Much of this book is designed to give you ideas about whether to day trade at all, what you want to trade, and how you want to trade it. That leaves one remaining issue: how much of your money to put on the line each time you trade. Risk too much, and you can be put out of business when you lose your capital. Risk too little, and you can be put of out business because you can’t make enough money to cover your costs and time.

Over time, many academic theorists and experienced traders have developed different systems of money management designed to help traders, investors, and even gamblers manage their money in order to maximize return while protecting capital. In this chapter, I explain how some of the better-known systems work so that you can figure out how to best apply them to your own trading.

Some of the material is related to leverage, which is borrowing money to trade. Leverage can dramatically increase the money that you have available to trade as well as the risk and return profile of the trades that you make, so it affects how you manage your money.

*What’s Your Expected Return?*
Before you can figure out how to manage your money, you need to figure out how much money you can expect to make. This is your expected return, although some traders prefer the word expectancy. You start by laying out your trading system and testing it. You are looking for four numbers:

- How many of your trades are losers?
- What’s the typical percentage loss on a losing trade?
- How many of your trades are winners?
- What’s the typical percentage gain on a winning trade?

Let’s say you determine that 40 percent of the time a trade loses, and it loses 1 percent. Sixty percent of the time, the trade wins, and winning trades are up 1.5 percent. With these numbers, you can calculate your per-trade expected return, like this:

% of losing trades × loss on losing trades + % of winning trades × gain on winning trades = expected return

Which in this example, works out to be:

.40 × –.01 + .60 × .015 = –.004 + .009 = .005

On average, then, you would expect to earn a half a percent on every trade you make. Make enough trades with enough money, and it adds up.

You are more likely to make more money if you have a high expectation of winning trades and if those winners are expected to perform well. As long as there is some probability of loss, you stand to lose money.

*The Probability of Ruin*
Expected return is the happy number. It’s how much money you can expect to make if you stay in the trading game. But it has a counterpart that is not so happy but is at least as important: the probability of ruin.

As long as there is some probability of loss, no matter how small, there is some probability that you can lose everything when you are trading. How much you can lose depends on how large each trade is relative to your account, the likelihood of each trade having a loss, and the size of the losses as they occur.

Shows the math for finding R, the probability of ruin.

A is the advantage on each trade. That’s the difference between the percentage of winning trades and the percentage of losing trades. In the expected return example discussed earlier, trades win 60 percent of the time and lose 40 percent of the time. In that case, the trader’s advantage would be:

60% – 40% = 20%

C is the number of trades in an account. Let’s assume that we’re dividing the account into ten equal parts, with the plan of making ten trades today. The probability of ruin today is 1.7 percent.

Now, 1.7 percent isn’t a high likelihood of ruin, but it’s not zero, either. It could happen. If your advantage is smaller, if the expected loss is larger, or if the number of trades is fewer, then the likelihood becomes even higher.

Shows you the relationship between the trader’s advantage, number of trades, and the corresponding probability of ruin, rounded to the nearest percentage.

Shows you the relationship between the trader’s advantage, number of trades, and the corresponding probability of ruin, rounded to the nearest percentage.

The bigger the edge and the more trades you can make, the lower your probability of ruin. Now, this model is a simplification in that it assumes that a losing trade goes to zero, and that’s not always the case. In fact, if you use stops, you should never have a trade go to zero. But you can see steady erosion in your account that will make it harder for you to make money. Hence, probability of ruin is a useful calculation that shows whether you will lose money in the long run.

The more trades you can make with your account, the lower your probability of ruin. That’s why money management is a key part of risk management.

*Why Size Matters*
As long as there is some chance of losing all your money, you want to avoid betting all of it on any one trade. But as long as there is a chance of making money, you want to have enough exposure to a winning trade so that you can post good profits.

Later, I describe some of the different money management systems that traders use to out how much money to risk per trade. But first, I want to explain the logic behind a money management system, so that you understand why you need one. That way, you can better manage your funds and improve the dollar returns to your trading.

*Valuing volatility*Expected return gives you an idea of how much you can get from a trade on average, but it doesn’t tell you how much that return might vary from trade to trade. The average of 9, 10, and 11 is 10; the average of –100, 10, and 100 is also 10. The first number series is a lot narrower than the second. The wider the range of returns that a strategy has, the more volatile it is.

There are several ways to measure volatility. One common one is standard deviation, which tells you how much your actual return is likely to differ from what you expect to get. The higher the standard deviation, the more volatile, and riskier, the strategy.

In the derivatives markets, volatility is measured by a group of numbers known as the Greeks: delta, gamma, vega, and theta. They’re based on calculus.

**Delta**is a ratio that tells you how much the option or future changes in price when the underlying security or market index changes in price. Delta changes over time.**Gamma**is the rate of change on delta. That’s because a derivative’s delta will be higher when it is close to the expiration date, for example, then when the expiration date is further away.**Vega**is the amount that the derivative would change in price if the underlying security became 1 percent more volatile.**Theta**is the amount that a derivative’s price declines as it gets closer to the day of expiration.

Day traders seek out more volatile securities, because they offer more opportunities to make money during any given day. That means they have to have ways to minimize the damage that might occur while being able to capitalize on the upward swings. Money management can help with that.

*Staying in the market*You only have a limited amount of money to trade. Whether it’s $1,000 or $1,000,000, once it’s gone, you’re out. The problem is that you can have a long string of losing trades before the markets go in a direction that favors you and your system.

Let’s say you trade 100 percent of your account. If you have one trade that goes down 100 percent, then you have nothing. If you divide your account into ten parts, then you can have ten total losers before you are out. If you start with ten equal parts and double each time you lose, you can be out after four losing trades.

The riskier your trading strategy, the more thought you need to put into money management. Otherwise, you can find yourself out of the market in no time.

On the other hand, if you divide your account into 100 portions, then you can endure 100 losing trades. If you trade fractions of your account, then you can keep going infinitely, or at least until you get down to a level that’s too low to place a minimum order. Money management can keep you in the game longer, and that will give you more opportunities to place winning trades.

*Considering opportunity costs*Opportunity cost is the value you give up because you choose to do something else. In trading, each dollar you commit to one trade is a dollar that you cannot commit to another trade. Thus, each dollar you trade carries some opportunity cost, and good traders seek to minimize this cost. During the course of the trading day, you may see several great trades, and some opportunities will show up before you are ready to close out a different trade.

If you have committed all your capital to one trade, you will miss out on the second. That alone is a good reason to keep some money on the table each time you trade.

*Money Management Styles*Over the years, traders have developed many different ways to manage their money. Some of these are rooted in superstition, but most are based on different statistical probability theories. The underlying idea is that you should never place all of your money in a single trade, but rather put in an amount that is appropriate given the level of volatility. Otherwise, you risk losing everything too soon.

Calculating position size under many of these formulas is tricky stuff. That’s why brokerage firms and trading software packages often include money management calculators.

This is only a sample of some methods. There are other methods out there, and none is suitable to all markets all the time. Folks trading both options and stocks may want to use one system for option trades and another for stock trades. If that’s your situation, you have one big money management decision to make before you begin: how much money to allocate to each market.

*Fixed fractional*Fixed fractional trading assumes that you want to limit each trade to a set portion of your total account, often between 2 and 10 percent. Within that range, you’d trade a larger percentage of money in less risky trades and at the smaller end of the scale for more risky trades.

Show the fixed fractional equation.

N is the number of contracts or shares of stock you should trade, f is the fixed fraction of your account that you have decided to trade, equity is the value of your total account, and trade risk is the amount of money you could lose on the transaction. Because trade risk is a negative number, you need to convert it to a positive number to make the equation work. Those vertical bars in the equation (||) are the sign for absolute value, and that means that you convert the number between them to a positive number.

This means that if you have decided to limit each trade to 10 percent of your account, if you have a $20,000 account, and if the risk of loss is –$3,500.

Of course, you probably can’t trade .57 of a contract, so in this case, you would have to round up to one.

*Fixed ratio*The fixed ratio money management system is used in trading options and futures. It was developed by a trader named Ryan Jones, who wrote a book about it. In order to find the optimal number of options or futures contracts to trade, N.

N is the number of contracts or shares of stock that you should trade, P is your accumulated profit to date, and the triangle, delta, is the dollar amount that you would need before you could trade a second contract or another lot of stock.

For example, the minimum margin for Chicago Mercantile Exchange E-Mini S&P 500 futures contract, which gives you exposure to the Standard & Poor’s 500 stock index, is $3,500. Until you have another $3,500 in your account, you can’t trade a second contract. If you are using fixed ratio money management to trade this future, your delta will be $3,500.

If your delta is $3,500, and you have $10,000 in account profits, you should trade 1.2 contracts. In reality, that means you can only trade one contract or two contracts, nothing in between. That’s one of the imperfections of most money management systems.

The idea behind fixed ratio trading is to help you increase your exposure to the market while protecting your accumulated profits.

*Gann*William Gann developed a complicated system for identifying securities trades. Part of that was a list of rules for managing money, and many traders follow that if nothing else.

The primary rule is: Divide your money into ten equal parts, and never place more than one 10-percent portion on a single trade. That helps control your risk, whether or not you use Gann.

*Kelly Criterion*The Kelly Criterion emerged from statistical work done at Bell Laboratories in the 1950s. The goal was to figure out the best ways to manage signal-noise issues in long-distance telephone communications. Very quickly, the mathematicians who worked on it saw that there were applications to gambling, and in no time, the formula took off.

To calculate the ideal percentage of your portfolio to put at risk, you need to know what percentage of your trades are expected to win as well as the return from a winning trade and the ratio performance of winning trades to losing trades. The shorthand that many traders use for the Kelly Criterion is edge divided by odds, and in practice, the formula looks like this:

Kelly % = W – [(1 – W) / R]

W is the percentage of winning trades, and R is the ratio of the average gain of the winning trades relative to the average loss of the losing trades.

I had an example of a system that loses 40 percent of the time with a loss of 1 percent and that wins 60 percent of the time with a gain of 1.5 percent. Plugging that into the Kelly formula, the right percentage to trade is .60 – [(1-.60)/(.015/.01)], or 33.3 percent.

As long as you limit your trades to no more than 33% of your capital, you should never run out of money. The problem, of course, is that if you have a long string of losses, you could find yourself with too little money to execute a trade. Many traders use a “half-Kelly” strategy, limiting each trade to half the amount indicated by the Kelly Criterion, as a way to keep the trading account from shrinking too quickly. They are especially likely to do this if the Kelly Criterion generates a number greater than about 20 percent, as in this example.

*Martingale*The martingale style of money management is common with serious casino gamblers, and many traders apply it as well. It’s designed to improve the amount of money you can earn in a game that has even odds. Most casino odds favor the house (roulette wheels used to be evenly black and red, but casinos found that they could make more money if they inserted a green slice for zero, thus throwing off the odds). Day trading, on the other hand, is a zero sum game, especially in the options and futures markets. This means that for every winner, there is a loser, so the odds of any one trade being successful are even. The martingale system is designed to work in any market where the odds are even or in your favor.

Under the martingale strategy, you start with a set amount per trade, say $2,000. If your trade succeeds, you trade another $2,000. If your trade loses, you double your next order so that you can win back your loss.

Under the martingale system, you will always come out ahead as long as you have an infinite amount of money to trade. The problem is that you can run out of money before you have a trade that works. The market, on the other hand, has almost infinite resources because of the huge volume of participants coming and going all over the world. That means that you have an enormous disadvantage. As long as you have a disadvantage, thoughtful money management is critical.

*Monte Carlo simulation*If you have the programming expertise or buy the right software, you can run what’s called a Monte Carlo simulation. In this, you enter in your risk and return parameters and your account value, let the program run, and it returns the optimal trade size. The system is not perfect — it is only a model that can’t incorporate every market situation that you’ll face and it has the fractional trade problem that the other systems do. But it has one big advantage: It can incorporate random changes in the markets in ways that simpler money management models cannot.

Monte Carlo simulation is not a do-it-yourself project, unless you have extensive experience creating these programs. If you are interested, you need to find a suitable program.

*Optimal F*The Optimal F system of money management was devised by Ralph Vince, and he’s written several books about this and other money management issues. The idea is that you determine the ideal fraction of your money to allocate per trade based on past performance.

If your Optimal F is 18 percent, then each trade should be 18 percent of your account — no more, no less. The system is similar to the fixed fraction and fixed ratio methods discussed earlier, but with a few differences.

Shows the equation for finding the number of shares of stock, N, to trade.

F is a factor based on the basis of historical data, and the risk is the biggest percentage loss that you experienced in the past. Using these numbers and the current price, you can find the contracts or shares you need to buy. If your account has $25,000, your biggest loss was 40 percent, your F is determined to be 30 percent, and you’re looking at a stock trading at $25 per share, then you should buy 750 shares.

The Optimal F number itself is a mean based on historical trade results. The risk number is also based on past returns, and that’s one problem with this method: it only kicks in after you have some trade data. A second problem is that you need to set up a spreadsheet to calculate it. Some traders only use Optimal F in certain market conditions, in part because the history changes each time a trade is made, and that history doesn’t always lead to usable numbers.

*How Money Management Affects Your Return*It’s one thing to describe why you need money management, but it’s more fun to show you how it works. And because I love making spreadsheets, I pulled one together to show you how different ways of managing your money might affect your return.

I started with the expected return assumptions that I used in the earlier example: 40 percent of the time a trade loses, and it loses 1 percent. 60 percent of the time, the trade wins, and winning trades are up 1.5 percent. I pick a hypothetical account of $20,000 and set up mock trades using these expected return numbers. Compares the performance of martingale and Kelly money management to betting the whole account each time.

You may notice that you end up with the most money from trading the entire account. That doesn’t mean you always get the most money this way, just that that’s how the numbers worked out in this case, given the 60/40 win ratio and a 3/2 winning size/losing size ratio.

This is just an example, applying some different strategies to different hypothetical returns. I’m not recommending any one system over another. The best system for you depends on what assets you are trading, your personal trading style, and how much money you have to trade.

*Planning for Your Profits*In addition to determining how much to trade each time you place an order, you need a plan for what to do with the profits that accumulate in your account. That’s as much a part of money management as calculating your probability of ruin and determining trade size.

Are you going to add the money to your account and trade it as before? Leverage your profits by trading them more aggressively than your core account? Pull money out and put it into long-term investments? Or a combination of the three?

*Compounding interest*Compound interest is a simple concept: Every time you get a return, that return goes into your account. You keep earning a return on it, which increases your account size some more. You keep earning a return on your return, and pretty soon, the numbers get to be pretty big.

In order to benefit from that compounding, many traders add their profits back into their accounts and keep trading them, in order to build account size. Although day traders earn little to no interest, the basic principle holds: By returning profits to the trading account to generate even more profits, the account should grow over time.

This practice of keeping profits in the account to trade makes a lot of sense for smaller traders who want to build their accounts and take more significant positions over time.

*Pyramiding power*Pyramiding involves taking trading profits and borrowing heavily against them to generate even more profits. Traders usually do this during the day, using unrealized profits in trades that are not yet closed as collateral for loans used to establish new positions. If the new positions are profitable, the trader can keep borrowing until it’s time to close everything at the end of the day.

This works great as long as the markets are moving in the right direction. If all the positions in the pyramid remain profitable, you can make a lot of money during the course of the day. But if one of those positions turns against you, the structure collapses and you end up with a call on your margin. Starts with an initial trade of $2,000 and assumes a return of 10 percent on each transaction — not realistic, necessarily, but it makes for a nice chart.

If the profits from each trade are used as collateral for borrowing, and if that 10 percent return holds all day, then the trader can make 17 percent by pyramiding those gains. If a reversal hits before the end of the trading session and the positions lose 10 percent, then pyramiding magnifies the losses — assuming your broker would let you keep borrowing. After all, the borrowed money has to be repaid regardless of what happens in the market.

Pyramiding is not related to a pyramid scheme. In trading terms, pyramiding is a way to borrow against your profits to generate even bigger profits. A pyramid scheme is a fraud that requires participants to recruit new members, and fees paid by the new members go to the older ones. Eventually, the pyramid collapses because it gets too difficult to recruit new members, and those at the bottom get nothing.

Some investment frauds have been structured as pyramid schemes, so bewary of deals that sound fabulous and also require you to recruit others.

Pyramiding increases your trading risk, but also your expected return. It’s a useful way to grow a portion of your trading account, especially when the market is favoring your trading system. It’s a good technique for a medium-sized account that would have enough money left over to stay in the market if a pyramid were to collapse on you.

*Regular withdrawals*Because day trading can be so risky, many traders look to diversify their total financial risk. One way to do this is to pull money out of the trading account to put into a less volatile long-term investment. Many traders routinely pull out a percentage of their profits and put that money into government bonds, a low-risk mutual fund, or real estate. None of these investments is as glamorous or exciting as day trading, but that’s the point:

Trading is hard work, and anyone can lose money any day, no matter how big their account is or how much money they have made so far. By moving some money out, a trader can build a cushion for a bad trading stretch, prepare for retirement, and have some money to walk away for a short period or even forever. That can greatly reduce the stress and the fear that go with trading.

The larger the account, the easier it is to pull money out, but even smaller traders should consider taking 5 or 10 percent of each quarter’s profits and moving them into another type of investment. Many brokerage firms can set up automatic withdrawal plans that zap money from your trading account to a stock or bond mutual fund, if you don’t trust yourself to do it.

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