A successful trader needs to have a sound and profitable trading system. Either discretionary or mechanical, a trading system is a collection of rules that provides some critical information and signals at what price level traders should enter and exit a market. It also guides how to manage trades and trading equity. However, many investors and traders spend their hard-earned cash on purchasing a trading system based merely on its performance, and that’s the wrong way to look at such an important purchase. This article is aimed at helping traders choose a winning trading system and saving disappointment and embarrassment about a poor decision.

There are two main criteria to consider in choosing a winning trading system: the system’s performance and the system’s compatibility with individual trading personalities. We’ll examine each of these criteria more closely in the following sections.

The System’s Performance
Needless to say, system shoppers should care about how a system has performed in the past and how the performance has been calculated. However, the mere performance and return figure for a system could be rather misleading. It’s important, too, to know how that performance has been synthesized and cultivated. To evaluate a system’s performance, analyze the following four Rs: Robustness, Reliability factor, Ratio of profit/loss and Risk of ruin. Let’s use the following example to expand on each of these four factors.

Example S&P day trading system:
Performance for trading one big single
S&P futures contract in the past 64 months

Number of total trades = 1,558
Number of winning trades = 1,194
Number of losing trades = 346
Number of break-even trades = 8
Average profit per trade = $1,168.07
Average loss per trade = $413.87
Total loss = $143,200
Total gains = $1,394,675
Net profit (excluding commissions
and slippage) =$1,234,225
Probability of winning trades: 77 percent
Probability of losing trades: 22 percent
Probability of break even trades: 1 percent
Monthly Gain Mean = µ = $19,284.77
Monthly Standard Deviation =σ = 8,504.12
Number of Months = n = 64

But Is It Robust?
A trend-following system usually works great in a strong bull or bear market. But, when the market swings in a range, the same system may perform badly. Therefore, how robust a system is under different market conditions comes into play. Some may also refer to robustness as the capability of trading a system in a wider selection of markets. For example, a system that works in the S&P market should work in bonds, currencies and other markets as well. However, the author asserts that each market behaves based on its internal dynamics, which in turn exhibits a set of dynamic behaviors according to its profile and personality. Therefore, in this article, a system is robust when it could perform under different conditions for one single market.

To test a system’s robustness or how consistently it has performed, a simple statistical test can be used. Here is how it works. Take one week or one month as a sample performance, depending on how the system’s performance has been tabulated and data gathered. Let’s call the system’s historical performance our “population performance.” In order to have a 95-percent confidence that the sample performance would be within the usual track record of the system’s performance, it should be within the following range:

µ ± 1.96 /?n
For our example system plugging in the values in the above formula we have:
19,284.77 ± 1.96 (8,504.12/8) = 19,284.77 ± 1.96(1,063.02) or $17,201.25 < sample month performance< $21,368.28

Now, if the sample month performance was within the calculated range, it could be concluded with 95-percent confidence that the system had performed within the system’s historical average performance. Otherwise, it would be necessary to look into other statistical tests and tools to determine more accurately if the system is performing properly independent of the market conditions.

Furthermore, check for any winning trades that could simply be “outliers” and, thus, increase the system’s performance out of proportion. For example, if it’s evident that the system has one or two big winning trades which have inflated the system’s overall performance in the past six months or so, take them out and see if the performance is still satisfactory. If not, one can safely assume that the overall performance in its future trading would be far off from stated performance and, consequently, rather disappointing.

Reliability Factors – A Flip of the Coin?
How reliable and profitable are the system’s trades? Does the probability of winning trades far exceed that of losing trades? Anything close to 50 percent winning trades would suggest a useless system simply because any one could flip a coin and have an equal or a better probability than 50 percent. When a fair coin is flipped many times, it would produce so many heads or tails, which may reflect a “hot hand.” This “hot hand” phenomenon can be explained by the “theory of run” in statistics. Therefore, even a fair coin should yield results better than 50 percent. To calculate the reliability factor for any system, simply divide the number of winning trades over total trades. If that ratio or number is greater than 0.50, there’s a probability of better than 50 percent of winning trades. For example, the depicted performance for the above system with 1,194 winning trades over 1,558 total trades yields a reliability factor of 1194/1558, or 77 percent.

Ratio of Profit/Loss
What is the profit/loss ratio for the system’s trades? Does the system garner four points for every two points possible loss? A profit/loss ratio close to one may just make a broker rich, but spell disappointment for the trader. Suppose a system claims that for every two points profit, there is a risk of two points loss. In other words, the ratio of profit to loss is just one. If with 20 trades, there are ten losing trades and ten winning trades, as well as the costs of commissions, slippage, data, equipment and the trader’s time, it would be a losing game. Even if the reliability factor is at 3/4 — because for every two points lost, there’s an expected two-points profit — when you include other necessary costs of trading as mentioned above, in the long run you are just making your broker rich.

A minimum ratio should be 2/1 – for every one-point loss, you stand to gain two points profit. The profit-to-loss ratio for the system depicted above is 1194/346 = 3.45. Because the system’s reliability is more than three to one, you just may have a winning system in your hands.

Risk of Financial Ruin
What is the risk of losing that chunk of trading capital trading with your system? Some systems may show a great performance, but looking into their trade details may be a surprise. Consider the example of the S&P day trading system with an average profit of $1,168.07 (about 4.7 points on the big S&P futures contracts) and average loss of $413.87 (less than two points per big S&P contract). Now, calculate how many losing trades the system should have before a trader loses his total trading capital, say for $15,000. To do this calculation, let’s use the following formula:

NL = (1 – PW)*C/L
NL = maximum number of losses in a row that you could have, PW = probability of winning trades, C = trading capital, L = average losing trade

Therefore, we have NL = (1- 0.77) (15,000)/ 413.87 = 8.33 or eight trades. This tells us that if the system makes eight consecutive losing trades, all of the available trading capital will be lost. It’s also possible to calculate the minimum probability that the system would lose all of its trading capital in the long run. Here’s the formula:

Pm = {1 – [Ln(1 + W/C – L/C)/ Ln (1- L/C)]}-1
In this formula, Pm stands for minimum probability, W = average winning trade, and Ln denotes natural log.
Pm = {1 – [Ln(1 + 1168.07/15000 – 413.87/15000)/ Ln (1- 413.87/15000)]}-1
Pm = 36 percent

Therefore, there is a 36-percent probability that the trader could lose his entire $15,000 trading capital to trade our example system. Because this is less than 50 percent, it indicates that the featured system is a rather strong and robust system, which has been producing profit in all types of markets in the past five years.

For comparison purposes, consider another system, which for every two points ($500 for big S&P futures contracts) has a risk of losing two points. This system would have a minimum probability of 100-percent losing the entire trading capital.

System Compatibility with Trader’s Personality
In reviewing whether each trader’s very individual personality is compatible with a system, explore the following factors.

Trading Method. Is the system a mechanical, discretionary or hybrid system? A system is a collection of trading rules that can provide entry and exit prices or signals, protective stops and money management. A trader may be able to program all of the rules into the computer to generate a mechanical system. On the other hand, traders can use the same rules and identify their entry and exit prices trading their favorite market – a discretionary system. A discretionary system requires the trader to analyze some vague information provided by the market based on the individual’s trading rules as opposed to the mechanical system, which requires him to be more or less a good operator.

The hybrid system is the combination of these two systems. It does provide some objective and mechanical elements, such as entry price and signal, but it requires following the rules using the trader’s own discretion to exit trades.
To achieve trading success, of course, the trader must make sure that he is choosing a trading method or system that is compatible with his trading personality. To identify your trading personality strengths and weaknesses, you might wish to take my Trading Personality Profile (TPP) test, based on Personality Traits Theory of Five Factor Model (see sidebar). This short test is a subset of a more detailed TPP test, but it can begin to help you identify which trading method might be best suited to you.

Trading Style. What about trading style? – day, swing or position trading? To obtain a maximum performance with a system, a trader should select a trading style that is compatible with who he is. In other words, his trading personality could influence his performance greatly.

If a trader has the holy-grail trading system for position trading, if his personality prefers more trades, using the same system could create a major financial disaster. If the TPP profile is compatible with day trading, the trader would require more trades and, therefore, would create extra trades, which are not provided by a position trading system. In other words, he would overtrade his position trading system, which could result in performance that greatly deviates from that of the system. Deviations from a system’s trading recommendations, regardless of the end result, can have negative impacts on a trader’s psychology. If, for example, a trader puts on a few trades that are not part of his system and ends up losing money, he could potentially begin criticizing himself. If, on the other hand, he obtains some good winning trades, this might cause him to implement a completely new system. Yet, it is unrealistic to expect this system to have the same performance as the initial system. This process has wasted valuable time and energy.

In the sidebar, there’s another short test to determine which style of trading may be most suitable for you.

Risk Preference. Traders differ, too, by the type of risk preference they possess. Some have more of an appetite for a risky trading system; they are able to endure larger losses and follow their systems despite big drawdown. However, others may be unable to handle big losses and large drawdown. Regardless of how good and robust a system might be, if a trader’s risk preference is not compatible with the system’s performance, that system is not worth the time and money spent.

To assess risk preference, it’s possible to use a utility function, which could offer some good proximity for it. Suppose the trader feels comfortable with a reliability factor for his trading of, say, 2/3 for every three trades, or two winning trades. Furthermore, he does not wish to have a loss of more than $100 in trading the E-mini (two points) for every $200 winning trade. His utility or risk preference is calculated according to the following equation:

U = W *PW + L*PL
where U = expected utility, W = average winning trade, PW = probability of winning trades, L = average losing trades, PL = probability of losing trades.
U = 0.666 * 2 + 0.333 *(-1) = 1.333 – 0.333 = 1
Now, consider an example of the S&P day trading system. The utility for that system is calculated as follows according to the above formula:

USystem = 0.77 * 1.168 + .22 * -0414 = 0.808 or 0.81

Because the system utility is only 0.81, which is less than the trader’s desire utility or risk preference, the example system would be compatible with his risk tolerance.

Draw Down and Number of Losing Trades in a Row. Here’s another consideration. A trader may like the system’s overall performance, but may get disappointed when he sees it could have fewer losing trades in a row than he can emotionally handle. To calculate the system’s draw down, find the first losing trade in the system’s historical performance and, from there, add all of the losing trades. If there’s a winning trade, he would deduct from his total losing trades in the series. If there are other winning trades, he would deduct them from his total losing trades amount. If he gets zero, the trader would need to find another losing trade after that. The total losing trades in a row should identify his total draw down in that period. Many individuals do not seem to have any problems with analyzing the total draw down with respect to the total gain and profit of a system. They are easily able to see that after some time, if they keep on trading the system consistently, they are able to recover the draw down and make some good profits as well.

However, since human beings are emotional beings, this type of analysis sometimes does not work in the real world. Therefore, it is important for traders to know how many losing trades they can withstand. This can be identified through the Trading Personality Profile. Depending on the TPP, a trader might be able to handle six losing trades in a row regardless of his account equity or financial standing. For another trader, three losing trades in a row may be the end of trading his system. This concept becomes more important if a trader has just purchased a great system, but as soon as he begins trading that system, he experiences more losses than he can handle.

Before choosing a system, know the probability of having a few losing trades in the first number of trades. Consider the trader that knows, based on his TPP, that he can handle no more than three losing trades at the beginning of his trading experience with any new system. Using the example S&P day trading system, let’s figure out the probability for having three losing trades for the first six trades. For this we use binomial probability distribution formula:

Ploss = [N! / L! (N-L)! ] PL (1-P)N-L
where L= number of losing trades, N= total number of trades, P = the probability of a loss and the symbol (!) stands for the factorial (e.g. 4! = 4*3*2*1 = 24)

Using the data from the above example day trading system, we have L = 3, N = 6, P = 22 percent and plugging these values into the formula:

Ploss = [6!/3! * 3!] (.22)3(.78)3 = [ 720/36](0.106)(0.475) = 1.007 or about 10 percent

The probability of having three losing trades in a row for the first six trades of that system is 100 percent. Now, if a trader’s TPP doesn’t agree with three losing trades in a row in his first trial of the system then this system, it’s not for him.

Again, to choose a winning trading system, the trader needs to consider two important criteria – the system’s performance and the trader’s trading personality compatibility with the system. Regardless of how profitable or good a trading system may look, to save your time, energy, money and future embarrassment, look carefully into each of the above-mentioned criteria.

Reference: How To Become A Successful Trader, The Trading Personality Profile: Your Key to Maximizing Your Profit with Any System, ISBN: 0595243894, by Ned Gandevani, MBA, PhD.

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