Stock Learning

You was a little shocked over what had happened in the market over the last three weeks - you had lost 70% of your account value. You are shaken, but still convinced that you could make the money back! After all, you had been up almost 200% before the market withered you down, you still have $4,500 left in your account. Sounds familiar? What advice would you give to a trader in this situation? Your advice should be, “get out of the market immediately. You don’t have enough money to trade speculatively.” 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 certain.

Experiment was done with a forty Ph.D.s. with a background in statistics or trading. The forty doctorates were given a computer game to trade. They started with $10,000 and were given a 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. This is a much better game than you’ll ever find in Las Vegas. Yet guess how many of the Ph.D’s 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.

Lets say you started the game risking $1,000. 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. Lets 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 be able 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 failure to understand the odds, and, in some cases, even 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 of their account size.

Table 1 - Recovery after Drawdowns

Look at Table 1. Notice how much your account has to recover from various sized draw-downs in order to get back to even. For example, losses as large as 20% don’t require that much of a corresponding gain to get back to even. But a 40% draw-down requires a 66.7% gain to break-even and a 50% draw-down 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.

Money Management Defined

Money management is the most significant part of any trading system. Since money management is the difference between poor performance and great performance - the difference between going broke and being a successful trader - it’s important to define it.

Money management is that portion of your trading system that tells you “how many” or “how much.” How many units of your investment should you putIn 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 loss potential 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.

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.

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 have 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. 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 position size when you make money. That holds for gambling and for trading and for 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 of 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 the elements in your 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. Controlling risk by determining the amount of loss if you are stopped out is not the same as controlling risk through a money management model that determines the size of your position. There are numerous money management strategies that you can use. In the remainder of this article, you’ll learn different money management strategies that work well. Some are probably much more suited to your style of trading or investing than others. Some work best with stock accounts, while others are designed for a futures account. All of them are anti-martingale strategies in that your position size goes up as your account size grows.

Money Management Models

All of the models you’ll learn about in this article relate to the amount of equity in your account. These models can suddenly become much more complicated when you realize that there are three methods of determining equity. Each method can have a different impact upon your exposure in the market and on your returns. These methods include the core equity method, the total equity method, and the reduced total equity method.
The Core Equity Method is simple. When you open a new position, you simply determine how much you would allocate to that position according to your money management method. Thus, if you had four open positions, your core equity would be your starting equity less the amount allocated for each of the open positions. Let’s assume you start with an account of $50,000 and you allocate 10% per trade. You open a position with $5,000 money management allocation, using one of the methods described below. You now have a core equity of $45,000. You open another position with a $4,500 money management allocation, so you have a core equity of $40,500. You open a third position with an allocation of $4,050, so that your core equity is now $36,450. Thus, you have a core equity position of $36,450 plus three open positions. In other words, the core equity method subtracts the initial allocation of each position and then makes adjustments when you close that position out. New positions are always allocated as a function of your
current core equity.
The Total Equity Method is also very simple. The value of your account equity is determined by the amount of cash in your account plus the value of any open positions. For example, suppose you have $40,000 in cash plus one open position with a value of $15,000, one open position worth $7,000, and a third open position that has a loss of $2,000. Your total equity is the sum of the value of your cash plus the value all of your open positions. Thus, your total equity is $60,000.
The Reduced Total Equity Method is a combination of the two methods above. It is like the core equity method in that the exposure allocated when you open a position is subtracted from the starting equity. However, it is different in that you also add back in any profit or reduced risk that you would receive when you move a stop in your favor. Thus, your reduced total equity is your core equity plus the profit of any open positions that are locked in with a stop or the reduction in risk that occurs when you raise your stop. (Note: This is sometimes called the Reduced Core Equity Method) Here’s how that works. Suppose you have a $50,000 account. You open a position with a $5,000 money management allocation. Thus, your core equity (and reduced total equity) is now $45,000. Now suppose the underlying commodity moves up in value and you have a trailing stop. Today, you only have $3,000 in risk locked because of your new stop. As a result, your reduced total equity today is $50,000 less your new risk exposure, or $47,000.
The next day, the value drops by $1,000. Your reduced total equity is still $47,000 since the risk to which you are exposed if you get stopped out is still $47,000. It only changes when your stop changes
to reduce your risk, lock in more profit, or close out a position. You now buy a second position, with a $4,000 money management allocation. The value of the first position moves up and you now lock in $11,000 worth of profit by moving up your stop. Your reduced total equity is now $50,000 minus the initial allocation of your second position ($4,000) plus the locked in profit of $11,000 on the first position. The resulting new value is $57,000.
The models below cover all size positions according to your equity. Thus, each model of calculating equity will lead to different position sizing calculations. Generally, I’ll refer to the total equity
method of calculating equity unless otherwise stated in the discussions of each of the models that follow.

Model 1 - Units per Fixed Amount of Money

Basicaliy, this method tells you “how much” by determining that you will trade one unit for every X dollars you have in your account. For example, you might trade one contract per $50,000 of your total equity. When you started trading or investing, you probably never heard about money management. If you knew something about it, your knowledge probably came from some book by an author who didn’t understand it either. Most books that discuss money management are about diversification or about optimizing the gain from your trading. Books on systems development or technical analysis don’t even begin to discuss money management adequately. As a result, most traders and investors have no place to go to learn what is probably the most important aspect of their craft. Thus, armed with your ignorance, you open an account with $20,000 and decide to trade one contract of everything in which you get a signal to trade (an investor might just trade 100 shares). Later, if you’re fortunate and your account moves to $40,000, you decide to move up to two contracts (or 200 shares) of everything. As a result, most traders who do practice some form of money management use this model. It is simple. It tells you “how much” in a straight-forward way.
The one unit per fixed amount of money has one advantage in that you never reject a trade because it is too risky. Let me give you an example of two traders: One trades one contract per $50,000 in equity, while the other limits his risk to 3% of equity and won’t open a position in which his exposure is more than that. Each is presented with an opportunity to trade very profitable contract. The person trading one contract, no matter what, takes the trade. The subsequent move in the equity is tremendous, so this person is able to produce the biggest monthly gain that he had ever experienced in his trading history. On the other hand, the other trader wouldn’t take the trade, even though his account size was $100,000, because the risk involved if the trade went against him exceeded his 3% limit. The second trader wouldn’t have a profitable month.
Of course, this also works in reverse. The first trader could have taken a large loss if the equity had gone against him which the other trader would have avoided. In presenting the results of all these systems, we will use a single trading system,- trading the same commodities over the same time period. The system is a 55day channel breakout system. In other words, it enters the market on a stop order if the market makes a new 55day high (long) or 55day low (short). The stop, for both the initial risk and profit taking, is a 21-day trailing stop on the other side of the market.
To illustrate, if you go long and the market hits a 21-day low, you exit. If you are short and the market makes a new 21-day high, you exit, This stop is recalculated each day, and it is always moved in your
favor so as to reduce risk or increase your profits. Such breakout systems produce above average profits when traded with sufficient money. This system was tested with a million dollars in start-up equity with a basket of 10 commodities in the years 1981 through 1991. Whenever data are presented in this report, it is based upon this same 55/21-day breakout system tested over the same commodities over the same years. The only difference between the tables is the money management model used. Table 2 shows the results with this system using the first money management model.

Table 2:
55/21 Day Breakout System with 1 contract per $X in equity
(Starting Equity is One Million Dollars)


Notice that the system breaks down at one contract per $20,000 in equity. At $30,000, you’d have to endure an 80% drawdown and you’d have to have at least $70,000 if you wanted to avoid a 50% drawdown.
To really evaluate this money management method, you’ll have to compare it with the tables developed from the other models (see Tables 3 and 5). Despite its advantage of allowing you to always take a position, I believe that the one unit per fixed dollars type of money management is limited, because
1. all investments are not alike and
2. it does not allow you increase your exposure very rapidly with small amounts of money.
In fact, with a small account, the “units per fixed amount model” amounts to minimal money management. Lets explore both of these reasons. All contracts are not alike. Suppose you are a futures trader and
you decide you are going to be trading up to twenty different commodities with your $50,000. Your basic money management strategy is to trade one contract of anything in that portfolio that gives you a signal. Lets say you get a signal for both bonds and corn. Thus, your money management says you can buy one corn contract and one bond contract. With T-bonds futures at $112 as of August 1995, you are controlling $112,000 worth of product. In addition, the daily range (i.e., the volatility) is about 0.775 so if the market moved three times that amount in one direction, you would make or lose $2,325. In contrast, with the corn contract you are controlling about $15,000 worth of product. If it moved three daily ranges with you or against you, your gain or loss would be about $550. Thus, what happens with your portfolio will depend about 80% on what bonds do and only about 20% on what corn does.
One might argue that corn has been much more volatile and expensive in the past. That could happen again. But you need to diversify your opportunity according to what’s happening in the market right now. Right now, based on the data presented, corn has about 20% of the impact on your account that bonds would have.

Cannot increase exposure rapidly. The purpose of an anti-martingale strategy is to increase your exposure when you are winning. When you are trading one contract per $50,000 and you only have $50,000, you will have to double your equity before you can increase your contract size. As a result, this is not a very efficient way to increase exposure during a winning streak. In fact, for a $50,000 account it almost amounts to no money management. Part of the solution would be to require a minimum account size of a million dollars. If you did that, your account would only have to increase by 5% before you moved from 20 contracts (1 per $50,000) to 21 contracts.
One reason to have money management is to have equal opportunity and equal exposure across all of the elements in one’s portfolio. You want an equal opportunity to make money from each element of your portfolio. In addition, you also want to spread your risk equally among the elements of your portfolio. Having equal opportunity and exposure to risk, of course, makes the assumption that each trade is equally likely to be profitable when you enter into it. You might have some way to determine that some trades are going to be more profitable than others. If so, then you would want a money management plan that gives you more units on the higher-probability-of-success trades - perhaps a discretionary money-management plan. However, for the rest of this article, we’re going to assume that all trades in a portfolio have an equal opportunity of success from the start. That’s why you selected them. The “units per fixed amount of money” model, doesn’t give you equal opportunity or exposure. But there are a
number of methods whereby you can equalize the elements of your portfolio. These include equating
1. The total value of each element of the portfolio;
2. The margin of each element in the portfolio;
3. The amount of volatility of each element in the portfolio;
4. The amount of risk (i.e., how much you’d would lose when you got out of a position in order to preserve capital) of each element in the portfolio.

Model 2 - Equal Units /Equal Leverage Model

The Equal Units Model is typically used with stocks or other instruments which are not leveraged. The model says that you determine “how much” by dividing your capital up into five or ten equal units. Each unit would then dictate how much product you could buy. For example, with our $50,000 capital, we might have five units of $1O,OOO each. Thus, you’d buy $10,000 worth of investment “A”, $10,000 worth of
investment “B”, $10,000 worth of investment “C” and so forth. You might end up buying 100 shares of a $100 stock, 200 shares of a $50 stock, 500 shares of a $20 stock, 1000 shares of a $10 stock, and 1429 shares of a $7 stock. Part of the money management in this strategy would be to determine how much of your portfolio you might allocate to cash at any given time.


Chart 1: Distribution of Funds as Shares
(each unit represents $10,000)

Chart 1 simply illustrates the number of shares, as a percentage of total shares, for each of the five $10,000 units. Notice that there is some inconvenience in this procedure. For example, the price of the stock may not necessarily divide evenly into $10,000 - much less into 100 share units. In futures, the equal units model might be used to determine how much value you are willing to control with each contract. For example, with the $50,000 account you might decide that you are willing to control up to $250,000 worth of product. And lets say you arbitrarily decide to divide that into five units of $50,000 of each. Gold is traded in 100 ounce contracts in New York, which at a price of around $900 per ounce, gives a single contract a value of $90,000. You couldn’t buy any gold, using this money management criterion, because you’d be controlling more product than you can handle with one unit. Corn is traded in units of 5,000 bushels. A corn contract, with corn at $5 per bushel, is valued at about $25,000. Thus, your $50,000 would allow you to buy 2 units of corn or $50,000 worth. A bond contract is currently worth about $116,000. You couldn’t buy any bonds either, using this money management criterion.
The Equal Units Approach allows you to give each investment or futures an approximate equal weighting in your portfolio. It also has the advantage in that you can see exactly how much leverage you are
carrying. For example, if you are carrying 5 positions in your $50,000 account, each worth about $50,000, you would know that you had about $250,000 worth of product. In addition, you would know that you had about 5-to-1 leverage, since your $50,000 was controlling $250,000. When you use this approach you must make a decision about how much total leverage you are willing to carry before you divide it into
units. It’s such valuable information, so I would recommend all traders keep track of the total product value they are controlling and their leverage. This information can be a real eye opener.
The equal units approach still has the disadvantage in that it would only allow you to increase “how much” very slowly as you make money. In most cases with a small account, equity would again have to double to increase your exposure by one unit. Again, this practically amounts to “no” money management for the small account.

Model 3 -Percent of Margin

The third model one might use for money management is to control your size according to the margin requirements of the underlying assets. Here, margin refers to the amount of money that the exchange (or your broker) requires that you put up in order to purchase one investment unit. If you have less money in your account than the margin requirements, you’ll need to add more money. The margin on buying most stock is 50%. Thus, you would have to have $25,000 in your account to purchase $50,000 worth of stock. In contrast, the margin on one S&P 500 E-Mini futures contract is currently $4,500. Thus, you could purchase one S&P 500 contract, controlling stock worth approximately $64,800 at today’s (August 8th 2008) price, with only $4,500 in your account. This would give you leverage of 14-to-l.
Since leverage can be so high with futures, you might want to control it by limiting your margin to a percentage of your equity. Here’s how that would work. You might decide to limit your trades to 5% of
margin. In a $50,000 account this would mean that the margin of your first purchase could be no more than $2,500. The margin of your second purchase would depend on the equity model you were using. Lets say you have one open position worth $2,500 and $47,500 in cash. With the total equity model, your next purchase could also have a margin of $2,500 - 5% of the total. However, with the core equity model or the reduced total equity model, you could only acquire margin in the second position of $2,375 - 5% of $47.500. Lets look at a few examples of additions using the Total Equity Model. Currently, the margin on corn mini is $405. When you divided $405 into your 5% level of $2,500, you get 6.17 contracts. Thus, you could buy 6 contracts. The margin on silver mini is currently $1,350 so your 5%
requirement would allow you to buy one contract. However, the margin on S&P 500 E-Mini is $4,500 so you couldn’t buy a contract until you had increased your equity. You might also limit the total margin of your account to some value such as 30%. If you did that, the margin on your total open positions could never total over $15,000 (i.e., 30% of your $50,000). If you wished to purchase a new position that would increase your total margin over that value, you could not do it. Method three is the first method that allows the smaller account to begin to increase its exposure as it makes money. It gives you strong control over your account and some control over the probability of margin calls. However, margin amounts can change daily for each contract, so you will have to keep track of them. In addition, the margin values are arbitrarily set by the exchanges and the brokerage houses. They tend to relate to both the volatility and the leverage in a particular contract, but the amount set is still quite arbitrary. As a result, the margin method of money management doesn’t necessarily give you equal exposure across all positions.


Model 4 - Percent Volatility

Volatility refers to the amount of daily price movement of the underlying instrument over an arbitrary period of time. It’s a direct measurement of the price change that you are likely to be exposed to - for or against you - in any given position. If you equate the volatility of each position that you take, by making it a fixed percentage of your equity, then you are basically equalizing the possible market fluctuations of each portfolio element to which you are exposing yourself in the immediate future. Volatility, in most cases, simply is the difference between the high and the low of the day. If IBM varies between $126.00 and $128.50, then its volatility is 2.5 points, However, using an average true range takes into account any gap openings. Thus, if IBM closed at $124.00 yesterday, but varied between $126.00 and $128.50 today, you’d need to add in the 2 points in the gap opening to determine the true range. Thus, today’s true range is between $124.00 and $128.50 or 4.5 points.
Here’s how a percent volatility calculation might work for money management. Supposed that you have $50,000 in your account and you want to buy gold. Let’s say that gold is at $860 per ounce and during the last ten days the daily range is $3.00. We will use a 4-day simple moving average of the average true range as our measure of volatility. How many gold contracts can we buy? Since the daily range is $3.00 and a point is worth $100 (since the contract is for 100 ounces), that gives the daily volatility a value of $300 per gold contract. Let’s say that we are going to allow volatility to be a maximum of 2% of our equity. Two percent of $50,000 is $1,000. If we divide our $300 per contract fluctuation into our allowable limit of $1,000, we get 3.3 contracts. Thus, our money management, based on volatility, would allow us to purchase 3 contracts. Lets do one more example, using a total equity model. Gold is now $864 per ounce, so the value of our open position has increased our equity by $400 per contract or $1,200. Thus our total equity is now $51,200.
We now want to buy a bond contract. Let's say, bonds have been fluctuating by about 0.75 points per day. Thus, the dollar value of the daily fluctuation is $750 (0.75 times $1,000 per point). Our money management says to limit our risk to 2% of equity, and 2% of $51,500 is $1,030. The daily $750 fluctuation in bonds, divided into $1,030 works out to be 1.37, allowing us to buy one bond contract. Notice that the daily fluctuation from bonds ($750) is about two and a half times the daily fluctuation in gold ($300). As a result, we’ve ended up with three gold contracts compared with only one bond contract. Thus, we can expect about the same amount of price fluctuation, in the short term at least, from both positions.
If you use volatility in your money management, you might also want to limit the total amount of volatility to which vour portfolio is exposed at any time. Five to ten percent is a reasonable number. Suppose, for example, that your exposure were 10%. Thus, you could have five positions, since your individual position limit is 2%. If all of your positions went against you at once in a single day, and you
stayed in the market, it would mean that you could lose as much as ten percent of the value of your portfolio in a single day. How would you feel if your $50,000 portfolio went down to $45,000 in a single day? If that’s too much then 2% and 10% are probably too big for you.

When you understand the concepts of Part 1 take a look at Part 2. In Part 2 you’ll learn five more money management models, giving you many additional ideas that could have a great impact on your bottom line profits. You’ll also learn how to design a system using these models to fit your particular objectives. In addition, we’ll also explore creative money management, so you can get some ideas where you really need to focus your attention in system development.