OPTIMAL TRADING QUANTITIES AND OPTIMAL F

Modern portfolio theory, perhaps the pinnacle of money management concepts from the stock trading arena, has not been embraced by the rest of the trading world. Futures traders, whose technical trading ideas are usually adopted by their stock trading cousins, have been reluctant to accept ideas from the stock trading world. As a consequence, modern portfolio theory has never really been embraced by futures traders.

Whereas modern portfolio theory will determine optimal weightings of the components within a portfolio (so as to give the least variance to a prespecified return or vice versa), it does not address the notion of optimal quantities. That is, for a given market system, there is an optimal amount to trade in for a given level of account equity so as to maximize geometric growth. This we will refer to as the optimal f. Here we propose that modern portfolio theory can and should be used by traders in any markets, not just the stock markets. However, we must marry modern portfolio theory (which gives us optimal weights) with the notion of optimal quantity (optimal f) to arrive at a truly optimal portfolio. It is this truly optimal portfolio that can and should be used by traders in any markets, including the stock markets.

In a nonleveraged situation, such as a portfolio of stocks that are not on margin, weighting and quantity are synonymous, but in a leveraged situation, such as a portfolio of futures market systems, weighting and quantity are different indeed. In this book you will see an idea first roughly introduced in Portfolio Management Formulas, that optimal quantities are what we seek to know, and that this is a function of optimal weightings.

Once we amend modern portfolio theory to separate the notions of weight and quantity, we can return to the stock trading arena with this now reworked tool. We will see how almost any non-leveraged portfolio of stocks can be improved dramatically by making it a leveraged portfolio, and marrying the portfolio with the risk-free asset. This will become intuitively obvious to you. The degree of risk (or conservativeness) is then dictated by the trader as a function of how much or how little leverage the trader wishes to apply to this portfolio. This implies that where a trader is on the spectrum of risk aversion is a function of the leverage used and not a function of the type of trading vehicle used. In short, this book will teach you about risk management. Very few traders have an inkling as to what constitutes risk management. It is not simply a matter of eliminating risk altogether. To do so is to eliminate return altogether. It isn’t simply a matter of maximizing potential reward to potential risk either. Rather, risk management is about decision making strategies that seek to maximize the ratio of potential reward to potential risk within a given acceptable level of risk.

To learn this, we must first learn about optimal f, the optimal quantity component of the equation. Then we must learn about combining optimal f with the optimal portfolio weighting. Such a portfolio will maximize potential reward to potential risk. We will first cover these concepts from an empirical standpoint (as was introduced in Portfolio Management Formulas), then study them from a more powerful standpoint, the parametric standpoint. In contrast to an empirical approach, which utilizes past data to come up with answers directly, a parametric approach utilizes past data to come up with parameters. These are certain measurements about something. These parameters are then used in a model to come up with essentially the same answers that were derived from an empirical approach.

The strong point about the parametric approach is that you can alter the values of the parameters to see the effect on the outcome from the model. This is something you cannot do with an empirical technique. However, empirical techniques have their strong points, too. The empirical techniques are generally more straightforward and less math intensive. Therefore they are easier to use and comprehend. For this reason, the empirical techniques are covered first. Finally, we will see how to implement the concepts within a userspecified acceptable level of risk, and learn strategies to maximize this situation further.

There is a lot of material to be covered here. I have tried to make this text as concise as possible. Some of the material may not sit well with you, the reader, and perhaps may raise more questions than it answers. If that is the case, than I have succeeded in one facet of what I have attempted to do. Most books have a single “heart,” a central concept that the entire text flows toward. This book is a little different in that it has many hearts. Thus, some people may find this book difficult when they go to read it if they are subconsciously searching for a single heart. I make no apologies for this; this does not weaken the logic of the text; rather, it enriches it.

One of the many hearts of this book is the broader concept of decision making in environments characterized by geometric consequences. An environment of geometric consequence is an environment where a quantity that you have to work with today is a function of prior outcomes. I think this covers most environments we live in! Optimal f is
the regulator of growth in such environments, and the by-products of optimal f tell us a great deal of information about the growth rate of a given environment. In this text you will learn how to determine the optimal f and its by-products for any distributional form. This is a statistical tool that is directly applicable to many real-world environments in business and science. I hope that you will seek to apply the tools for finding the optimal f parametrically in other fields where there are such environments, for numerous different distributions, not just for trading the markets.

For years the trading community has discussed the broad concept of “money management.” Yet by and large, money management has been characterized by a loose collection of rules of thumb, many of which were incorrect. Ultimately, I hope that this post will have provided traders with exactitude under the heading of money management.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s