tOU | |||||||||||||||
ouu | |||||||||||||||
w £.'J1 | |||||||||||||||
n, fauu 150 | |||||||||||||||
n | nil | OMiT |
1000 2000
-3000 -2000 -1000
Figure 4.6 A histogram of the 65sma-3cc system over a narrower range of profits and losses. Notice that only a small number of trades show large profits.
Developing New Trading Systems
measurements will follow a normal distribution. The normal distribution is a bell-shaped probability distribution of the relative frequency of events. The standard normal is a special case of the normal distribution with a mean of zero and standard deviation equal to one. To compare the distribution of the 65sma-3cc trades to the standard normal distribution, we first have to "normalize" the bin sizes. The comparison is shown in Figure 4.7.
The 65sma-3cc curve is more sharply peaked than the standard normal curve. To generate a normal distribution that would fit our data, I used a Microsoft Excel 5.0 spreadsheet and employed an iterative process of manually tweaking the values. The fitted normal curve, with a mean of-0.16 and standard deviation of 0.18 is shown in Figure 4.8. The fitted normal distribution shows that the actual 65sma-3cc distribution has "fat" tails. This simply means that there is a larger probability for the "big" trades than would be expected from the normal distribution. This chart shows that unusually large profits or losses are more likely than might normally be expected.