To begin, I want to introduce to you the primary rule upon which our success is based. It s a rule that you can never forget.

Transcription

1 Welcome to the casino secret to profitable options trading. I am very excited that we re going to get the chance to discuss this topic today. That s because, in this video course, I am going to teach you to be THE HOUSE. To do that, we re going to start by looking at some concepts first. Then we re going to open the black box. That s where I will introduce you to key formulas, then we ll look at some images generated by those equations. So let s get started. To begin, I want to introduce to you the primary rule upon which our success is based. It s a rule that you can never forget. That rule is: In all speculations -- whether it s investing or wagering -- you make money when the collective misprices the odds. 1

2 My goal is to get you to think like a casino. And while it may sound unpleasant, Casinos are takers 2

3 So if casinos are takers, why would I suggest that you start thinking that way? Being a taker doesn t sound very nice. Well, let s begin by looking at one of the fundamental facts about options. Options are not like stocks. Options are a zero sum game. Stocks are not. Options are more like a casino game where, for every winner, there is a lower. Casinos make money by taking from players. Options traders make money by taking it from somebody else. The people you are trying to take money from are usually pretty good at what they do. It s an indisputable fact: most options volume comes from pros, not other individuals. 3

4 So if the options market is a zero sum game, and the other partcipants are so good, how does one succeed? The only way to beat the best the only way to beat those professionals is to change your mindset. Change the way you think about making money. My goal is to get you to think of trading as if you are a casino operator. I want you to put away the notions you ve had in the past, and here s why: As Ray Dalio, chairman of the most successful hedge fund in history said, if you're going to come to the poker table, you're going to have to beat me, and you're going to have to beat those who take money. I want you to learn the principles of the takers. Be a giver with the rest of your life, not your trading. 4

5 To become a trading taker, we going to Harness Proven Success Formulas Casinos Use to Generate Option Profits Successful option traders, just like top level professional poker players and card counters NEVER know that they are going to make money on a single hand. The casino never knows whether that one roll of the dice or that one pull of the slot machine arm is going to win or lose. What they ALWAYS know, for every play: Probability Reward Risk EDGE 5

6 I will show you how you can use the same concepts that some of the most profitable businesses on earth casinos, plus insurance companies, even government run lotteries use to generate profits that are almost unimaginable. 6

7 The types of companies I just mentioned generate their profits due to their mastery of probability. Casinos and lotteries make money when you do not win the jackpot. So they need to know what the odds are that you won t win. Similarly, insurance companies make money when you do not have a wreck. So they need to know what the probability is that you won t have a wreck. 7

8 But it s more than just probability You need to know risk and reward Auto insurance companies need to know how much they will have to pay in the unlikely event that you do have a wreck (their risk), so they know how much to collect in premiums to have enough money to pay your claim, plus make money for themselves (their reward). The odds of you wrecking influence the premium you pay (the insurance company s reward) and their risk. 8

9 Lottery organizations need to know how many tickets they re likely to sell (their reward), so they know how big the prize can be when they award the jackpot (their risk). They price their games in a way that makes it unfair for the player. 9

10 So here is a key concept: these businesses make money from mispricing Casinos, lotteries and insurance companies make money when something is mispriced when it s UNFAIR for the other guy. If buying what these companies sold was good for the buyer, then the companies would be the losers. If betting in casinos was good for the bettor, casinos wouldn t be able to stay in business. If insurance was a good bet for the insured, then insurance companies would LOSE money! That doesn t mean insurance isn t good from a risk distribution perspective and your peace of mind. It just means that the premiums are priced to the point where it s not a good financial bet for the customer. People are willing to pay for that peace of mind and the loss prevention. 10

11 And that gets to the crux of the matter. These probability companies do lose in individual situations. Like when there is a claim, or a jackpot winner. But think about this: If there was no need to ever file a claim, then there would be no need for insurance. If no one won the jackpot, no one would play. But their overall profit is STAGGERING. 11

12 Now I am going to give you a very quick and simple example of what I mean by mispricing. This is a simple lottery game, let s say there are 100 unique tickets for sale. Each ticket cost $2. The winning ticket receives a $100 jackpot. The lottery collects $200, but only pays out $100. That means the lottery keeps $100. That s not fair. The lottery is a taker. What that tells you is that with those odds, the ticket was really only worth $1, not $2. It s mispriced. 12

13 At those prices, for the lottery to have been fair, the number of tickets should have been just 50. That is, the risk and reward can tell us the fair odds. So the price can tell us the fair odds. And the odds can tell us the fair price. 13

14 Now, you re never going to hear one of these businesses say so. But the basic success formula for casinos and lotteries is to make sure that the odds are unfair for their customers. Casinos, lotteries and insurance companies make money because things are mispriced relative to the fair odds. Casinos, lotteries and insurance companies have an edge. That edge is their knowledge of probability. Knowing the fair odds means they know the true value of any proposition, speculation or investment. So how do we translate that to the market? 14

15 With Options, It s about mispricing and it s impact on probability, risk and reward Just like that $2 lottery ticket, you make money when something is mispriced. With options just like with those other businesses the thing that is distorted is probability. Specifically, it s the probability that a stock is going to make a certain sized move within a certain time frame. That probability mispricing is reflected in the risk and reward of the trade. Risk and reward is reflected in the price. 15

16 I want to use another game of chance to illustrate this point. By the way, this game could just as easily be a certain type of option trade. Here are the payoffs of the game: When you win, you win 4. When you lose, you only lose 1. Risk and reward are VERY GOOD! Add an additional crucial ingredient. Your odds of winning are 10%. So 1 time in 10 you win 4 And 9 times in 10 you lose 1. 16

17 If we play that game 10 times, we have the following result: 1 win of 4 equals +4 9 losses of 1 equals 9 For a net is a loss of 5 No rational player is going to play this game. That s because the expected profit/loss is 0.5 ( 5/10) Rational participants only play if there are fair odds. Therefore, with reward of +4 and risk of 1, what do the probabilities have to be for the odds to be fair? 17

18 For the odds to be fair in a game with reward of +4 and risk of 1, the odds of winning have to be 20%. The odds of losing have to be 80%. If they re better than that, then the other participant won t play unless they re going to Vegas or playing the lottery. That leads to the following important implication: RISK AND REWARD CAN BE USED TO DETERMINE THE FAIR ODDS OF THE GAME. 18

19 Similarly, the price of an option, with its own risk and reward characteristics, can be used to determine the probability assessments of the market participants. Risk and reward tell us what traders think the fair odds or probability of a move are. When options are mispriced, it tells us that the option buyers have a distorted sense of probability. Overpriced options means buyers are overestimating the likelihood of a certain size move over a certain period of time. 19

20 So how do we know the probability assessment is distorted? Well, we know that we can determine expected probabilities from risk and reward. We showed how that was easy using a game of chance. Option pricing models allow us to determine what those expected probabilities are for any option trade imaginable. We can then compare these results to the what has actually to see if the expected probability matches reality! 20

21 There are a few things to remember. First, always remember, your edge in a speculation occurs when something is mispriced. That comes from knowing something that the market doesn t. With options, price equals probability. Therefore, our edge occurs when we find that the probability assumption does not match reality. Then we know that others have a distorted sense of probability. That means the options are mispriced 21

22 Welcome to the chapter on option pricing and probability. I want to begin with this thought If your edge is knowing that the probability assessment is distorted, you need to know the magnitude of the distortion. 22

23 In option pricing theory, as in many aspects of finance, there are a lot of assumptions Trading is continuous and the stock price follows a geometric Brownian motion. Volatility is constant. There are no restrictions on short selling. The problem is, THESE ASSUMPTIONS ARE UNREALISTIC!, as you ll see when we get to a later chapter. By the way, these aren t the only assumptions in option pricing theory. There are other assumptions. But they re not relevant to this discussion. 23

24 This is the famous Black Scholes Model. It s a partial differential equation. When you break it down, you get this formula. That N represents the Cumulative Distribution Function. That tells us that we re going to use the bell curve. Think of it as the area under the bell curve to the left of d1 24

25 Now here is the bell curve. To generate this, we created a distribution that almost perfectly matches the bell curve. Then we ran a monte carlo simulation to see how closely it matched the perfect theoretical bell curve. The bell curve is the line. The simulation results are shown in the columns. As you can see, they are very nearly an exact match. Now I want to show you something else. To do that, let s look at another game of chance. One that involves throwing a dice. 25

26 Here is the probability distribution of a game that involves throwing 2 6 sided dice. As you can see, there is only one way to come up with snake eyes, or a total of two. There is also only one way to come up with box cars, or a total of twelve. But there are six ways to come up with 7. There are 36 possible combinations. So the odds or rolling a 7 are 6 out of 36, or 1/6 th, or 16.67%. Also notice these nice straight lines. Now let s add another dice to the game and see what changes occur. 26

27 Here s what it looks like when you have three dice. Notice that the maximum probability is less than 16.67%. Also notice that the line is not as straight. Let s add another dice to the game. 27

28 The max probability shrinks even further, and the graph is curving even further. Now, let s imagine that we added an infinite number of dice to the game. 28

29 This is what you get. This is what the probability graph looks like if the dice game has an infinite number of dice. That should look very familiar. I showed these charts in my ODDS Advantage video. And we also saw the chart 29

30 Here. We saw this when we were discussing N, which is that key part of the Black Scholes option pricing model. 30

31 That leads to this extremely important concept in options trading. The Assumed Distribution of the Market is Identical to the Distribution of a Game of Chance with Infinite Possibilities. No wonder the comparison to casinos is so appropriate! 31

32 We ve arrived at the point where it s time to start discussing the formulas This video hasn t had a bit of fluff in it so far, and it s not about to. In fact, it s going to get even more intense. For those who want to do this yourself, I hope you remember your higher level maths. Fortunately, those who don t want to get into the math, there is software that can perform most of these equations, providing you with a simple solution. You do NOT need to do this at home. We re showing you this so you re not flying blind. So you understand the concepts of why the casino like approach works. 32

33 This is a standard normal distribution, otherwise known as the probability density function. Simply plug in x, and it will give you the y value. For instance, if you plug in 1, you ll get approximately Plug in 0, and you ll get approximately 0.4. By the way, this chart like the charts before it and the charts you ll see later was generated in Excel. 33

34 This is that same formula, except instead of using Excel, I used a free web site called Wolfram Alpha. You input the formula here. It generates the graph down here. Wolfram Alpha is not necessary. I am only using it to show you that there are free ways to do this yourself! 34

35 To calculate probability is a three step process: Determine a target in terms of price. Convert the price into standard deviations. Calculate the area under the bell curve. 35

36 Let s look at an example. Let s say we have a stock index at 1000 We have a volatility of 15% I came up with a random target. In this case, our target price is We want to determine the probability that the index will be at or above one month from now. 30 calendar days or 21 trading days 36

37 We re going to plug that information into this equation to convert the price target into a standard deviation. 37

38 Again, for those of you who want to do this yourself, and don t want to spend any money, here is Wolfram Alpha. The formula goes here 38

39 If you plug in the values in the appropriate spot You get this result. We re going to round it to one. 39

40 Here we have that standard deviation marked. The blue bar indicates the point on the bell curve. So we ve done step 1 and step 2. Now we have to figure out the probability by calculating the area under the curve. To find the area under the curve, you get the integral. But integrating the bell curve function is impossible, so we have to use an approximation. The formula for that is on the next page. 40

41 Here it is. Please don t get overwhelmed. I know it looks like a monstrosity. Fortunately, software makes it easy. In Excel, it s normsdist. All probability software, including ours, has this function built into it. 41

42 This is what that equation is going to provide to us. If we plug in our standard deviation, which was 1, into the equation on the prior slide, the result will be the area under the curve to the left of 1, which is shaded in blue. 42

43 Again, you don t have to do this if you don t want. There is software that performs these probability calculations for you. But if you want to do this yourself, here is the formula in Wolfram Alpha 43

44 And here is what it looks like when we input our standard deviation of 1 into the formula. And here is the result. 44

45 So that s the answer we re looking for. We now have the theoretical probability. The probability of being less than is 84%. The probability of being greater than is 16%. Now, let s look at a simple way to calculate actual probability. 45

46 We re going to use that same example: We have a stock index. It s still at 1000 Our target price is still at Our time horizon is still a month, which corresponds to 21 trading days. Now we change that target to a logarithmic change. That equates to over 21 trading days We go to our table and count how many times there were 21 day moves where the log change was greater than We then compare that to how many times there were 21 day moves less than Let me repeat that we count! 46

47 Here s a table of index prices. We need to determine the 21 day change in log terms. We look at the price on day 1. The price is Then we look at the price on day 21. That price was We then calculate the log change. As shown in the table, the log change was Now let s look at day 2. The price was days later, the price was We see that the log change was Let s look at day 3. The price was days later the price is The 21 day log change was We do this for as many time periods as we want, count how many exceed our target, how many don t, and that gives us the probability. Not hard, but very tedious. Again, software makes it much, much easier. 47

48 So let s take a minute to review. Options are a zero sum game. To make money trading, you must take it from the less informed. The only way to take money is to have an edge. Our edge is knowing the actual probabilities. Because probability is directly related to risk and reward, and because we can observe when probabilities are wrong, we can also determine when options are mispriced. We can also determine when they are correctly priced! 48

49 So we ve learned why this is important. And we ve seen some of the most important equations. Now let s look at some charts that will give us a clear picture of true market probability. 49

50 This is a chart of the S&P 500 going back to The reason we chose that date is because that is when weekend trading ended. For those of you interested in market history, the market used to be open on Saturdays until May

51 To begin, we need to determine theoretical probability. For this demonstration, we re going to use the actual volatility of the stock market. Statistical Volatility over this entire period was 15.66% On December 31, 2012, implied volatility of the January SPX options was 15.98%. Very close to volatility over the past 60 years! 51

52 Once we know our volatility, we do three things: Calculate Count Compare 52

53 When we re done, this is what we get. This is a comparison to the theoretical probability to the actual probability for that entire period. The line is the theoretical, the columns are the actual. You can see that it s a close match, but not quite exact match. The peak in the middle is slightly higher. There is a slight shift to the right. At either end, on the tails, there is a slight bump, especially on the low end. By the way, the x axis is the log change, divided up into standard deviations. For instance, the minus 13% on the left, is 4 standard deviations below. That means a log change of worse than 0.13 over a 21 day period is more than 4 standard deviations down. This is why the theorists believed it was appropriate to use the bell curve as an approximation. It s not a perfect match, but it s pretty close. 53

54 Now we re going to look at a portion of that 60 year time frame. From the beginning of 1995 through the end of Note how persistently and steadily the market move higher. This was a bullish period of modest volatility. 54

55 Here is that comparison. The peak height of the actual distribution is nearly a perfect match to the theoretical. It s almost dead on. The left tail is smaller. But the actual probability distribution is skewed to the right. That tells us the actual moves were biased to the upside, and the size of the moves were relatively normal. It confirms what we saw in the prior chart. 55

56 Now let s look at a bear market period. This covers the period from the beginning of 2000 to the low in

57 Here is what it looks like when you compare theoretical and actual during this period. There are several things to note. First, there is a substantial deviation from theoretical. First, the curve is flatter at the top. Second, the whole thing is skewed to the left Third, there is a substantial bulge above the theoretical line on the left side. Fourth, look at the fat tails on either end. Basically, this is telling us that the market moved far greater than normal, and the moves were biased to the down side. If you were an investor during this period bear market period, that information is not a surprise. But what may be a surprise is that many people were using the bell curve to value options! 57

58 Now let s look at what happened during the worst bear market since the Great Depression. 58

59 As you can see, the actual price action didn t come even close to mimicking the bell curve. The highest point is actually 4 standard deviations down!. The next highest point is 4 standard deviations up. The level of volatility was ridiculous. In fact, research I did in October 2008 showed that volatility during that time period the period was the 4 th highest in history. You had to go back to October 1929, October 1931, and October This is why so many traders and investors who relied on models like the Black Scholes, which are based on a bell curve, blew up. Options were horribly mispriced, because the probabilities calculated by that N function in the models wasn t even close to reality. By the way, there are a lot of names for the bell curve. It s also known as a normal distribution, is graphed using a formula called the probability density function. The bell curve is also known as a Guassian distribution, named after the mathematician who discovered the bell curve, Carl Friedrich Gauss. I mention that because the bell curve was widely used to manage bank risk. They used formulas called Value at Risk and Gaussian copulas to manage their exposure. As you can see, that probability assumption was very nearly a fatal flaw. The only reason banks survived is because of the taxpayer funded government backstop. 59

60 Enough history. Let s get back to the application of this information to trading. Up till now, we ve seen that there is a directional bias. But remember, one assumption in the markets is that if there is a risk free trade, you can extract it. One of the ways to do that is through short selling. We said something about that earlier when we talked about the assumptions. When you extract a risk free profit by taking advantage of a pricing imbalance between two assets, it s called an arbitrage. So the fact that there is no limit to extracting a risk free profit means that there can be no directional bias. The distributions must be symmetrical. Let s look at how our charts have changed when we add that factor. 60

61 Here is that entire 60 year time period. Note the peak in the middle and the small tails at either extreme. 61

62 Here is 1995 to It is nearly a perfect match. 62

63 Here we have Again, it s flatter 63

64 And during the financial crisis, the actual curve is even flatter still with those two wild fat tails. 64

65 What these charts do is allow you to visualize probability. You can see it. We can see theoretical probability. We can see actual probability. This lets us visually compare theoretical to actual probability! You can actually see your edge. 65

66 When we get those probabilities, and we can see the difference between theoretical and actual, we are able to visualize our edge. As you ll see, this is very similar to knowing when the deck is stacked either in our favor, or against us. If it s against us, we don t play. But if it s in our favor, we know we have an edge. 66

67 Our EDGE Is That We Know the Actual Probabilities The options market is pricing in certain probabilities derived from option pricing models. We measure probabilities based on the actual movement of the stock. That allows us to determine when probability assessments are distorted. Remember, probability determines risk and reward. 67

68 Because the probability assessment is distorted, the risk and reward must also be distorted. That means option prices are distorted. We then do what no one else is capable of doing: We value the options based on actual probabilities. We know by what quantity theory and reality deviate. THAT IS OUR EDGE! 68

69 It s as if we re playing Black Jack, and we re allowed to count cards, so we know when the deck is stacked We don t know with certainty that we have a winning hand. But the probabilities, risk and reward are all in our favor. 69

70 We re now in a position to be a taker The Business Of Running A Casino Is To Make Sure The Odds Are Always Bad For The Other Guy and to take his money. But not take so much that the other guy doesn t ever win. The Casino can t win every play. Otherwise, no one would ever speculate. But they can make sure that odds are unfair. Players odds are unfairly bad. The house s odds are unfairly good! 70

71 Now, I want to speak about risk. Like I said, the casino has to lose every now and then to get players to continue gambling. Our edge is that we know the actual probabilities compared to what the market is expecting. This gives us a far higher probability of profit than one would expect. A higher probability of profit does NOT provide certainty! 71

72 So to make sure the required loss doesn t ruin us, risk control is vital. We do that three ways: Never put on a trade that you don t understand or you can t control. ALLOCATION IS THE KEY. If you trade wisely, you don t need to allocate huge portions of your portfolio to make a good return. We only allocate 5% to 10% of our model portfolio to a single trade, and never more than half to any particular style of trade. 72

73 And I do have one other caveat. The principles I outlined are actually relatively simple. That monstrosity of an equation was really nothing more than multiplication, division, subtraction and addition. Plus a square root, a logarithm, and an exponential function. These can all be done on a calculator or Excel. The thing is, they re tedious. Simple, but tedious. If you want to automate this, the concept is simple too. But the implementation is difficult. That s because the data requirements are massive. And the ability to process that data in a reasonable time frame is also quite difficult. But it can be done, especially if you want to concentrate on just a stock or two. For instance, the S&P 500 SPDR ETF. 73

74 So that s it. My hope is that your perception about trading has changed for the better. Instead of thinking like a gambler, I want you to think like a casino. For every play, I want you to know your odds. For every play, I want you to know your edge. You have a choice: IN THE MARKETS, YOUR EITHER A TAKER OR A GIVER. As far as the rest of your life is concerned, be a giver. But when it comes to trading, you can either take, or be taken. I want you to BE THE HOUSE. 74