therefore, we are not as certain that the sliding scale works at all lev-els. The best we can expect is that the technique has a sound premise, is well defined, andthe profile of performance is improved.
. lf we follow that logic further, we eventually come to the adaptive, or self-adjustingmethod, in which the most fundamental elements of a calculation can vary based on pricelevel, volatility, or a broad choice of patterns, The methods in this chapter focused on twoareas that have not been presented elsewhere in a collected manner, The first is the vari-ation of the trend period itself. The choice of a single trend does not serve us best for pro-longed periods in the market, Slower trends are reliable, but give back much of theirprofits before ending; faster trends work only during periods when prices move quicklyand uniformly. The obvious solution is that the calculation period should change, speed-ing up when there is a short-term; fast-moving price pattern. At other times, it shouldfocus on the long-term direction. This concept is perfectly reasoriable, although formu-lating the rules to vary the period has not been perfected. The methods shown here may448 ADAPTIVE TECHNIQUES
 
work better than a static period, but should only be the beginning of a road on which tomove forward.
The other adaptive method is the centering of an oscillator to avoid prolonged periodsin which the value of the indicator loses significance by pushing against the upper or lowerlimits. By recording the high and low values of a past time interval, the oscillator values canbe continually readjusted to provide a more useful tool. Analysts are encouraged to lookfurther into these methods as an excellent way to improve system robustness.18
Price Distribution Systems
 
a new bar or point recorded to the right of the previous prices. There are many appli-
cations that need to look at the way prices cluster, or distribute, rather thansequences of patterns. In options, it is important to evaluate the current market volatilityto decide the chances of prices remaining in a specific range for a specific amount of time.To get that value, we use the standard deviation calculation first introduced in Chapter 2.The standard deviation gives the most basic measure of price distribution. From the valueof 1 standard deviation we can estimate the chances of a price remaining within a rangeover time. The key values to remember are that 1 standard deviation defines 68% of theprice movement (both up and down), 2 standard deviations contain 95%, and 3 standarddeviations contain 99% of all price movement based on the sample of data used to calcu-late the standard deviation value.
P= movement is usually viewed as a chart on which each new time period is seen as
USING THE STANDARD DEVIATION
The data used to determine the standard deviation is very important. Because it is a statis-tical measure, it is most accurate when a large amount of data is applied. For example, youmight find that 1 standard deviation of the crude oil daily price move is only $0.25 per bar-rel when measured over the past 10 years, but during the 6 months of the Gulf War thesame measurement yielded $.50, twice as large.
Most trading applications using the standard deviation tend to apply short data inter-vals to its calculation, such as 20 days. This short period is not likely to represent the sameprice distribution as a 10-year calculation; therefore, the probabilities given by the result-ing standard deviation value must be interpreted differently. While it is less likely that theprice will make a move of 3 standard deviations compared with 1 standard deviation, theprobabilities can be misleading. Statistics tell us that there is only a 1% chance that priceswill move a distance of 3 standard deviations higher or lower; however, that value is reli-able only when measured over a long data period. If you selected 20 days of unusually lowvolatility, the chance of a 3-standard deviation move would be very high.
The frequency distribution is another very practical approach to measuring price dis-tributions. This was also described in Chapter 2. It has the advantage of having a muchclearer visual interpretation. While the standard deviation gives us what appears to be ahighly mathematical probability, the large error factor that is caused by small amounts ofdata may make its usefulness about the same as the frequency distribution. In the follow-ing sections, both techniques will be used.
Standard Deviation Bands
Bollinger bands, discussed in Chapter 5 (“Trend Systems”), are a very popular applicationof price distributions. They do not detrend price, but calculate the standard deviation ofprices over a period of 20 days and form a band of 2 standard deviations around the trend-line. It is common for traders to vary both the period and the number of standard devia-450 PRICE DISTRIBUTION SYSTEMS
 
tions used to construct the Band. Once calculated, Bollinger bands can be displayed on anyprice chart and used to generate buy and sell signals, much the same as any other channelbreakout system. Using a smaller Bollinger band, for example, 1 standard deviation, willgive many more signals than using one of 3 standard deviations. At the same time, a bandof 3 standard deviations translates into risk that is 3 times greater than 1 standard devia-tion. Signals produced with a larger band tend to be more reliable, but have greater risk.
Bollinger bands also describe market volatility. A relatively narrow band translates intolow volatility. By comparing a 21-period Bollinger band with a 65-period band, you can seethe relative difference between shorter-term and longer-term market volatility in Figure18-1. The thicker lines, representing the 65-period calculation, cross the short-term bandat points that show relative overbought and oversold situations. If this was a daily ratherthan a 15-minute chart, the 21-period band would give monthly volatility and the 65-period band would be quarterly volatility, useful values for options traders.
Problems in Using Moving Standard Deviations
Applying any technique to a rolling time interval of the most recent N bars is a commonmethod of keeping in tune with current market conditions. In the case of a simple movingaverage, we should be very familiar with the lag that is introduced. For trends, when pricesare moving steadily higher, the lag causes the trendline to be much lower.
There is a similar lag when using the most recent N bars to calculate a standard devia-tion, even when the data has been detrended. If we are measuring the volatility of the mar-ket, and prices rally quickly, the volatility rises. This will be seen in the larger value of 1standard deviation measured over a fixed number of days, or bars. If we are looking for aconfirmation of a buy signal based on an increase in volatility, we should get it.
However, the volatility represented by the standard deviation will not decline as fast aswe expect because of the same lag. Once higher volatility has occurred on a single day, it
 
FIGURE 18-1 Comparison of 21- and 65-period Bollinger bands.
Bees
 
aaa Gano Want” “U2 12H3
 
Source: Chart created with TradeStation® by Omega Research, Inc.USE OF PRICE DISTRIBUTIONS AND PATTERNS TO ANTICIPATE MOVES 451
 
will remain part of the standard deviation value until it passes completely out of the calcu-lation window. That will prevent a new volatility event from being recognized soon after ashort decline in volatility. It will also make it difficult, if not impossible, to get a timely exitsignal on reduced volatility, because the lag keeps the volatility appearing high until at leastpart of this new, more active price movement begins to pass out of the end of the calcula-tion window. This can also be seen in Figure 18-1, where the 65-period bands expandquickly and narrow slowly.
USE OF PRICE DISTRIBUTIONS AND PATTERNS TO ANTICIPATE MOVES
Prices often form patterns that can be evaluated using probability methods, or simplyviewed in much the same way as a frequency distribution, or histogram. Because the con-cepts are sound, but the statistical analysis is often difficult because of limited amounts ofdata or changing conditions, analysts have taken a much more empirical approach towardstudying price distributions. The following section will look at some innovative ways tolook at price distributions and how they are interpreted into trading opportunities.
Analysis of Zones
Rather than using standard deviations to identify the chance of a price move above orbelow yesterday’s closing level, Bruce Gould observed that historic prices could be dividedinto five zones, each 20% of the price range over the previous 3 years. Using this long-termapproach, it is easy to see that selling in zone 1 (the lowest price levels) would have lessopportunity for profit than selling in zone 2, just above it. Similarly, buying in zone 5, thehighest band, would carry both the greatest risk and the least opportunity of profit. This islikely to remain the case unless prices move to much higher levels and all zones need read-justing. - .
J.T. Jackson! has used this concept to define five short-term zones, based only on yes-terday’s prices, which can be associated with the strength or weakness of today’s move.These daily zones, which are popular with floor traders, are calculated as:
 
 
Calculation Zone If Price ts Above ThenHigh2 = Average + High! - Low] 6 Strong upHigh! = 2*Average ~ Low 5 Moderate upAverage = (High + Low + Close) / 3 4 Mildly upLowl = 2+*Average — High 3 Mildly downLow2 = Average + Low! — High! 2 Moderately down
t
Strongly down _
 
where the High, Low, and Close are yesterday’s prices. Note that there are five calculationsbut six zones needed to separate them. A test of how the S&P 500 falls into these relativerankings gives:
 
Zone 6 5 4 3 2 !S&P frequency 20% 44% 83% 79% 42% 20%
 
"J.T. Jackson, Detecting High Profit Day Trades In The Futures Markets (Windsor Books, 1994).452 PRICE DISTRIBUTION SYSTEMS
 
which shows the slightly upward bias expected of the overall equities market. These distri-butions may vary depending on the interval used in their calculation and whether there isa dominant trend during that period. A longer interval that includes bull, bear, and side-ways markets would be safest; otherwise, there is the chance that the calculations will cre-ate a bull market profile, while some trading will occur during a bear market reaction.Although you can avoid trend bias by using longer intervals for the calculations, the zonestend to get very large.
The strategies for trading price zones focus on short-term trends and holding periods.For example, you can sell when prices move into zone 4 (mildly up) with a stop in zone 5.If you consider zones 3, 4, and 5 as containing mostly market noise, then selling at the topof zone 4 and closing out that trade at about the average, or buying near the bottom ofzone 3 and closing out at about the average, could capture the majority of price moves thathave no direction.
Nonrandom Patterns
In evaluating the zone approach, the markets that offer the greatest potential for this strat-egy are those that show an abnormal distribution of prices within the six zones. For exam-ple, if the six zones were all equal in size, and the frequency of prices declined by one-halfas they moved from the center to the extremes, there would be a perfectly random distrib-ution and no profit potential:
 
Zone of Equal Size. 6 5 4 3 2 1Normal distribution 1% 14% 28% 28% 14% 7%
 
 
If the distribution is normal, but zones 3 and 4 are much wider than the outer zonés,then the risk of selling at the top of zone 4 with a stop at the top of zone.5 and a profit tar-get at the average (of zones 3 and 4) would result in an equal number of profits and losses,but the profits would be larger. If the zones are of equal size, the opportunities come whenthe distribution is clustered in the center:
aZone of Equal Size 6 s 4 3 2 {
Normal distribution 2% 8% 40% 40% 8% 2%
 
In this case, selling at the top of zone 4 would result in many more profits than losses,although profits and losses would be of equal size.
Applying a Moving Average Distribution
To extend the time frame and include trend bias within the zone values, the same zonesmay be created by using the moving average values applied to the close, high, and low sep-arately. For example, if three separate 21-day moving avérages are calculated on the high,low, and closing prices, the moving average values can be substituted for yesterday’s high,low, and close to give new zones. In using this approach, a strong upward trend wouldcause al] the zones to lag below today’s prices, making current values strongly overbought.Zones created from the history of these averages will reflect the relative overbought andoversold price levels within trends. In a strong upward market, however, prices can remainin Zone 6 while they are steadily moving higher in much the same way that an oscillator canremain over 80%.DISTRIBUTION OF FriCES 453
 
Using moving average values is likely to change the way in which you trade thesezones, For example, you might want to enter long positions only in zone 5 and look to exitin zone 6. You might find that, if prices close in zone 6 (very strong), they are likely to openin zone 4 (slightly higher).
Zones for Forecasting Range and Risk Control
Statistics have proved that, barring a superior forecasting method, the best estimate fortomorrow’s price is today’s price. That is, under most conditions, we cannot predict withany certainty that prices will go up or down tomorrow; therefore, the best estimate is to saythat prices will be unchanged. However, if a trend system, such as a moving average, hasbeen 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 tomorrow’s price to cre-ate a set of zones used to control risk or project the probable trading range.”Using a 10-day moving average of the daily price changes,
A = @Avg(@AbsValue(close - close{i}),10)
where close[1] represents the previous close. Taken as positive numbers, zones are cre-ated that center around the current price and expand according to the average pricechange (volatility) using the following calculations:
H2 = close{i]:+2*AHl = close(i] +A(1 = close{i]"- A(2 = closeti] -2*A
Five zones are then created by the areas above H2 and below L2, and the three rangesbetween H2, H1, L1, and L2, all of which change in proportion to the n-day volatility. Thesevolatility levels, or bands, represent a very similar scenario to channel breakouts. The mar-ket often trades in a range defined by a normal or average level of volatility. When a newpiece of information affects the price, it jumps to a new level, then trades with similarvolatility (or slightly higher at first) at the new level. Most often, the first breakout of anexisting trading range puts prices in a zone just above the old range, making the patternappear to be divided into equal zones. This same philosophy is the reason that standardprofic targets for a price breakout are equal to the previous trading range. Readers can findadditional 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 dis-tributions can explain whether the market is trending, Sideways, or unstable. Some ofthese patt€rns are clear and others need interpretation; in addition, the combination ofpatterns within patterns can become complex. The following is intended as a basicapproach to interpreting price distributions, although each group of markets has specialcharacteristics. Before engineering a systematic approach to trading, it is best to under-stand how prices are expected to distribute. This approach avoids surprises and the riskthat goes with them.
Long-Term Price Distributions
A quick observation of price data for most tangible products, such as soybeans or gold, showsthat we should expect a skewed long-term price distribution, with prices clustering at lower
? Based on Tushar Chande and Stanley Kroll, The New Technical Trader (John Wiley & Sons, New York, 1994, p. 172).454 PRICE DISTRIBUTION SYSTEMS
 
levels and a long tail representing extreme high prices. In the case of gold, we should remem-ber that prices peaked briefly at $675 per ounce (New York cash price) in 1980, but haveremained below $400 most of the time before and after. If we consider $375 as the approxi-mate normal price of gold, then the rise to $800 is a gain of $425 per ounce. If $375 were theaverage price, and distributions were symmetric, then gold would be able to decline an equalamount, 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 soybeansonly gained a small percentage every year based on inflation, price forecasting would bevery simple. Expectations, however, are based on carryover stocks (inventories), exports,weather, and government programs, all of which cause sharp price adjustments. Theseshifts up and down appear as steps on a price chart. Once a new step is reached, prices willfluctuate in a range with a new perceived base price. Within the period when the step is intransition, unexpected news will normally cause short-lived price peaks. Normally, pricestrade at the lower end of the range.
Patterns of Market Groups
Those markets representing physical commodities, such as gold, soybeans, and coffee,have a cost of production that forms a practical lower bound to price movement. Whenthere is ample supply, or low demand, prices decline to those cost levels, or slightly lower,volatility drops, and there is little price activity. This also applies to the interest rate marketviewed in terms of yield. At low yields, volatility is proportionally low and prices move side-ways with an occasional spike (downward for prices) in anticipation of change.
Currency markets are very different from physical commodities because they do nothave a production cost, nor can you distinguish high from low. All currencies are quotedin terms of other currencies, What is high, relative to one country, might be low comparedwith another. A stable political situation, low inflation, and a controlled balance of tradeputs a currency at equilibrium provided that it is quoted in terms of another stable cur-rency. With no expectation of surprises, the currency will trade in a narrow range, showinglow volatility. Unexpected economic news moves the foreign exchange rate sharply up ordown; normalization of the problem allows prices to return to a quiet equilibrium. Thispattern can appear to be similar to a normal distribution.
Frequency Distributions
If we remember the qualities of a standard deviation when measuring price distribution, itassumes a symmetric pattern; therefore, a simpler frequency distribution can be used toprovide a more convenient representation of price distribution. The frequency distribu-tion makes no assumptions about the shape of the curve, but records the amount of timethat prices remained within a specified range. For example, if we look at the history of goldfrom 1976 through 1993 (see the bold line in Figure 18-2), prices have varied from $100per ounce in 1976 to $675 per ounce in 1980. Because the first 3 years would lower theaverage, 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 his-tory of monthly closing prices into the 20 slots from $227.60 to $251. 20, $251.21 to$274.80, and so forth, we get a frequency distribution spanning the full range of goldprices, each bar indicating the number of months that the average monthly price fell in thatbar. That distribution, seen in Figure 18-3, shows peak frequencies (gray bars) from $392to $445, significantly below the midpoint price. —-
The total number of months from 1979 through 1993 is 228, therefore, we can find theapproximate price that occurred at the 90% level by summing the frequency of the barsbeginning at the highest price. Because 10% of 228 is 23, the bar that causes the total fre-DISTRIBUTION OF P... ES
455
 
 
FIGURE 18-2 Cash gold prices, CPi, and deflated gold prices.
 
700
600
US$ per ouncea os a8 8 8
Sy8
100
 
 
Consumer Price Index (1967 = 100)
 
 
 
 
 
 
 
 
FIGURE 18-3 Frequency distribution of gold. Gray bars show the distribution of cash prices.The dark bars show the distribution of deflated cash prices. The deflated prices are skewedmuch further to the left.
 
35
            
30
25
no°o
Frequencya
°
 
 
 
 
 
 
       
 
 
4 es
57.9 605.0 652.2
510.7 5:
Deflated ~~456 PRICE DISTRIBUTION SYSTEMS
 
quency to exceed 23 will he the target price range for the 90% level. This works well forskewed distributions; the 90% level may be 3 bars from the top of distribution, while the10% level may be the lowest bar of the distribution, For cash gold, the highest 10% of theprices span the highest 9 bars, while the lowest 10% are in the bottom 2 bars. This showsan extremely skewed distribution.
Adjusting for Inflation
One way of correcting for the apparent bias in the long-term charts is to adjust prices forinflation. That is, if we have a table of monthly Consumer Price Index values, all prices canbe divided by the monthly percentage increase in the CPI. Therefore, if today’s gold priceis $400 per ounce, and inflation last year was 5%, today’s price of $400 is divided by 1.05to get $381. If the actual price of gold was $380 last year, it was very close to normal. In Fig-ure 18-1 the CPI appears as a steady increase which, when used to adjust the cash goldprices, shows that 1993 prices had returned to 1979 levels on an inflation-adjusted basis.The frequency distribution of the adjusted prices, seen in Figure 18-3, shows a muchbroader frequency at lower levels and a smaller, longer tail at higher prices. These patternsare fundamental to understanding and using price distributions.
Structural Changes
Despite the need to correct for inflation, structural changes will affect the smooth patternof the frequency distribution. For gold, cash prices below $100 per ounce are part of his-tory. that we can choose to ignore for now. By creating a new frequency distribution thatreflects prices beginning in 1979, some of the price inconsistencies can be eliminated. Forother markets this may not be as easy, because the structural changes may occur within thenormal range of historic prices.
Medians and Means
Although the inflation-adjusted long-term distributions show that prices spend much moretime at lower levels, there is a tendency to consider the average price of a market as themidpoint between the highest and lowest prices. Using the gold example, the midpoint for1979 to 1993 was $451. The average of all monthly prices will give a reasonable approxi-mation ofa normal price; however, the best measure is the median, or middle, value whenall monthly prices are sorted from high to low. The median value for gold over the sameperiod was $381. If we look back at Chapter 2 (“Basic Concepts”), we find that skewness ismeasured as the difference between the mean and the median, as a percentage of the stan-dard deviation. In this case, the difference of $70 is a very large value, indicating a distrib-ution with a peak far to the left of center. For price distributions, the median is a muchmore useful value than the average, although not as convenient to calculate, The mediannaturally adjusts for the skewness in the price patterns.
Short-Term Distributions -Unlike the predictable patterns of the long-term price distributions, the distribution pat-terns of short intervals can vary widely and have been interpreted in many ways. Short-term distributions are not anchored to a base level because the entire period of analysismay be at prices that are significantly above intrinsic value or production costs, and awayfrom equilibrium. Keeping in mind the normal shape of price distribution for each marketgroup, a different configuration can be a strong indication of expected price movement.Three distribution patterns are shown in Figure 18-4 (6-d), along with the larger, long-term distribution (@). The first short-term distribution (see Figure 18-44) shows a patternwith a long tail toward the higher prices and a jarge accumulation near lower price levelsin a manner very similar to a long-term chart, but with the extended tail much shorter andDISTRIBUTION OF PriCES 457
 
a little more extension on the bottom. This is most likely to occur at low price levels, wheremost activity is near the bottom with occasional short excursions up. This can be a smallsegment of a normal pattern or a temporarily higher level that is stable. Figure 18-4c is abell-shaped, symmetric curve that could indicate a congestion area or short-term equilib-tium. When prices trade equally within a range they do not exhibit any likelihood of favor-ing an immediate breakout either up or down.
The fourth distribution (see Figure 18-4) is most interesting, because it is skewed ina pattern opposite to (8) and to the normal long-term distribution. For this pattern to havedeveloped required a relatively short, quick move to a higher price level, then a congestionarea formed at the higher level. You can be certain from this pattern that prices are higherthan normal. By the very nature of the pattern, we can say that this price level is unstable,and that prices are more likely to go down than up. This last conclusion does not requirestatistics, because prices at high levels must not necessarily continue to rise, but they musteventually fall.
Identifying Potential Price Moves
From the patterns just described, the combination of a distribution of a long tail towardhigher prices, but at a relatively low level, offers no promise of a potential price move.
 
FIGURE 18-4 Three short-term distribution patterns. (a) A traditional, long-term distribu-tion. (b) A short-term distribution indicating stable prices at a temporarily higher level, or apermanent change. (c) A bell-shaped curve representing congestion but not indicating futuredirection; the market is in suspension or temporary equilibrium. (d) The tail points to lowerprices with most activity at higher prices; the market is unstable and has substantial downsidepotential. ‘
Increasing Prices ——»'
 
a. Normal long-term b. Short-term normal c. Beil-shaped -d. Skewed oppositedistribution, pattern indicates pattern indicates "pattern impliesmoderate stability. temporary equilibrium. unstable prices.
 458 PRICE DISTRIBUTION SYSTEMS
 
Prices that are not near the base level are always likely to move, and the farther they getfrom the base level, the more volatile they become. Three formations show that there is agreater chance for a move. :
1, A broad, often erratic formation indicates volatile, current movement. Prices havenot remained at one level and have not yet established a well-defined pattern ortrading range.
2. A skewed distribution (with the tail toward higher prices), the mode well above thebase level, and where the current price is at the extreme away from the tail (lowerprices) indicates a likely move down.
3. A skewed distribution (with the tail toward lower prices), the mode well above thebase level, and where the current price is in the tail (lower prices) indicates a likelymove down,
Any time prices form a distribution that is not the same as a long-term distribution, and notat low levels, there is potential for movement and volatility.
STEIDLMAYER’S MARKET PROFILE
Market Profile, the effort of J. Peter Steidlmayer, appears to be a frequency distribution ofintraday price movement but has used time, rather than volume, as its key element. Steidl-mayer formalized this technique in 1985 while at the Chicago Board of Trade. The Boardconsidered this such a unique insight that they copyrighted his work as Market Profile andLiquidity Data Bank. \t was intended to provide detailed information to traders about -how trading was facilitated. Market Profile offers much more than a count of how: manytimes a price traded at one level. With proper studying, traders are able to separate partic-ipants by time frame and even identify their trading patterns. Figure 18-5 shows this tech-nique as it originally appeared, with letters denoting sequential 30-minute time periods,and an analysis of who participated in the trade at each price.> Called a customer tradeindicator (CTI), these categories are CTI 1, the local floor traders; CTI 2, the commercialclearing members; CTI 3, clearing members who fill for other members and nonclearingcommercial traders; and CTI 4, clearing members who fill orders for the public or othercustomers not included in the previous groups (outside paper). This information, onwhose behalf the trade was executed, is only available after the close of trading.
To understand what is described in Market Profile and the Liquidity Data Bank, youmust know that the locals and commercial clearing members, CTI 1 and CTI 2, account forthe largest part of volume (over 65%), and both have trading styles that are very differentfrom the off-floor speculators who form groups 3 and 4. The locals take smaller positions,often counter to the current price moves and hold that trade for a period spanning sec-
“Onds to a few hours. Most locals even up at the end of the day, which avoids the need tofinance their positions. The commercials might be a bank that is hedging an existing cur-rency exposure or arbitraging a gap between two or more short-term rates in the cash mar-ket. These positions may move the market but can be insensitive to current price directionand flow into the market at arbitrary times. - _
Outside paper, a term that refers to customer accounts, range from individual spec-ulators to major fund managers. Because they trade from off the floor, their style of trad-ing favors holding positions for more than 1 day, and a large majority will be trendfollowers. The style of CTI 3 is similar to CTI 4; that is, both tend to be directional, andthe two can be combined for the purposes of evaluation. Although they account for asmaller portion of the volume, they are more influential in the short-term direction. Fig-
> BM. “Doc” Haynie, “Stretching the ‘profile’ to cover 24-hour markets," Futures (February 1992). 
 
 
 
 
 
 
 
 
 
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