How Large A Position Should You Take?

• September 28, 1999
• Bob Pisani

Suppose you have $100,000 in your trading account. You see a profit-making opportunity in an option, and need to decide how large a position you should take.

Two factors, reward and risk, must be weighed against one another before you can make a rational decision about your position size

Of course, there is risk in any position. The larger a position you take, the greater your potential profit–but also the greater your risk. These two factors, reward and risk, must be weighed against one another before you can make a rational decision about your position size. With options, you have a way of measuring these quantities, and option trading seems to be uniquely suited to making these kinds of measurements. The problem is to take these measurements and combine them in such a way that you maximize account growth.

This problem has been solved–theoretically–for options and any other investment situation. The guiding principle: choose a position size that will make the expected logarithm of your return as large as possible. This is called the “Kelly Criterion,” popularized by Ralph Vince as “optimal f.” If you are uncomfortable with the mathematical character of this principle, don’t worry. Let’s talk a bit about what the Kelly Criterion can do for you, and we’ll get into the math later.

Several facts have been demonstrated mathematically about the Kelly Criterion in a theoretical setting. Speaking loosely, suppose you follow this allocation policy and I follow a different allocation policy. The following two facts will emerge:

1. Your fortune will multiply at a rate far greater than mine, and we will arrive at a time when your fortune is twice mine, and later four times mine, and, in fact, a time when your account is any given multiple of mine that you want to choose. Of course, the larger the multiple, the longer it will take–but we will get there.
   
2. If we both have a goal of reaching a certain account size, say $1 million, your expected time to reach that goal is less than mine.
   

These two facts seem to argue persuasively for using the Kelly Criterion to determine the best position size. But before you jump ahead and start studying non-linear programming and other related subjects, wait until you read my next commentary, in which I’ll show you how the Kelly Criterion works in a very simple situation.