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Options Trading Math 101

Hey everyone, this is Kirk, here again at, where we show you how to make smarter trades. And today, we’ve got an awesome video tutorial for you: Breaking down trading math, and specifically, options trading math. And it’s basically a 101 course on why we have the methodologies that we do about the markets and about trading. So, welcome back to statistics class. And you’re probably thinking, “Oh..” But don’t worry. Undoubtedly, more important than understanding the Black Scholes model for pricing which we purposely don’t cover in any video tutorial that we have because it’s pointless to cover, you don’t need to know it to be successful. But besides that, your ability to understand just basic statistics and probabilities is paramount to your ability to be successful in this business. So, if you don’t get the math behind the trades, here’s my promise to you: You will fail at trading options long-term if you don’t understand the math behind it, and more importantly, the statistics and the probabilities behind it. You can make a couple of trades here and there and be successful. But to do this long-term, to generate consistent monthly income long-term, you’ve got to understand the math.

So, swallow your pride, head back to school with us as we talk in depth about standard deviations, probabilities, and statistics in this advanced tutorial. But before we do that, let’s first have a talk about one real quick thing, and that’s market efficiency. So, this whole idea about market efficiency is really important, and you probably heard us talk about it in the other videos that we have to trade liquid products and liquid underlying stocks. But this whole idea of market efficiency is this concept that the markets are super-efficient, and especially in the US markets where there are millions and millions of different market participants, all with their own individual ideas. The markets are incredibly efficient and incredibly fast. Data or information that anybody receives on a stock or a company is immediately priced into the market. And as a guy who’s been on both sides of the Chinese wall, basically, I was an M&A analyst in New York for Deutsche Bank, and so, I was on the private side, dealing with mergers and acquisitions. And then, I was on the other side of the Chinese wall in Tysons in DC and dealing with the retail side as an analyst.

So, I’ve been on both sides of the wall, and I can definitely tell you, the markets are incredibly efficient. There’s no edge that you can get a knowing information about a company in advance or having some sort of insider knowledge. In most cases, most CEO’s have no clue where their stock is going to go or how it’s going to react to the market, regardless of how well they think they might be doing. So, to that end, we have to understand that. As we said before, we have no clue where a stock is going to go. And nobody else does either. Myself included, I have no idea where a stock is going to go in the future. I might have an assumption, an opinion. But at the end of the day, we’re all no better than 50/50 on our guesses. So, what this leads to then is to this probability distribution. And what we call a normal distribution or you probably have seen before as a bell curve. Now, this is really important because this is how distributed, or this is how a efficient market distributes its returns.

So, basically, what you have here is you have most of the returns are probably somewhere around even or par. And that’s basically what this kind of zero line here is. But it’s saying that most of the time, the distribution of returns will be within a certain confidence range or within about one standard deviation. This is what this one standard deviation is that I’m kind of highlighting here on the chart. So, this is saying that 34.1% of the time up, and 34.1% of the time down, we might see this confidence within this given range. And we can define that range in stocks, in every particular stock that we look at. And we’ll show that to you later on here. But you just have to understand that when a market has normal movements and an efficient movement, it’s going to have a normal distribution of returns. Now, this means that most stocks are going to kind of land inside of that normal distribution. Sure, you’re going to have the stocks that go outside of that distribution, so they make a three standard deviation move, so whatever most stocks are doing, they do three times that move.

These are going to be stocks that are really high flyers, right? The one in a million stock that goes from $5 to $500 or whatever the case is. And then of course, you’re also going to have stocks that make a three standard deviation move to the downside. So, these are going to be your stocks that go from $100 down to $10. It’s the one in a million chance that the stock goes bankrupt or the company goes bankrupt, whatever the case is. Remember, this is a normal efficient market, so most of the time, stocks are going to return some sort of normal average in the middle. And that bulk average here is what we’re working for when we start to place trades, just understanding that this is how a stock is distributed. Now, when we look at the same graph and kind of tilt it on its side here, we can see that this same concept applies to a stock distribution of its price movement over time. So, I’ll say that again. The same distribution will apply to a particular stock’s price movement, going forward in the future. So, what I always like to do is I always like to say, “Okay, at certain points in the future..” And let’s just draw a line down here and say, “Okay, at this point in the future versus this point in the future, we can estimate based on the entire trading history of the stock going back in time, how likely the stock is to rally or fall within a given range.” Again, we can use the data from the stock going back all the way to its beginning, as much data as we have on that stock, to automatically and accurately calculate how far the stock is likely to move in a given range by a certain date.

So, in this case, if we’re looking at this stock which is just the S&P at some point in the future that we’ve taken this chart, then you can see that by the time that we reached this date or this line here, this expiration date, as a stock is trading, it might end up trading somewhere in this range, okay? And that’s a good likelihood of happening because the stock doesn’t have that much time. And so, based on its entire trading history, it’s not likely to make a move all the way up here or all the way down here, given such a short time period.

So, we know we can calculate that. As we go further out in time, the stock is likely to make more of a volatile move. So, it’s as more time here – And so, you can see it can widen out its breath of movement. And again, that’s true because as you can see, going forward here on the S&P, the longer we went in timeframe, the more the stock could move over time. And so, that happens here too. And again, just continuing now into the future, you can see the stock can then really move as we start to go further and further out on the expiration cycle. So, this same type of distribution can then be applied to where the stock moves over time. Now, most of the time, the stock is going to move with the inside of this one standard deviation movement.

And this one standard deviation movement is about 68% of the time. Now, we can exactly calculate this probability inside of most broker platforms. So, I’m going to show you how we do it at the end of this video. But again, just trust me that this one standard deviation move is about 68% of the time. And so, it’s really, really helpful to understand where a stock might move 68% of the time because then, we can build a strategy around that movement or take advantage of that possible movement, and this is how we get to high probability trading. Now, as we go forward, let’s first do a quick review of volatility because all of this normal distribution and stock distribution stuff has a hinge, and that hinge is a volatility, and volatility in option pricing. So, let’s take two stocks in this example. Both stock start out at the same price which is $100. So, in this case, stock A is the stock that’s in black on this chart. And you can see it has very little volatility which means that it moves more or less right around $100, give or take maybe $5 or $10 in the opposite direction.

So, it’s moving very, very slowly around $100. It has low volatility. The frequency and the magnitude of its moves are very small. Compare that to stock B which is going to be the stock that’s in blue. You can see they both start out and end at the same price, but stock B has much higher and much more volatile moves in its price as it gets to that average of $100. So, you can say that stock B which is again, the one here in the blue, has higher implied volatility than stock A. Again, stock A which is the one here in black, lower implied volatility, still the same stock, still around $100. It’s just the level of movement or the frequency of movement that that stock makes. Now, this drives us to our next topic which is Implied Volatility. Now, implied volatility is basically an expectation of where the stock might move in the future. And depending on how volatile or not a stock is, that will cause option pricing to increase or decrease as a result to compensate for that implied volatility.

So, we take our normal distribution graph which is really the one here in blue. This is that one from one of the other screens. So, again, just a normal distribution or kind of average volatility in the market. You might see the stock have a range of between here and here, right? So, the two extremes with again, something around the median or the mean as far as its distribution going out into the future. Now, if implied volatility for that stock is a lot lower – So, remember option A or stock A from the slide before? That black line that was kind of hovering around $100? If implied volatility is a lot lower, then that creates this distribution graph to get taller and skinnier, and that’s this red graph here. And so, you can see that it still has a normal distribution, but it’s much more centered on the stock making very small movements out into the future. So, instead of movements all the way out here, now the extreme movements or the kind of three standard deviation moves are much, much closer to the mean of the stock.

Again, our standard deviations have moved in from a further out area. So, the implied volatility in the stock is lower, and that means that the likely range of the stock going forward is going to be much smaller. It’s not going to have the greatest magnitude of movement. Now, if we have a stock that has implied volatility that’s extremely high. So, it’s making a lot of jagged and very quick moves like that stock we looked at in the slide before, that blue line. It’s all over the place, still centered around $100, but all over the place. And what that does is that slams down this distribution graph and it makes it much shorter and fatter. And so, this distribution graph looks like this. It’s much more distributed this way. It’s very flat, very wide graph. And you can see because it’s very volatile, the stock can rally really high.

It can go that high or it can go that low. Now, most of it is going to be around some sort of average or mean, but you’ll notice that the average and mean has expanded. And now, 68% of the time, it trades within this range which is all the way out towards the end of its shading. So, 68% of the time in high implied volatility, the range of the stock is much lower. Compare this with 68% of the time when implied volatility is low. It’s going to have a much shorter or narrow window to trade within.

So, you can see now that implied volatility is a critical ingredient to your ability to be successful. But it’s also this understanding of how implied volatility shapes and molds this distribution graph that we used. So, as implied volatility increases or what’s commonly called “Vega” in option pricing, an options price will increase as well to compensate for the higher probability of being in the money at expiration. Remember, as a stock starts to make more frequent moves, that options price is going to increase because now, these options at the further extreme have an opportunity to be in the money at expiration.

And the options down below also have a further chance of being in the money at expiration because the stock is making huge, huge moves in either direction. Now, this is why we specifically suggest that you sell options when implied volatility is high, because option pricing is going to be very much expensive and rich and swollen because of implied volatility. And this is also why we suggest that you buy options generally when implied volatility is low. And that’s because option prices are generally going to be really low and have the propensity maybe to increase in the future. Now, with all of this hard data behind both volatility and possible ranges in the stock, we can actually build option strategies that target any probability of success we want. And this is really the key ingredient here. It’s that with the options, you have the ability to target any possible win rate that you want.

If you’re trading stocks, your win rate is 50/50. You have a 50% chance that the stock goes up. You have a 50% chance that the stock goes down. But with options, we have the awesome ability to target any probability of success that we want. So, let’s look at a really specific example here. This is a trade tab of SPY which is the S&P 500 index. And currently, SPY is trading right at 20423. Now, in the next month, (these are the February contracts, the next month out is February contracts which are 29 days out) you can see that we are in a position right now where we’re selling a spread or selling options above the market at the 208 strike price.

So again, the stock is trading at 204 and were trading options all the way out at 208. Based on all the trading history of SPY at this point and all of the volatility in SPY at this point, the probability of our option being in the money at expiration – Again, using that distribution graph that we looked at a couple sides ago. The probability right now, hard numbers that our option is in the money at expiration and loses is 29.35%. So, the probability that a stock goes up to our level and closes above that level is 29.35%. So, let’s use that same probability, and again, go back to our stock distribution graph. And let’s just say that the SPY which is currently right about here is trading at about 203, 204, right where I was in slide before. Now, if our strike price is up here at 208, if this is the level that we don’t want SPY to cross or breach, because we want SPY to close anywhere below this level for us to make money, then what we’re saying here is with this distribution graph, is that there’s about a 30% chance that that happens.

Now, we again, showed you where we got that number from and how we derived it. But there’s a 30% chance the SPY from where it’s at right now, goes up to and closes beyond our strike price by expiration. Now, if there’s a 30% chance of this happening, that also means there’s a 70% chance that it doesn’t happen. And so, a 70% chance that SPY never makes it up there and closes beyond that level at expiration. And this is where we get our very high probability of success trade. In this instance, the trade that we are actually truly in right now (and you can see this with the position markers) is a trade that has a 70% chance of success as it stands right now.

Now, the beauty of options, like we said, is that you can pinpoint your chance of success at any level that you want. In this case, if you want a higher level of success, you can go out to these options which are the 210 options. Those have about a 19% chance of being in the money or losing at expiration. That means if they have a 19% chance of losing at expiration, then they basically have about an 81% chance of being a winner at expiration. Now, of course, the market is going to compensate you and reduce a little bit of the money that you make because you have a little bit higher chance of success. So, with these options, we sold those for $145 and we only have a 70% chance of success. And I say 70% chance of success like it’s some lower number. But you know it’s like an extremely high probability versus going out to the 210 strike which is over here. The 210 calls have about a 20% chance of losing, so at 80% chance of success and you’re only going to get $for the option.

So, again, you can see the markets are extremely efficient. They know that that further out option has a higher likelihood of winning, and therefore, you’re not going to make as much money. So, there’s definitely a sweet spot in there. But you can see, you can pin your probability of success anywhere you want. Again, just to drive home the point again, we can go all the way out to the 2calls and you can see the probability of losing on those is 9.56%, so about 10%, meaning that this is about a 90% chance of success trade. So, it’s really, really powerful how we can use these probabilities when trading to pinpoint our chance of success, and we cannot replicate this with stocks because stocks always have a 50/50 probability of success. So, with all of this said, (I’m kind of wrapping up here) your only goal moving forward to be successful in trading options is to make as many small high probability trades as you can on the right side of volatility.

Period. End of story. That is the ultimate goal with trading. It’s to make as many small, (very small positions, you don’t take on too much risk) high probability trades like we just showed you that have a high likelihood or chance of success on the right side of volatility. Just understanding if implied volatility is low or relatively high, so that you’d know if the market could expand in price or can contract in price. Remember that we want to sell options when implied volatility is high, and we want to buy them when implied volatility is low.

So, I really hope you enjoyed this video. I know it was a more advanced tutorial, but we’re getting into a lot more concepts as we get through this part of the course here. And as always, if you have any comments or questions, please ask them right below. Until next time! Happy trading! . – Welcome back to statistics class. Undoubtedly more important that understanding the Black Scholes model for pricing (which we purposely don’t cover) is your ability to understand statistics and probabilities on a deep level.

We would even venture to say that your understanding of the “math” behind our trading system is directly related to your success rate and end of the year profit.

If you don’t get the math behind the trades you will fail – guaranteed!

Swallow your pride and head back to school with us as we talk in depth about standard deviations, probabilities and statistics in this advanced tutorial.


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