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141

of the day. The actual price distribution W is the maximum that couid be expected from such a sjstem; in reality, the first day is usualiy a ioss

TREM5S ) NOISE

Throughout this book there are techniques that try to find the underijing trend when the price direction is noi ciear. The investor who bujs sooner is more profitable, but oniy if the maiket moves higiier. Wiiat makes it so difficult to identify the frend is noise. Noise is the erratic movement of price; by definition it is unpredictabie, yet it has very definite statistical atfributes.

Noise is the product of the market participants bujing and seliing at different times for different piwposes. Each has their own objectives and time frame. Noise can also be a price shock-an unexpected event that may or may noi cause a iasting price change. Noise has most of the qualities of a sequence of random numbers. Neariy half of ali price moves change direction from the previous move; about 25° a of ali price moves continue in the same direction for two periods, and so on. These pattems shouid alreadj be famiiiar to analjsis. The size of a price move, or price shock, also appears to be random; that is, 50°o are quite smi, 25°a are twice as iaige, I2.5>o are four times as iarge, and afew are very iarge

Then how can you teii if a price move up is an indication of a new direction or simpiy more noise? The answei is that you cant teii by shidjing oniy price untii after the direction has continued. There are situations, of course, where the news wiii give us information to show that the price junp was a shnctural change (for exampie, when the Federal Reserve iowers interest rates). But price alone wont teii us.

We can improve our chances of seiecting the frend direction based on a net price move by choosmg oniy the iaigest moves. This is the reason why a iong-term trend is more reiiabie than a short one. To see this cieariy, considei Figure 20-5 to be random numbers, or market noise. Most of the time prices remain beiow the ievei PI, but a price move that reaches P2 (twice as iarge) is stiii fairiy common. Less often, price wiii junp to ievei P3 but oniy rareiy wiii it reach PS. Lets say that, out of 1,000 price moves, P i is reached 500 times, P2 occurs 250 times, P4 occurs 64Y2 times and PS about 4 times. If we use a breakout sjstem to decide the price frend, and our breakout criteria is iess than P2, then there wouid have been 250 total signals (both iong and short) in which to find the right trend direction, if there were 10 confirmed trends during this period, you needed to reject or fiiter 240, or 96°o, of ali moves. Suppose your criteria was PS instead of P2, and because the size of the subsequent price trend must be bigger due to the iarger enfry criteria, there was oniy one good trend during this period. Then you have a I-in-4 chance of being correct, far better than the I-in-25 using avery smali frend criteria

it is the magnitude of the market noise that determines the criteria needed for entering a frend. For a broadly traded maiket, the noise pattem is very predictabie, whiie maikets that have iow voiume might not conform cioseiy to a traditional statistical profiie.

FIGURE 20-5 Random occurrence of price ieveis.

P8------------------------------------------

Noise can be measured using the same calculations as voiatiiity, given at the beginning of this chapter, or as Kaufrnans efficiency ratio found in Chapter 17 (Adaptive Techniques").

EXPERT SYSTEMS

An expert sjstem is one in which you draw conclusions based on an accumuiated knowledge base, which has been stored as data, facts, and relationships in the form of if-then-else rules. For our piwposes, these would include price and economic data as wen as the knowledge that, for exanple, highly correlated maikets move together, and high volatility means high risk. -When the first expert sjstems were developed, the core information was actually g



by interviewing experts, which is how the name expert sjstem was derived. The success of this method depends upon the quality and completeness of the knowledge base.

The knowledge base is used by an inference engine, which is abie to draw conclusions from the facts stored in the knowledge base Therefore, if we have the foiiowing information,

FACT 1: U.S. bonds are more voiatiie than Eurodoiiars.

FACT 2: The S&P 500 is more voiatiie than U.S. bonds.

FACT 3: Voiatiiity is directly proportional to risk.

then the inference engine can create the new faa

FACT 4: The S&P is ridaer than Eurodoiiars.

The inference engine provides a straightforward, iogical process; however, there may be many relationships to resoive, not ali of which may appiy to the probiem you wouid iike to soive. For exanpie, if we also have the foiiowing facts

FACT 5: The S&P has ahigh degree of noise

FACT 6: Eurodoiiars have a iow degree of noise.

FACT 7: The S&P is currentiy frading beiow its 200-day moving average.

FACT 8: The S&P is currentiy frading above its 20-day moving average.

FACT 9: The S&P has been above its 200-day moving average for 80°o of the past 20 years.

FACT 10: Eurodoiiar rates are driven by monetary bank poiicy.

FACT 11: Current monetary poiicy is dominated by concems of inflation.

FACT 12: Inflation resuits in higher interest rates.

FACT 13: Net trading retums for the S&P have been 40° per annum.

FACT 14: Net trading retums for the Eurodoiiar have been 20°o per annum.

then human iogic might conclude that Eurodoiiar yieids are iikeiy to rise because of concems over inflation. In addition, the S&P has greater risk, erratic behavior, and is currently not as sfrong as it has been on average over the past 20 years, although it is now rising. Compared with Eurodoiiars, there is greater risk frading the S&P but its retums have been higher.

How can this expert conclusion be duplicated by a computer? By addmg a set of ruies that paraiieis the thinking of experts, a computer can theoretically arrive at the same conclusions. For exanple,

RULE la: IF the Producer Price Index rises by more than the annualized rate of 4>o, THEN we have inflation.

RULE 2a: IF there is high noise, THEN there is less chance of a trend.

RULE 3a: IF there is high noise, THEN there is greater nd;.

RULE 4a: IF the faster trend is above the slower frend, THEN prices are frending up.

For each positive rule 1 through 4, there should also be a negative rule:

RULEIb:lF the Producer Price Index does not rise by more than 40 annualized, THEN we do not have



RULE 2b IF there is low noise, THEN there is a greater diance of a trend. RULE W IF there is low noise, THEN there is lower rid;.

RULE 4b: IF the faster trend is below the slower trend, THEN prices are trending down.

Even with the negative rules there are some ambiguous cases. For example, in Rule 4 there is the case in which the two trends are in conflict. In other situations, the positive rule might be true, but the negative rule may not be as strong. In Rule lb, we see that the effect is that "we do not have inflation" rather than-wehave deflation."

Forward Chaining

The process of combining the rules and facts to yield an expert opinion is called forward chaining. For example, beginning with FACT 6, "Eurodollars have a low degree of noise," we find the relevant rule, RULE 3b: IF there is low noise, THEN there is lower risk," and create a new fact: "Eurodollars have (relatively) low risk " Note thai in each case, the terms low, high, and faster are all relative.

Once we have this new fact, that Eurodollars have relatively low risk, and we similarly conclude that the S&P has relatively high ride we can also conclude that Eurodollars have lower rid; than the S&P The process of following the path of each fact as it is handled by various rules is called forward chaining. It will lead to other rules and other facts; it may be that the expert opinion will be found along this route, or that the combination of new facts, such as the relative risk between the Eurodollars and the S&P, will provide the ef ert opinion.

This example shows only a few facts that can be easily summarized., however, there are thousands of pieces of information about performance characteriatics, relationships to other markets, and fundamental factors that might alter expectations. If accumulated by asking experts, it is also likely that there will be conflicting information. While the human brain has a remarkable ability to sort through these items and select the information it considers most relevant, some important items can be overlooked when there is too much to

consider. An expert sjstem is expected to use all of the data and reduce it to a single decision. In doing this, it must also select the most significant fds and resolve conflicts associated with the proper order of events and the time horizon of the investor.

A Technical Expert Sjstem

An expert sjstem can treat indicator values as expert opinions and create sjstems without the fundamental relationships shown in the previous section. An example by Fidiman, Barr, and Loick, applied to the DJIA, defines rules as the relationships between the various indicators and calculations, and the facts as the values of those items. The piwpose of this expert sjstem is to inapect trending and nontrending characteristics of price movement to give the probability of a continued trend. The following example is adapted from their article:

Rule I: IF ADX := 18 AND ADX:== ADX[21

(AND nonfrending is false or undefined),

THEN there is a 95>o chance the market is trending.

Rule 2: IF ADX =: 3U AND ADX =:= ADX[2]

(AND frending is false or undefined),

THEN there is a 90°o chance the market is nontrending.

Rule 3: IF the market is trending,

THENNLCD = probability of .8 AND SD = probability of 5 (850o).



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