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A Primer on Position Sizing and Compounding a Winner

In trading, controlling the risk in a portfolio is determined by position sizing.  Most trading firms employ a fixed fractional contract position sizing method.  Under this methodology, positions are determined using the following formula:

Fixed fractional bet sizing:
Amount risked per trade = closing equity * fixed percentage risked per trade (e.g. 25bps)

Once the Fixed-Fractional Contract Position Sizing Formula has been used to calculate the amount of risk to put on with a trade (in dollar terms), the Risk-Basis Position Sizing method is employed to determine how many shares or contracts of an instrument to buy or sell.  The Risk-Basis Position Sizing method considers the risk for each security, where risk per share is the entry price minus the stop-loss point.  It divides the total risk allowance (e.g. 25bps in dollar terms) by the risk per share to determine the number of shares to trade.  Legendary systems and Trend Following trader Ed Seykota offers the following insight on this method, “over time the fixed-fraction system grows exponentially and surpasses the fixed-bet system that grows linearly.”  In other words, one is trading larger size positions (in dollar terms) as the account balance expands.  This is when one’s trading is at its best.  Conversely, one trades the smallest when experiencing a drawdown or when a trading process is out of favor. 

While this form of position sizing offers a solid starting place for building a trading system, there are many deviations employed by professional traders. For example, position sizing algorithms can be customized according to position volatility or correlations across the portfolio. In other words, if a security or market exhibits larger price swings over a specified time period a process can be built to allocate less risk to this position so that the position moves will not be excessively large and cause too much disruption in the equity curve. Additionally, if a proposed trade behaves too similarly with existing holdings (i.e. it displays a high correlation)  the trade can either be ruled out or scaled down since it ultimately will be nearly the same as adding to the existing position’s risk budget.

In addition to position sizing traders must determine a method for scaling into a position that works in one’s favor. In his book “Trading Systems and Methods” Perry Kaufman offers three solutions for systems traders when profits accumulate after initiating a position. These compounding structures offer different forms of leverage and risk management. The first is called the Scaled-Down Size or Upright Pyramid. Each incremental addition to the initial trade is progressively smaller and offers only a little compounding. The second option allows the addition of equal amounts of risk on each trade for a position. This is commonly referred to as an inverted pyramid and offers the most compounding. Lastly, the Reflecting Pyramid provides leverage and profit taking. When building a position using a Reflecting Pyramid, it will resemble the upright pyramid where incremental risk units diminish in size. However, when closing out of the position a trader gradually scales down the risk proportionately.

Having a foundational understanding of position sizing and compounding of a position will better equip traders to run profitable trading businesses and take advantage of an opportunity get the most from a winning trade, respectively. Through back-testing as well as actual trading an ideal position size can be determined based on the risk tolerance of the trader. The style of compounding will require some experimentation as well as rules are established for the system design and testing. Ultimately, a trader must find a process that best fits his or her personality while providing the most desirable risk adjusted returns. 

As always, please feel free to contact me with any questions.

JD
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