Monday, June 27, 2005

Position Sizing Trials

I've been experimenting off and on with different position sizing methods for years now. One of those things that are always on the back burner, so to speak.

And since sizing techniques by and large are not giving away an edge...I figured I'd write a bit about techniques I use. Especially since John Tait over at Fickle Trader wrote a nice little post about small positions and their effect on trading. Read the post and comments here.

I use a baseline of 10% for my weekly system testing and sometimes will drop down to 5% if the number of trades generated become too large. That 10% is what I call my Equity Risk (ER). Now, that's just for a system testing baseline. What I typically use for my actual Equity Risk (ER) in live trading is much lower. Usually around 2% of equity risked.

I then apply a Stock Risk (SR) of some percentage point or range of price of the stock I'm trading. This Stock Risk can actually be quite high at times...up to 17% on some positions or systems in fact. Which is better here? Range or percentage? Ah, depends on the system traded. I'll sometimes even use a combination where the percentage acts as a maximum stock risk and then adjust downard for the volatility of the stock.

Now, from here I can go real simple and just use the standard formula most people use: trunc(ER / SR). For example, if my total equity is $50,000, I'm willing to risk 2% of equity, current stock price is $25.00/share, and I'm using a percentage stop of 10% then...
ER = $50,000 * 0.02 = $1,000
SR = $25.00 * 0.10 = $2.5
Number of shares = trunc($1000 / $2.5) = 400 shares
Dollar Amount = num shares * share price = 400 shares * $25 = $10,000
If cash on hand is less than this amount then I will just take the cash on hand and divide it by the price of stock. Let's say my cash on hand was only $5,000 then I would buy: $5,000 / $25 = 200 shares of stock. Simple enough.

Now, to get a little more complicated we can go with adjusting the size of the shares purchased by the volatility of the stock. Take the same logic above but now we calculate the current range of the stock and compare it against the historical range.

I use various methods to calculate the range of a stock. Sometimes just taking the high minus the low of the past x days and divide by the historical max. Another way is to use the average true range. Regardless of the method, the point is to reduce size when stock is volatile and increase size when quiet.

Here's one of the many formulas I use:
Current Range (CR) = 10 day high - 10 day low
Maximum Range (MR) = highest value of the (10 day high - 10 day low)
Shares = trunc((1 - (CR / MR)) * ER) / SR)

Equity Risk (ER) = $50,000 * 0.02 = $1,000
Stock Risk (SR) = $25.00 * 0.10 = $2.5
Current Range (CR) = $30.00 (10day high) - $20.00 (10day low) = $10.00
Maximum Range (MR) = $60 back a few years ago.
Shares = (1 - ($10 / $60)) * $1,000) / $2.5 = trunc(336) = 330 shares
Dollar Amount = 330 shares * $25 = $8,250

Now, what's the advantage of using volatility to adjust your positions? Well, for one, it does help in evaluating systems from one time period to another. But, that's a whole nother story. The key for me is it usually smooths out my equity curve. In other words, reduces drawdowns which can lead to an increase in totals profits for the system. Just depends on how the volatility is used and the nature of your system. And for how aggressive you want to get.

There are others ways to adjust your positions that involve the overall market volatility. And if you want to get real fancy you can play with your equity curve. But, it's late and I'm sure you're bored to tears already.

For those who are interested, Stephen Vita posted a few weeks ago the position sizing he uses. Check it out.

Good Night,



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