Money Management & Position Sizing

John was a little shell-shocked over what had happened in the market over the last three days. He'd lost 70% of his account value. He was shaken, but still convinced that he could make the money back! After all, he had been up almost 200% before the market withered him down. He still had $4,500 left in his account. What advice would you give John?

Perhaps your answer is, "I don't know. I don't have enough information to know what John is doing." But you do have enough information. You know he only has $4,500 in his account and you know the kind of fluctuations his account has been going through. As a result, you have enough information to understand his money management -- the most important part of his trading. And your advice should be, "Get out of the market immediately. You don't have enough money to trade." However, the average person is usually trying to make a big killing in the market, thinking that he or she can turn a $5,000 to $10,000 account into a million dollars in less than a year. While this sort of feat is possible, the chances of ruin for anyone who attempts it is almost 100%.

Ralph Vince did an experiment with forty Ph.D.s. He ruled out doctorates with a background in statistics or trading. All others were qualified. The forty doctorates were given a computer game to trade. They started with $1,000 and were given 100 trials in a game in which they would win 60% of the time. When they won, they won the amount of money they risked in that trial. When they lost, they lost the amount of money they risked for that trial.

Guess how many of the Ph.Ds had made money at the end of 100 trials? When the results were tabulated, only two of them made money. The other 38 lost money. Imagine that! 95% of them lost money playing a game in which the odds of winning were better than any game in Las Vegas. Why? The reason they lost was their adoption of the gambler's fallacy and the resulting poor money management.

Let's say you started the game risking $1000. In fact, you do that three times in a row and you lose all three times -- a distinct possibility in this game. Now you are down to $7,000 and you think, "I've had three losses in a row, so I'm really due to win now." That's the gambler's fallacy because your chances of winning are still just 60%. Anyway, you decide to bet $3,000 because you are so sure you will win. However, you again lose and now you only have $4,000. Your chances of making money in the game are slim now, because you must make 150% just to break even. Although the chances of four consecutive losses are slim -- .0256 -- it still is quite likely to occur in a 100 trial game.

Here's another way they could have gone broke. Let's say they started out betting $2,500. They have three losses in a row and are now down to $2,500. They now must make 300% just to get back to even and they probably won't do that before they go broke.

In either case, the failure to profit in this easy game occurred because the person risked too much money. The excessive risk occurred for psychological reasons -- greed, the judgmental heuristic of not understanding the odds, or in some cases, the desire to fail. However, mathematically their losses occurred because they were risking too much money.

What typically happens is that the average person comes into most speculative markets with too little money. An account under $50,000 is small, but the average account is only $5,000 to $10,000. As a result, these people are practicing poor money management just because their account is too small. Their mathematical odds of failure are very high just because they open an account that is too small.

Hundreds of thousands of hopefuls open up their speculative accounts yearly, only to be lead to the slaughter by others who are happy to take their money. Many brokers know these people don=t have a chance, but they are happy to take their money in the form of fees and commissions. In addition, it takes many $5,000 accounts to feed a single multi-million dollar account that consistently gets a healthy rate of return.

Look at the table below. Notice how much your account has to recover from various sized drawdowns in order to get back to even. For example, losses as large as 20% don't require that much larger of a corresponding gain to get back to even. But a 40% drawdown requires a 66.7% gain to breakeven

and a 50% drawdown requires a 100% gain. Losses beyond 50% require huge, improbable gains in order to get back to even. As a result, when you risk too much and lose, your chances of a full recovery are very slim.

Managing Other People's Money

In the futures industry, when an account goes down in value, it's called a drawdown. Suppose you open an account for $50,000 on August 15th. For a month and a half, the account goes straight up and on September 30th, it closes at a high of $80,000 for a gain of 60%. At this point, you may still be in all of the same trading positions. But as a professional, your account is "marked to the market" at the end of the month and statements go out to your clients indicating what their respective accounts are worth.

Now, lets say that your positions start to go down in value around the 6th of October. Eventually, you close them out around the 14th of October and your account is now worth about $60,000. And let's say, for the sake of discussion, that your account at the end of October is worth $60,000. Essentially, you've had a peak-to-trough drawdown (peak = $80,000, trough = $60,000) of $20,000 or 25%. This may have occurred despite the fact that all of your trades were winners. It doesn't really matter as far as clients are concerned. They still believe that you just lost $20,000 (or 25%) of their money.

Let's say that you now make some losing trades. Winners and losers, in fact, come and go so that by August 30th of the following year, the account is now worth $52,000. It has never gone above $80,000, the previous peak, so you now have a peak-to-trough drawdown of $28,000 -- or 35%. As far as the industry is concerned, you have an annual rate of return of 4% (i.e., the account is only up by $2,000) and you are now labeled as having 35% peak-to-trough drawdown. And the ironic thing is that most of the drawdown occurred at a time in which you didn't have a losing trade -- you just managed to give back some of your profits. Nevertheless, you are still considered to be a terrible money manager. Money managers typically have to wear the label of the worst peak-to-trough drawdown that they produce for their clients for the rest of their lives.

Think about it from the client's viewpoint. You watched $28,000 of your money disappear. To you it's a real loss. You could have asked for your money on the first of October and been $28,000 richer.

Trading performance, as a result, typically is best measured by one's reward-to-risk ratio. The reward is usually the compounded annual rate of return. In our example, it was 4% for the first year. The risk is considered to be the peak-to-trough drawdown which in our example was 35%. Thus, this traders reward-to-risk ratio was 4/35 or 0.114 -- a terrible ratio.

Typically, you want to see ratios of 2 better in a money manager. For example, if you had put $50,000 in the account and watched it rise to $58,000 you would have an annual rate of return of 16%. Let's say that when your account has reached $53,000, it had drawn down to $52,000 and then gone straight up to $58,000. That means that your peak to trough drawdown was only 0.0189 ($1,000 drawdown divided by the peak equity of $53,000). Thus the reward-to-risk ratio would have been a very respectable 8.5. People would flock to give you money with that kind of ratio.

Let's take another viewpoint and assume that the $50,000 account is your own. How would you feel about your performance in the two scenarios? In the first scenario you made $2,000 and gave back $28,000. In the second scenario, you made $7,000 and only gave back $1,000.

Let's say that you are not interested in 16% gains. You want 40-50% gains. In the first, scenario you had a 60% gain in a month and a half. You think you can do that several times at year. And you're willing to take the chance of giving all or most of it back in order to do that. You wouldn't make a very good money manager, but you might be able to grow your own account at the fastest possible rate of return if you could "stomach" the drawdowns.

Both winning scenarios, plus numerous losing scenario, are possible using the same trading system. You could aim for the highest reward to risk ratio. You could aim for the highest return. Or you could be very wild, like the Ph.D.s in the Ralph Vince game and lose much of your money by risking too much on any given trade.

Interestingly enough, a research study (Brinson, Singer, and Beebower, 1991) has shown that money management (called asset allocation in this case) explained 91.5% of the returns earned by 82 large pension plans over a ten year period. The study also showed that investment decisions by the plan sponsors pertaining to both the selection of investments and their timing, accounted for less than 10% of the returns. The obvious conclusion is that money management is a critical factor in trading and investment decision making. (Determinants of Portfolio Performance II: An Update, Financial Analysts Journal, 47, May-June, 1991, p 40-49.)

You now understand the importance of money management. Let's now look at various money management models, so that you can see how money management works.

Money Management Defined

Money management is that portion of one's trading system that tells you "how many" or "how much?" How many units of your investment should you put on at a given time? How much risk should you be willing to take? Aside from your personal psychological issues, this is the most critical concept you need to tackle as a trader or investor.

The concept is critical because the question of "how much" determines your risk and your profit potential. In addition, you need to spread your opportunity around into a number of different investments or products. Equalizing your exposure over the various trades or investments in your portfolio gives each one an equal chance of making you money.

I was intrigued when I read Jack Schwager's Market Wizards in which he interviews some of the world's top traders and investors. Practically all of them talked about the importance of money management. Here are a few sample quotes:

"Risk management is the most important thing to be well understood. Undertrade, undertrade, undertrade is my second piece of advice. Whatever you think your position ought to be, cut it at least in half." -- Bruce Kovner

"Never risk more than 1% of your total equity in any one trade. By risking 1%, I am indifferent to any individual trade. Keeping your risk small and constant is absolutely critical." -- Larry Hite

"You have to minimize your losses and try to preserve capital for those very few instances where you can make a lot in a very short period of time. What you can=t afford to do is throw away your capital on suboptimal trades." -- Richard Dennis

Professional gamblers play low expectancy or even negative expectancy games. They simply use skill and/or knowledge to get a slight edge. These people understand very clearly that money management is the key to their success. Money management for gamblers tends to fall into two types of systems -- martingale and anti-martingale systems. And investors and traders should know about these models.

Martingale systems increase winnings during a losing streak. For example, suppose you were playing red and black at the roulette wheel. Here you are paid a dollar for every dollar you risk, but your odds of winning are less than 50% on each trial. However, with the martingale system you think you have a chance of making money through money management. The assumption is that after a string of losses you will eventually win. And the assumption is true -- you will win eventually. Consequently, you start with a bet of one dollar and double the bet after every loss. When the ball falls on the color you bet, you will make a dollar from the entire sequence of wagers.

The logic is sound. Eventually, you will win and make a dollar. But two factors work against you when you use a martingale system. First, long losing streaks are possible, especially since the odds are less than 50% in your favor. For example, one is likely to have a streak of 10 losses in a row in a 1,000 trials. In fact, a streak of 15 or 16 losses in a row is quite probable. By the time you reached ten in a row, you would be betting $2,048 in order to come out a dollar ahead. If you lose on the eleventh throw, you would have lost $4,095. Your reward-to-risk ratio is now 1 to 4095.

Second, the casinos place betting limits. At a table where the minimum bet was a dollar, they would never allow you to bet much over $50 or $100. As a result, martingale betting systems, where you risk more when you lose, just do not work.

Anti-martingale systems, where you increase your risk when you win, do work. And smart gamblers know to increase their bets, within certain limits, when they are winning. And the same is true for trading or investing. Money management systems that work call for you to increase your risk size when you make money. That holds for gambling and for trading and investing.

The purpose of money management is to tell you how many units (shares or contracts) you are going to put on, given the size or your account. For example, a money management decision might be that you don't have enough money to put on any positions because the risk is too big. It allows you to determine your reward and risk characteristics by determining how many units you risk on a given trade and in each trade in a portfolio. It also helps you equalize your trade exposure in a portfolio.

Some people believe that they are "managing their money" by having a "money management stop." Such a stop would be one in which you get out of your position when you lose a predetermined amount of money -- say $1000. However, this kind of stop does not tell you "how much" or "how many", so it really has nothing to do with money management.

Nevertheless, there are numerous money management strategies that you can use. In the remainder of this report, I'm going to present different money management strategies that work. Some are probably much more suited to your style of trading than others. Some work best with stock accounts, while others are designed for futures account. All of them are Anti-martingale strategies.

Money Management / Position Sizing 

Money management is a very confusing term.  When we looked it up on the Internet, the only people who used it the way that Van was using it were the professional gamblers.  Money management as defined by other people seems to mean controlling your personal spending, giving money to others for them to manage, risk control, making the maximum gain, plus 1,000 other definitions. 

To avoid confusion, Van elected to call money management "Position Sizing."  Position sizing answers the question, "How big of a position should you take for any one trade?"

Position sizing is the part of your trading system that tells you “how much.” 

Once a trader has established the discipline to keep their stop loss on every trade, without question the most important area of trading is position sizing. Most people in mainstream Wall Street totally ignore this concept, but Van believes that position sizing and psychology count for more than 90% of total performance (or 100% if every aspect of trading is deemed to be psychological).

Position sizing is the part of your trading system that tells you how many shares or contracts to take per trade.  Poor position sizing is the reason behind almost every instance of account blowouts.  Preservation of capital is the most important concept for those who want to stay in the trading game for the long haul.

Imagine that you had $100,000 to trade. Many traders (or investors, or gamblers) may just jump right in and decide to invest a substantial amount of this equity ($25,000 maybe?) on one particular stock because they were told about it by a friend, or it sounded like a great buy, or perhaps they decide to buy 10,000 shares of a single stock because the price is only $4.00 a share (equating to $40,000).

They have no pre-planned exit or idea about when they are going to get out of the trade if it happens to go against them and they are subsequently risking a LOT of their initial $100,000 unnecessarily.

To prove this point, we’ve done many simulated games in which everyone gets the same trades. At the end of the simulation, 100 different people will have 100 different final equities, with the exception of those who go bankrupt.  And after 50 trades, we’ve seen final equities that range from bankrupt to $13 million—yet everyone started with $100,000 and they all got the same trades.

Position sizing and individual psychology were the only two factors involved. 

Van says that this just shows how important position sizing is.

So how does it work?

Suppose you have a portfolio of $100,000 and you decide to only risk 1% on a trading idea that you have.  You are risking $1,000.

This is the amount RISKED on the trading idea (trade) and should not be confused with the amount that you actually INVESTED in the trading idea (trade).

So that’s your limit, you decide to only RISK $1,000 on any given idea (trade). You can risk more as your portfolio gets bigger, but you only risk 1% of your total portfolio on any one idea.

Now suppose you decide to buy a stock that was priced at $23.00 per share and you place a protective stop at 25% away, which means if the price drops to $17.25 you are out of the trade.  Your risk per share in dollar terms is $5.75.  Since your risk is $5.75, you divide this value into your 1% allocation (which is $1,000) and you are able to purchase 173 shares, rounded down to the nearest share. 

Work it out for yourself, so you understand that if you get stopped out of this stock (i.e., the stock drops 25%), you will only lose $1,000 or 1% of your portfolio. No one likes to lose, but if you didn't have the stop and the stock dropped to $10.00 per share, you can see how quickly your capital vanishes.

Another thing to notice is that you will be purchasing about $4000 worth of stock.  Work it out for yourself.  Multiply 173 shares by the purchase price of $23.00 per share and you’ll get $3979.  It would probably be around $4000 when you add commissions. 

Thus, you are purchasing $4000 worth of stock, but you are only risking $1000 or 1% of your portfolio.

And since you are using 4% of your portfolio to buy the stock ($4000), you can buy a total of 25 stocks this way without using any borrowing power or margin, as the stockbrokers call it.

This may not sound as “sexy” as putting a substantial amount of money in one stock that “takes off,” but that strategy is a recipe for disaster and very rarely happens. Therefore it is best left on the gambling tables in Las Vegas.

To continue to trade and stay in the markets over the long term, learning position sizing and protecting your initial capital is vital. 

Van believes that people who understand position sizing and have a reasonably good system can usually meet their objectives through developing the right position sizing strategy.

Position Sizing—How much is enough?

Start small.  So many traders that are trading a new strategy start by risking the full amount that they plan on using for the long term with that strategy.  The most frequent reason given is that they don’t want to “miss out” on that big trade or long winning streak that could be just around the corner.  The problem is that most traders have a much greater chance of losing than they do of winning while they learn the intricacies of trading the new strategy.  Therefore, start small (very small) and minimize the “tuition paid” to learn the new strategy. Don’t worry about transactions costs (such as commissions), just worry about learning to trade the strategy and follow the process.  Once you’ve proven that you can consistently and profitably trade the strategy over a meaningful period of time (months, not days), then you can begin to ramp up your position sizing.

Manage losing streaks.  Make sure that your position sizing algorithm helps you to reduce the position size when your account equity is dropping.  You need to have objective and systematic ways to avoid the “gambler’s fallacy.”  The gambler’s fallacy can be paraphrases like this: after a losing streak, the next bet has a better chance to be a winner.  If that is your belief, then you will be tempted to increase your position size when you shouldn’t.

Don’t meet time-based profit goals by increasing your position size.  All too often, traders approach the end of the month or the end of the quarter and say, “I promised myself that I would make “X” dollars by the end of this period.  The only way I can make my goal is to double (or triple, or worse) my position size.  This thought process has led to many huge losses.  Stick to your position sizing plan!

We hope this information will help guide you toward a mindset of capital preservation on your journey toward successful trading. 

I have talked to many folks who have blown up their accounts.  I don’t think I have heard one person say that he or she took small loss after small loss until the account went down to zero.  Without fail, the story of the blown up account involves inappropriately large position size or huge price moves, and sometimes a combination of the two. ~D.R.Barton

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