Beyond analysis: Sizing your trade

Money management is mostly about how much to bet. While your trading system or analysis techniques tell you what, when and how to trade, a money management strategy tells you how much to trade.

When asked where money, or risk, management ranks with other aspects of a trading plan, most professional traders respond as trader Fred A. Kingery of the commodity trading advisor (CTA) AM Grace Trading Co. in Volant, Pa.: "It's paramount. It's numero uno."

Still, money management is not something most beginners consider, says trader Michael Dever of the CTA Brandywine Asset Management Inc. in Thorton, Pa. "It's trading strategies that are fun to develop."

But money management strategies make the most difference between success and failure, Dever adds.

George Pruitt, who runs Futures Truth in Hendersonville, N.C., with John Hill, says money management is so important, traders should spend 60% of their time and resources developing money management strategies and the other 40% developing their actual trading strategies and portfolio makeup.

Trader accolades of money management fill books, but the fundamentals will help you the most. (See Jack Schwager's book Market Wizards if you're still not convinced that money management matters.) Here, we look at some of the underlying mathematics and show where these can be applied in your own trading plan. We also look at several distinct approaches and apply two of them to a simple trading system.

The first steps
Before you can decide how to manage your money, you must put your objectives and abilities in perspective. Most experts highlight three areas you must analyze before taking your money management any further:

  • The volatility of the market(s) you trade.
  • The success you expect from your analysis techniques.
  • Your trading capital.

Market volatility is an often overlooked part of money management. You will fail if the maximum risk you can endure is $500 and the interday fluctuations of the market you want to trade are $3,000. If you can't afford to trade the S&P 500 or coffee, you must admit it.

You also must have a grasp of the viability of your analysis. Unless you know your average loss should be $1,500, how can you plan for it? With extensive backtesting or paper trading, you can estimate such parameters. Then some simple formulas can help you get an even better picture of your potential success.

Your expected payoff is a function of how often you expect to win or lose and the amount you expect to win or lose. The formula for the expected payoff (often referred to as the mathematical expectation) is:

EP = P1 * W - P2 * L, where

P1 is the probability you will win.
P2 is the probability you will lose.
W is the amount you can win.
L is the amount you can lose.

The expected payoff must be positive if the system is worth trading.

While an exact measure can't be known due to fluctuating wins and losses, most experts suggest using the average winner for "W" and the average loser for "L," which your backtesting or paper trading will help you determine. And while it's also not fixed in trading, you can use the percentage of winning trades for "P1" and the percentage of losing trades for "P2." In the book Schwager on Futures: Technical Analysis, these figures are used to compute the expected net profit per trade.

Having enough capital to trade is probably the most important area of money management. If you aren't well-capitalized, an extended drawdown eventually will wipe you out. There is no hard figure needed to start with, such as $15,000, $25,000 or $100,000. Of course, what you need must mesh with what you can afford.

By calculating your risk of ruin, or the chance that you'll lose so much you must stop trading, you can estimate whether you have enough capital. What risk of ruin you settle on is subjective, but experts say anything over 10% is too high. The formula for risk of ruin is:

RoR = ((1 - A) / (1 + A))C, where

A is your trading advantage.
C is the number of units you have.

To figure A, subtract the percent chance you have to lose from the percent chance you have to win. So, if you expect to win 55% of your trades, your advantage would be 10% (0.55 - 0.45 = 0.1). To figure C, divide one by the percent of your capital you'll risk on each trade. So, if that's 4%, you have 25 units (1 / 0.04 = 25).

"Risk of ruin" (below) depicts the chance you'll blow out given certain trading advantages. The number of units you have has a clear impact on the outcome. Overly aggressive trading - betting a high percentage of your stake on each trade - may give you some big winners, but it also will take you down in the end.



An important caveat with this risk of ruin calculation is it assumes your winners and your losers will be equal - an unlikely occurrence. Nevertheless, this still can be a good measure of the viability of your techniques.

The math to calculate your risk of ruin for winners and losers that differ is much more involved.

Mike DeAmicis-Roberts discusses some IBM-compatible software in "Balancing Act," Futures, September 1995, that will calculate this for you. See the download section of Futures' Web site for a free copy of this software.

Limiting loss
Stops are orders you give your broker to liquidate a given position if it moves against you a specified amount. While stops can be one way to get a more exact idea of your greatest potential loss, they also can affect the overall profitability of your techniques.

The bane of stops is they can force you out of a position that initially goes against you but ends up moving in your direction. That's why most experts suggest using stops that fluctuate with market volatility.

"I don't believe in fixed money management stops," Pruitt says. Overly constrictive stops, such as those many have employed in the volatile S&P 500 in recent years, will "deteriorate" systems, he says.

A better way is to use wider stops as volatility increases. For example, increase them by some dollar or percentage value as the standard deviation of closes or average true range reaches certain levels.

Other than using stops, you could find a strategy that by its nature seems to avoid large losses based on historical tests. (Of course, the danger is past performance may not match future performance.) This approach appeals to purists who favor sticking to a system and not "polluting" their results with fixed stop loss points, profit objectives, etc. Proponents of stop-and-reverse strategies, which always stay in the market by going directly from long to short positions and vice versa, also lean toward depending on the system to limit risk.

For illustration's sake, we'll look at a simple 20-day, 40-day moving average crossover system that's always in the market. (That is, if we're long and we get a sell signal, we sell to offset our long position, then we sell again to initiate a new short position.) We tested the system on 10 years of daily Treasury bond data, from Jan. 1, 1987, to Jan. 1, 1997. We assumed $100 for slippage and commissions.

Our total net profit for the period would have been $41,294 on a maximum intraday drawdown of -$13,913. The test shows 58 trades would have been made, 28 or 48% of which would have been winners. The average winning trade would have been $3,668, while the average loser would have been -$2,047.

Based on a starting capital of $25,000, our maximum loss would have been high as a percentage of our capital at the time (see "Sizing up our losses," below). But our average loss on losing trades was 5%. We can use this simple system to demonstrate two strategies for managing position size.



Gauging growth

As a simple illustration of what money management can do, we'll apply two popular money management strategies - fixed percentage and optimal f. These simulations are based on the trades indicated by our basic moving average crossover system with additional slippage and commissions subtracted for additional contracts traded. Results are shown to supplement the discussion of the various techniques and should not be used as the basis for judging one strategy superior to the others (see "Maximizing growth," below).





Fixed percentage money management sizes positions as a percentage of account equity. While this percentage can be determined a number of ways, we'll use loss figures from our T-bond test.

Tests show that our maximum loss over the period was 12% of our capital. If we feel comfortable with this maximum loss, which many would say is too high but can be used for illustrative purposes, we then could determine how many contracts to trade. First, we find our account size right before the loss, which was $28,619. Assuming the 12% is a good proxy for the maximum percentage loss we could expect in the future, we could trade one contract for every $28,619 in our account. But this would have us trading one contract until we amassed more than $57,238, which doesn't happen in our simulation until Feb. 8, 1996.

If we wanted to be more aggressive, we could risk, say, a maximum loss of 20% of our equity. To find the contracts you would trade with this, find the dollar value of the largest loss, -$3,506 in our case, and divide that by 20%. Our answer is $17,530. So, we would trade one contract for every $17,530 in our account. This occurs as early as February 1991 in our simulation. These are the results shown in "Maximizing growth" for the fixed percentage increase strategy. (Be careful adjusting percentages and other money management parameters. As with the techniques in your actual trading system, these can be over-optimized as well. Any other settings you derive should be tested extensively on out-of-sample data.)

Probably the most well-known technique is optimal f, developed by Ralph Vince, president of First October Trading Co. in Gates Mills, Ohio. (See "In the library," page 69, for where to find more on optimal f.)

We used a spreadsheet to calculate optimal f for our simple system and determine how many contracts we would trade at that level. (See Futures' downloads section for money management related spreadsheets and other tools.) With an optimal f of 32%, this technique had us trading the most contracts (11 by September 1996 on an account equity of $129,694).

One source explains optimal f as "pull-your-hair-out trading." While that may be harsh, it's indicative of the high volatility and sharp drawdowns that tend to accompany optimal f. Optimal f bases the number of contracts to be traded on the account size, win/loss percentages, etc. It does not attempt to anticipate streaks of underperformance and counter that with abrupt decreases in contracts traded to limit the drawdowns. But who knows when the drawdown will end? If you're trading the full number of contracts, you'll be well positioned to take full advantage of the turnaround.

Still, despite that benefit, "optimal f is too highly leveraged," Pruitt says. "Ninety percent of the time, trading at optimal f, you're going to get killed."

Pruitt's casual advice is only slightly exaggerated. Risking 32% of your equity on each trade with a 5% advantage over the market, you stand a 74% chance of losing it all if your winners equal your losers. With a 1% advantage (you win 50.5% of your trades), your risk of ruin is 94%.

Pruitt suggests small traders approach money management on a trade-by-trade basis. First, determine how much you want to risk on a trade. Second, calculate how much risk is in the market, either by looking at volatility, or support and resistant levels. Third, divide the risk you will accept by that in the market to see how many contracts you can trade. For more flexibility, Pruitt suggests you use the fractional contracts traded at the smaller exchanges, such as the MidAmerica Commodity Exchange.

Building pyramids
These methods addressed the size of initial positions, not adding to current positions. While a valid option for improving your performance, adding to positions can lead to severe overtrading.

Assuming you're adding to a winning position, pyramiding increases your average cost. For example, if you're long corn at $2.80 and it rises to $3, persuading you to buy another contract, your average cost now is $2.90 on two contracts. If recent support is at $2.88, and price tests that support, you're now in a losing trade. (The $2.80 entry makes 8¢, but the $3 entry loses 12¢ for an overall loss of 4¢. Looked at another way, your average cost of $2.90 lost 2¢ per contract, or a total of 4¢.)

"Identify [support] on the downside [for a long position], then make sure you don't raise your average cost to that level," says Jim Bianco with Arbor Trading Group in Barrington, Ill. Bianco emphazises that unrealized profits (paper profits on open positions) should be treated like actual equity.

"People call [paper profits] the 'house's money,' and that is one of the single worst things you can do," he says.

Bianco likes the "4-3-2-1" rule for adding to positions. That is, add contracts at a decreasing rate once the market suggests your original position was right.

As with trading systems, many money management strategies exist, including those you can buy. Considering how powerful money management can be, software vendors have not overlooked it.

Ryan Jones, president of Rumery and Lehman Inc. in Colorado Springs, Colo., is such a vendor. He claims his methodology, fixed ratio trading, is one of the most dynamic available.

A basic notion of fixed ratio trading, and what makes it so dynamic, is it alters the position size based on factors other than the account size. For example, with fixed ratio trading, you may trade five contracts as your account grows, but then after a loss or two, you will drop down to one or two contracts, despite how much you actually lost from your account.

Jones, who sells software that applies his method, would not discuss the math behind fixed ratio trading for this article. But a few basic aspects of fixed ratio trading are clear: Increase position size based on the number of contracts currently traded and some fixed ratio; decrease position size faster than you increase it to protect from extended drawdowns. This is a fundamental notion of money management that professional traders have preached for decades.

And as with trading systems, money management strategies often make unrealistic promises.

The Martingale - not a realistic strategy for traders but popular with gamblers before casinos imposed limits on bets - says with each losing bet, you should double up the amount lost to that point, with a little extra thrown in. The logic is sound: Odds say you can't lose forever, and when you do win, you'll make back all your losses plus the little extra. But in practicality it's flawed: Starting with $1,000, after 10 consecutive losses you would have to bet more than $1 million just to get even.

The Kelly formula, also popular with gamblers, suggests you trade (N / B) * E, where N is the advantage per bet, B is what the bet pays, and E is your current account equity.

All money management techniques have the same objective: to optimize your trade size and loss parameters for better performance. But regardless of the strategy, this is clear: You'll never realize your full potential trading without both a winning ensemble of analysis techniques and a sound money management system.

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