Friday, February 17, 2006

Position Sizing with Leverage

After running through the calculations from the previous post I noticed that one position with a 2% of total equity risk size gobbled up 25% of my account equity. I don't like holding only 4 positions just because I like to get a little diversification. So I got back to thinking about the hedge fund guys and commodity trading advisors that leverage several positions. I ran a couple of calculations with 2x leverage that you can get with stocks, and 4x and 7x that futures traders can use. I'll use the same example with ANTP even though I'm not sure there are futures contracts for it.

Risk size is still 2% of $15,000 of total equity = $300/position

2x Leverage
In this case because I'm levered at a 2x rate, I know my loss can only be $150. This will dictate a smaller position size than the non-levered position. I will say that interest is negligible for the sake of easier calculations.

Position Risk = Commissions - margin costs- (transaction costs)Position Size
$150 = $20 + ($16.08-$14.92)*Position Size
$130 = $1.16*Position Size
112 shares = Position Size
112 shares * $16/share = $1793
% of total equity = 11.9%

Now that I'm trading with leverage, I can only risk 112 shares instead of the 241 shares that I could risk with no margin. I can also have up to about 9 positions of similar size.

Now to futures contracts:
4x Leverage
With the same equity risk I'm going to have to reduce the margin portion to $75 ($300/4).

$75 = $20 + (1.16)* Position Size
$55 = 1.16*Position Size
47 shares = Position Size
47 shares * $16/share = $752
$752/$15000= 5% of total portfolio equity in this position

Now the portfolio can hold a fairly well diversified selection of positions; up to around 20.

7x Leverage
This is more like options and more levered futures contracts. The margin risk size has come from $300 with no leverage to $42 with 7x leverage. Note that commission costs eat up half of this positions equity risk.

$42 = $20 + ($1.16) Position Size
$22 = $1.16 * Position Size
19 shares = Position Size
19 shares * $16/share = $304
$304/$15,000 = 2% of total portfolio equity

Now the portfolio can hold around 50 positions. Note that if you only have $15,000 and/or a mechanical system that can easily keep track of your 50 positions, then you probably do not want 50 positions. You probably don't want 10 positions. Commission starts to eat up large portions of position risk with such a small account. This is why professional traders suggest having a good bit of money ($50k - $100k) to trade before even starting. From what I've seen, many professional money management firms will trade 30-50 positions.

In summary, the effect of leverage is that it can actually increase diversification, which may or may not be a good thing to you. If you crave volatility in your account then you can increase your position size. I personally only like upside volatility :). Negative volatility or drawdowns are a part of every trend following system, but there are ways to reduce drawdowns and still have good returns. Once again, I will be using this information in my own mechanical system, so it definitely has some practical applicability in both mechanical and discretionary trading.

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