# Position Sizing Methods

The following are the position sizing methods available in Trading Strategies:

• Fixed Size: Buys a fixed number of shares/contracts/units.

• Fixed Dollar: Buys a fixed dollar amount of shares/contracts/units.

• Account Balance: Buys as many shares/contracts/units as possible with the current account equity. Shares Traded = (Current Account Balance / Entry Price) rounded down to the nearest whole number of shares.

(Power User only)

• Percent of Account: Buys as many shares/contracts/units as possible with the specified percent of account equity.

• Fixed Leverage: Buys the number of shares/contracts/units that limits trading to the specified leverage of the account equity.

• Fixed Fractional: Buys the number of shares/contracts/units that risks the specified fraction of account equity per trade, where risk per trade is the size of the initial protective stop or the largest historical trade loss when a trade has no initial protective stop.

• Kelly formula: Buys the number of shares/contracts/units that risks the fraction of account equity per trade calculated by the Kelly Formula, which takes into account the systems history of winning and losing trades. Risk per trade is the size of the initial protective stop or the largest historical trade loss when a trade has no initial protective stop. Note that the Kelly Formula can result in suggesting 0 or negative shares/contracts/units be traded for a strategy with a losing history, in which case NeuroShell Trader simply uses 1 share/contract/unit for trading to reduce risk to a minimum level.

• Optimal f: Buys the number of shares/contracts/units that risks the fraction of account equity per trade calculated to maximize the systems end profit. Risk per trade is the size of the initial protective stop or the largest historical trade loss when a trade has no initial protective stop. Developed by Ralph Vince.

• Secure f: Buys the number of shares/contracts/units that risks the fraction of account equity per trade calculated to maximize the systems end profit when limited to the specified maximum system drawdown. Risk per trade is the size of the initial protective stop or the largest historical trade loss when a trade has no initial protective stop. Developed by Leo Zamansky and David Stendahl.

• Profit Risk: Buys the number of shares/contracts/units that risks the specified fraction of initial account equity and the specified fraction of closed trade profits per trade. Risk per trade is the size of the initial protective stop or the largest historical trade loss when a trade has no initial protective stop.

• Volatility Risk: Buys the number of shares/contracts/units that risks the specified fraction of account equity per the current Average True Range of price movement

When using Fixed Ratio position sizing, a necessary starting balance required to buy one share is calculated such that as the account equity grows geometrically the number of shares purchased never outruns the money available, especially when margin is being utilized.  That necessary starting balance to purchase one share is determined by the formula: StartingBalanceForOneShare = CostToBuyOneShare * CostToBuyOneShare / \$ProfitPerShare – ((2 * CostToBuyOneShare / \$ProfitPerShare – 1) ^ 2 – 1) / 8 * \$ProfitPerShare.  Once the necessary starting balance is determined, then the actual number of shares bought is then calculated as NumberShares = 0.5 * ((1 + 8 * (AvailableAccountBalance – StartingBalanceForOneShare) / \$ProfitPerShare) ^ 0.5 + 1).

For a full understanding of this position sizing method, read the twenty eight pages (pages 80 ‘ 97) that Ryan Jones devotes to the topic in his book “The Trading Game” cited in the notes below.

• Margin + Drawdown Sizing: Buys the number of shares/contracts/units such that the account equity will cover the margin requirement and the specified multiple of the largest historical system drawdown.

• Fixed Dollar Amount per Unit: Buys one share/contract/unit for every specified dollar amount of account equity.

• Fixed Dollar Risk: Buys the number of shares/contracts/units that risks the specified dollar amount per trade, where risk per trade is the size of the initial protective stop or the largest historical trade loss when a trade has no initial protective stop.

Notes:

• For detailed information about the calculation and use of the position sizing methods, please see the following books and articles:

“Portfolio Management Formulas” by Ralph Vince, John Wiley & Sons, New York, 1990.

“Trade Your Way to Financial Freedom” by Van K. Tharp, 2nd edition, McGraw-Hill, New York, 2007.

“The Trading Game” by Ryan Jones, John Wiley & Sons, New York, 1999.

“Secure Fractional Money Management ” by Leo J. Zamansky, Ph.D., and David C. Stendahl, July 1998 issue of Technical Analysis of STOCKS & COMMODITIES magazine.

“The Definitive Guide to Futures Trading (Volume II)” by Larry Williams, Windsor Books, 1989.