## How to Win the Stock Market Game. V. Daragan

If the number of trades is large it is a good idea to analyze the trading performance by using a histogram. Histogram (or bar diagram) shows the number of trades falling in a given interval of returns. A histogram for returns per trade for one of our trading strategies is shown in the next figure. As an example, we have considered distribution of returns for our Low Risk Trading Strategy (see more details in http://www.stta-consulting.com) from January 1996 to April 2000. The bars represent the number of trades for given interval of returns.

The largest bar represents the number of trades with returns between 0 and 5%. Other numbers are shown in the Table. For this distribution the average return per trade is 4.76%. The width of histogram is related to a very important statistical characteristic: the standard deviation or risk.

To calculate the standard deviation one can use the equation. The smaller the risk-to-return ratio, the better the trading strategy. If this ratio is less than 3 one can say that a trading strategy is very good. We would avoid any trading strategy
for which the risk-to-return ration is larger than 5. For distribution in Fig. 1.2 the risk-to-return ratio is equal to 2.6, which indicates low level of risk for the considered strategy. Returning back to our hypothetical trading strategies one can estimate the risk to return ratios for these strategies. For the first strategy this ratio is equal to 3.2. For the second strategy it is equal to 5.9. It is clear that the second strategy is extremely risky, and the portion of trading capital for using this strategy should be very small.

How small? This question will be answered when we will consider the theory of trading portfolio. The definition of risk introduced in the previous section is the simplest possible. It was based on using the average return per trade. This method is straightforward and for many cases it is sufficient for comparing different trading strategies. However, we have mentioned that this method can give false results if returns per trade have a high volatility (risk). One can easily see that the larger the risk, the larger the difference between estimated total returns using average returns per trade or the average growth coefficients. Therefore, for highly volatile trading strategies one should use the growth
coefficients K.

Using the growth coefficients is simple when traders buy and sell stocks every day. Some strategies assume specific stock selections and there are many days when traders wait for opportunities by just watching the market. The number of stocks that should be bought is not constant. In this case comparison of the average returns per trade contains very little information
because the number of trades for the strategies is different and the annual returns will be also different even for equal average returns per trade. One of the solutions to this problem is considering returns for a longer period of time. One month, for example. The only disadvantage of this method is the longer period of time required to collect good statistics.

Another problem is defining the risk when using the growth coefficients. Mathematical calculation become very complicated and it is beyond the topic of this publication. If you feel strong in math you can write us (service@stta-consulting.com) and we will recommend you some reading about this topic. Here, we will use a tried and true definition of risk via standard deviations of returns per trade in %. In most cases this approach is sufficient for comparing
trading strategies. If we feel that some calculations require the growth coefficients we will use them and we will insert some comments about estimation of risk. 