scenario should develop you know you won't be jumping out of the window. Hope for the best but prepare for the worst. If you haven't done these exercises, then close this book now and keep it closed. Nothing can help you if you do not have this foundation to build upon.
MATHEMATICS NOTATION Since this book is infected with mathematical equations, I have tried to make the mathematical notation as easy to understand, and as easy to take from the text to the computer keyboard, as possible. Multiplication will always be denoted with an asterisk (*), and exponentiation will always be denoted with a raised caret (^). Therefore, the square root of a number will be denoted as ^(l/2). You will never have to encounter the radical sign. Division is expressed with a slash (/) in most cases. Since the radical sign and the means of expressing division with a horizontal line are also used as a grouping operator instead of parentheses, that confusion will be avoided by using these conventions for division and exponentiation. Parentheses will be the only grouping operator used, and they may be used to aid in the clarity of an expression even if they are not mathematically necessary. At certain special times, brackets ({ }) may also be used as a grouping operator. Most of the mathematical functions used are quite straightforward (e.g., the absolute value function and the natural log function). One function that may not be familiar to all readers, however, is the exponential function, denoted in this text as EXP(). This is more commonly expressed mathematically as the constant e, equal to 2.7182818285, raised to the power of the function. Thus: EXP(X) = e^X = 2.7182818285^X The main reason I have opted to use the function notation EXP(X) is that most computer languages have this function in one form or another. Since much of the math in this book will end up transcribed into computer code, I find this notation more straightforward.
SYNTHETIC CONSTRUCTS IN THIS TEXT As you proceed through the text, you will see that there is a certain geometry to this material. However, in order to get to this geometry we will have to create certain synthetic constructs. For one, we will convert trade profits and losses over to what will be referred to as holding period returns or HPRs for short. An HPR is simply 1 plus what you made or lost on the trade as a percentage. Therefore, a trade that made a 10% profit would be converted to an HPR of 1+.10 = 1.10. Similarly, a trade that lost 10% would have an HPR of 1+(-.10) = .90. Most texts, when referring to a holding period return, do not add 1 to the percentage gain or loss. However, throughout this text, whenever we refer to an HPR, it will always be 1 plus the gain or loss as a percentage. Another synthetic construct we must use is that of a market system. A market system is any given trading approach on any given market (the approach need not be a mechanical trading system, but often is). For example, say we are using two separate approaches to trading two separate markets, and say that one of our approaches is a simple moving average crossover system. The other approach takes trades based upon our Elliott Wave interpretation. Further, say we are trading two separate markets, say Treasury Bonds and heating oil. We therefore have a total of four different market systems. We have the moving average system on bonds, the Elliott Wave trades on bonds, the moving average system on heating oil, and the Elliott Wave trades on heating oil. A market system can be further differentiated by other factors, one of which is dependency. For example, say that in our moving average system we discern (through methods discussed in this text) that winning trades beget losing trades and vice versa. We would, therefore, break our moving average system on any given market into two distinct market systems. One of the market systems would take trades only after a loss (because of the nature of this dependency, this is a more advantageous system), the other market system only after a profit. Referring back to our example of trading this moving average system in conjunction with Treasury Bonds and heating oil and using the Elliott Wave trades also, we now have six market systems: the moving average system after a loss on bonds, the moving average system after a win on bonds, the Elliott Wave trades on bonds, the moving average system after a win on heating oil, the moving average system after a loss on heating oil, and the Elliott Wave trades on heating oil. -7-
Pyramiding (adding on contracts throughout the course of a trade) is viewed in a money management sense as separate, distinct market systems rather than as the original entry. For example, if you are using a trading technique that pyramids, you should treat the initial entry as one market system. Each add-on, each time you pyramid further, constitutes another market system. Suppose your trading technique calls for you to add on each time you have a $1,000 profit in a trade. If you catch a really big trade, you will be adding on more and more contracts as the trade progresses through these $1,000 levels of profit. Each separate add-on should be treated as a separate market system. There is a big benefit in doing this. The benefit is that the techniques discussed in this book will yield the optimal quantities to have on for a given market system as a function of the level of equity in your account. By treating each add-on as a separate market system, you will be able to use the techniques discussed in this book to know the optimal amount to add on for your current level of equity. Another very important synthetic construct we will use is the concept of a unit. The HPRs that you will be calculating for the separate market systems must be calculated on a "1 unit" basis. In other words, if they are futures or options contracts, each trade should be for 1 contract. If it is stocks you are trading, you must decide how big 1 unit is. It can be 100 shares or it can be 1 share. If you are trading cash markets or foreign exchange (forex), you must decide how big 1 unit is. By using results based upon trading 1 unit as input to the methods in this book, you will be able to get output results based upon 1 unit. That is, you will know how many units you should have on for a given trade. It doesn't matter what size you decide 1 unit to be, because it's just an hypothetical construct necessary in order to make the calculations. For each market system you must figure how big 1 unit is going to be. For example, if you are a forex trader, you may decide that 1 unit will be one million U.S. dollars. If you are a stock trader, you may opt for a size of 100 shares. Finally, you must determine whether you can trade fractional units or not. For instance, if you are trading commodities and you define 1 unit as being 1 contract, then you cannot trade fractional units (i.e., a unit size less than 1), because the smallest denomination in which you can trade futures contracts in is 1 unit (you can possibly trade quasifractional units if you also trade minicontracts). If you are a stock trader and you define 1 unit as 1 share, then you cannot trade the fractional unit. However, if you define 1 unit as 100 shares, then you can trade the fractional unit, if you're willing to trade the odd lot. If you are trading futures you may decide to have 1 unit be 1 minicontract, and not allow the fractional unit. Now, assuming that 2 minicontracts equal 1 regular contract, if you get an answer from the techniques in this book to trade 9 units, that would mean you should trade 9 minicontracts. Since 9 divided by 2 equals 4.5, you would optimally trade 4 regular contracts and 1 minicontract here. Generally, it is very advantageous from a money management perspective to be able to trade the fractional unit, but this isn't always true. Consider two stock traders. One defines 1 unit as 1 share and cannot trade the fractional unit; the other defines 1 unit as 100 shares and can trade the fractional unit. Suppose the optimal quantity to trade in today for the first trader is to trade 61 units (i.e., 61 shares) and for the second trader for the same day it is to trade 0.61 units (again 61 shares). I have been told by others that, in order to be a better teacher, I must bring the material to a level which the reader can understand. Often these other people's suggestions have to do with creating analogies between the concept I am trying to convey and something they already are familiar with. Therefore, for the sake of instruction you will find numerous analogies in this text. But I abhor analogies. Whereas analogies may be an effective tool for instruction as well as arguments, I don't like them because they take something foreign to people and (often quite deceptively) force fit it to a template of logic of something people already know is true. Here is an example: The square root of 6 is 3 because the square root of 4 is 2 and 2+2 = 4. Therefore, since 3+3 = 6, then the square root of 6 must be 3. Analogies explain, but they do not solve. Rather, an analogy makes the a priori assumption that something is true, and this "explanation" then masquerades as the proof. You have my apologies in advance for the use of the analogies in this text. I have opted for them only for the purpose of instruction.