Position Sizing Strategies: Why Equal Risk Beats Equal Dollar Investing
by D.R. Barton, Jr., Contributing Editor
Wednesday, January 17, 2007: Issue #387
“That’s the way we’ve always done it.”
This one phrase has killed more useful projects and progressive ideas than perhaps any other.
The same logic applies to the trading world. But when done properly, diversification and using position sizing strategies can offer good protection and alleviate risk.
However, you need to know that the classic way of diversifying a portfolio by investing equal amounts of cash into different stocks is not always the best. In fact, this strategy can be dangerous, as it unintentionally adds extra risk to your portfolio. Let’s see how that can happen – and show you how position sizing your stocks, the right way, will help you to get the most out of your investments.
Two Position Sizing Strategies: Equal Dollar vs. Equal Risk
When investing, you have a couple of choices when position sizing: Equal dollar weighting, versus equal risk.
To compare the two, let’s look at how each is done. For simplicity, I’ll talk about stocks, but the same concepts can be applied to futures, options and currencies.
- Equal Dollar Weighting: Splitting your money into equal parts has always been an easy way to allocate money across trades. For example, if you have $100,000 to invest, and want to distribute it in five equal parts, you’d simply buy $20,000 worth of each stock. So if you’re taking a position in a $100 stock, you’d buy 200 shares; for a $50 stock, you’d buy 400 shares, etc.
- Equalizing Risk Across All Your Trades: Instead of buying the same dollar amount in each stock, you use your stop-loss level for each position to determine the risk per share that you’re taking for a given trade (you are using stop losses, aren’t you?) Once you know your risk amount for each trade, you can calculate how many shares to buy, based on how much of your total portfolio you would be willing to risk for each trade.
And it’s this risk-based part of the equation that I’ll talk about here. So let’s do a quick calculation to see how it would work…
Let’s say you’re willing to invest $100,000 and are okay with a 1% downside risk per trade. That’s $1,000.
When the first trade comes along, your strategy dictates that you’ll get out if the stock moves $2.00 against your position. Since you’re only risking $1,000 total on the trade, here’s the math for how many shares to buy:
- $1,000 (risk per trade) divided by $2.00 risk per share) = 500 shares to purchase.
And when you compare this risk-based method with just allocating equal dollar amounts across trades, you have an advantage. Let’s take a look at the numbers…
Why The Equal Risk Position Sizing Strategy Beats Equal Dollar Investing
To do this comparison, we’ll look at two portfolios that contain the same two stocks. To make this even easier, we’ll say both stocks are $50 each.
However, Stock A is a slow-mover with very low volatility, so we set our stop-loss/trailing stop just $1 below the entry price. But Stock B has a very high volatility, so we set the stop-loss $4 below the entry price.
- Equal Dollar Portfolio: This one is easy. We simply buy $50,000 dollars worth of each stock, or 1,000 shares. ($50,000 divided by $50 per share = 1,000 shares). ~ For Stock A (the slow-mover with the $1 stop-loss), we buy 1,000 shares ($1,000 risk per trade divided by $1 risk per share = 1,000 shares).
- Equal Risk Portfolio: We determine how many shares to buy, based on risking 1% – or $1,000 per trade. ~ For Stock B (the volatile stock with the $4 stop loss), we buy 250 shares ($1,000 risk per trade divided by $4 risk per share = 250 shares).
Let’s look at what happens if we encounter a little bit of market weakness and we hit the trailing stops on both stocks:
So it’s easy to see that for stocks with widely varying stops, an equal dollar portfolio can take on too much risk – especially if stocks are lower priced and volatile.
Another scenario is when the more volatile stock hits its trailing stop and the less volatile stock wins an amount equal to its stop amount.
In this scenario, you have one winner and one loser, yet in the equal dollar portfolio, you wind up losing big, while breaking even in the equal risk portfolio.
Without drawing a new table, you can easily see that if the both stocks move in your favor, you do actually make more money with the extra money invested in the equal dollar portfolio. But the increased profit is in equal proportion to the increased risk.
And in general, when taking on one unit of extra risk, you don’t want to only get the possibility of one unit of extra return. But since we obviously can’t guarantee which trades will work and which ones won’t, a strategy that equalizes risk makes intuitive sense.
One final note: If your strategy uses a set percentage for a stop-loss or trailing stop (25% of a stock’s price, for example), then the “equal dollar amount” and “equal risk” portfolio position size becomes mathematically the same!
So folks that are using a 25% trailing stop are, in fact, using an equal risk strategy if they put equal dollar amounts into each trade.
D. R. Barton, Jr.