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Position sizing

Fixed fractional position sizing

Fixed ratio position sizing

Position sizing optimization

Monte Carlo analysis

Trade dependency

Significance testing

Equity curve trading

Performance statistics


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Michael R. Bryant, Ph.D. Position Sizing

 by Michael R. Bryant




Most trading experts agree that money management is one of the most critical aspects of trading. Position sizing -- also known as trade sizing, bet sizing or betting strategy -- is one of the key elements of money management. Whatever you call it, it's the process of determining how much to trade. If you trade stocks, it's the number of shares to trade. If you trade futures or options, it's the number of contracts. Position sizing can be used to increase returns, reduce risk, improve the risk/return ratio, and smooth the equity curve, among other goals.


Position sizing is particularly important when leverage is involved, as with futures trading. If you trade too many futures contracts, a string of losses could force you to stop trading. In fact, with the built-in leverage of futures, you could lose more money than you have in your account. On the other hand, if you trade too few contracts, much of your account equity will sit idle, which will hurt your performance. Finding the right balance is a key element of risk management.


There are many different ways to vary the number of contracts or shares when trading. Some of the most commonly used methods are listed below.


Fixed size. The same number of contracts or shares is applied to each trade; e.g., two contracts per trade.


Fixed dollar amount of equity. A fixed dollar amount of account equity is needed for each contract or share; e.g., $5000 of account equity per contract.


Fixed fractional (also known as fixed risk). The number of contracts or shares is determined so that each trade risks a specified fraction of the account equity; e.g., 2% of account equity is risked on each trade. Fixed fractional position sizing has been written about extensively by Ralph Vince. See, for example, his book “Portfolio Management Formulas,” John Wiley & Sons, New York, 1990.


Fixed ratio. The number of contracts or shares increases by one for each "delta" amount of profit earned per contract. For example, if the delta is $3000, and the current number of contracts is two, you'll need $6000 of profit before increasing the number of contracts to three. Fixed ratio position sizing was developed by Ryan Jones in his book “The Trading Game,” John Wiley & Sons, New York, 1999.


Margin Target. Margin target position sizing sets the size of each position so that the chosen percentage of account equity will be allocated to margin. For example, if you choose a margin target of 30%, then 30% of the account equity will be allocated to margin.


Leverage Target. This method sets the position size so that the leverage of the resulting position matches the selected target. Leverage is defined as the ratio of the value of the position to the account equity. For example, if 1000 shares of a $30 stock are purchased with a $25,000 account, the leverage would be $30,000/$25,000 or 1.2.


Percent Volatility. The percent volatility method sizes each trade so that the value of the volatility, as represented by the average true range (ATR), is a specified percentage of account equity. This method is attributable to Van K. Tharp. See, for example, his book "Trade Your Way to Financial Freedom," 2nd ed., McGraw-Hill, New York, 2007, pp. 426-8.


With each of these methods, except for fixed contract position sizing, the number of contracts or shares increases as profits accrue and decreases as the equity drops during a drawdown. Position sizing methods that use this approach are known as antimartingale methods. Antimartingale methods take advantage of the positive expectancy of a winning trading system or method. If you have an "edge" with your trading (i.e., your trading method is inherently profitable), you should use an antimartingale method, such as those listed above.


The alternatives, known as martingale methods, decrease the amount at risk after a win and increase the amount at risk after a loss. A commonly used example is "doubling down" after a loss in gambling. Martingale methods are most often used by gamblers, who trade against the house's advantage.


Provided you have a profitable trading method, antimartingale methods are always preferable over the long run because they're capable of growing your trading account geometrically. However, it's sometimes possible to lower your risk by taking advantage of patterns of wins and losses, similar to martingale methods. Two ways to do this are via dependency rules and using equity curve trading. Both of these methods can be used in addition to whichever position sizing method you choose.


While martingale methods are not recommended by themselves, these adjustments to the antimartingale methods listed above can sometimes prove beneficial. For example, if your trading system or method tends to have long winning and losing streaks, it might be beneficial to skip trading after a loss until the first skipped trade would have been a winner. Resume taking the signals until a loss is encountered. This is an example of a dependency rule for systems with positive dependency. Alternatively, you might try trading the equity curve. For example, you could stop taking the trading signals when the moving average of the equity curve crosses below the equity curve line. Resume trading when the moving average crosses back above the equity curve.


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