The Percent Risk Model: Size Does Matter

The Percent Risk Model: Size Does Matter

It's time now, once again, to dispel those ugly rumors that "size doesn't matter" Indeed, size does matter in investing, and it matters just as unambiguously as when parallel parking a Buick in heavy traffic. The difference being (among other things) that in parking a 'land shark' like a Buick, it is the 3-mile long hood and the cavernous trunk, that clouds up the process. In trading or investing, it is the even more often 'inopportune' impact of emotions that clouds our clarity and takes us out of our game plan. Let's go back to what our "game-plan" is, whether it be for trading or more long-term investing, and that is capital gain within a solid risk management mantra.

Let's first talk about how we could apply the 'position sizing' aspect, and then we will talk about the advantages and disadvantages to this approach. To begin with, the position sizing aspect can be the most important part of a trading system. If you have a good, positive expectancy system, then most of your profit or loss will come from sizing techniques.

First, we use positions that are based on risk tolerance, or a percent risk model. Let's say you have a $1,000,000 marginable trading account. Depending on your risk tolerance, you may choose to size your positions equally based upon a dedicated risk relative to your overall account. For instance, lets chose a 1% risk tolerance on a portfolio of that size. Depending on your risk tolerance or aggressiveness, you may adjust that risk percentage from .5% to 4%, but typically not beyond. Using a 1% risk, meaning that each position will be sized so that the risk is no more than 1% of your $1,000,000 account. One percent of one million dollars is $10,000, so that will be our risk for our first position. So let's now approach that single position based on our calculated risk.

Position Sizing Example XYZ: In this example we will use our old favorite XYZ. Since we know (can determine) our stop loss point for our trade in stock XYZ, we would determine the distance from our entry point to our stop loss point, and then divide that into our $10,000 risk for the position. The resulting value will be the number of shares that we can purchase to stay within our 1% risk tolerance. Here's an example, XYZ gave us a 'buy' signal at $50 yesterday and all of the technical and fundamental work suggests we want to play this move. We will maintain a stop loss of $45 for traders, which will break a double bottom negating the positive pattern that was developing, and the stock has opened this morning at $49. So our entry price right now would be $49, and our risk on this trade is $4 ($49-$45). We now divide our $10,000 risk for this position, by our $4 risk per share to give us a lot of 2500 shares. Naturally, as the distance to your stop loss point decreases, your share purchase will increase; likewise the opposite will occur when you are considering stocks trading further from your stop point.

An Anti-Martingale Approach: Two basic principles underlie our position-sizing process. First, you are increasing the size of your trades when the market environment is favorable and your success rate is fairly high. As well, when a murky environment exists for an extended period of time (i.e. last year for example) your position sizes will naturally contract on the way down. Let me explain:

You may have heard the term "Martingale system", which is what you would employ at the roulette table in Vegas, a method of increasing your position size with each play that goes against you. In Wall Street terms that would translate into "double-up to catch up!" Unfortunately, it only makes reasonable sense in Vegas because laws of probability suggest that each result of "red," for example, increases the likelihood of an occurrence of "black" in a given sample size. So if your risk tolerance allows you staying power at the table, you can expect that within a reasonable number of spins you will payoff and have a big position placed to participate. On Wall Street that methodology has no place in a proper risk management scheme.

This method of position sizing is an anti-martingale strategy, in that the 'bet' increases as our equity increases. This is opposed to a martingale strategy above where your bet would increase to compensate for losses in a portfolio. This anti-martingale approach allows our position sizes to increase as our portfolio grows. Let's say our portfolio began at $1,000,000, but after a year of trading was now at $1,500,000 of total equity. Well, using the same position sizing technique our risk for each position would now be $15,000 (1% of $1,500,000) while still only risking 1% of our overall account per trade. So let's say that a similar trade presented itself with XYZ, our position size would now have grown to 3750 shares ($15,000 divided by $4).

** You may note that we will sometimes cost average down or cost average on long positions; this would always done within the context of our 1% limit. For instance, we may initiate a .5% position and add another .5% position at a later date. The sum is an approximate 1% risk position.

Discounting Your Emotions: The second fundamental aspect of this approach deals with emotions. You have heard it before, and it is somewhat of a cliche, but that doesn't make it any less of a profound statement. To be an effective trader or investor you must discount emotion. Perhaps you are emotionally tied to the stock, but don't let it be the reason you ruin your returns for a year. The percent risk model takes some of the emotional influence out of the process by forcing you to make smaller 'bets' when the market dictates, and forcing you to make sequentially equivalent bets on each trade. When our market indicators are bullish, we will take a 1% position in every trade, regardless of how bullish our emotions are telling us we should be on any single trade. This keeps any single position from beating us, and allows for our trading system to work.

Using this percent risk model, you can imagine the results in a favorable environment. Those of you that have positioned by size in a good moving stock know how this model can help boaster returns to the upside. In essence, it is one way to keep up with some of the capitalization weighted indexes during a bull market. We know that as the NASDAQ, for instance, rises, each rising stock is placed a larger 'bet.' So to compete with such an index in a bullish environment, your 'bets' should be allowed to grow with the portfolios growth as well. But what about the extreme cases in a negative direction, such as in 2000 and so far this year?

Let's say you were to raise your percent risk to 3%, a little more aggressive but still a reasonable number. Let's then suppose you had 20 losing trades in a row, you would have lost 46% of your investment, because the position sizes decreased after each loss. The first hit would take 3% from your portfolio, leaving you with 97% of your original capital, but your second trade would then only be sized at 2.91% of that original capital. So even after 20 trades, losing full positions, you would still retain more than half of your capital. Likewise, if a $1 Million portfolio kept an equal dollar sizing strategy that began at 3% or a $30,000 investment, you would retain only 40% of your original capital after a 20-loss streak. Or worse, let's say you increased your risk to 10% per position after a great year of 1999 because you felt invincible. (Disclaimer: Anything above 4-5% is considered a far too "emotional" number) After 20 losses in that "juiced up" scenario you would report a loss of 95%. That hurts.

After a draw down of 46%, you would have to return just under 100% to break even. That's an ugly number, but when compared with the unmanageable 900% you would have to yield after a 95% decline, it is feasible at least. It is important to know what your maximum draw down can be, however, and we can discuss that further in follow up conversations. While a percent-risk model gives you advantages to the upside, you must be willing to accept a certain draw down (dependant upon % risk chosen) during weak periods to achieve the expected return over time.

Extrapolation of Van K. Tharp's research, the equal share and equal dollar method vastly under perform the percent risk method. If you are interested in explanations on other various ways to size positions within a portfolio, we recommend purchasing Trade Your Way to Financial Freedom, by Van K. Tharp, Ph.D. There is a chapter on position sizing where Tharp covers a percent risk model as well as a percent volatility model, in addition to discussing the limitations of equal dollar and equal share models. I would definitely recommend this book, as it explains very clearly the advantages and disadvantages to particular position sizing techniques.

In his study, the same number of trades/signals were taken regardless of the position sizing model. (See his book for all the details of the research study). I am merely trying to summarize the vast difference in returns that can exist as a result of what position sizing model you choose. This study was conducted over a 5.5-year time span, and was based upon a $1 Million initial investment.