Bulkowski’s Position Sizing

Written and copyright © 2008-2010 by Thomas N. Bulkowski. All rights reserved.

Below are two simple methods to size positions for trading stocks.

Background

I have always used a fixed dollar amount for money management when buying stocks. At the beginning, it was $2,000. That bought me 100 shares of a $20 stock. I thought that’s the method that everyone used. As I learned about the stock market, I knew there were better ways to size a position (money management) but I didn’t know what they were.

In the August 2007 issue of Active Trader magazine ( www.activetradermag.com), Volker Knapp (see Trading system lab: "Percent-volatility money management") tests a system that uses volatility to determine the position size. I already use volatility to determine stop placement (see Stop Placement), so this is a welcome addition. The article is based on Van K. Tharp's book Trade Your Way to Financial Freedom.

Percent-Risk Position Sizing

The first method, percent-risk position sizing, is well-known and it’s based on risk to determine the position size. For example, if you are looking to buy a stock with a price of $20 and a stop loss of $19, with a maximum loss of $2,000, you should buy 2,000 shares.

The formula for this approach is:

DollarRiskSize/(BuyPrice - StopPrice)

In this example, the DollarRiskSize is $2,000, the BuyPrice is $20 and the StopPrice is 19 giving a result of $2,000/($20 - $19) or 2,000 shares.

Percent-Volatility Position Sizing

This method adjusts the risk for volatility of the stock. Tests described in the article says it performs much better than the percent-risk method.

Here’s the formula.

PositionSize = (CE * %PE) / SV

Where CE is the current account equity (size of portfolio)

%PE is the percentage of portfolio equity to risk per trade.

SV is the stock’s volatility (10-day EMA of the true range).

For example, if the current account equity (CE) is $100,000, the percent of portfolio equity we want to risk (%PE) is 2%, and the stock’s volatility is $1.25, then the result is: ($100,000 * 2%) / $1.25 or 1,600 shares.

Instead of calculating the 10-day exponential moving average of the true range, I just calculate the volatility using Patternz, which provides it at the click of a button.

The downfall of these two methods is that if your portfolio is $100,000, then the trade just described would chew up 1,600 shares x $20 buy price or $32,000. Thus, you can buy just over 3 stocks, giving you a concentrated portfolio. The percent-risk method would be even worse with $40,000 used for just one stock. (Of course this assumes that the stocks share the same buy price, volatility, and so on).

One way to avoid the concentrated portfolio problem is to divide the $100,000 into $10,000 allotments (or whatever size you feel comfortable with that would lead to a diversified portfolio), one for each stock. Use the same formula to determine the share size. In the percent-volatility example, the computation would be: ($10,000 x 2%) / 1.25 or 160 shares.

I don’t know what this does to the profitability of the method because the article’s author didn’t discuss this. In any case, this page is about position sizing and not portfolio theory.

Excel Spreadsheet Template

I have an Excel spreadsheet template which does the math for both techniques. To use the spreadsheet, first download it and then fill in the yellow cells with the appropriate information. The position size appears in the blue cells. The following shows what the template looks like.

-- Thomas Bulkowski

Copyright © 2008-2010 by Thomas N. Bulkowski. All rights reserved. Exercising adds minutes to your life. That means you’ll spend 5 additional months in a nursing home at $5,000 per month.