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Oct
31
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 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
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)
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
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)
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
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
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
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)
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)
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)
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
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
Chapter Six
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:
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:
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
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
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
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
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 sh