We have already explained that every backtest, whether automated or discretionary, is performed for the purpose of evaluation of trading systems´ performance. In this chapter we will introduce the basic tools for assessing a trading system´s performance. Our goal should always be to detect such trading systems the backtesting of which will then show stable profits.

**Equity Curve **

First have a look at an equity curve (see Fig. 1). We have mentioned this term already in the previous chapters. The equity curve gives us the initial signal that the system we are testing may be profitable.

**Fig. 1****: Equity curve of a potentially profitable trading system **(*Created in **TradeStation)*

In Fig. 1 you can see the historical equity curve of one of the systems which I use in my live trading. (And I should say that I have had a lot of success with using this system so far!) I added this system to my live trading portfolio in early 2013.

So what information gives us the equity curve?

- In the headline of the figure you can see that the curve covers trades carried out between September 3, 9. 2003 and September 3, 9. 2013, i.e. during the last 10 years.
- On the horizontal axis you can see that the system executed nearly 1,200 trades (namely 1,178) in the last 10 years.
- The vertical axis gives us information that over the last 10 years the system earned approximately $ 110,000 (namely $ 106,629) by a conservative trading of one futures contract.
- You can see that this system´s equity curve tends to continuously create new peaks. It means that after periods of losses (drawdowns) the trading system has the power create new price peaks again, i.e. to enter into series of profitable trades.
- In the period between the trade no. 500 and the trade no. 600 the equity curve rose very steeply. It is a very interesting phenomenon because these profits were generated at the beginning of the crisis – from approximately June 2008 to March 2009 when markets were falling sharply.
- Since this system is based on utilising strong business trends, every economic bubble causing steep Long-side or Short-side movements is very favourable for it.
- You can also see that about the last 200 trades were very profitable (i.e. trades no. 1,000 – 1,200) and that the curve created new and new peaks. Such trading systems which show a steady growth also in the close historical periods give us a higher probability that they will work well in the future.
- We must not forget that within the backtesting this trading system executed nearly 1,200 trades during the last 10 years, which is a very good statistical sample. Here applies the rule: The more the better.
- Another positive fact is that we backtested 10 years of quality and accurate data. The data include all market situations – a crisis period, stagnation period, and a period of strong economic growth. It is not so easy to get quality historical intraday data these days as data providers usually charge considerable fees. But as you can learn in a series of articles on my web portal or in my courses, there are some very interesting and cheap alternatives. It is of course necessary to be familiar with this sphere and have a certain know-how. I will be happy to help you with both. Never underestimate the quality of data and the sufficiently long historical sample!

So you can see how much useful information can be read from the equity curve. From my perspective, it is one of the most essential and useful graphical tools for evaluating performance of trading systems. Strength of the equity curve lies mainly in the fact that it can show us very quickly whether our trading system is stable. That is, whether it tends to generate profits and created new and new price peaks in the long term.

Now we will focus on the basic parameters of a trading system´s performance expressed in numerical form. If you are a discretionary trader and you keep your trading diary in e.g. MS Excel, it should be easy for you to calculate the individual performance parameters of your system. If your trading approach is based on automated trading, then software platforms can save you a lot of time because performance evaluation reports are already their integral parts.

Let’s explain what performance indicators we should pay attention to.

**Net Profit (Total Net Profit)**

Net profit is the sum of all winning (Gross Profit) and losing (Gross Loss) trades. Its value can be both positive and negative.

To illustrate, imagine backtests of two trading systems, both with 5-trade samples with the following results:

*$320, $260, $50, $400, $720*.*The total profit of $430.**$200, $750, $3 000, $30, $5 200.***The total profit of $1,680.**

Question for novice traders: “Which of these two trading systems would you trade with a real account?” Many of you would, seemingly logically, choose the system with the higher net profit of $1,680.

By this simple example I´m trying to explain that it is necessary to start to think in a broader context. Of course, our primary goal will always be to earn the most money possible. Yet trading, just like any other business, is also about a risk. So now let’s look at the two examples from the perspective of the accumulated loss:

- In the first case you would be exposed to the accumulated loss of
*-260 + 50-400 =***$-610** - in the second case the cumulative loss is
*-750 -3,000 =***$3,750**

Now you surely understand that evaluating a trading system solely on the basis of a single indicator would be very short-sighted and could end by an early bankruptcy. It is always necessary to assess trading systems by the use of more information and indicators. Therefore, never and under no circumstances consider the net profit indicator as a decisive and the only relevant indicator of your trading system´s quality!

Also remember that the net profit should reflect the costs associated with brokerage fees (commissions) and slippage in order execution.

**Drawdown**

Drawdown is the difference between the historical peak of our equity curve and the subsequent cumulative price decline. It does not necessarily mean a loss, it may be only a price collapse. It can be expressed as the amount of money or percentage of the largest cumulative decline in capital in our historical trades or backtests. Its value or a multiple of its value are often used to determine the size of the account for live trading in a particular market and to determine the maximum acceptable risk and stop loss before we start to trade live. For example, if our maximum historical drawdown in a particular market was $5,000, we can say that our business strategy requires an account with at least a triple drawdown value, i.e. $15,000.

**Profit Factor **

Profit factor is the ratio of all winning (Gross Profit) and losing (Gross Loss) trades. Its lowest value is 0, the highest value is not limited. Yet from my own experience I know that strategies with a sufficient number of trades (more than 500) and the profit factor higher than 2 are rather exceptional. There are traders who use the profit factor as the absolutely essential indicator. For example, their rule is not to use a strategy with the profit factor lower than 2.5. However, I personally do not agree with this strict rule because I know from my own experience that also a strategy with the profit factor of about 1.5 can be very profitable. Therefore, perceive the profit factor as an indicator that is variable in time.

**Fig. ****2****: Periodic Analysis of Performance Report **(*Created in **TradeStation)*

In Fig. 2 you can see the annual backtesting results of a strategy traded for 10 years (from 2003 to 2013). An ideal robust strategy should have approximately the same profit factor every year.

Now imagine an extreme situation in which our strategy achieved a profit factor 6.5 in one year. But in the previous 9 years the profit factor was lower than 1. In other words, we were losing for 9 years. Only one year our strategy showed enormously good results. Therefore, the sum of all profits and losses would be a high profit, but only thanks to a single year.

Now imagine a strategy with a profit factor 1.5, but all 10 years were profitable with the profit factor higher than 1. Which of the two strategies would you choose for live trading? The strategy that brought you more money after 10 years but with which you were in a loss for 9 years? Or the lower-profit-factor strategy that was steadily generating smaller profits year after year?

In terms of statistical robustness you should choose the second (stable) strategy with the profit factor higher than 1 in each year.

**Total Number of Trades**

Please, always remember one crucial rule. The larger the sample of trades, the better. Those familiar with the probability theory and the basics of statistics do not need a further explanation. You surely understand that the larger statistical sample of data we have (backtest data in our case), the smaller the deviation from reality (live trading).

A classic example are surveys of election results. We all know the situation very well – an opinion research agency conducts survey on election results by the use of a statistical sample. Such a statistical sample typically contains a few thousand inhabitants, i.e. an insignificant part of the total number of inhabitants. The most important thing is that the sample contained all age groups, social classes, ethnicities, both genders, etc. in an even distribution. Based on this statistical sample are then estimated the overall results of the actual polling.

Please note that in these surveys they always speak about a few-percent **statistical deviation**. There is one inflexible rule here – the closer is the statistical sample (subset) to the total number (entire set), the smaller the statistical deviation. In the Czech Republic there are approximately 10 million inhabitants. Now imagine that for an election survey will be chosen two relevant statistical samples (subsets), the first with 10,000 inhabitants and the second with 100,000 inhabitants. It is clear the sample with 100,000 inhabitants will be more statistically relevant.

Similarly, now let’s have a look at a trading system. You surely understand that a system with 30 trades has a completely different informative value than a system with 600 trades. I have met traders who in no case would trade a system with less than 500 backtested trades. This applies primarily to systems based on short-term trades (mostly for intraday trading). However, more advanced traders are well aware that it is virtually impossible to obtain such a large statistical sample for testing of positional systems. Thus it is necessary to be more benevolent in the case of positional trading. As a completely sufficient sample are considered 200-300 trades here.

The point is to always backtest:

- the longest period possible for the given market with the largest amount of trades possible,
- the largest sample of market situations possible (e.g. chops, strong trends, sudden price reversals, limit movements, high and low-volatility periods, extreme situations, etc.).

**Risk Reward Ratio (RRR)**

RRR indicates a ratio used by traders for comparisons of the expected profit per trade and the acceptable loss per trade. Mathematically, this ratio is calculated as the amount that we are willing to risk in one trade (for example, $300 Stop Loss) divided by the expected profit if the market moves in the desired direction ($ 600 Profit Target). When using the values in brackets the RRR would therefore be 1: 2. RRR is important for managing risks within trading strategies. The aim of the trader is to set SLs and PTs that are consistent with his strategy´s RRR and that will bring stable profits. This ratio is independent on actual results of individual trades (i.e. whether they were winning or losing).

**Percentage of profitable trades (Percent Profitable)**

If we take the number of winning trades and divide it by the total number of trades and then multiply the result by 100, we get the percentage of successful trades. The question is to what extent this is a decisive indicator for us. There are strategies with only 30% of profitable trades that generate much higher profits in the long run than strategies with 60% success rates. There may be even strategies with 60% of profitable trades that are losing in total. The answer therefore lies more in the average profit and the average loss for all trades and their ratio.

Let’s explain this on an example. We have two strategies each of which we tested on 1,000 trades:

**1. The first strategy **has the average profit of $1,000 and the average loss of $400.

**The profit-to-loss ratio**s 1 000/400 = **2.5**.

The Percent Profitable value is **35%**.

**The total profit/loss **is:

Total profit/loss = the number of trades * (average profit * 0.35 – average loss * 0.65) = 1000 * (350-260) = **$90,000**

Thus despite the low percentage of successful trades the strategy is profitable in the long run thanks to a high **ratio of the average profit to the average loss**.

**2. The second strategy **has the average profit of $1,000 and the average loss of $1 800.

**The profit-to-loss ratio **is therefore **0.55**.

The Percent Profitable value is **60%**.

**The total profit/loss **is:

Total profit/loss = 1000 * (600-720) = **– $120,000**

Although the strategy has 60% profitable trades, it led to a substantial loss after 1,000 trades due to the very low **ratio of the average profit to the average loss**.

The example clearly shows that like in other indicators, Percent Profitable cannot be seen in isolation, but always in the context of the **ratio of the average profit to the average loss.** It is therefore a very important indicator because the entire trading is about searching of a “Logical edge” (statistical advantage). A problem in strategies with a low percentages of profitable trades is that the trader asks a logical question: Is the low probability of a winning trade a result of a demanding exit strategy or is it a mere coincidence that occurred only in backtesting and will not appear again in the future?

There is no unequivocal answer. However, from my personal experience I know that it is possible to find strategies with a high percentage of successful trades and a sufficient **ratio of the average profit to the average loss.** From a psychological point of view, such strategies are far easier to trade. It is always psychologically easier to use strategies that generate more frequent, though smaller profits than strategies with high **ratio of the average profit to the average loss** and less frequent winning trades. But of course it depends on the nature and disposition of each trader.

**Average profit/loss per one trade (Average Trade Net Profit)**

This indicator can give us a lot of useful information in trading. It´s calculation is very simple – it is the arithmetic average of all trades, i.e. both the winning and losing ones. It can be both positive and negative. If the indicator´s value is positive it means that the overall backtesting result was a profit. If the value is negative, the backtesting showed that the strategy brought a loss.

There is one truly fundamental rule. The higher the average profit per trade, the better. Yet again, you must also take into account other indicators, like Profit Factor, standard deviation of the system, number of trades, drawdowns, etc. In no case you can simply choose a strategy because it has the highest average profit per trade!

In this chapter we introduced the concept of trading systems´ performance evaluation. We have explained the equity curve and its purpose in trading. We also introduced the basic numerical indicators that help traders to find out whether they are on the right way to creating a really good trading strategy. Do not forget to always compare these indicators within backtesting, papertrading, and live trading results. The results of a really good trading system should be more or less the same in all three cases. If backtesting of individual indicators or the equity curve brought the expected results but the results were not confirmed in papertrading, do not risk your capital by live trading via this system. Your goal is to eventually find such a trading system that proves its qualities in any conditions. As novice traders you do not need other indicators than those introduced in this chapter. In the long run, it is advisable to learn more about evaluating trading systems´ performance.

**Petr**

**(c) AOStrading.cz**

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