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Position Sizing Background

For most of my investing career, I 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 that there were better ways to position sizing (money management) but I didn’t know what they were.

In the August 2007 issue of Active Trader magazine, Volker Knapp (see Trading system lab: “Percent volatility money management”) tested a system that used volatility to determine the position size. I already use volatility to determine stop placement (see Stop Placement), so this was a welcome addition. The article was based on Van K. Tharp’s book Trade Your Way to Financial Freedom.

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.

The percent volatility position sizing method adjusts the risk according to the stock’s volatility. Tests described in the article say 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.

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. *Click the image to make it larger.*

When a bear market begins, I cut my position size to limit losses. Recently, I decided to derive a mechanism to achieve that. The following table shows the rules for this new method to limit losses in a bear market.

By definition, a bear market begins when an index (I use the S&P 500) drops 20% below a peak. When that occurs, cut the amount allocated to each trade by half. If my position size is $20,000, I will cut it to $10,000.

If the market drops another ten-percentage points, then cut the position size in half again — from $10,000 to $5,000 in my case. Continue cutting the position size by half until it reaches $2,500 (or whatever value you choose).

The advantage of this position-sizing algorithm is obvious. As the bear market begins and worsens, your have the potential to lose less and less of your trading capital. However, this method does keep you in the market, so you can shop for bargains among a variety of stocks. That promotes diversity, which is also a good thing.

If there is a drawback, it’s that at a bear market bottom, you are investing few dollars in the market. When the bull market resumes, that’s when you want to pile back in. Of course, it’s often difficult to determine when a bear market ends and a bull market begins, so prematurely ramping up the position size can lead to larger losses.

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How do you size the positions in your portfolio, assuming you wish to make multiple buys per stock (or just once)?

To get the position size (shown in the above table as $20,000 then $10,000), take the value of the trading account and divide it by the number of positions you want to hold. The number of positions you choose is up to you. Many will say to hold no more than 10 to 12 with at least 7 to 8 positions to give adequate diversity. As I write this, I own 22 positions with an eye to 30. Think of this as my own private mutual fund. I’m a skilled investor/trader with 30+ years of experience, so owning this many is not a problem…but that’s just me.

For example, say you have a portfolio currently valued at $300,000, and want to hold 30 positions, then each position would be $10,000. Within 20% of a bull market peak, you’d start with 10k per position. When the bear market begins, you’d cut that in half, to 5k and then 2.5k as the bear market worsens.

That gives you the amount to invest in each stock. Now, let’s adjust the position for volatility. The more volatile the stock the fewer shares you should own.

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I saw one algorithm that compared the current stock’s volatility with its historical range. The “current” period used a 10-day high-low calculation but they didn’t specify what was meant by “historical.” In their example, they said “a few years ago” (whatever that means).

That bothered me. A company could have had a drug failure, dropping the stock by 70% in one session (huge historical volatility) and then sold the division. You might not know that unless you read the press releases or discovered it some other way.

I have a better idea. Why not compare the stock’s volatility to the market’s? Here’s the formula.

Shares = (PositionSize * (MarketVolatility / StockVolatility)) / StockPrice

PositionSize comes from the above table, so it’s adjusted for the market conditions.

MarketVolatility is the daily change of the market over the last month, averaged, expressed as a percentage.

StockVolatility is the daily change of the stock over the last month, averaged, expressed as a percentage.

For the two volatility calculations, I calculate the high-low difference of the stock or market index (I use the S&P 500 index) each day for 22 trading days (about a month), average it, and divide it by the most recent close. This is nearly the same calculation that I use for a volatility stop, so check that link for an example. You can use the ATR, but it’s not as effective.

This will give you the number of shares to invest per position. You can have multiple positions per stock.

In short, take the ratio of the two volatilities to further adjust the bucks you spend and divide that by the current share price to get the number of shares.

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We adjusted the amount spent per trade for the market conditions, and then we adjusted the number of shares for the stock’s volatility. The third leg of the algorithm is to use a volatility stop. That calculates a stop loss order based on a stock’s volatility in a manner similar to the above volatility calculation.

Thus, you have three pieces: Adjusting the position size for the market conditions, adjusting it for the stock’s volatility versus the market’s, and using a volatility stop to limit losses.

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Let’s assume we want to buy Gap (GPS) stock. It closed Friday, December 17, at 21.19. Our portfolio has a current value of $100,000 and we want to hold 10 stocks in the portfolio.

The S&P index is down less than 20% from it’s high a few days ago (it’s down less than 1% from the high). Thus, we’d spend the full $10,000 for this trade (that’s $100,000 / 10 stocks = $10,000). To find the number of shares, the market volatility is 0.009 (0.9%) and the stock’s volatility is 0.0213 (2.1%) — I have a program that calculates the two volatilities automatically. Plugging this into the formula, we get,

Shares = ($10,000 * (0.009 / 0.0213)) / 21.19 or 200 shares (I round up to the nearest 100 shares). They would be worth 200 * 21.19 or $4,238.

The volatility stop would be placed at 20.15, or 5% below the current close.

That gives us plenty of dollars to spend on the stock sometime in the future, to increase the position. The volatility and portfolio value will have changed by then, so you’d run another calculation to get the next investment amount.

— Tom Bulkowski

Copyright (c) 2011 by Thomas Bulkowski. All rights reserved. Reprinted with permission.

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