# Preface

It's been estimated that 90% of traders lose money. To trade profitably, you've got to do things differently. One way to do things differently is to look at financial data differently.

This book is about simple trading strategies that work, based on the perspective that financial time series can be viewed as a random binary string with possibly some hidden order embedded in it. From this fundamental approach, we present strategies flexible enough to be profitable regardless of trend direction or market type (bull, bear, or going-nowhere).

Our motivation is to show that there are ways to exploit hidden and unknown trends in a stochastic process, that is a process dominated by probability and not certainty. We show that you can get a positive expectation if trends exist, even without knowing their direction.

There are two parts to this book. The first, Strategies (Chapters 1-14), looks at various strategies and how well they performed in the past on instruments in different asset classes. We start with simple strategies based on a single asset. We then look at ways of using one asset to trade another. Next we show how to use one asset to determine the strategy to use on another. Markov models are introduced next. We show how to construct these models for assets based on price alone and price with volume information. We show examples of using all the strategies and a summary of their performance. The examples were chosen to represent equities, bonds, commodities, and precious metals. The final chapter of part one gives suggestions for further research into more sophisticated strategies.

Any trading strategy must be based on a model of how the asset you are trading behaves. There are two ways to come up with a trading strategy. One way is to first find a good model for how the asset behaves and then determine the optimal strategy based on the model. The other way is to simply look for a good strategy without worrying about the model. But there will always be an implicit model behind the strategy, just as there is always an implicit philosophy behind peoples lives. If the implicit model is not correct and robust then the strategy will eventually break down. So in any case it is important to understand the model behind a trading strategy.

The second part of the book, Models (Chapters 15-17), takes a detailed and more mathematical look at some of the models that are implicitly behind the trading strategies in part 1. These are models for a binary random process that produces a sequence of two values: 1 or 0, up or down, heads or tails. To make things concrete we use the example of flipping coins to generate the binary sequence. We examine models based on one, two, and three coins. The behavior of the models becomes more complex as more coins are used. We look at the probabilities and statistics of the models and how to bet on them in a simple gambling game. For those readers interested in a deeper insight into the strategies presented in part 1, this part of the book should provide it. The relevant mathematical background for this part of the book is provided in two appendices.

The outline of the book is as follows.

Chapter 1 introduces the idea of how a financial time series, for the purpose of trading, can be viewed as a random binary string.

Chapter 2 discusses the binary random process: how to estimate its probabilities, the mean square error for the estimate, and its expectation and variance.

Chapter 3 presents the simplest strategies for dealing with a binary random process whose probabilities are both unknown and changing in time: BSP (bet same as previous) and BOP (bet opposite as previous). We come to the remarkable result that the BSP strategy has a positive expectation when there is some bias, regardless of its direction. This means you don't need to know the direction to use the strategy. These two simple strategies can be viewed as the basis for all possible strategies. Chapter 4 gives examples of BSP and BOP in action.

Chapter 5 introduces a simple extension of BSP and BOP, which we call BSP-XY and BOP-XY, that uses one binary random process to predict another, or in our case, using one stock to predict another. Chapter 6 shows examples of these strategies in action.

Chapter 7 discusses one way to model a switching bias, which we call XY strategy switching. This is based on the fact that on any given day, either the BSP or BOP strategy will be correct, which leaves the question of when to switch. Here we use one binary random process (stock) to decide which strategy to use on another stock. Chapter 8 gives some examples of XY strategy switching.

Chapter 9 presents another way to model a switching bias, a Markov model. Here we use a stock's own price history to anticipate when the bias switches. This leads to the question of what is the optimal history length to use. Chapter 10 shows examples of using the Markov model.

Chapter 11 takes the Markov model one step further by using both price and volume information. This doubles the model's states from 2 to 4. Chapter 12 has examples of using the Markov model with both price and volume.

Chapter 13 concludes by ranking all the examples by profit, discusses the results and the practical consequences in the choice of time period.

Chapter 14 talks about ways to extend the simple strategies we have discussed, and continue beyond the content of this book.

Chapters 15 through 17 are about the single biased coin model, the 2-coin model, and 3-coin models, respectively.

The appendices provide background, for those who need it, on discrete probability (Appendix A), as well as the Cayley-Hamilton Theorem (Appendix B) used in the 2-coin and 3-coin models.

This book's web page is: http://quantwolf.com/doc/simplestrategies/simplestrategies.html

We can be reached by email at:

stefan[at]exstrom DOT com richard[at]exstrom DOT com

Stefan Hollos and Richard Hollos

QuantWolf.com

Exstrom Laboratories LLC

Longmont, Colorado, U.S.A.

September 2011