notation that can be found mixed together. Of course, the standard mathematical formulas for most methods sppear as they had in the previous editions. Added to that are spreadsheet examples, using Corels Quattro code, which is very similar to Microsofts Excel. Readers should have no trouble transferring the examples found here to their own choice

Finally there is extensive program code with examples in Omegas Easj Language. Although these programs have been entered and tested on TradeStation, there are occasional errors introduced during final editing and in transferring the code into this book. Readers are advised to check over the code and test it thoroughly before using it. In addition, there are times when only a single line of code is shown along with the standard mathematical formula to help the reader translate the technique into a more practical form. Because of the many different forms of formulas, you may find that the standard deviation fiinction takes the spreaddieet form of (fflstd rather than the Easj Language notation (fflstddev, or that (fflavg sppears instead of (average. Please check these formulas for notation consistent with your needs.

basic concepts

... economics is not an exact science, it consists merely, of laws of probability. the most prudent investor therefore, is one who pursues only a general course of action which is "normally" right and who avoids acts and policies which are-normally-wrong.

l.l.b. angas

there will come a time when we no longer will know how to do the calculation for long division, because miniature voice-activated computers will be everj-where. we might not even need to be able to add; it will all be done for us. we m-ill just assume that it is correct, because computers dont make mistakes. in a small way this is happening now. -not everyone checks their more complicated spreaddieet calculations by- hand to be certain they are correct before going fiirther. nor does everyone print the intermediate results of computer calculations to verify their accuracy computers dont make mistakes, but people do

with computer software rapidly maldng technical analj-sis easier, we no longer think of the steps involved in a moving average or linear regression. a few years ago -we used correlations only when absolutely necessarj, because they were too complicated and time consuming to calculate. it would even be difficult to know if you had made a mistake without having someone else repeat the same calculations, -"sc" we face a different problem-if the computer does it all, we lose our understanding of why -1, amoving average trendline differs from a linear regression. without looking at the data, we dont see an erroneous outlier. by not reviewing each hypothetical trade, we miss seeing that the slip page can tum a profit into a loss.

to avoid losing the edge needed to create a profitable tradmg shiegj. the basic tools of the trade are explained in this chapter. those of you alreadj familiar with these methods may skip over it; others should consider it essential that they be able to perform these calculations manually.

about data and

the law of averages

the law of averages is a greatly misunderstood and misquoted principle. its most often referred to when an abnormally long series of losses is expected to be off-set by an equal and opposite run of profits. it is equally wrong to expect a maitet that is currently overbought to next become oversold. that is not what is meant by the law of averages. over a laie sample, the bulk of events will be scattered close to the average in such a way as to overwhelm an abnormal set of events and cause them to be insignificant.

this principle is illustrated in figure 2-1, where the addition of a small abnormal grouping to one side of a balanced group of near-normal data does not affect the balance. a long run of profits, losses, or price movement is simply abnormal and will be offset over

time by the laie number of normal events. further discussion can be found in-thetheory of runs" (chapter 22). bias in data

avhen sampling is used to obtain data, it is common to divide entire subsets of data into discrete parts and attempt a representative sampling of each portion- these samples are then weighted to reflect the perceived impact of each part on the whole. such a weighting will magnify or reduce the errors in each of the discrete sections. the result of such weighting may cause an error in bias. even large numbers within a sample cannot overcome intentional bias infroduced by weighting one or more parts

price analj-sis and frading techniques often introduce bias in both implicit and explicit waj-s. a weighted average is an overt way of adding a positive bias (positive because it is intentional). on the other hand, the use of two analytic methods acting together may unknowingly rely doubly on one statiatical aspect of the data; at the same time, other data may he used only once or may be eliminated by offeetting use. the daily high and low used in one part of a program and the daily range (high to low) in another section would introduce bias.

how much data is enough?

Technical analj-sis is fortunate to be based on a perfect set of data. Each price that is recorded by the exchange IS exact and reflects the netting out of all information at that moment. Most ottier statiatical data, although it might appear to be very specific, are normally an average value, which can represent a broad range of numbers, all of them either larger or smaller. The average price received by all farmers for corn on the 15th of the month cannot be the exact number. The price of Eurodollars at 10:05 in Chicago is the exact and only price.

AVhen an average is used, it is necessary to collect enough data to make that average accurate. Because much statistical data is gathered by sampling, particular care is given to accumulatmg a sufficient amount of representative data. This will hold ttue with prices as well. Averaging a few prices, or analyzing small market moves, will show more erratic results, it is difficult to draw an accurate picture from a very small sample.

AVhen using small, incomplete, or representative sets of tbta, the approximate error, or accuracy, of the sample should be known. This can be found by using the standard deviation as discussed in the previous section. A laie standard deviation means an extremely scattered set of points, which in tum makes the average less representative of the data. This process is called the testing of significance. The most basic of these tests is the error resulting from a small amount of data. Accuracy usually increases as the number of items becomes larger, and the measurement of deviation or error will become proportionately smaller.

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FIGURE 2-1 The law of averages.The normal cases overwhelm the unusual ones. It is not necessary for the extreme cases to alternate-one higher, then the other lower-to create a balance.

Therefore, using only one item has an error factor of 100° o; with four items, the error is 50" o. The size of the error is important to the reliability of any trading sj-stem. if a sj-stem has had only 4 trades, whether profits or losses, it is very difficult to draw any conclusions about performance expectations. There must be sufficient trades to assure a comfortably small error factor. To reduce the error to 5>o, there must be 400 frades, which presents a dilemma for a very slow frend-following method that may only generate 2 or 3 trades each year. To compensate for this, the identical method can be applied to many markets and the sample of trades used collectively. By keeping the sample error small, the rid; of trading can be better understood.

ON THE AVERAGE

In discussing numbers, it is often necessarj to use representative values. The range of values or the average may be substituted to change a single price into a general claracteriatic to solve a problem. The average (arithmetic mean) of many values can be a preferable substitute for any one value. For 1 , the average retail price of one pound of coffee in the northeast is more meaningful to a costof-living calculation than the price at any one store However, not all data can be combined or averaged and still have meaning. The average of all futures prices taken on the same day would not say anything about an individual maitet that was part of the average. The price changes in copper, com, and the German DAX index, for example, would have littte to do with one another. The average of a group of values must meaningfully represent the individual items.

The average can be misleading in other waj-s. Consider coffee, which rose from 40c to $2.00 per pound in one year. The average price of this product may sppear to be $1.40; however, this would not account for the time thai coffee spent at various price levels. Table 2-1 divides the coffee move into four equal price intervals, then shows that the time intervals spent at these levels were uniformly opposite to the price rise. That is, price remained at lower levels longer, and at higher levels for shorter time periods, which is very normal price behavior.

AVhen the time spent at each price level is included, it can be seen that the average price should be lower than $1.40. One way to calculate this, knowing the specific number of daj-s in each interval, is by using a weighted average of the price and its respective interval