a one-dimensional asset. It doesn’t matter how long it takes for the stock to move, just as long as it moves in the right direction.

As an analogy, you car moves in one dimension – horizontally. An airplane, on the other hand, can move in two-dimensions – horizontally and vertically. It is this second dimension that makes flying an airplane so much more difficult than driving a car. Just because you may have driven a car accident-free for 20 years does not mean you should just jump into an airplane and start flying. There is a second dimension you’re not used to dealing with. Likewise, just because you may have been trading stocks successfully for 20 years does not mean you should just jump into the options market and start trading options based on direction. That’s an equally bad idea.

In this example, the $20 call option trader got the stock direction right but not the speed; it took too long for the stock to get there. If the stock had moved to $21.18 in a shorter time, say a day or two (rather than six), the $20 call would certainly have made money. It is this second dimension of speed that makes options trading so much more difficult than stock trading. Notice that a stock trader would have made money by purchasing the stock for $18.81 and selling at $21.18. The speed at which the stock rises doesn’t matter. So while both traders guessed the stock direction correctly, only the stock trader made money.

This example shows that call options are not necessarily a direct substitute for stock. If you think a stock is moving higher, you cannot just buy a call in place of the stock and expect to make money if you are correct. Yet most option traders mistakenly apply this one-dimensional stock trading technique to options and, consequently, end up losing money. What is responsible for this speed component? It’s the time premium of the option. If the time premium is relatively high, then the breakeven price is pushed too high and the option may lose money even though the underlying stock moves favorably. In order to prevent that from happening, option traders must learn to separate the price of an option from the value.

To be continued…..

Oct

30

The Jellyroll Options Trading Strategy

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The Jellyroll

When we want to buy a calendar (time) call spread or to buy a calendar put spread, we look for which once is the least expensive. If we are buying the June-May $25 call spread, it is the same thing as buying the June-May $25 put spread adjusted for interest and dividend. To figure out what the call spread value is, we need to consider the effects of interest and dividend. To do that, we need to subtract the interest less the dividends.

For example, if the May-June $25 call spread is trading for $1.30 and the put spread is trading for $1.25 we would need to find out the interest and the dividends if applicable. If the interest between May and June is 10 cents and there are no dividends to be paid out, the call should be trading at $1.35. Why? Because the call spread should be trading higher than the put spread by the amount of interest minus dividend. In this case, the call spread is selling for 5 cents less than it should. This, the call is under valued.

As a general rule, we want to buy the cheapest spread and sell the more expensive one. What if we’re already in the long time spread; we bought the call spread because it was a better value than the put spread. Now, we’re looking to get out and we’re noticing that the put spread is effectively priced higher. Now that it’s time to sell, it’s the put spread that’s more expensive. We want to sell the more expensive one. It makes perfect sense. When you do that- buying the call spread and then getting out by selling the put spread or buying the put spread and getting out selling the call spread- you’ve set up an arbitrage called a “jelly roll”.

According to Ron Ianieri, co-founder of the Options University, the jelly roll is to the time spread in the same way “the box” is to the vertical spread. Remember, the box helps us to mathematically relate two corresponding vertical spreads to each other. The jelly roll does the exact same thing for time spreads.

The jelly roll is two corresponding time spreads in combination; one long, one short the call time spread, short the put time spread. We can do this because the call time spread and its corresponding put time spread are the same thing. Because they are the same thing, we can buy one and sell the other. To understand how the jelly roll works, we need to polish our understanding of its synthetics.

Let’s say we bought the July $50 call and we short the May $50 call and we can say that’s the same thing as buying the July $50 put and selling the May $50 put. When it was time to get out, we noticed that the put spread was still priced higher. So, we sold the put spread against our long call time spread. What is left is long the call time spread and short the put time spread. The long call time spread is the same thing as the long put time spread. Buying the long call is the same as buying the long put so selling the put is the same as selling the call. Or, buying the call and selling the put works the same way.

Herein lies the secret:

Instead of looking at it horizontally, let’s look at it vertically. Going back to our synthetics, what is short May $50 call, long May $50 put? Indeed, that’s a short stock position. That is synthetic short stock. We’re synthetically short stock in May. What is Long July $50 call, short July $50 put? That’s synthetic long stock. What do we have here? We have a synthetically long stock. Do you see it?

What is a same strike short stock and a long stock? Nothing. No position. Zero. It becomes a straight arbitrage; we bought stock and we sold stock at the same time and captured the difference between months.

For more on all things about stock options including basic through advanced online courses, mentoring and trade shadowing, go to the Options University website at: www.optionsuniversity.com

Oct

29

Pricing Time Spreads Options Trading Strategy

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Pricing Time Spreads

Remember, when trading time spreads (aka:calendar spreads) we’re not really trading strikes, we’re trading time and the time value between one option month to another option month. Both options must be equally reflected in the difference between one month to the other-regardless if we’re using calls or puts. The difference in time between a May $25 call and a June $25 call is the exact same difference in value as the difference in time between the May $25 put and the June $25 put. They are the same; buying the call time spread is the same thing as buying the put time spread.

If this is so, that means when we look at a call spread we can look at the corresponding put spread and know that the two are supposed to be equal. But according to the Options University, before we buy the call time spread we might want to look at the put time spread. If we’re going to buy a spread, we want to buy the cheaper one if they are both going to do the same thing.

A call spread will normally trade higher than its corresponding put spread by the amount of interest minus dividend. If there is no dividend, the call spread should trade higher than it’s corresponding put spread by the amount of interest.

The following is an example taken from the Options Mastery Course put out by the Options University. Suppose we’re looking at the May $25-June $25 (could be a call or put) and we’re saying that if the May-June $25 call spread is trading for $1.30 and the put spread is trading for $1.25. In this example, there is no dividend. To see it the rule holds true, we need to know what the interest between May and June is. Let’s say the interest between May and June is 10 cents. The rule is telling us that this call spread should be trading 10 cents higher than the put spread- but it’s not.

The call spread is only trading 5 cents higher. It should be trading 10 cents higher. That means the call spread is slightly under valued versus its corresponding put spread. Remember this is for corresponding options. In this scenario, we would rather buy the June $25-May $25 call spread at $1.30 than we would want to buy the May $25-June $25 put spread at $1.25 even though it has a higher price. However, in reality the call is 5 cents under priced.

Now, things get interesting. In this example, we would buy the call spread and when it was time to get out or if we are a seller of the spread instead of a buyer of the spread, we would sell the put spread. Why? Because the call spread should trade higher than the put spread by the amount of interest minus dividend. With no dividend then the call spread should trade higher than the put spread by 10 cents. Right now it’s not. That means the call spread is under valued.

If the call spread were trading for $1.40 instead of $1.30 things are different.

If the interest is the same at 10 cents and there is no dividend, the call spread is trading higher than the 10 cents and is thus over valued. If we are going to buy a time spread, we want to buy the corresponding put spread at $1.25 because in theory it’s like buying the call spread for $1.35 because the call spread is always supposed to be 10 cents higher.

Four times a year, on dividend paying stocks, we might have the put spread actually trading higher than the call spread. For example, what if there’s a 25 cent dividend? Then the call spread should be trading higher than the put spread by 10 cents minus 25 cents.

In Summary, if one spread is more expensive than the other, and we’re a buyer, we want to get in the cheaper one. As a seller, we want to obviously sell the more expensive one

For information on all things stock option, go to www.optionsuniversity.com

Oct

29

Fair Value Depends on Perspective When Trading Options

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We can even use computer simulation to see if we’re right. Figure 6-2 shows a computer model with the number of tosses on the horizontal axis and our total profit or loss on the vertical axis:

Figure 6-2: Computer Simulation of Fair Value (Paying $1 to Win $1)

Figure 6-2

You can see that after 500 tosses, we’re about back at breakeven. However, prior to that, we can certainly end up winning or losing due to chance. But in the long run, we’d expect to just break even. The “zero” horizontal mark in Figure 6-2 acts like a magnet for a fairly valued bet in that the profit and loss line doesn’t get too far from it. The profit or loss line can stray from zero but it cannot just move away from it indefinitely. The profit and loss line just tends to oscillate around zero.

Let’s use this same formula to see what it says about paying $1.50 for the $1 reward:

(0.50) * +$1.00

+ (0.50) *-$1.50

Expected value = -25 cents

The formula shows that we are expected to lose 25 cents per flip. Paying $1.50 for this bet is therefore too high a price, since we would expect to end up with certain losses over time. Figure 6-3 shows that a computer simulation agrees with the formula:

Figure 6-3: Computer Simulation Above Fair Value (Paying $1.50 to Win $1)

Figure 6-3

In fact, mathematically, after 500 tosses we would expect to end up at 500 tosses * -.25 cents = -$100 and that’s roughly where the computer simulation ended. Curiously enough, notice that even though we’re paying above fair value it’s still possible for us to end up on the winning side in the short run. Figure 6-3 shows that we ended up on the winning side even after 100 flips. But that is just due to some short-term good luck on our side. We had significant winnings to cover our losses after 100 flips. But if we stay in the game long enough, the profit and loss line does not tend to get pulled toward zero. Instead, it moves into a definite downward path and never returns. Once again, this shows that $1.50 is too high of a price to bet on this coin flipping game.

Let’s see what the formula has to say about wagering 50 cents for the $1 reward:

(0.50) * +$1.00

+ (0.50) * -$0.50

Expected value = +25 cents

Wagering only 50 cents to win $1.00 at the flip of a coin is a good deal for us, as we now expect to win about 25 cents per flip. Figure 6-4 shows a computer simulation of this arrangement:

Figure 6-4: Computer Simulation Below Fair Value (Paying 50 cents to Win $1)

Figure 6-4

Again, we would expect to have 500 tosses * +25 cents = $100 profit after 500 flips and that’s about where this computer simulation ends. Notice too, however, the chart shows we actually lost money after 75 flips even though the odds were on our side. That’s because the profit and loss line dips below zero up until the 75th flip mark. At that point, we head into uninterrupted profits. This profit and loss line is not pulled toward zero in the long run. Although we could certainly lose in the short run, we will end up on the winning side after numerous flips, which is confirmed in Figure 6-4.

Only when the price of the bet is $1.00 can we say that it is “fair” for both parties. As a reminder, just because the bet is fair does not mean you cannot end up on the winning or losing side. The fair price for both just means that, over the long run, neither side is expected to end up on the winning or losing side.

Fair Value Depends on Perspective

In the coin toss example, we calculated that $1.00 was the fair value of the bet. However, that result is due to our assumption that the chance of winning (and losing) is 50%. Obviously, if we used different probabilities, we would get different results. This means the fair value of any bet depends on our perspective; it depends on our views of the probability of winning.

For example, let’s assume that somebody offers to wager $1.50 for this bet. There are two ways we could look at it. First, we could assume there is a 50% chance of winning and losing and assume that is too high of a price since it results in an expected loss of 25 cents per flip:

(0.50) * +$1.00

+ (0.50) * -$1.50

Expected value = -25 cents

However, we could also look at this bet another way. We could assume that it’s priced fairly since nobody should intentionally pay more than what they think is fair. If someone offers to pay $1.50, we could say that the gambler must think it is a fair price to pay. In order for that to be true, the gambler would have to think his chances of winning are 60% since that results in a fairly valued bet:

(0.60) * +$1.00

+ (0.40) *-$1.50

Expected value = 0

If a gambler were willing to pay $1.50 for this bet, we would say he is implying that his chances of winning are 60%. In other words, just by the fact he is willing to pay $1.50 for such a bet we can back into it mathematically and assume he believes his chances of winning are 60%; otherwise he would not bid so high.

This shows there are two ways of looking at any bet. First, if we believe there is only a 50% chance of winning then paying $1.50 is too high a price. Second, we can assume the $1.50 is a fair price and adjust the probabilities to make the expected value equal to zero. We can back into this figure algebraically and, in this case, we’d say the gambler willing to pay $1.50 for this bet is implying that there is a 60% chance of winning the $1.00 prize and a 40% chance of losing the $1.50 wager.

Now, as gamblers, it’s up to us to decide which viewpoint is more realistic. Should we assume the chances of winning are 50% and be willing to pay only $1.00? Or is 60% a better assessment? Notice that if we assume 50% is the better guess we will be outbid by another gambler if he feels 60% is the more realistic probability. We would only be willing to bid up to $1 for the bet while he would be willing to pay up to $1.50. It is critical that we are confident in our assessments. If 60% sounds like too high of a probability, we’re probably better off forgoing the bet and letting someone else make it. It’s better to miss out on some reward rather than lose our money.

Whether we should use 50%, 60% (or something else) to value this coin flip is an important question. It’s even more important when valuing options. However, few option traders ever check to see how the price of an option compares to their assessment of value. Failure to do so is the leading reason that option traders lose with options. In order to make that assessment, option traders need to use the Black-Scholes Model.

The Black-Scholes Option Pricing Model

We briefly mentioned the Black-Scholes Model in Chapter Five. There are many mathematical pricing models that can tell us what the price of an option “should be.” Naturally, there will be minor variations in the answers depending on the assumptions in the model. The most famous is the Black-Scholes Option Pricing Model named after Fischer Black and Myron Scholes. Its development was no small feat, as the model relies on complex mathematics and arbitrage pricing relationships to determine what the price of an option should be and is considered to be one of the biggest breakthroughs in the modern financial era. In fact, the 1997 Nobel Prize in Economics was awarded to Myron Scholes for its development (unfortunately, Fischer Black died in 1995 and the Nobel prize is not awarded posthumously).

According to the Black-Scholes Model, there are six factors needed to determine the price of a call and put option:

Stock Price
Exercise Price
Risk-Free Interest Rate
Time to Expiration
Dividends
Volatility

Notice the last factor, volatility. Of these six inputs, volatility is the most important for the fact that it’s the only true unknown factor. For example, assume the risk-free interest rate is 5% and hundreds of traders are trying to value a 30-day, $100 call option on a stock trading for $95. We’ll also assume the stock pays no dividends over the life of the option. Notice all of the factors are automatically determined except volatility:

Stock Price = $95
Exercise Price = $100
Risk-Free Interest Rate = 5%
Time to Expiration = 30 days
Dividends = 0
Volatility = ?

To be continued…..

Oct

28

Advanced Options Trading – Time Spread Volatility

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Time Spread Volatility

Often, when people do spreads, they want to know what the volatility of the spread is. They want to know what the implied volatility of each option in the spread is. Traders will say something like “I sold 34 volatility, I bought 32 volatility, so it’s like I have a combined volatility of 33. That statement is incorrect.

At the Options University, they point out that you can’t just take the two options and average them. When you average something you normally are making a simple assumption that both values are weighted equally. But in the case of spreads, it’s a bit different. When you’re doing a spread and trying to figure out the volatility of the spread, you need to understand that implied volatility in the front month and implied volatility of the out month are not weighted equally. Why? Because of Vega- the amount that the price of an option changes compared to a 1% change in volatility- is what weights volatility sensitivity and we know that the front month is not going to have the same Vega as this out month.

Before we can determine the actual volatility of the spread, we must first equalize the volatility of both options. Perhaps the best way to explain it is do an actual example. Suppose I bought the 34 volatility for $3 and I sold the 32 for $2. The option that’s at 34 volatility is trading at a volatility level that’s two ticks higher than the 32 volatility option and we know this option’s Vega is 8 cents. We know that the 32 volatility option is trading for $2, we know that we can bring this option up to the 34 volatility option’s level very easily. At 32 volatility it’s worth $2 and we know that Vega is 8 cents. So, if we move up from 32 volatility to 34 volatility we would move up 2 ticks times 8 cents. At volatility 34, the Vega would have the value at $3.16.

Now that we have brought the theoretical value of this option up to a volatility level that matches both options, we can figure out that at 34 volatility this spread should be worth $3.16 minus $2, or $1.16. This spread is worth $1.16 at 34 volatility.

The underlying idea is that we take 32 volatility up to 34 volatility. If you aren’t confused yet, try this one on: We found out that the spread is worth $1.16, but now we traded it at $1.20. How do we figure out what volatility we traded the option at? Now that we’ve got it equalized we can use the spread’s Vega to compute the difference between the two values. We did a spread at $1.16 and as we said it’s a 34 volatility and now we need to figure out what $1.20 volatility is. Both have their own Vega and we are long one and short the other. If I know that the Vega difference between the two options is 3 cents, this gives us a spread Vega of 3 cents. If I take volatility up one tick to 35 volatility it’s going to take this value up 3 cents making it $1.19 which is right around $1.20. The implied volatility of this spread is 35.

Whenever you’re doing two options with different strikes, different Vega values you can’t just sit there and average them out. Where this becomes important, especially is when a trader is trying to hedge their volatility exposure. But that story is for another time.

For information on all things stock option, go to www.optionsuniversity.com

Oct

27

An Introduction to Volatility in Trading Stock Options

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An Introduction to Volatility

In Chapter Two, we talked briefly about volatility and how it affects an option’s price. It was there we found out that the uncertainty of stock prices – the volatility – is what gives an option its value. The higher the volatility of the stock, the higher the option’s price. However, the definition alone is not enough to trade options successfully. New and experienced traders must understand the role it plays in determining the fair value of the option as well as how it is possible to lose with options even though the underlying stock moves in their favor.

The Frog and the Roo

To understand the role of volatility and option prices, imagine that you are at a carnival with a very unusual game – a frog jumping game. A frog starts in the middle of a floor and can only jump left or right. The frog moves randomly, jumping right or left with equal probability. At the end of one minute, the frog’s final destination is marked and you are paid $1 for every foot the frog is to the right of the starting point. If the frog happens to land anywhere to the left of the starting point, you win nothing:

frog

How much would you pay to play this game? There is no right or wrong answer but think about it for a moment and pick a number that you think sounds reasonable. Now let’s change the mechanics of the game a bit. Imagine there is another game that is played with the same set of rules except this one uses a kangaroo:

Roo

How much would you pay to play this game now? As before, there is no right or wrong answer but think again for a moment and come up with your best estimate as to what this game is worth to you. It should be obvious that no matter which price you chose for the frog you should be willing to pay a higher price to have it replaced by a kangaroo. Why? Because the kangaroo has the ability to jump further, and that means you could win far more money, so the game is worth more to you. Notice that while both games offer potentially different rewards, neither has a mirror-image downside risk. In other words, you do not lose one dollar for every foot to the left of the starting point — once you place your bet that’s the most you can lose. So the only thing that matters to you is the upside potential. The game with the most upside is the one that is worth the most. It is the asymmetrical payoffs of these games that makes the kangaroo game more valuable.

In order to understand how volatility affects options prices, just replace the frog and kangaroo with at-the-money calls on two different stocks. One stock hardly moves like a big blue-chip stock such as General Electric (GE). The other bounces all over the board like Google (GOOG). Which call is more valuable to you? It’s the one that has the highest ability to move; in other words, it is the stock with the highest volatility. If you own a call option, you’re not as concerned with the downside risk as you are when holding a stock. If you own a stock, you can make dollar-for-dollar on the upside but also lose dollar-for-dollar on the downside. Put-call parity showed us that when you buy a call option, you are doing the same thing as someone who buys stock and buys a put option. In other words, call options provide downside protection so we are not concerned with the downside in the same way as when you own stock. Likewise, if you own a put option, you are doing the same thing as someone who shorts stock and also buys a call to protect them from the upside risk. Therefore, when you own an option, your maximum loss is limited. What determines the value of the call (or put) is the likeliness for the stock to make large moves – the volatility.

We can mathematically measure the volatility of a stock. The calculation is quite easy, although tedious, but is not really necessary to understand for our purposes. Just be aware that we can measure how far a stock price typically moves from its average. Volatility is typically measured in percents; the bigger the percentage, the more volatile the stock. A high-volatility stock is one that exhibits large price swings throughout the day or over time. Conversely, low-volatility stocks are those whose prices do not move much. The volatility range is not limited to 0 and 100 like many might suspect when dealing in percentages. Most stocks will probably fall in the 15% to 30% categories while 50% and higher would probably constitute a relatively-high-volatility stock. However, ranges can extend into the thousands during unusual circumstances.

One of the exercises in Chapter Two asked you to look up at-the-money quotes for Google and McDonald’s and see which is more expensive and then asked why. If you did that exercise, you found that the options on Google were far more expensive than for McDonald’s. From the brief discussion on volatility in that chapter, you should have realized that Google options are more expensive because the stock is more volatile. Now let’s see if we can gain a better understanding of what we meant. Take a look at Figure 6-1, which shows historic price charts for Google and McDonald’s over the same six-month time frame:

Figure 6-1

Figure 6-1

Think of the pictures as roller coasters. You can see the Google is a much “wilder ride” since there are bigger drops between the peaks and valleys. McDonald’s, on the other hand, had a relatively steady climb and doesn’t exhibit price swings like Google. Another way we can tell that Google is more volatile than McDonald’s over this time period is by the heights of the individual bars. The heights of those bars are determined by the high and low stock prices during the day. It is evident that the bars are much taller for Google than for McDonald’s, on average, and that means Google had much larger price swings during the day. So whether you look at the charts intraday or across time, Google had bigger price fluctuations than McDonald’s and that means we’d expect it to have a higher volatility number. Granted, these two charts are on different scales but they still give a good visual representation of the concept of volatility. If we were to look up actual volatility numbers during this time frame, we’d find that Google had 40% volatility while McDonald’s had 20%, which confirms what we just visually interpreted.

It’s important to understand that high volatility does not necessarily mean better performance. Higher volatility just means that there are larger price fluctuations over the time period; it says nothing about the performance of the stock. In fact, in Figure 6-1, you can see that Google had a low around $360 and a high of about $490 over the time period, or a 36% increase. McDonald’s had a low and high of $34 and $45 respectively, or 32%. So the performances are similar even though the volatilities are vastly different. The higher volatility for Google just means that the movements across the chart exhibited bigger “jumps” than were realized for McDonald’s.

In the same way, the kangaroo game is more volatile than the frog game. This simply means that the sizes of the jumps are much bigger for the kangaroo so there is more potential for upside gains. But this doesn’t necessarily mean that the kangaroo will always win. It is certainly possible for the frog to win. High volatility just means there are bigger fluctuations during the day and across time; it says nothing about performance.

A Simple Pricing Model

The size of the jumps – the volatility – in a stock’s price is the key to determining what an option is worth. In order to gain a better understanding of how volatility affects an options price, let’s make a very simple model and assume that a stock is trading for $50 and that it can only rise or fall by $5 at expiration with equal probability. (To make the calculations simple, we’ll assume there is no cost of carry; that is, interest rates are zero.)

This means that only two final prices are possible, $45 and $55. What is the $50 call option worth? We can figure that out intuitively. Half the time it will be worth $5 (the call has $5 intrinsic value) when the stock ends at $55, and half the time it would be worth nothing when it ends at $45 (the $50 call expires worthless).

Now let’s consider some prices to pay for the call. If you pay $5 for the $50 call then half the time you’ll break even and half the time you’ll lose $5. This means you can’t win but could certainly lose, so $5 is too much to pay for the call. What if you paid $1? In this case, you’d make a $4 profit half the time and lose $1 half the time, which means you’ll make money for sure over the long run. This price is certainly a good deal for you, but that also means you’ll likely get outbid by another trader so it will be too low a price in an actual market.

To be continued…..

Oct

27

Morphing Time Spreads Options Trading Strategy

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Morphing Time Spreads

As you recall, a time spread-also known as a calendar spread-involves a front and an out month. One of the considerations that must be taken into account is what happens when the front month expires? If we were in a long time spread, our front month short call expires and we are left with a naked long call in the out month. If we were long a put time spread, we will also be long a put. What should we do?

We have a few things that we can do. We can leave it as it is. Maybe we think the stock is going to trade down and you might be long the naked put. The reverse might be in play for a long call time spread where the price may be moving up. Either way, you’re naked long this option from the previous month. We must either morph it, hold it or close it out.

If we’re short the time spread, we’re going to have a naked short option remaining and we know that’s unacceptable. According to Ron Ianieri, co-founder of Options University, when we’re short a naked option in our short spread, either short a put or short a call, that position must be addressed on expiration day of that front option.

In the Options Mastery training course offered by the Options University, they use the following example. Let’s say we’ve got a long the May and short the June, a short time spread. On the day that this option expires you must do something to this position and we cannot let this position become naked into the next month. If we’re short a time spread, we must take care of that out month short option on expiration day of the front month.

If you were in a short time spread and are stuck in a naked short put position at the end of the front month expiration, and the stock suddenly plummets, you could be in real trouble. When stocks breakdown, they usually do it in a hurry and can shed points like a dog shaking off water. Before you know it, the stock can lose 50% of its value. If this happens and you have sold a put, you will be assigned and obligated to buy the stock at the strike price, which could be way above the current price. On the other hand, if you are long a time spread, you will be naked long and the worst that can happen is the loss of premium.

To find out all about stock options, contact the Options University at www.optionsuniverstiy.com

Oct

26

Advanced Options Trading – More on Time Spreads

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More on Time Spreads

The Short Time Spread

According to Ron Ianieri, co-founder of the Options University, in situations of high volatility where the straddle might be very expensive, we can look to selling the time spread. We know that with a short time spread we’re short the out month option. That also means we’re short Vega and we’re short volatility sensitivity. If volatility increases and we’re short volatility, we’re going to lose money. Likewise, if volatility decreases and we are short Vega, we’re going to make money. It all depends on where volatility goes.

We also know that we don’t want to be short a time spread and have time go by and nothing going on. Why? Well, we’re long the front month option and Theta is decaying extrinsic value like crazy; indeed, we are going to lose money when nothing happens and time passes when we’re short the time spread. We need movement away from the strike for the short time spread to work.

To reiterate, if you think a stock is going to move but you aren’t sure of which direction and volatility is so high that you’re straddles and strangles aren’t a good alternative because of price, then you might substitute with a short time spread.

Time Spread P & L

The most we can lose in a long time spread is the amount of money we spent to put on the position. At the outset, we have established what the maximum potential loss would be. Because of this fact, we are said to be fully hedged in this position. We know exactly how much we can lose at the absolute very worst scenario.

As far as profits are concerned, because of the two different months, things can get complicated. As both options end at different points in time, it means they are more susceptible to a greater amount of different potential variables. For example, for a long time spread at expiration of that front month, whatever your profit or loss is at that point you are now going to be long a naked call and you will be subject to the risks and rewards of that naked long call for as long as you have it on. That adds into the mix of the risk and rewards; in other words, you know your max losses only when both options are still in play. Once the front month expires, the whole situation changes.

For the short time spread, the situation is different. The most you can make is what you sold the option for. On the risk side of the equation, if that front month expires then we end up with an out month option; a short naked out month option, and we know we don’t like that. Indeed, there is not enough to gain compared to what could be lost.

Because there are two different months involved, when the front month expires we need to take action; the position we’re left with has to be adjusted, closed or moved.

For more on all things stock options, go to www.optionsuniversity.com

Oct

26

Trading Stock Options – Chapter Five Answers

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Chapter Five Answers

1) Which of the following represents a synthetic long call?

d) Long stock + long put

Using the basic formula S + P – C = 0, we can rearrange it to solve for a long call. This can easily be done by simply taking the – C to the other side of the equal sign. Once we do, we see that a long call is synthetically equivalent to long stock plus a long put.

2) The put-call parity formula shows us that an at-the-money call will be priced higher than the at-the-money put. How much higher will the price of the call be?

a) Stock – Pv (E)

The put-call parity formula can be arranged to show that C – P = S – Pv (E). This shows that the difference between a call and put (same strike) is equal to the difference between the stock and present value of the exercise price. In other words, the call will cost more than the put by the interest that could be earned on the exercise price. *explain why doesn’t work with pricing model *

3) A call option’s price can be broken down into three components. The first is the intrinsic value. The second is the cost of carry on the exercise price. What is the third component?

d) Long put

Call options have an implicit put option built into their price. It is this put that gives the call the limited downside risk.

4) Which of the following is a synthetic T-bill (or long bond)?

a) Long stock + long put + short call

The combination of long stock, long put, and a short call behaves just like a T-bill. You will purchase the three assets at a discount from the exercise price and will collect the full exercise price at expiration.

5) Which of the following is a synthetic long put?

c) Short stock + long call

Using the basic formula S + P – C = 0, we can rearrange it to solve for a long put. Since the put is already “+” or long on the left side, we just need to bring the S and C over to the right side of the equal sign and change their signs in the process. The result is P = -S + C, which means that a long put is equal to short stock plus a long call.

6) Which of the following is synthetic long stock?

d) Long call + short put

The formula S + P – C = 0 can be rearranged to solve for long stock. Since the stock is already long on the left side, we just need to bring the P and C over to the right side of the equal sign and we end up with S = C – P. This tells us that the synthetic equivalent to long stock is a long call plus a short put.

7) Which of the following is synthetic short stock?

a) Short call + long put

Once again, we just need to rearrange the formula S + P – C = 0 to solve for short stock, which we can do by moving the S to the right side of the equal sign thus changing its sign to negative. The result is P – C = – S, which means that a long put plus a short call is the synthetic equivalent to a short stock position.

Which of the following is a variation of the put-call parity equation?

a)S + P – C = Pv (E)

9) Which of the following is one of the biggest advantages of the put-call parity equation? It can identify:

c) The most efficient trades

10) When using the put-call parity equation, you will end up with plus and minus signs with each variation. What do these signs represent?

a) Plus = long position, Minus = short position

11) In the put-call parity formula, what does S + P – C equal?

a)The present value of the exercise price

12) Which of the following is the technical name for the three combined position: S + P – C?

a)Conversion

These three positions together make up a conversion, which is a “locked” trade meaning that it has no risk. If the opposite set of transactions were taken (-S, -P, +C) then it is called a “reverse conversion” or reversal.

13) Which of the following is a synthetic short put?

b) Long stock + short call

If you buy stock and sell a call you are doing exactly the same thing as someone who sells (shorts) a put.

14) Which of the following is a synthetic short call?

b) Short stock + short put

If you buy stock and sell a put you are doing exactly the same thing as someone who sells (shorts) a call.

15) Put-call parity shows that call options are really put options and vice versa depending on:

a)How the calls or puts are paired with the underlying stock

16) Any time you see the negative of the present value of the exercise price, – Pv (E), in the put-call parity formula, that represents:

d) Borrowing of funds

If you are short the present value of the exercise price it means that you have borrowed the present value and must repay the exercise price at expiration. It is similar to selling a bond. Bond sellers receive cash up front (borrow money) but must repay the higher face value at maturity (pay back with interest).

17) Before exercising a call early to collect a dividend, you should check the bid of the corresponding (same strike as the call) put. If the bid price is higher than the dividend, you should:

d) Sell the put

By selling the put, you have created a synthetic long stock position, which is effectively what you are doing by exercising the call. However, because the bid of the put is higher than the dividend, you have more money for not taking on any additional risk when compared to exercising the call.

18) Put-call parity can show us why it is not optimal to exercise a call option early. When you exercise a call option early, you are throwing away the value of the:

d) Both a and c

If you exercise a call option early, you are effectively throwing away the interest that could have been earned on your money by paying for the stock too early. In addition, you also throw away the protective value of the put option.

19) Interest rates are 5%. You observe that ABC stock is trading for $20 per share. The one-year, $20 call is $3 and the one-year $20 put is $1. Using put-call parity, what would you expect to happen to the call and put prices?

b) Call prices should fall and put prices rise

This one is tricky. You could borrow money and buy 1,000 shares of stock for $20,000. Then you could sell 10 $20 calls and receive $3,000 and buy 10 $20 puts for $1,000. The net cost to you is $18,000, which you could borrow at 5% thus owing $18,000 * .05 = $900 in interest for a total of $18,900 at the end of one year. However, the position (conversion) is guaranteed to have a value of $20,000 at expiration thus paying back far more money than you own. At these prices, you could create a risk-free money machine. As traders discover this, they will continue to demand conversions thus putting buying pressure on the puts and selling pressure on the calls. This means that the call prices will fall and put prices will rise.

20) Interest rates are 5%. You observe that ABC stock is trading for $20 per share. The one-year $20 put is $1. Using put-call parity, what would you expect to see the one-year $20 call trading for?

a) $1.95

Put-call parity tells us that S + P – C must equal the present value of the exercise price. In this case, a one-year $20 call has a present value of $20/1.05 = $19.05 if interest rates are five percent. We now know that the three-sided package containing S + P – C must be worth $19.05. The stock is worth $20 and the put is $1 so $21 – C = $19.05. We find that the call must be worth $1.95. You should have recognized that answers C and D could not be correct as they are less than the value of the put and we know that the same-strike call must always be more than the put by the cost of carry.

To be continued…..

Oct

25

Trading Stock Options – Chapter Five Questions

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Key Concepts

1) Stock + Put – Present value of the exercise price = Risk-free position (Conversion).

2) The opposite of a Conversion is a Reversal (Short stock – Put + Present Value of the exercise price).

3) The value of a put option equals the time value of the call (above the cost-of-carry).

4) Any synthetic position can be found by solving the formula S + P – C = Present value of E for a single variable.

5) Buying calls is synthetically equivalent to buying stock on margin and buying a put for insurance.

Chapter Five Questions

1) Which of the following represents a synthetic long call?

a) Long stock + short call

b) Short stock + long call

c) Long stock + short put

d) Long stock + long put

2) The put-call parity formula shows us that an at-the-money call will be priced higher than the at-the-money put. How much higher will the price of the call be?

a) Stock – Pv (E)

b) Stock + Pv (E)

c) Stock – call

d) Stock – put

3) A call option’s price can be broken down into three components. The first is the intrinsic value. The second is the cost of carry on the exercise price. What is the third component?

a) Present value of the exercise price

b) Short put

c) Long stock

d) Long put

4) Which of the following is a synthetic T-bill (or long bond)?

a) Long stock + long put + short call

b) Short stock + short put + long call

c) Long stock + long call + long put

d) Short stock + long put + short call

5) Which of the following is a synthetic long put?

a) Long stock + long call

b) Long stock + short call

c) Short stock + long call

d) Short stock + short call

6) Which of the following is synthetic long stock?

a) Short call + long put

b) Long call + short stock

c) Long call + long put

d) Long call + short put

7) Which of the following is synthetic short stock?

a) Short call + long put

b) Long call + short stock

c) Long call + long put

d) Long call + short put

Which of the following is a variation of the put-call parity equation?

a)S + P – C = Pv (E)

b) S + P + C = Pv (E)

c) S – P – C = Pv (E)

d) S – P + C = Pv (E)

9) Which of the following is one of the biggest advantages of the put-call parity equation? It can identify:

a)Guaranteed trades

b) Superior strategies

c) The most efficient trades

d) Market direction

10) When using the put-call parity equation, you will end up with plus and minus signs with each variation. What do these signs represent?

a)Plus = long position, Minus = short position

b) Plus = high probability trade, Minus = low probability trade

c) Plus = market ends up, Minus = market ends down

d) Plus = hedged position, Minus = unhedged position

11) In the put-call parity formula, what does S + P – C equal?

a)The present value of the exercise price

b) The exercise price

c) The future value of the exercise price

d) The present value of the stock price

12) Which of the following is the technical name for the three combined position: S + P – C?

a)Conversion

b) Reversal

c) Parity

d) Arbitrage

13) Which of the following is a synthetic short put?

a) Short call + long put

b) Long stock + short call

c) Long put + short stock

d) Long call + short put

14) Which of the following is a synthetic short call?

a) Short stock + short put

b) Short stock + short call

c) Long put + short stock

d) Long call + short put

15) Put-call parity shows that call options are really put options and vice versa depending on:

a)How the calls or puts are paired with the underlying stock

b) How the calls or puts are exercised

c) The length of time until expiration

d) Any arbitrage opportunities that may exist

16) Anytime you see the negative of the present value of the exercise price, – Pv (E), in the put-call parity formula that represents:

a)Loaning of funds

b) Borrowing stock

c) Shorting stock

d) Borrowing of funds

17) Before exercising a call early to collect a dividend, you should check the bid of the corresponding (same strike as the call) put. If the bid price is higher than the dividend, you should:

a)Exercise the call and short the stock

b) Buy the put and sell the call

c) Buy the put

d) Sell the put

18) Put-call parity can show us why it is not optimal to exercise a call option early. When you exercise a call option early, you are throwing away the value of the:

a)Put option

b) Stock

c) Interest that could be earned on the exercise price

d) Both a and c

a)Call prices should rise and put prices fall

b) Call prices should fall and put prices rise

c) Call prices and put prices should remain the same

d) Call and put prices will both fall

20) Interest rates are 5%. You observe that ABC stock is trading for $20 per share. The one-year, $20 put is $1. Using put-call parity, what would you expect to see the one-year $20 call trading for?

a)$1.95

b) $2.15

c) $0.85

d) $0.75

Answers will be presented in next post.

Oct

25

The Dynamics of a Calendar Spread Options Trading Strategy

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The Dynamics of a Calendar Spread

Time is at the heart of a calendar spread. You see, due to the nature of Theta, as an option approaches expiration date, its extrinsic value goes non linear and starts to plunge as it approaches about 15 days out from expiration.

If we buy a long calendar spread, we will sell the front month and buy the out month.

As the front month approaches its expiration, its extrinsic value burns off much more rapidly than does the out month. As a result, the spread between both options widens.

As the out month extrinsic value is higher, it creates a debit spread and as the front

month decreases faster than the out month, the gap between the prices of both widens. Basically, We’re trying to find a stock that is stagnant, that is trading sideways around the strike and we’re just allowing the natural effects of time decay, of Theta, to make our money for us and to expand the spread between the two options.

Let’s use an example taken from the online Options Mastery Course put on by the Options University. Let’s use this time spread. We’re going to be short the 30 day option and long the 60 day option. In 30 days however, that spread is going to increase and the reason is because of the time decay slope. Our 60 day option for the next 30 days is not going to decrease as much as in the front month. The Theta of that 60 day option is going to be much smaller than the Theta of our 30 day option.

If the front month had a value of $2.00 and the out month had a value of $2.70 (remember, both options are one-to-one and at the same strike price) and the front month expires, it will have a worth of zero whereas the out month might have a value of $2.00. The spread has widened from .70 cents to $2.00. In effect, all we are doing here is trading time.

The reason we use the at-the-money option for this type of trade is because that’s where all the highest time premium and extrinsic value is. Intrinsic value does not decay.

Sound good so far? Well, let’s talk about some of the risks of calendar spreads. The most obvious is if the stock moves away from the strike. If that happens, instead of a widening gap over time, it is going to start to shrink. We know that being long the time spread the last thing we wanted to do was shrink. We are looking for opportunities where the stock is going to stay in a general area.

Spreads are not a standardized contracts as are exchanged traded put and calls and there is NO spread market. As a result, the "market" cannot be "held" to a price. Additionally, spreads are executed at the discretion of a market maker and may require more time to fill. There are other technical ramifications of trading spreads and it is suggested that all spread investors be familiar with the differences between a spread and a legged spread position.

For information on all levels of stock options, courses in options, mentoring and trade shadowing, contact the options university at www.optionsuniversity.com

Oct

24

Creating a Call Option

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Creating a Call Option

Synthetic options provide tremendous insights into the role of options in the marketplace. Assume you wish to buy a stock but are either afraid to because of the recent volatility or simply because you do not have enough money. So rather than buy the stock, you decide to buy a call option.

When your order is received, the market maker must create a call option. Remember, call options are simply contracts between two people; they do not exist in actual form such as shares of stock. In order to create that long call, the market maker must buy stock and buy a put, which is a synthetic long call. He can then transfer that over to you buy selling the call. Note what these actions by the market maker create:

Market maker buys stock

Market maker buys the put

Market maker sells you the call

Hopefully you remember these three actions – long stock, long put, short call – as a conversion, which is a risk-free, or “locked” trade. Because you did not want to take the risk of holding the stock, the market maker bought the stock for you and then bought a put to protect that downside risk. Doing so, he created a synthetic call. When he sells you the call, he has effectively transferred the long stock plus long put positions over to you.

So the reason you were able to buy a call is because the market maker was able to buy a put. The person who sold him that put must be willing to buy the stock (that’s the obligation of the short put). By purchasing the call, you have the right to buy the stock. This means that the market maker has a guaranteed sale of stock at expiration.

If the stock’s price is above the strike price, he will be assigned and required to sell the stock. If the stock’s price is below the strike, he will exercise his put and sell the stock. The market maker is fully protected from any adverse movements in the stock’s price. Notice that the option’s market created a sale of stock (to the market maker) when nobody wanted to buy it at that point in time. It was only because of the option’s market that stock was traded.

The options market creates more buyers of stock. If you buy a call option, somebody else is buying stock. The options market just creates an easy way to “find” these other people. If you want to buy a call, all you have to do is look at the quote board and see if the price is right. If you buy it, somebody somewhere in the world must be taking the other side of the trade and you will never know who that person is.

Are Options Bad for the Market?

Put-call parity provides powerful insights for option traders. Despite this quality, there is perhaps a bigger problem that it solves. That is, put-call parity formula can shed some light on one of the most polarizing debates in finance: Are options bad for the market? One group adamantly says yes; the other says no with equal conviction. Can put-call parity help solve the debate?

There are many investors who adamantly refuse to buy or sell options because they hear how “speculative” they are. They insist on holding only stocks. However, if you refuse to use options, you are speculating. Options were created as hedging tools or as a way to decrease risk. Whenever you hedge your long stock, perhaps by purchasing a put or selling a call, you give up some upside profits in exchange for some downside protection. So if you buy stock and refuse to buy or sell options, you are speculating that nothing will go wrong with your long stock position. You are willing to hold out for more profit at the expense of downside exposure to a price of zero. It can be argued that investors who don’t use options are among the most speculative of all! However, if you’re still in doubt, would you believe that stock can be viewed as an option?

Valuing Corporate Securities as Options

Advanced option traders know to consult with an option pricing model of some kind before entering a trade. We’ll talk more about option pricing models and why we use them in Chapter Six. For now, just understand the most famous of pricing models is the Black-Scholes Option Pricing Model developed by Fisher Black and Myron Scholes. When Black and Scholes developed this option pricing model, they were certain there were many uses for it other than just valuing call options. One of the uses they suggested was in valuing corporate securities.

Consider a firm that has issued one zero-coupon bond that matures to a value of $1,000,000 in five years. A zero-coupon bond just means that the corporation doesn’t make quarterly payments; instead, they make one lump-sum payment of 1,000,000 in five years. In exchange, they receive less money than the 1,000,000 face value. With this money, the firm produces products and hopes to have a value in excess of this $1,000,000 in five years and pay off its debt, leaving the stockholders with whatever remains in value. However, if the firm’s value is less than $1,000,000 at maturity of the bond, the stockholders will simply turn over the assets to the bondholders and will be free of further liability.

Let’s look at the payoffs for stockholders and bondholders at maturity:

If the value of the firm is less than $1,000,000, say, $800,000:

Bondholders get: $800,000
Stockholders get: $0

Total value of firm = $800,000

If the value of the firm is greater than $1,000,000, say $1,200,000 at maturity:

Bondholders get: $1,000,000
Stockholders get: $200,000

Total value of firm is $1,200,000

We see with the above payoffs that the total value of the firm is partitioned between the stockholders and bondholders. Notice how the stockholders get nothing at expiration if the value of the firm is below the value of the matured debt. But if the value of the firm is greater than the matured debt, stockholders receive the excess value.

Now compare this bondholder and stockholder relationship to options. Assume you own 100 shares of stock and have sold, or written, a $100 call option against it. This means that you have been paid for the potential obligation to sell your shares. (If this sounds like a nice arrangement, it is a strategy called the “covered call” and we’ll talk much more about it in Chapter Seven.)

At expiration, if the value of the stock is less than $100, say $80:

You get: $80
Call buyer gets: $0

Total value of your position is $80

In other words, if the value of the stock is below the strike at expiration, you end up holding the stock at its current value of $80. The long call owner receives nothing since it expires worthless.

However, if the value of the stock is greater than $100, say $120 at expiration:

You get: $100
Call buyer gets: $20

Total value of positions is $120

If the value of the stock is above the strike at expiration, you will be assigned and receive the $100 strike price; that’s the most you will ever receive. The call owners will receive the stock and pay the strike for a value of the stock price minus the strike price. The call owners, in this case, receive what’s left over after you have been paid. If you look closely, you will see that the payoff for the call option above exactly resembles the payoffs to the stockholders for the corporation discussed earlier.

Using the Black-Scholes Model

Recall the put-call parity formula:

Stock + Put – Call = Present value of the exercise price

We can rewrite this for the above corporation as:

Stock + Put – Call = Present value of the debt

Which can be rewritten at maturity as:

Stock + Put – Call = Total value of debt

Stock – Call = Total value of debt – Put

So the Black-Scholes Option Pricing Model tells us the value of the covered call position (left side of equation) is equal to the debt at maturity with a put written against it (right side of equation).

This means the bondholders have, in essence, written a put against the firm. In other words, if the value of the firm is less than the debt that is due at maturity, the stockholders "put" the firm back to the bondholders and walk away losing only what you paid for the stock – just as when you buy a call option. The value of this “put” is part of what gives your stock its value.

If you like owning stocks for this reason then there’s no reason you should feel that options are bad for the market. In fact, Pricing Principle #5 from Chapter Two showed that the price of an option with a zero strike price and an unlimited time to expiration would equal the price of the stock. Options allow you to do what stockholders have always done – but for a lot less money. Why? Because they have strike prices. They allow you to partition the unlimited range of possible stock prices into segments that you wish to control. Options can also be used to create downside hedges in exchange for upside profits. Because of these uses, investors can create better risk-reward profiles that are simply not possible with stock alone.

To be continued…..

Oct

24

Calendar Spreads Options Trading Strategy

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Calendar Spreads

Floor traders used to call calendar spreads, “Time spreads”. The reason calendar spreads are also called time spreads is that they try to take advantage of the non linear decay of Theta- also known as time decay. What we are trying to take advantage of is the passage of time with two options decaying at different rates.

Construction

Long

The most popular way people set up time spreads is a long time spread where we will be long an outer month option and short a nearer term option of the same strike in a one to one ratio. This is a premium collection strategy. For example we might be long the May $25 call and short the April $25 call, or long the June $70 put and short the May $70 put. We’re always trying to be long the out month option and short the nearer term option.

This trade is done most of the time at-the-money. The reason for that is because that is where the biggest amount of premium is; that’s where all that big fat extrinsic value is. It’s obvious when you think about it; one more little step and it moves from at to in-the-money where parity and intrinsic value starts to kick in.

It doesn’t matter if we want to do a call spread or a put spread, we are looking at selling the front month option, buying the out month option and as close to at-the-money as possible. Our strategy is to take advantage of the front month’s more rapid rate of decay.

Short

Where the long function described above is really a premium collection strategy trying to take advantage of a stock that’s either consolidating or stagnating and trading sideways, the short time spread is a little different. Obviously it is the opposite of the long time spread.

With a short time spread, we’re going to be short the out month option and long the nearer term option. Of course, we use the same strike and in a one to one ratio. So, why would somebody do that type of trade?

As a matter of fact, the short time spread trades very much like a straddle. According to Ron Ianieri, co-founder of the Options University, if we sold a time spread and the stock started moving away from the strike, in either direction away from the strike, we would profit, much like a long straddle. The difference here is that with the long straddle we have an unlimited potential reward. With the short calendar spread, that is not true. We have a limited potential reward but we have that limited potential reward as the stock moves in either direction away from the strike and you’ll find it to be a much cheaper way to play a non-specific directional trade.

For all things stock option, go to www.optionsuniversity.com

Oct

23

How to Create a Synthetic Short Stock Position

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Synthetic Short Stock

If synthetic stock is just a long call plus a short put what would synthetic short stock be? Once again, all we have to do is change the signs of our previous answer and find out that a long put plus a short call will behave just like a short stock position. This is great to know for all traders involved in short selling. With synthetic options, it is now possible to short stock without an uptick or when stock is not even available for shorting.

Question

You wish to short a stock, which is trading for $100. Your broker informs you that the stock is not marginable and therefore cannot be shorted. How can you effectively enter a short sale?

Answer

Enter a synthetic short by selling the $100 call and buying the $100 put.

How much will it cost to enter an at-the-money synthetic short stock trade? Think back to put-call parity. One variation was:

C – P = S – Present value E

This tells us that if we buy the call and sell the put (left side) it should be worth the difference between the stock price and present value of the exercise price (right side). Because we are doing the reverse and buying the put and selling the call, the transaction should result in a slight credit.

Realistically though, because of bid-ask spreads and commissions, the trade may result in a slight debit. Regardless, it will not be a major cash outlay to enter this position (please keep in mind that there will be significant margin requirements to do so). However, they should not exceed (and will usually be much less) than the 150% Reg T margin required to short a stock. So not only can synthetics allow trades that otherwise cannot be done, they usually allow it to be done in a more efficient way by requiring less capital to take the same position.

Example: Figure 5-16 shows a chart of the S&P 100 (OEX). Between May 17 and June 3, 2002 (the area to the right of the dotted vertical line), the OEX took another. While there is usually no way to short the OEX index through the stock market, you could have done it synthetically in the options market.

Figure 5-16

Figure 5-16

On May 17, the index was trading at 550 and the 550 calls were $13.00 with the 550 puts at $11.80. As we showed earlier, an at-the-money synthetic short will usually result in a slight credit, which was the case here. Selling 20 calls and buying 20 puts would result in a net credit of 20 contracts * 100 * $1.20 credit = $2,400. Just 17 days later, at the close of the trading, the puts were worth $38.20 and the calls 0.80. The synthetic short position could have been closed out for a credit of $37.40 * 20 * 100 = $74,800. For no money down (in fact, a credit of $2,400) you could capture a $70,000 profit in a relatively short time. Of course, this trade does not come without risk. The risk is that the index traded higher, which would have left you with an equally big loss if the index had risen by the same amount. We’re just trying to show that synthetics allow you to initiate positions that others will tell you cannot be done. The more agile and efficient you are at establishing positions, the better trader and investor you will become. Synthetics give you those abilities.

Added Insights into Synthetics

All combinations of synthetics can be created by Formula 5-15 which is:

S + P – C = 0

Now that you understand synthetics, it is easier to see why the formula works. Assume you are long stock and also have another asset in your portfolio. You don’t know what this asset is but you are told that it makes your long stock position risk free. What does that tell you about the other asset? If you have no risk, then the other assets must be short stock. If you are long stock and short stock, then you are effectively flat and have no risk. Now think about our synthetic formula. If you are long stock and have other assets (shown by the box) and are also told that you have no risk then the boxed assets (long put + short call) must be equal to short stock and that’s exactly what we found out.

S + P – C = 0

To find any synthetic equivalent, all you need to do is isolate the variable(s) you’re trying to solve for and the answer will be immediately visible. Let’s try another. If you want to find out the synthetic equivalent to a long put, just isolate that +P position:

S + P – C = 0

If that long put is paired with other assets so that it has no risk, then the other assets must be equal to a short put. This immediately shows that long stock plus a short call must be equal to a short put.

It turns out that no matter which asset you pick, the other two are the synthetic opposite and fully hedge the risk. It should make sense, then, that we could also pick any two assets and know that the third will fully hedge those two.

All Combinations of Synthetics

It is great practice to run through Formula 5-15 and figure out the various combinations of synthetic trades. If you are really motivated, try to draw the corresponding profit and loss diagrams. All of the combinations are listed below for your reference. Note that the short positions are exactly the opposite of the long positions.

Asset	Synthetic Equivalent
Long stock	Long call + Short put
Short stock	Short call + Long put
Long call	Long stock + Long put
Short call	Short stock + Short put
Long put	Short stock + Long call
Short put	Long stock + Short call

Synthetic trades may seem complex at first but, in reality, are actually quite simple. Many think they are a needless academic exercise and of no practical use but nothing could be further from the truth. If you plan to actively trade options, it is crucial to understand synthetics. Market makers make their living with the put-call parity relationship so don’t think it’s a waste of your time to gain a basic understanding. A little time invested will make option investing worth your time.

All combinations of synthetic positions are derived from the put-call parity equation.

Real Applications for Synthetics

Are synthetics really useful? In Chapter Four we found that it is never advantageous to exercise a call option early except to collect a dividend. When you exercise a call option, you give up the rights with the call option in exchange for the stock. If you exercise a call to gain the stock, you are holding all of the downside risk of the stock in exchange for collecting the dividend. Now that you understand synthetics, we can perhaps find a better way to do this. When you are long the call, rather than exercising it, you could, instead, sell the same strike put. This creates a synthetic long stock position (since you are long the call and short the put), which is effectively the same position you were going to have if you exercised the call. While the synthetic long stock position does not allow you to collect the dividend, it does let you collect the premium of the put. In many cases, this put premium will be of greater value than the dividend on the stock while either choice exposes you to the same downside risk. In addition, by choosing the synthetic long call position, you can hold onto the exercise value of the cash a little longer to earn interest. In other words, if you choose to exercise the call, you must pay for the stock today.

By entering the synthetic long stock position, you will end up buying the stock at the same price but at a later date. Why? For the synthetic long stock position, you are long the call and short the put. If the stock price is above the strike at expiration, you will exercise the call and buy the stock for the exercise price. If the stock’s price is below the strike, you will be assigned on the put and buy the stock for the strike price. No matter where the stock’s price is at expiration, you will pay the strike price and receive the stock, which is exactly what you would have done had you exercised the call only at a later date. This allows you to hold onto the cash for a longer period of time to earn interest. As long as the put premium plus interest earned exceeds the value of the dividend, you are better off with the synthetic long stock position. This means that it may still be advantageous to use the synthetic stock strategy even if the put premium is less than the dividend. You must compare the put premium plus interest earned to the dividend. Only when the dividend exceeds the value of the put plus interest should you exercise the call for the dividend. Please keep in mind that we are not saying that you should always capture either the dividend or put premium. In many cases, neither choice may warrant holding all of the downside risk of the stock whether synthetically or not.We just mean that if you have decided it is worthwhile, then you should consider the synthetic long stock version before exercising the call.

The mathematics behind put-call parity work no matter how you may choose to attack a particular problem. For example, we could have solved the problem of early exercise by considering what would happen if you actually exercised the call to get the dividend. If you exercise the call, you are buying stock and effectively selling your call. If you buy stock and sell a call, what have you done synthetically? You have sold a put. Different investors and traders see synthetics in different ways. But no matter how you view them, you’ll arrive at the same answer as long as you are properly applying the put-call parity formula.

To be continued…..

Oct

23

Advanced Options Trading – Some Vertical Spread Morphs

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Some Vertical Spread Morphs

Let’s say you are long a call spread. The stock suddenly starts trading down and the next thing you know it’s now breaking down and you’re definitely in the wrong position. Here is a simple morph for this situations.

All you need to do is buy the put of the strike that’s corresponding to your short call. If you’re short the June $65 call, you buy the June $65 put. That creates a synthetic short stock position at $65. You haven’t sold anything.

If you are bearish and things start moving up and you are long the put spread; the stock starts to trade up. If you bought the call, you’d be long call and short put at the $60 strike. That makes you long synthetic stock; you are long synthetic stock and long the actual put. Long stock and long put equals long call with the stock now breaking out to the up side.

Let’s go over that one more time. You are long a put spread and expect the stock to go down. But, it turns on you and now you are in the wrong position and want to morph into a long position.

I think the sock is going down

Long Put Spread	Put
Long	$ 65
Short	$ 60

Oops. Its going the other way. Wait for me!

Morph to Synthetic Long	Put	Call
Long	$65	$60
Short	$60	Synthetic long stock

Long stock and long put equals long call

Genrally, for debit call and put vertical spreads, if things go against you, look at the short option, go to its counterpart and buy it. That works for either a debit call spread or a debit put spread.

To recap:

If we’re in the right direction but we want to get more in the right direction, buy back the short option.
If we’re in the wrong direction and we need to spin the position around, we go to where the short option is and buy the corresponding option.

For all things stock options, go to www.optionsuniversity.com

Oct

22

The Box and Trading the Vertical Spread Options Trading Strategy

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The Box and Trading the Vertical Spread

The first thing we need to do is find the charting patterns. Are we looking at an up trading or a down trading stock? What is our anticipation of the stock movement? If we think it’s going to go up, we’re going to enter into a bull spread. We ‘re either going to buy the call spread or sell the put spread.

To help us decide which strategy is the best, we are going to base that decision on “the box”.

To do that, we are going to add the call spread and its corresponding put spread together and come up with the difference between the two strikes. If we find that we are below that difference, then we want to be a buyer of the call spread. If we are above, then we want to be the seller of the put spread.

For example, if the chart displays that the stock is heading down, we would normally want to get into a bear spread; we would either want to buy the put spread or sell the call spread. At this point, we look to the box to decide which one we would want to do. We want to add the two corresponding spreads together and subtract the result from the spread between strikes-in this case $5. If the result of the difference is below $5, we would want to be a buyer of a put spread or seller of a call spread.

Remember, we know that the value of the two of them has to equal the difference between the two strikes. If we have a call spread trading for $3, its corresponding put spread must be trading for $2 and we’re assuming a $5 box, a $5 difference between the two strikes. Whenever these boxes add up to below the strike spread, we want to do the debit side, no matter if it’s a call spread or a put spread, bull spread or bear spread, it doesn’t matter. If it adds up below, we do the debit side.

The nice thing about a vertical spread is it has a limited loss and a limited gain and it makes or loses money in a pretty tight range. There is not a lot of adjusting to be made. However, according to Ron Ianieri, co-founder of the Options University,” there are a couple of real easy morphs that we can do to take advantage of a changing environment while we’re in a vertical spread”.

Morphing is actually the changing of strategy and not shutting down one trade and reopening another. Let’s look at a couple of easy morphs we can do out of the debit spread.

Let’s assume a long vertical call spread. We buy the June $60s and sell the June $65s; we’re expecting the stock to trade up. Suddenly the stock breaks out of its range. It’s now a break out; the stock is no longer going to trade up a little bit, it’s going to fly and here we are in our vertical spread and we’ve got a limited up side because we sold the $65s. To remove our cap, we simply buy the short option back, which makes us totally long and clears the way on the upside. It also works the same way with a put spread if we have a debit put spread on and the stock is trading down.

For more on all things stock option, go to www.optionsuniversity.com

Oct

22

How to Create Synthetic Call Positions

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To find the synthetic version of any of these three assets, all we need to do is reference Formula 5-15 for the answer.

To start, we need to get the asset that we’re trying to replicate (either the stock, put, or call) by itself and with the correct sign. Let’s stick with our same example and find the synthetic equivalent value of a long but this time we’ll use Formula 5-15. To do so, we need to get a +C (remember, we are using “+” to denote a long position) on one side of the equation. Using some basic algebra, if we add C to both sides of the equation we get: S + P = C and there’s the answer; long stock plus long put (left side of the equation) will behave just like a long call (right side of equation). Therefore, if you hold long stock and a long put, you have a synthetic call position.

insert fig61-1

According to Formula 5-15, an investor who owns stock and a put will share the same profit and loss diagram as one who is long a call. Remember, this does not mean that both investors will have the same portfolio values since we’re not accounting for the borrowed funds. But the two portfolios should respond the same way to stock price changes at expiration. Let’s assume one investor buys stock plus a $50 put for $5 while another buys a $50 call for $5 and check the profit and loss diagrams to see if we’re correct:

insert fig61-2

As you can see, there is no difference between long stock + long $50 put purchased at $5 (left chart) and the long $50 call purchased at $5 (right chart). The person holding the long stock and long put raised the cost basis of his stock from $50 to $55; that’s why his breakeven point is now $55. However, he still participates 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 he paid for the put; therefore the maximum loss is $5.

For the call holder (right chart), he paid $5 so his maximum loss is also $5 but he too participates 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, since he has the right to buy stock at $50 but paid $5 for that right. This makes his breakeven price $55 as well.

We can use this information to gain some trading advantages. For example, most firms do not allow investors to buy call options in their IRA (Individual Retirement Account) but now you know that it can be done in a roundabout way with synthetics. You simply buy the stock and put, and you are effectively long a call option. Now, your return on investment will be much lower using long stock plus a long put as compared to the person who buys only the call. This is due to the difference in capital required to purchase the stock, but the two positions will behave the same in terms of net gains or losses at expiration.

Synthetics are useful for understanding option-pricing behavior as well. In Chapter Two we showed that out-of-the-money options respond slower to changes in stock prices because of the number of zeros used in the averaging process. Synthetics can show us another view as well. Assume that a stock is trading for $100. We can create an out-of-the-money call, such as the $105 strike, by purchasing the stock for $100 and also buying the $105 put. Remember that the “bend” in any profit and loss diagram occurs at the strike price, so a long stock position plus a $105 put will look exactly like a $105 call in a profit and loss diagram. As the stock rises from $100 toward $105, the long stock position will obviously make dollar-for-dollar. However, the long $105 put is losing intrinsic value nearly dollar-for-dollar up to the $105 stock price. The net result is that the long stock and long put positions nearly cancel each other out, and there is no change in value.

In other words, the long stock plus long $105 put combination will hardly budge in value as the stock climbs toward $105. But once the stock price rises above $105, then the put has no more intrinsic value to lose but only some time value. The stock, on the other hand, continues to increase dollar-for-dollar and the long stock plus long $105 put combination now starts to increase in value if the stock continues to climb above $105. This is exactly how a long $105 call would behave. The next time you’re tempted to buy an out-of-the-money call because it’s cheap, think about synthetics. If you’re really bullish and want to buy the stock, would you buy an in-the-money put (that’s going to lose dollar-for-dollar) to protect it? If not, then think twice about that out-of-the-money call because it is the same thing.

Using Formula 5-15, we can figure out any synthetic position. Notice that there are only three assets in the equation – stock, puts, and calls. A very simple property of synthetics is that the synthetic equivalent of any one asset will be some combination of the other two. In other words, stock can be formed by some combination of puts and calls. Calls can be replicated by some combination of stock and puts. The synthetic equivalent will never include the asset you’re trying to replicate. For example, a synthetic long call will not include a call option in the answer. If you come up with that, a mistake has been made. The only thing left now is to figure out whether those combinations are long or short, and that’s where Formula 5-15 helps.

Now that you have Formula 5-15, let’s work through some examples to see how to figure out – and understand – synthetic options.

Synthetic Long Stock

Can we use the basic put-call parity formula (Formula 5-15) to see if there’s a way to own stock synthetically? Without looking ahead, see if you can use the equation S + P – C = 0 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, which changes their signs. Once we do, you will find that S = C – P. This tells us that a trader holding a long call and short put (right side of equation) is doing the same thing as someone holding stock (left side). That is, a long call plus a short put is synthetically equivalent to long stock.

Let’s check the profit and loss diagrams for each and see if we’re correct:

insert fig61-3

Again, we see there is no difference between 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 is 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. Many traders wonder how these two positions can be exactly the same. Isn’t there some time premium on the call option and doesn’t that change the profit and loss diagrams? Refer back to Figure 5-10, which is reprinted below:

insert fig61-4

This showed that the time value of the call (over the cost-of-carry) is equal to the value of the put. If you buy the call and sell the put, you have eliminated the entire time premium in the call.

Another way to understand why the long call plus short put combination is equal to long stock is to think back to our lesson on the deltas of calls and puts. We determined that the absolute delta values must sum to one. If the call delta is 60, then the put delta is -40. So if you bought this call and sold the put, you are long 60 deltas and short 40 deltas, or +60 – (-40) = 100 deltas. The delta of stock is always 100 since it always gains and loses point-for-point with itself. Buying a call and selling a put is exactly the same thing as owning stock from a profit and loss standpoint. Of course, it is much different on a leveraged basis since we are not accounting for the cost of carry since we ignore the Pv (E) from our original put-call parity equation. In an earlier section, we mentioned that Gordon Gekko would have done much better had he purchased the calls and sold the puts. Now you see why; he would have been holding synthetic long stock.

To be continued………….

Oct

21

Advanced Options Trading – Introduction to The Box

Filed Under Advanced Options Trading | Leave a Comment

Introduction to The Box

Vertical spreads used in combination create something called a “box”. Normally, a box is composed of a long call spread and a long put spread or a short call spread and a short put spread.

The value of the two spread positions in a box is equal to the difference between the two strikes. For example, if you have a call spread trading for $3 and a corresponding put spread, it must be trading for $2 assuming a box of $5, the difference between the strikes. This means the value of the call spread plus the value of the put spread have to equal the difference between the two strikes, in this case $5.

If we bought both a call spread and its corresponding put spread, one is going to make money in one direction while the other is going to lose the same amount of money at the same rate; remember they are corresponding options. So who would want to do that? It appears to be a no win situation; a wash.

The answer is that we don’t have to buy and sell both spreads.

In the example we’re using, the call spread is worth $3 ant the corresponding put is worth $2. But what if the put spread is actually selling for $1.90? But its not supposed to do that; it should always be worth $2 if the spread between strikes is $5. What happened? Instead of the total price of both spreads equaling the difference in strike price, in this case $5, it is really selling for $4.90.

It usually means that one of the spreads is too cheap. If you see that the combination price is below the difference in strike price, you want to buy the call spread. Why?

The market will adjust one of the two spreads up 10 cents. You don’t know which spread but if the price will be raised, its best to be long the call. If the put is adjusted, it will have no effect. But if you are long the put and that is adjusted upward, you would be losing money.

Box Secrets

The Box is an arbitrage play where the market is out of kilter for a short time and an opportunity presents itself to profit when the proper adjustment is made. At options University, they teach how to best choose which spread will be adjusted; there is a definite need for nimbleness, but the opportunities do present themselves.

Suppose you are long a May 25 call, short a May 30 call and long a May 30 put, short a May 25 put. Looking at it a little differently, you are long a May 25 call and short a May 25 put. This is the synthetic representation of a long stock position. You are also short a May 30 call and long a May 30 put: this is a synthetic short stock. You are in exactly the same position as if you were long stock and short stock.

So, what you have is a synthetic long stock at $25 (long May25 call and short the May25 put). You are also short stock at $30 (short May30 call, long May 30 put). Long stock at $25, short stock at $30 what is the value? $5. Thus our long box created by being long the call spread and long the corresponding put spread simultaneously is going to be worth $5 and it’s an arbitrage if you paid less than the $5 value. This is an example of a long box and the short box works exactly the same way.

For more on all things stock option, go to www.optionsuniversity.com

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