Chapter 6
Managing Your Money and Positions
IN THIS CHAPTER
Calculating expected return
Knowing your probability of ruin
Mulling over the many methods of money management
Figuring out what money management has to do with returns
Deciding what to do with your profits
You can’t trade if you don’t have money. Sure, your brokerage firm will loan you some funds, but only if you have some of your own funds to stake as margin. You have to keep some powder dry.
So how much of your money should you 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 out of 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 such a way as 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. Doing so can help you protect your trading funds and figure out what size trades to enter so that you can stay trading as long as you like.
Note: Some of the material in this chapter is related to leverage, which is borrowing money to trade. Because 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, it affects how you manage your money. Flip to Chapter 9 for more information on leverage and why you may want to use it.
Setting Your Earnings Expectations
Return is a function of risk. If you want a guaranteed return, go down to your bank and open a federally insured deposit account. The returns will be almost comically low, but you’ll have no risk. If you want anything higher than what your bank is quoting, well, you have to take on at least a little bit of risk. When you take on risk, you increase both your likelihood of return and your likelihood of loss.
Successful day traders lose money all the time, but they’re able to keep trading. If you’re looking at a trade with even a 0.5 percent chance of 100 percent loss, the odds indicate that you would lose everything over the course of 200 trades — but only if you put all your money into each trade. If you put only some of your money in that trade, then you’ll never lose everything in it. Sure, you won’t get all of the upside potential, but you’ll be able to hit the potential high return more often because you can make that trade more often.
The key term in investing is diversification: If your money is spread out among different assets, your long-return return will be higher for less total risk than if you commit to only one asset.
Trading isn’t investing, but the power of diversification holds. If you divide your money among a few different trades or always keep some cash on hand in your account for the next trade, you’ll almost definitely make more money in the long run than if you put all your money on one idea. Sure, risking everything on one idea may work a few times, but are you that lucky? If you’re smart about your money management, you don’t need luck.
Finding 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 amount is your expected return, although some traders prefer the word expectancy. You start by laying out your trading system and testing it (refer to Chapter 16). You’re 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?
Say that you determine that a certain trade loses 40 percent of the time, 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
0.40 × –0.01 + 0.60 × 0.015 = –0.004 + 0.009 = 0.005, which is the same as 0.5%.
On average, then, you would expect to earn 0.5 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 probability of loss exists, you stand to lose money.
Determining your 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, while not so happy, is at least as important: the probability of ruin.
Yes, ruin.
As long as some probability of loss exists, no matter how small, there is some probability that you can lose everything when you’re 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. (Don’t think it can happen? That’s what the top executives at AIG, Bear Stearns, Lehman Brothers, and Washington Mutual said.)
Many traders who have winning trading strategies find themselves shut down because a few bad trades ruined them. Every trader has some losses, but these losses don’t have to end your trading career if you know the probability of ruin and how to use it. The equation you use to calculate the probability of ruin (R) is
In this equation, 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 everything 40 percent of the time. In that case, the trader’s advantage would be
60% – 40% = 20%
And c is the number of trades in an account. Assume that you’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, as shown in this equation:
Now 1.7 percent isn’t a high likelihood of ruin, but it’s not zero, either. It can 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.
Figure 6-1 shows you the relationship between the trader’s advantage, number of trades, and the corresponding probability of ruin, rounded to the nearest percentage.
© John Wiley & Sons, Inc.
FIGURE 6-1: Adding trader’s advantage to the mix.
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 (automatic buy and sell orders, described in Chapter 2), you should never have a 100 percent loss. 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’ll 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.
Gaining Advantage with a Money-Management Plan
As long as there’s some chance of losing all your money, you want to avoid betting it all on any one trade. But as long as there’s a chance of making money, you want to have enough exposure to a winning trade so that you can post good profits. How do you figure out how much money to risk?
Later in this chapter, I describe some of the different money-management systems that traders use to figure 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.
Minimizing damage while increasing opportunity
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 may vary from trade to trade. The average of 9, 10, and 11 is 10; the average of –90, 10, and 110 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.
Day traders seek more volatile securities because they offer more opportunities to make money during any given day. For this reason, they need to have ways to minimize the damage that may occur while being able to capitalize on the upward swings. Money management can help with that.
Staying in the market longer
You have only a limited amount of money to trade. Whether it’s $1,000 or $1,000,000, once the money’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.
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’re out. If you start with ten equal parts and double each time you lose, you can be out after four losing trades.
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 indefinitely, or at least until you get down to a level that’s too low to place a minimum order. (That’s the philosophy behind the Kelly criterion, described later in this chapter.) Money management can keep you in the game longer, and that gives you more opportunities to place winning 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.
Getting out before you lose everything
A money-management system works best if the trader using it knows when to close out a position. You have to have a trading plan and know when you’re willing to get out: at the recent high? A few ticks below the most recent high? A few ticks up from where you entered? A few ticks below where you entered, to limit your losses?
Sometimes the market will go nuts, and you won’t be able to get out as quickly as you’d like. In these situations, those tiny chances of losing everything kick in, and good money management offers the most protection.
On more ordinary trading days, be sure to supplement your position size and capital protection efforts with ordinary trading tools: trade planning and use of stop and limit orders. You can review these in Chapter 2.
Accounting for 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.
Because a money-management system holds back some of your capital, you are more likely to have funds to take advantage of these opportunities than if you allocate your cash willy-nilly. Your plan may cause you to miss some trades, and that’s okay. If you believe that you are missing too many, though, you may want to experiment with another system to see whether it gives you better results. Whatever you do, don’t ignore money management.
If you have committed all your capital to one trade, you miss out on the second. That alone is a good reason to keep some money on the table each time you trade.
Examining Styles of Money Management
Over the years, traders have developed many different ways to manage their money. Some money-management strategies 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. Instead, you should put in an amount 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. Check Chapter 11 for more information on the brokers and Chapter 12 for more on different software and research services.
In the following sections, I offer a sampling of the many different money-management methods available. Other methods are out there, and none is suitable to all markets all the time. If you trade both options and stocks, you may want to use one system for option trades and another for stock trades. And 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!
Limiting portions: 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 trade a larger percentage of money in less risky trades and a smaller amount of money for more risky trades. (In other words, this method isn’t all that “fixed,” but no one asked me to pick a name for the system!)
Here’s the fixed fractional equation for calculating fixed-fractional trade proportions.
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.
Here’s an example that uses the equation. Assume that you’ve decided to limit each trade to 10 percent of your account, you have a $20,000 account, and you are looking at contracts with a value of $3,500. You want to set your trade based on the assumption that the contracts go to zero, to look at the worst-case scenario. Plugging the numbers into the equation and doing the math gives you
Of course, you probably can’t trade 0.57 of a contract, so in this case, you would have to round up to one.
Protecting profits: Fixed ratio
Developed by a trader named Ryan Jones, the fixed-ratio money-management system is used in trading options and futures. The idea behind fixed-ratio trading is to help you increase your exposure to the market while protecting your accumulated profits.
To find the optimal number of options or futures contracts to trade, you use this equation
N is the number of contracts or shares of stock that you should trade, P is your accumulated profit to date, and Δ (delta) is the dollar amount you would need before you could trade a second contract or another lot of stock. (Don’t confuse this delta with the delta used to measure of volatility; see the sidebar “Measuring volatility” for more information.)
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 use fixed-ratio money management to trade this future, your delta is $3,500.
Here’s an example that uses fixed-ration calculation. Assume your delta is $3,500 and that you have $10,000 in account profits. If you plug in the numbers and calculate, you see that you should trade 2.94 contracts:
What this means is that you can trade only one or two contracts, nothing in between. That’s one of the imperfections of most money-management systems.
Sticking to 10 percent: Gann
William Gann developed a complicated system for identifying securities trades. Part of his system was a list of rules for managing money, and many traders follow that if nothing else.
The primary rule is this: Divide your money into ten equal parts and never place more than one 10 percent portion on a single trade. This strategy helps control your risk, whether or not you use Gann. (I discuss Gann in Chapter 7.)
Finding the ideal percentage: Kelly criterion
The Kelly criterion lets you determine the ideal percentage of your portfolio to put at risk. To calculate how much of your portfolio to put at risk, you need to know what percentage of your trades are expected to win, 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:
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.
To see this formula in action, consider 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. (Look familiar? I used this same example at the beginning of the chapter.) Plugging that info into the Kelly formula, the right percentage to trade is 33.3 percent:
In this situation, as long as you limit your trades to no more than 33 percent 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 can 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 it does in this example.
This money-management method 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 it could be applied to gambling, and in no time, the formula took off. In fact, a math professor, Edward O. Thorpe, used the Kelly criterion with great success to win big at blackjack in Las Vegas in the early 1960s, which led to a change in casino rules.
In a casino, the rules are against you. If you find an edge, in no time, you’ll be asked to leave, and the rules may be changed. In the financial markets, the odds are even or slightly in your favor, so you have a better opportunity to make money by practicing your strategies.
Doubling down: 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. 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 (after you close or limit the first trade) so that you can win back your loss. (You may have heard gamblers talk about doubling down? Well, this is what they’re doing.)
Under the martingale system, you always come out ahead as long as you have an infinite amount of money to trade. See the problem? 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. In short, you’re at an enormous disadvantage. As long as you have a disadvantage, thoughtful money management is critical.
Letting a program guide you: Monte Carlo simulation
If you have the programming expertise or buy the right software, you can run what’s called a Monte Carlo simulation, named for the famous casino town. In this calculation, you enter in your risk and return parameters and your account value and let the program run. It then returns the optimal trade size. The system is not perfect; it 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.
There are different schools of thought about the statistical theories that go into a Monte Carlo simulation. Fortunately, you don’t have to know them to use the system’s estimates of the return in the market to help you determine your position sizes as the market changes.
A Monte Carlo simulation is more dynamic than most of the other money-management systems, but it isn’t as easy to use. For that reason, it isn’t a do-it-yourself project unless you have extensive experience creating these programs. If you are interested, you need to find a suitable program. Many brokerage firms include Monte Carlo simulation packages in their day trading platforms.
Considering past performance: 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 (see the appendix for more information). 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.
To find the number of shares of stock, N, to trade under Optimal F, you use this equation:
F is a factor based on the basis of historical data, risk is the biggest percentage loss that you experienced in the past, equity is the amount of money in your account, and price is the current price. Using these numbers, you can find the contracts or shares you need to buy.
Here’s an example: Assume your account has $25,000, your biggest loss (risk) was 40 percent, your F is 30 percent, and you’re looking at a stock trading at $25 per share. Plug in the numbers and calculation to find that 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 kicks in only after you have some trade data. A second problem is that you need to set up a spreadsheet to calculate it (so read Ralph Vince’s book if you want to try it out). 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.
Seeing How Money Management Affects Your Return
Describing why you need money management is one thing, but showing you how it works is more fun. And because I love making spreadsheets (we all need a hobby, right?), I pulled one together to show you how different ways of managing your money may affect your return.
In Figure 6-2, 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. The trade wins 60 percent of the time, 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. Then I compared the performance of martingale and Kelly money management to betting the whole account each time.
© John Wiley & Sons, Inc.
FIGURE 6-2: How money management affects your return.
As the calculations in Figure 6-2 show, 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. (Keep in mind that if you were using a Kelly or martingale system, you’d probably be doing something with the rest of the account rather than just letting it sit there.)
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’re 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? The following sections explore some of your options.
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.
To benefit from that compounding, many traders add their profits back into their accounts and keep trading them as a way to build account size. Although day traders earn little to no interest (which is compensation for loaning out money — say, by buying bonds), 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.
Pyramiding 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, then the structure collapses and you end up with a call on your margin.
Figure 6-3 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.
© John Wiley & Sons, Inc.
FIGURE 6-3: Pyramiding magnifies returns and losses.
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 recruiting new members gets too difficult and those at the bottom get nothing. Be aware that some investment frauds have been structured as pyramid schemes. Steer clear of deals that sound fabulous and 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. This technique is good for medium-sized accounts, which have enough money that, if a pyramid were to collapse on you, you’d still have enough to stay in the market.
Making 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 his account is or how much money he’s 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. Having money in low-risk investments 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.