Forex Talking

The determination of the size of the trading position is the third, and in the eyes of many, the most important component of a trading strategy. Simply stated, trade sizing determines our bet size, or the amount of capital to be risked on each trade.

Definition: A position sizing rule determines the number of contracts or shares that are committed to each trade. It is very easy to see the impact of position sizing at either extreme. If we trade a position size that is too small—for example, one S&P contract per $1,000,000—our trading equity is not being used at optimal levels. Conversely, a position size that is too large—for example, 100 S&P per $100,000—for our capital can increase our risk of ruin to certainty. Only the most naive and inexperienced of traders will be ensnared by either of these extremes. It is in the area between these two opposite ends of the spectrum, however, where a sizing rule will have the most impact on strategy performance, whether positive or negative.

The best and most efficient sizing principle will be the one that applies our trading capital in an optimal manner so as to achieve maximum returns with an affordable risk.

The problem of efficient position sizing is difficult. One of the primary reasons for this difficulty, however, arises from the non-Gaussian (especially fat-tailed) distributions that are typical of financial markets and the returns that are produced by them. Such distributions reduce the effectiveness of traditional statistical estimation methods that are employed in more sophisticated sizing methods.

Another level of difficulty in sizing arises from the lack of statistical robustness of many of the measures that are employed in sizing rules. Last, but not least, position sizing takes on another level of complexity when a trading strategy is incorporated in a portfolio of markets.

We will look at four position sizing examples:

1. Volatility adjusted

2. Martingale

3. Anti-Martingale

4. The Kelly method

A volatility adjusted sizing rule uses the size of the account and the size of the risk assumed per contract per trade.

Definition: Volatility adjusted position sizing determines the number of contracts or shares per trade as a fixed percentage of trading equity divided by the trade risk.

For example, assume:

1. A risk size of 3 percent of equity

2. A risk per contract of $1,000

3. An account size of $250,000

The trade unit would be seven contracts and is calculated as follows: Total Equity to Risk = $7,500($250,000 × .03) Number of Contracts = 7($7,500/$1,000 = 7.5 rounded down = 7) An example of a well-known money management rule is the Martingale strategy. It is derived from a gambling money-management method.

Definition: The Martingale sizing rule doubles the trade size after each loss and starts at one unit after each win. There are a number of variations on this theme. One such variation is anti-Martingale.
Definition: The anti-Martingale sizing rule doubles the number of trading units after each win, and starts at one unit after each loss.

Optimal f (Fixed fractional trading) was introduced by Ralph Vince in 1990. It is based on a formula derived from the Kelly method, which was, in turn, applied by Professor Edward Thorpe to gambling and
trading. Let us look at one implementation of the Kelly formula.


Kelly % = (Win% − Loss %)/( Average Profit/Average Loss)

For example, assume a strategy that has a winning percentage of 55 percent, an average win of $1,750, and average loss of $1,250. The Kelly percent will tell us what percentage of our trading capital to risk is on the
next trade.

Kelly % = (55 − 45)/($1,750/$1,250)

Kelly % = 10/1.4

Kelly % = 7.14%

Let us use this to calculate our position size. We have our risk size of 7.14 percent of equity from the Kelly formula, a risk per contract of $1,000, and an account size of $250,000. The trade size would be seventeen
contracts and is calculated as follows:

Total Equity to Risk = $250,000 × .0714

Total Equity to Risk = $17,850

Number of Contracts = $17,850/$1,000 = 17.65

Number of Contracts = 17.85 rounded down = 17 contracts

Recall from our earlier discussions that these numbers are often lacking in statistical robustness. Another way to look at these numbers is to recognize that they are a bit fuzzy. Because of a limited sample size and
large variance, the numbers used in this formula will, in turn, introduce a significant degree of variance in the results of the Kelly formula. It is this very fuzziness that introduces a level of inaccuracy in the use of formula such as Kelly or Optimal f.

There are many different formulations of position sizing rules. They all share a way of setting the number of contracts or shares per trade. These methods are presented here as examples and not as recommendations.

It is worthy of notice that many of these sizing algorithms are derived from the gambling literature.
Position sizing is a critical component in trading system design. The problems that exist should in no way deter the strategist from exploring and evaluating such methods. The trader should be very aware, however,
of the statistical limitations of their accuracy and their inherent limitations. There is a large body of work developing in this area, since many involved with trading have finally come to accept that financial markets have a non-Gaussian distribution. Furthermore, some have now come to accept the fractal distribution of these markets.