Understanding the Math

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Hey, everyone. This is Kirk, here again at optionalpha.com where we show you how to make smarter trades. Today, we've got an awesome video tutorial for you, breaking down trading math and specifically, options trading math.

It’s a 101 course on why we have the methodologies that we do about the markets and trading. Welcome back to statistics class. 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.

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.

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. This whole idea about market efficiency is really important, and you’ve probably heard us talk about it in 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. Especially in the US markets where there are millions and millions of different market participants, all with their 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. 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 I was on the private side dealing with mergers and acquisitions, and then I was on the other side of the Chinese wall in Tyson’s in DC and dealing with the REIT retail side as an analyst.

I’ve been on both sides of the wall, and I can tell you, the markets are incredibly efficient. There’s no edge that you can get in knowing information about a company in advance or having some insider knowledge.

In most cases, most CEOs 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.

To that end, we have to understand that as we’ve 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.

What this leads to then is to this probability distribution and what we call a normal distribution or what you probably have seen before as a bell curve. This is really important because this is how an efficient market distributes its returns.

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 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 about one standard deviation. This is what this one standard deviation is that I’m highlighting here on the chart.

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. 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. This means that most stocks are going to 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 high flyers, the one in a million stock that goes from $5 to $500 or whatever the case is. Then, of course, you’re also going to have stocks that make a three standard deviation move to the downside.

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 normal average in the middle, and that bulk average here is what we’re looking 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 tilt it on its side here, we can see that this same concept applies to a stock distribution of its price movement over time. I’ll say that again. This same distribution will apply to a particular stock’s price movement going forward in the future.

What I always like to do is I always like to say at certain points in the future… Let’s just draw a line down here and say 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.

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.

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 the stock is trading, it might end up trading somewhere in this range.

And that’s a good likelihood of happening because the stock didn't have that much time and 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 gave such a short 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. It adds more time here, and you can see it can widen out its breath of movement.

That’s true because as you can see going forward here on the S&P, the longer we went in the timeframe, the more the stock could move over time, and that happens here too.

Again, just continuing down to the future, you can see the stock can then really move as we start to go further and further out on the expiration cycle. This same type of distribution can then be applied to where the stock moves over time.

Most of the time, the stock is going to move with the inside of this one standard deviation movement. This one standard deviation movement is about 68% of the time. We can exactly calculate this probability inside of most broker platforms.

I’m going to show you how we do it at the end of this video, but just trust me that this one standard deviation move is about 68% of the time.

It’s 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.

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 volatility and volatility and option pricing. Let's take two stocks in this example. Both stocks start out at the same price which is $100.

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.

You can say that stock B which is 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.

This drives us to our next topic which is implied volatility. Implied volatility is an expectation of where the stock might move in the future. 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.

We take our normal distribution graph which is the one here in blue. This is that one from one of the other screens, so just a normal distribution, our average volatility in the market.

You might see the stock have a range of between here and here, so the two extremes with something around the median or the mean as far as its distribution going out into the future. If implied volatility for that stock is a lot lower…

Remember stock A from the slide before? That black line that was 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.

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. Instead of movements all the way out here, now the extreme movements or the three standard deviation moves are much, much closer to the mean of the stock.

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’ve looked at in the slide before, that blue line, it’s all over the place, still centered around $100.

But all over the place, then what that does is that slams down this distribution graph, and it makes it much shorter and fatter. This distribution graph looks like this. It’s much more distributed this way.

It’s a very flat, very wide graph. You can see because it's very volatile, the stock can rally high, it can go that high, or it can go that low.

Most of it is going to be around some average or mean, but you'll notice that the average and mean has expended and now 68% of the time, it trades within this range which is all the way out towards the end of its shading.

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.

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 use.

As implied volatility increases or what's commonly called Vega in option pricing, an option’s 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 option’s 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.

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 going to be 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 build option strategies that target any probability of success we want. This is the key ingredient here, is that with 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 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.

Let’s look at a specific example here. This is a trade tab of SPY which is the S&P 500 index, and currently, SPY is trading right at 204.23. 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.

Again, the stock is trading at 204, and we’re 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 using that distribution graph that we looked at a couple of slides ago.

The probability right now, hard numbers that our option is in the money at expiration and loses is 29.35%. The probability that a stock goes up to our level and closes above that level is 29.35%.

Let's use that same probability and 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 it was on the slide before.

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 with this distribution graph is that there’s about a 30% chance that that happens.

We showed you where we got that number from and how we derived it, but there’s a 30% chance that SPY from where it’s at right now goes up to and closes beyond our strike price by expiration.

If there’s a 30% chance of this happening, that also means there’s a 70% chance that it doesn't happen and a 70% chance that SPY never makes it up there and closes beyond that level at expiration.

This is where we get our very high probability of success trading. In this instance, the trade that we are 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.

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 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.

With these options that we’ve sold, we sold those for $145 and we only have a 70% chance of success (I say 70% chance of success like it’s some lower number, but you know it’s 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 an 80% chance of success and you’re only going to get $78.5 for that option. You can see the markets are extremely efficient; they know that further out option has a higher likelihood of winning and therefore, you’re not going to make as much money.

There’s a sweet spot in there, but you can see, you can pin your probability of success anywhere you want. Just to drive home the point again, we can go all the way out to the 212.5 calls, and you can see the probability of losing on those is 9.56%, so about 10%, meaning that this is a 90% chance of success trade.

It’s real, 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.

With all of this said and wrapped 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, is 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 know if the market can 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.

I hope you enjoyed this video. I know it was a more advanced tutorial, but we’re getting to a lot more concepts as we get through this part of the course here. As always, if you have any comments or questions, please ask them right below. Until next time, happy trading!