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Position Sizing to Maximize your Stock Trading Returns
By: Trader Jack

Of all the aspects of stock trading, one of the most difficult is deciding what size position to open. Unless you are using a strictly mechanical system that explicitly defines your trade size, figuring out exactly how much of your hard earned cash to 'put on the line' can be extremely hard to decide. Rules of thumb such as 'never risk more than 5% of your portfolio' are fine, but may leave you in the dust on fast moving days. As we here at www.traders101.com would say, faint heart never won fair lady, yet look before you leap! Oftentimes, what looks like an average trade starts to run away as the stock market climbs, and you end up wishing that you had taken a large position. And conversely, if you get it wrong, you can end up banging your head against your computer screen and wishing forlornly that you had been a little more 'prudent' in your trading size.

Not to worry. There is, in fact, a fairly simple formula you can use to determine the correct position size for your stock trades, as long as you are looking for long term growth. Known as the 'Kelly Formula', this is a useful little equation that is simple to understand, and simpler to apply. You will need to have done some trades before, and have the stats at hand (the ratio of your winners to losers, and the size of those winners and losers). Lets say that 'WP' means 'Winning Percentage' and 'WL' means 'Historical Average Win Size divided by Historical Average Loss Size'. The 'Kelly Formula' is then:-

Kelly Forumula = ((WP * WL) - (1 - WP)) / WL

Ouch! Scary maths! Not! To understand this formula, let's take an example, based on a series of 15 trades. Lets say that you made money on 10 of these trades, at an average of $200 profit per trade, and lost money on 5 at $100 per trade (you cut your losses! Good man!). Substituting the figures into the formula, we have:-

An average win size of $200, an average loss size of $100, so the 'WL' number is 2. The Winning Percentage (or 'WP') is 10 / 15 or 0.67

Kelly = ((0.67 * 2) - (1 - 0.67)) / 2

The result is 0.505. In other words, if your win / loss ratio is consistent, you will maximize your returns by only risking about 50% of your equity on each trade. Now the problem you can see is that risking anything above 5% or 10% of your equity on a single trade would be regarded by most traders (and certainly everyone at www.traders101.com) as insanely brave. So the next step is to ask yourself 'What is the absolute maximum I would be happy losing on a single trade'? You then multiply this absolute maximum drawdown by the Kelly number and voila - your position size. If your maximum acceptable drawdown while stock trading is (e.g.) $1000, then your optimum position size would be 1,000 * 0.505 = $505.

What about if your winners were only good for an average of $100, whereas your losers ate up an average of $120? Let's have a look. The 'WL' number is 100/120 = 0.83. The 'WP' or winning percentage is still 0.67. The substitution then gives you:-

Kelly = ((0.67 * 0.83) - (1 - 0.67)) / 0.83

which is 0.274 or about 27.5%. Multiplied by your 'maximum acceptable drawdown' of $1000 this is $275. So as you can see, the formula adjusts as your ratio of winners to losers changes, and also as the size of your winners and loser changes. One final note - this topic ties in with 'Expectancy'. Expectancy is defined as:-

(% of wins x Avg Win Size ) - (% of Losses x Avg Loss Size) = Expectancy

Just remember that you should NEVER trade with money you aren't prepared to lose!

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About The Author

Trader Jack likes to write for www.traders101.com - the free stock trading site from traders Initiative helping traders get up to speed fast!

This article was posted on September 15, 2005

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