using the moving average values applied to the close, high, and low separately. For exanple, if three separate 2 1-day moving averages are calculated on the high, low, and closing prices, the moving average values can be substituted for yesterdays high, low, and close to give new zones. In using this approach, a strong upward trend would cause all the zones to lag below todays prices, making current values sfrongly overbought. Zones created from the history of these averages will reflect the relative overbought and oversold price levels within trends, in a sfrong upward marfcet, however, prices can remain in zone 6 while they are steadily moving higher in much the same way that an oscillator can remain over 80°o.

Using moving average values is likely to change the way in which you frade these zones. For example, you might want to enter long positions only in zone 5 and look to exit in zone 6. You might find that, if prices close in zone 6 (very strong), they are likely to open in zone 4 (slightly higher).

Zones for Forecasting Range and Risk Confrol

Statistics have proved that, barring a superior forecasting method, the best estimate for tomorrows price is todays price. That is, under most conditions, we cannot predict with any certainty that prices will go up or down tomorrow; therefore, the best estimate is to say that prices will be unchanged. However, if a trend sjstem, such as a moving average, has been profitable, then its forecast for tomorrow is better than the mean. Market volatility; based on price changes, can be used with a directional forecast of tomorrows price to create a set of zones used to confrol risk or project the probable trading range.

Using a 10-day moving average of the daily price changes,

A = @Avg(@AbsValue{close - close[l]),10)

where close[l] represents the previous close. Taken as positive numbers, zones are created that center around the current price and expand according to the average price change (volatility) using the following calculations:

H2 = close[l] + 2 * A

Hi = close[l] + A

Ll - closem - A

12 •= closem - 2 • A

Five zones are then created by the areas above H2 and below L2, and the three ranges between H2, H I, LI, and L2, all of which change in proportion to the n-day volatilitj. These volatility levels, or bands, represent a very similar scenario to channel breouts. The maitet often trades in a range defined by a normal or average level of volatility. When a new piece of information affects the price, it jumps to a new level, then trades with similar volatility (or slightly higher at first) at the new level. Most often, the first breakout of an existing trading range puts prices in a zone just above the old range, making the pattem appear to be divided into equal zones. This same philosophy is the reason that standard profit taigets for a price breakout are equal to the previous trading range. Readers can find additional trading range projections in Chapter 15 ("Pattern Recognition")

DISTRIBUTION OF PRICES

in the search to understand how prices move, and what to expect, an analysis of price distributions can explain whether the maitet is trending, sidewajs, or unstable. Some of these pattems are clear and others need interpretation; in addition, the combination of pattems within pattems can become complex. The following is intended as a basic approach to interpreting price distributions, although each group of maitets has special characteristics. Before engineering a sjstematic approach to frading, it is best to understand how prices are expected to distribute This approach avoids surprises and the rid; that goes with them.

Long-Term Price Distributions

A quick observation of price data for most tangible products, such as soybeans or gold, shows that we should expect a stewed long4erm price dishibution, with prices clustering at lower

Based on Tushar nian.le and Stanley E-U. The New Tecimical Tra.ler (J..lii, Wiley & Sons, New York, ISM, p 17j.

levels and a long tail representmg extreme high prices. In the case of gold, we should remember that prices peaked briefly at $675 per ounce (New York cadi price) in 1980, but have remained below $400 most of the time before and after. If we consider $375 as the approximate normal price of gold, then the rise to $800 is a gain of $425 per ounce. If $375 were the average price, and distributions were sjinmeU-ic, then gold would be able to decline an equal amount, which would put the low price at negative $50 per ounce, which is not possible.

The process in which prices move up and down is not uniform. If the price of soybeans only gained a small percentage every year based on inflation, price forecasting would be very simple. Expectations, however, are based on carrjover stocks (inventories), exports, weather, and government programs, all of which cause sharp price adjustments. These shifts up and down appear as steps on a price chart. Once a new step is reached, prices will fluctuate in a range with a new perceived base price. Within the period when the step is in transition, unexpected news will normally cause short-lived price peaks. Normally, prices trade at the lower end of the range.

Pattems of Maitet Groups

Those maitets representing phjsical commodities, such as gold, soybeans, and coffee, have a cost of production that forms a practical lower bound to price movement. When there is ample simply, or low demand, prices decline to those cost levels, or slightly lower, volatility drops, and there is litfle price activity This also applies to the interest rate maitet viewed in terms of yield. At low yields, volatility is proportionally low and prices move sidewajs with an occasional spike (downward for prices) in anticipation of change.

Currency maricets are very different from phjsical commodities because they do not have a production cost, nor can you distinguish high from low All currencies are quoted in terms of other currencies. What is high, relative to one countrj might be low compared with another. A stable political situation, low inflation, and a confrolled balance of frade puts a currency at equilibrium provided that it is quoted in terms of another stable currency. With no expectation of surprises, the currency will trade in a narrow range, showing low volatility. Unexpected economic news moves the foreign exchange rate sharply up or down; normalization of the problem allows prices to retum to a quiet equilibrium. This pattem can appear to be similar to a normal distribution.

Frequency Disfributions

if we remember the qualities of a standard deviation when measuring price disfribution, it assumes a sj-mmefric pattem; therefore, a simpler frequency disfribution can be used to provide a more convenient representation of price disfribution. The frequency disfribution makes no assumptions about the shape of the curve, but records the amount of time that prices remained within a specifled range. For example, if we look at the history of gold from 1976 through 1993 (see the bold line in Figure 18-2), prices have varied from $100 per ounce in 1976 to $675 per ounce in 1980 Because the first 3 years would lower the average, we will consider only the period from 1979 through 1993, which had a low of $228. Dividing the price range into 20 parts, we get bars of $23.60. Accumulating the history of monthly closing prices into the 20 slots from $227.60 to $25120, $25121 to $274.80, and so forth, we get a frequency disfribution spanning the full range of gold prices, each bar indicating the number of months that the average monthly price fell in that bar. That distribution, seen in Figure 18-3, shows peak frequencies (gray bars) from $392 to $445, signiflcantly below the midpoint price.

The total number of months from 1979 through 1993 is 228; therefore, we can find the approximate price that occurred at the 90°o level by summing the frequency of the bars beginning at the highest price. Because 10°o of 228 is 23, the bar that causes the total fire

FIGURE 18-2 Cadi gold prices, CPl, and deflated gold prices.

FIGURE 18-3 Frequency distribution of gold. Gray bars show the distribution of cadi prices. The dark bars show the distribution of deflated cash prices.The deflated prices are dcewed much further to the left

----10.7 557.---------

227 274.6 322.0 369 1 416.3 463.5 5)0.7 557.s 605.0 6525

Gold Deflated

quency to exceed 23 will be the target price range for the 90% level. This works well for dcewed dishibutions; the 90>o level may be 3 bars from the top of distribution, while the I0°o level may be the lowest bar of the dishibution. For cadi gold, the highest I0°o of the prices span the highest 9 bars, while the lowest I0°o are in the bottom 2 bars. This shows an exttemely dcewed dishibution.

Adjusting for Inflation

One way of correcting for the spparent bias in the long-term charts is to adjust prices for inflation. That is, if we have a table of monthly Consumer Price Index values, all prices can be divided by the monthly percentage increase in ttie CPI. Therefore, if todays gold price is $400 per ounce, and inflation last year was 50 o, todays price of $400 is divided by 1.05 to get $381. If ttie actual price of gold was $380 last year, it was very close to normal, in Figure I8-I the CPI sppears as a steadj increase which, when used to adjust the cash gold prices, shows that 1993 prices had returned to 1979 levels on an inflation-adjusted basis. The frequency dishibution of the adjusted prices, seen in Figure 18-3, shows a much broader frequency at lower levels and a smaller, longer tail at higher prices. These pattems are fundamental to understanding and using price dishibutions.

Sfruaural Changes

Despite the need to correct for inflation, shnctural changes will affect the smooth pattern of the frequency dishibution. For gold, cash prices below $100 per ounce are part of history that we can choose to ignore for now. By creating a new frequency dishibution that reflects prices beginning in 1979, some of the price inconsistencies can be eliminated. For other maikets this may not be as easj, because the stractural changes may occur within the normal