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The Market Unit
By Donald L. Jones, March 17, 2005
Copyright 2005

Foreword

Auction market analysis is based on value. Day value from Market Profile/ Meta-Profile and longer term value from Overlay Demand Curve. (Market Profile is from a CBOT Liquidity Data Bank, Meta-Profile is from tick data.) Constant value defines a market in balance. Changing value (trend) starts from balance, runs directionally, stops changing and ultimately ends back in a balance. The process of balance-to-trend and back to balance is a Market Unit. The elapsed time of a market unit varies from unit to unit. A series of market units forms a new, deeply revealing sort of market data. The length of time and the price range of the balance and the amplitude, range and time of the trend offers traders quantitative knowledge of their market.


We begin by a simple examination of the structure of markets in general. Markets move in waves, from high to low and low to high etc., continuously. The time to complete a wave varies from wave to wave. One cycle might be 10 days and the next can be 30 days in a completely irregular manner. Likewise, the amplitude from top to bottom of a wave varies widely. For instance from April 7 to September 2003 for the SP there were 5 complete waves. The number of days per wave varied from 13 days to 28 days. An example of wave dates and their amplitude illustrates the irregularity.

                                Wave
             High    Low       Period   H-L Amplitude
  Apr  7   900.00
  Apr 11           865.50        28         34.5
  May 15   945.30
  May 20           913.50        18         31.8
  Jun 17  1015.60 
  Jul  1           960.50        18         55.1
  Jul 14  1014.30
  Jul 21           973.60        13         40.7
  Jul 31  1003.70
  Aug  6           958.50        26         45.2
  Sep  9  1034.60
In this short run (under six months), wave periods varied by over a factor of two. In the earlier months of 2003 the variation in period was a factor of three. Such variations are found in all markets. We conclude that markets show little regularity. A consequence is that 'smoothing', as with a moving average, is on a slippery slope indeed. These results play a role in the general ineffectiveness of technical analysis based on moving averages and oscillators. However, we are primarily interested in the support lent to the market unit studies by this look at market variability. Market unit analyses flesh out our bare-bones study of market waves.

A market unit of an auction market is defined by the markets progression: from the start of a balance, to the end of the balance (breakout), through a trend phase and then back to the start of the next balance. Balance, or short term equilibrium, is a non-directional, volatility dominated time period. Breakout from the balance initiates a directional, or trend, phase. As the trend decays, a new balance initiates the next unit. The market over time is merely the conjoining of the separate market units as they evolve. Balances and trends are market defined and hence market units have neither a standard time period nor a standard amplitude for their trends. Market condition (balancing or trending) is a local descriptor of the current state of the market and defies generalization (e.g. the previous market unit was ten days, so this one will be around ten days). Knowing where you are within a market unit is imperative to the trader. Inside the balance you are dealing with non-directional volatility. In the trend, market movement is dominated by directionality, with volatility secondary.

The market unit is the fundamental element of market structure. It is the primary element of information for market understanding. As a market unit develops, the first phase, balance, arises out of the dying trend. Then, breakout from balance signals a potential change in market condition from balance to directional. The directional phase includes any trending and the prelude, consolidation, to end of trend. As the market returns to non- directionality, the balance phase of the next market unit begins.

Market units break a market into discrete pieces. Each piece follows it's own scenario; spending time in balance and then being driven in the directional phase.

The Balance Phase
A balance may may be completed in a few days or may continue for many days or weeks. Over time, the balance range (support/resistance) may change slowly as the market responds to low level changing demand. A surge in demand will cause price to exceed the balance limits, causing a breakout.

The Directional Phase
Increasing demand drives the market directionally, e.g. in a trend. During the directional phase support/resistance is poorly defined. As the buying/selling pressure decays the trend loses steam and price movement slows. This effect is measurable as an increase in congestion. Directional markets often pass through several such slowings (pauses) until the final congestion grows into a new balance.

Discovering a Market Unit
Analysts typically use price in their work. In most cases this is a mistake. Price has a large volatility component. Value is a better choice. The early work of Steidlmayer [1] identified the "Market Profile" as a way to find value for one day's trading. Market Profile value is found from cleared volume, with the center of value located at the highest volume. Meta-Profiles are built from half-hour range bars to find frequency of occurrence at each price. In the Meta-Profile, the center of value is at the price with the most frequent trading. Profiles decode the market feedback into value. In this study, Meta-Profiles are the source of all values used. The Meta-Profile for the DJIA future for April 1, 2004 in Figure 1 shows the day's half-hour bars on the left coalesced into the profile on the right. The profile displays the aggregated trading by price. As typical of all markets, there is little trading at the day's extreme top and bottom prices and quite a lot in the middle. Steidlmayer named the central seventy percent of trading the "value area". Value is the winner of the the price popularity contest.

Longer term value is found from the Overlay Demand Curve (ODC) [2]. The ODC is a linear aggregation of Meta-Profiles.
Market/Meta Profiles Background
Overlay Demand Curve Background
Figure 2A is an ODC of the four days March 29 through April 1 (day symbols 6, 7, 8, 9). Trading is concentrated between 103800 and 102800; labeled Upper Limit and Lower Limit respectively. The single quasi-rectangular shaped distribution indicates the DJIA is balancing between upper and lower limits. Overlays are the source of the information that defines market units. In Figure 2A you see the balance that will ultimately move into a breakout, which with the ensuing trend, completes a market unit.

A five day Overlay, Figure 2B, shows the vestiges of an earlier balance that ended on March 26 (prices 102400 to 101700, day symbol 5). Lastly, Figure 2C, a nine day Overlay, displays an earlier balance between 101000 and 99900 (March 22 through 25, day symbols 1, 2, 3, 4). Call this balance 1. An upside breakout on March 25 (around 10:25 am) continued into March 26 (day symbols 4, 5, 6). Call this trend 1; it ended about 10:50 am March 26. That was the beginning of the new four day balance (although the fact that a new balance was developing would not be completely determined for a couple of days). You now have a mapping of a market unit that began with a balance (99900 to 101000) broke out into a trend (101100 to 102800) and ended with the beginning of the next balance.

The completed market unit 3/22 through 3/31 and the partial next unit is shown in the symbol/date table:


  Symbol   1     2     3     4     5     6     7     8     9
  Date    3/22  3/23  3/24  3/25  3/26  3/31  3/29  3/30  4/01
          Bal1..............Bal1
                            Tnd1........Tnd1
                                        Bal2..............Bal2
                                                          Tnd2......
The beginning balance (symbols 1, 2, 3 and 4) covered the price range 101000 to 99900, denoted on the symbol/date table as Bal1. The trend phase, Tnd1, starting on March 24 continued into March 31 (symbols 4, 5 and 6). This completes the unit. In all it lasted six days and the balance to balance price change (amplitude) is 102700 - 101100 or 1600. Converted to dollars, the amplitude is $1,600, a significant price change. The new balance (Bal2, on day 6) signals the start of the next market unit.

Balances and the units associated with them have a somewhat fractalish nature. A longer timeframe, say twenty days, can include shorter units and at times the shorter ones can lose their identity through mixing. To completely define a market unit one needs Overlays with different time bases. Experience with futures shows a good set for market surveillance is 5, 10, 15 and 20 days. One can use a time base as large as desired, but the annual length used in much of equities analysis is sorely lacking in detail.

The example below follows the behavior of the Dow Index future through the period March 22, 2004 through April 1, 2004, a period of nine trading days, culminating in Figure 2c. In this nine days the market created a four day balance (March 22 - 25), a three day directional move (March 25 - 29) and then a four day balance (March 29 - April 1). This unusually compact market unit was selected because of it's compactness. It displays the initial balance (March 22 - 25), how that balance evolved into a directional move, including a pause in the middle and then the later balance. An examination of the second balance would show it initially began as a pause (March 29 - 30), only evolving into a clear balance by April 1.

Figure 1. Short Timeframe Value from the Meta-Profile
Market value is described by price but it is not itself a price. For instance, think of a trading day, say April 1, 2004 for the Dow Jones Index. Split the day into half hour time periods from the open at 7:20 am to the close at 3:15 pm. Give each time block an identifier: y for 7:20 to 7:30, z for 7:30 to 8:00, A for 8:00 to 8:30, B for 8:30 to 9:00 and so on alphabetically for the rest of the day, where N identifies trading from 3:00 to 3:15 pm. These letters are called TPOs (time-price-opportunity, or that- price-occurred). TPOs show time - trade matches. As you will see, value is price-over-time and TPOs provide the measure.

Meta-Profile for the Dow Index on April 1, 2004.

                 META-PROFILE REPORT FOR 04 01 04

COMMODITY  --  DJIA (CBOT)  DAY      JUN 04        LENGTH OF FIRST PERIOD =  10 MINS

        Half - Hour Bars  =  Segmented Auction                 Market Profile 
                                                                      TPOs
 103950                   D                                    103950 D
 103900                   D  E                                 103900 DE      
 103850                   D  E                                 103850 DE    
 103800                   D  E                                 103800 DE      
 103750                   D  E  F             K                103750 DEFK    
 103700                   D     F          J |K |L        P    103700 DFJKLP  
 103650               C       |  |G |  |  |J |K |L |  |  |P    103650 CGJKLP <== VAu
 103600               C    |  |  |G |H |  |J |K |L |M |  |P    103600 CGHJKLMP
 103550      z        C |  |  |  |  |H |I |  |K |L |M >N >P    103550 zCHIKLMNP
 103500      z       |C |  |  |  |  |H |I |  |  |L |M |N |P    103500 zCHILMNP
 103450     |z |A |  |C |  |  |  |  |H |I |  |  |  |M |N |     103450 zACHIMN   
 103400     |z |A |B |C |  |  |  |  |H |  |  |  |  |M |N |     103400 zABCHMN   
 103350  |y |z |A |B |C |  |  |  |  |  |  |  |  |  |M |N |     103350 yzABCMN <== VAl
 103300         A |B |C |  |  |  |  |  |  |            N       103300 ABCN    
 103250            B  C |  |  |  |  |  |                       103250 BC      
 103200            B  C    |  |  |                             103200 BC      

   VALUE AREA: Central 70% of TPOs
     UPPER      103670
     LOWER      103320

Fig 1. Half-Hour Bars (left) and Meta-Profile (right), June 04 delivery, Trading on April 1, 2004. Price compression times 5.

The vertical bars on the left labeled z, y, A, B,... identify the trading range for each time period from 7:20 am to 3:15 pm. The vertical dashed lines accompanying the half-hour bars are a running measure of the developing value area.

Meta-Profile, letters on the right (TPOs), give price and time of day that price was traded (example: 103250 traded in the 8:30 to 9:00 am period (B) and also in C period, 9:00 to 9:30.

Features of Fig 1. (From the Meta-Profile)
1) Price 103950 traded in only one period, the high of the day
2) Prices 103900 to 103800 and 103250 to 103200 traded in only two periods
3) The most popular price, 103550 was visited in nine of the day's 17 periods
4) Seventy percent of the TPOs, the value area, lie between 103670 and 103320.
5) The shape of the TPO distribution is a single bell shaped curve.

Explanation of Figure 1. The Features
1) Little trading at the top four prices shows the market rejected these prices
2) Little trading at the bottom two prices shows the market rejected these prices
3) 103550 won the day's popularity contest
4) The bulk of the trading (70%) lies between 103670 and 103320 which is named the "Value Area".
5) The single distribution (bell shape) shows balance.

Conclusion: You found the price range the market selected on April 1 for its best estimate of value. Value is not a price, but rather the price range 103670 to 103320.

Overlay Demand Curves: Collective Value for Multiple Days, Figures 2A, 2B, 2C
The Meta-Profile value area locates market determined value for a single day. Longer timeframes are handled by the Overlay Demand Curve, a linear summing of the individual profiles. The Overlay determines 'market condition', visually identifying balances, trends and other more complicated states of the market. The thesis is similar to that applied to profiles: a single distribution indicates balance, a run shows a trend and distributions that are neither balance or trend are defined and 'other'. Market distributions are continually evolving, following the general system of balance to trend to balance. More correctly there are five steps: balance to transition to trend to transition to balance. Starting from balance the next step is a breakout into a transition. The transition may continue into a trend or move back into balance. A third possibility is to move into a choppy phase where neither balance or trend exist. This is one of the 'other' conditions where the market may zig and zag apparently at random.

In the Overlay discussion that follows we examine market condition over the eleven day time period March 22 to April 1, 2004 for the Dow Jones index, June Delivery. In the displays below, each day is represented by a symbol in the ROT PROFILE column, which stands for a date:

  Symbol   1     2     3     4     5     6     7     8     9
  Date    3/22  3/23  3/24  3/25  3/26  3/31  3/29  3/30  4/01
where ROT PROFILE identifies those dates each price traded. A price may trade in several periods of a day, e.g. 103750 traded only on day 9 (4/01) with that price occurring in three different half-hour time periods.

A Four Day Balance
TPO VOLUME OVERLAY AND PRICE ROTATION PROFILE JUN 04 DJIA (CBOT) DAY 03 29 04 TO 04 01 04

 PRICE DYS  L/F ROT PROFILE *  TPOS TPO VOL OVERLAY *
 
103900  1    9    9               2 XX
103800  2    9    89              4 XXXX <== Upper Limit
103700  2    9    89              9 XXXXXXXXX
103600  3    9    789            15 XXXXXXXXXXXXXXX
103500  3    9    789            15 XXXXXXXXXXXXXXX
103400  3    9    789            15 XXXXXXXXXXXXXXX
103300  3    9    789            17 XXXXXXXXXXXXXXXXX
103200  4   69    6789           16 XXXXXXXXXXXXXXXX
103100  3   6     678            21 XXXXXXXXXXXXXXXXXXXXX
103000  3   6     678            17 XXXXXXXXXXXXXXXXX
102900  3   6     678             8 XXXXXXXX
102800  2   6     67              5 XXXXX <== Lower Limit
102700  1   6     6               1 X
102600  1   6     6               1 X
102500  1   6     6               1 X
102400  1   6     6               3 XXX
 
Figure 2A. Dow Jones Index, June 2004 delivery, March 29 to April 1. Price compressed times 10. 
Legend:
  PRICE: Trading price
  DYS:   Number of days in which that price traded
  L/F:   L = Last symbol (earliest day, 6); F = First symbol (latest day, 9)
  ROT PROFILE:  Day symbols for each price (6 for Mar 29, 7 for Mar 30,...)
  TPOS:  Number of total half-hour periods traded
  TPO VOL OVERLAY:  TPOS extended with X's for a visual of trading activity
The DYS and ROT PROFILE columns are two ways to estimate general trading density. TPO VOL OVERLAY is a pictorial of the trading density at price.

The four day Overlay of Figure 2A shows a single distribution (where the minimum distribution has at least three TPOs with four contiguous prices). The upper and lower limits of the distribution are 10385 and 102800. Outside those limits are vestiges of previous distributions or just noise.

Market perceived value for the four day period is no particular price, rather it is a 'value region' between 10385 and 102800. This longer term value may be contrasted with the 'value area' of April 1 of Figure 1: 103670 to 103220. Now you have a longer timeframe value with a local value nested inside.

Market condition is a function of the timeframe. If the market is in a long timeframe balance you might find not only, say a month balance, but internediate periods (4 day, 7 day, 15 day, etc.) all in balance as well. We define this as an 'equilibrium' situation. A change in price level is often manifested by first, a shorter term movement (a 4 or 5 day breakout), then a 10 day breakout, and so forth. Likewise a trend coming to an end will be seen first as a short term balance, then longer balances, until the longest timeframe is balanced.

An Out of Balance Market Coming into Balance

TPO VOLUME OVERLAY AND PRICE ROTATION PROFILE JUN 04 DJIA (CBOT) DAY 03 26 04 TO 04 01 04


 PRICE DYS  L/F ROT PROFILE *  TPOS TPO VOL OVERLAY *
 
103900  1    9    9               2 XX
103800  2    9    89              4 XXXX <== Upper Limit     |
103700  2    9    89              9 XXXXXXXXX                |
103600  3    9    789            15 XXXXXXXXXXXXXXX          |
103500  3    9    789            15 XXXXXXXXXXXXXXX          |
103400  3    9    789            15 XXXXXXXXXXXXXXX        Balance
103300  3    9    789            17 XXXXXXXXXXXXXXXXX        |
103200  4    9    6789           16 XXXXXXXXXXXXXXXX         |
103100  3         678            21 XXXXXXXXXXXXXXXXXXXXX    |
103000  3         678            17 XXXXXXXXXXXXXXXXX        |
102900  3         678             8 XXXXXXXX                 |
102800  2         67              5 XXXXX <== Lower Limit    |
102700  1         6               1 X
102600  1         6               1 X
102500  1         6               1 X
102400  2   5     56              4 XXXX <== Upper Limit (previous)
102300  1   5     5               4 XXXX
102200  1   5     5               6 XXXXXX
102100  1   5     5               6 XXXXXX
102000  1   5     5               4 XXXX
101900  1   5     5               5 XXXXX
101800  1   5     5               7 XXXXXXX
101700  1   5     5               3 XXX <== Lower Limit (previous)
101600  1   5     5               1 X
Figure 2B. Dow Jones Index, June 2004 delivery, March 26 to April 1. Price compressed times 10.
Figure 2B. illustrates a double distibution day. The later, upper distribution, is the one of Figure 2A. The lower distribution is obsolete, having been superceded. You would suspect that there was an earlier distribution that defined a lower value, but it is not possible to tell from a single day.

Stepping from One Value to Another

TPO VOLUME OVERLAY AND PRICE ROTATION PROFILE JUN 04 DJIA (CBOT) DAY 03 22 04 TO 04 01 04


 PRICE DYS  L/F ROT PROFILE *  TPOS TPO VOL OVERLAY *
 
103900  1    9    9               2 XX
103800  2    9    89              4 XXXX <== Upper Limit            |
103700  2    9    89              9 XXXXXXXXX                       |
103600  3    9    789            15 XXXXXXXXXXXXXXX                 |
103500  3    9    789            15 XXXXXXXXXXXXXXX                 |
103400  3    9    789            15 XXXXXXXXXXXXXXX               Balance 2  
103300  3    9    789            17 XXXXXXXXXXXXXXXXX               |
103200  4    9    6789           16 XXXXXXXXXXXXXXXX                |
103100  3         678            21 XXXXXXXXXXXXXXXXXXXXX           |
103000  3         678            17 XXXXXXXXXXXXXXXXX               |
102900  3         678             8 XXXXXXXX                        |
102800  2         67              5 XXXXX <== Lower Limit           |
102700  1         6               1 X                     |
102600  1         6               1 X                     |    
102500  1         6               1 X                     |
102400  2         56              4 XXXX          |       |
102300  1         5               4 XXXX          |       |
102200  1         5               6 XXXXXX        |       |
102100  1         5               6 XXXXXX        |     Trend 1
102000  2         45              5 XXXXX         |       |
101900  2         45              8 XXXXXXXX      |       |
101800  2         45             10 XXXXXXXXXX  Pause     |
101700  2         45              5 XXXXX         |       |
101600  2         45              4 XXXX          |       |
101500  1         4               3 XXX           |       |
101400  1         4               1 X                     |
101300  1         4               2 XX                    |
101200  1         4               2 XX                    |
101100  1         4               1 X                     |
101000  3   1     124             4 XXXX <== Upper Limit (previous) |
100900  3   1     124            17 XXXXXXXXXXXXXXXXX               |
100800  4   1     1234           20 XXXXXXXXXXXXXXXXXXXX            |
100700  4   1     1234           19 XXXXXXXXXXXXXXXXXXX             |
100600  3   1     123            15 XXXXXXXXXXXXXXX                 |
100500  3   1     123            21 XXXXXXXXXXXXXXXXXXXXX           |
100400  3   1     123            25 XXXXXXXXXXXXXXXXXXXXXXXXX     Balance 1
100300  3   1     123            20 XXXXXXXXXXXXXXXXXXXX            |
100200  3   1     123            15 XXXXXXXXXXXXXXX                 |
100100  2   1     13              8 XXXXXXXX                        |
100000  2   1     13              7 XXXXXXX                         |
 99900  2   1     13              3 XXX <== Lower Limit (previous)  |
 99800  1         3               1 X

Figure 2C. Dow Jones Index, June 2004 delivery, March 22 to April 1. Price compressed times 10.
A longer view of the DJ index behavior through April 1 clearly shows a stepped equilibrium. The three days March 22 - 24 (symbols 1, 2, 3) and part of March 25 describes a nicely balanced market with a value region 101000 to 99900. On March 25 (symbol 4), around 10:25 am, price broke above 101000. The breakout initiated a trend that moved quickly up to 102000. The next two days, March 26 and 27 (symbols 5 and 6), the trend continued up to as high as 103250. In the middle of the trend, around 101800, upward movement stopped for as long as ten half hour periods. Such interruptions of a trend, called pauses, are a normal part of many trends. The Overlay display format makes pauses clearly evident. This trend, from breakout to trend end, 2250 points, is a 2.2 percent move, or $2,250 for the DJ future.

The ensuing four day period (symbols 6, 7, 8, 9) described the new balance value region 102800 to 103800. The previous balance at 99900 to 101000 is about 3000 points lower.

This example illustrates the clarity and definition of the balance regions as well as the intensity of the intervening trend. Four or five day balance breakouts are often the precursors, the early alerts for major market movements. However,large market movements are less frequent. Longer balances of ten or twenty days are more stable, of course. However, longer timeframe balances are harder to achieve. In the year 2002 (250 trading days) we found 139 five day balances, 169 ten day, 120 fifteen day and 116 twenty day balances. There were 77 days of true equilibrium where all four timeframes were balanced. The longest continuous run with all four balances maintained was only nine days.

Variation Over Time
Most technical analysis methods assume regularity, but markets are anything but regular. For the Dow Index in the first quarter of 2004 the market created five units. The shortest was four days, a two day balance followed by a two day directional period. The longest was 20 days, fifteen in balance, five directional. The five units and their dates are listed below (B is balance, D is directional). Within the period of Jan 6 to Mar 16 encompassed by the March future, price started at 105070 and went from a high of 107500 to a low of 101150, closing at 10185 on Mar 16.

The variability of market units presented in this table is not unusual. For all of 2003 the average balance period was 7.4 days, with individual balance periods ranging from 2 to 15 days. In the same period the average directional period of 5.8 days came from periods ranging from 2 to thirteen days.

A trader finds opportunity in the directional markets. These begin with a movement out of balance and end with the start of a new balance. Predicting when a breakout will begin starts with an understanding of the balance itself, from the Overlay Demand Curve. Overlay Demand Curve Background

Locating the end of the directional phase of a market requires the identification of a phase change, the change of the directional phase into the congestion that is the beginning of a new balance. A moving, directional market does so under the impetus of demand. The best tool for reading demand change is the Market Profile, described by J. Peter Steidlmayer in 1985 (1). Market Profile uses volume from the CBOT LDB data bank. The LDB depends on the clearing process and lags the market within the day. Most traders use the Meta_Profile, developed by Jones in 1987 (3). Meta-Profile comes from a tick database and is real time. Market Profiles Background
             A Brief Table of Dow Index Market Units, First Quarter 2004

0106 0107 0108 0109 0112 0127 0128 0203 0204 0206 0209 0212 0213 0305 0308 0312 0316 0319 0322 0408
  B = 2     D = 2     B = 11    D = 5     B = 3     D = 4     B = 15    D = 5     B = 4     D = 13
or
Balance:      2 days  0106-0107
Directional:  2 days  0108-0109     Market Unit = 4 days

Balance:     11 days  0112-0127
Directional:  5 days  0128-0203     Market Unit = 16 days

Balance:      3 days  0204-0206
Directional:  4 days  0209-0212     Market Unit = 7 days

Balance:     15 days  0213-0305
Directional:  5 days  0308-0312     Market Unit = 20 days

Balance:      4 days  0316-0319
Directional: 13 days  0322-0408     Market Unit = 17 days



One Year of Market Units for DJ, Basis 5, 10 and 15 day Overlays

The time lengths of Market Units differ depending on the time scale examined. The table below is for the Dow Index for 2004. Length of a Market Unit is defined as the period encompassed from the beginning of one balance to the beginning of the next.

 Days in Unit      5 Day Overlay      10 Day Overlay      15 Day Overlay
                           Sum                 Sum                 Sum
      2                                     1    2              2    4
      3                 7   21             10   30              8   24
      4                 9   36             13   52             10   40
      5                 3   15        M=>   4   20        M=>   7   35
      6                 2   12              6   36              3   18
      7            M=>  9   63             10   70              7   49
      8                 7   56              1    8              0
      9                 3   27              5   45              4   36
     10                 3   30              2   20              1   10
     11                 3   33              3   33              1   11
     12                 1   12              0                   0
     13                 1   13              0                   1   13
     14                 0                   0                   0
     15                 1   15              3   45              0
     16                 1   16              0                   1   16
     17                 0                   0                   1   17
     18                 0                   0                   0
     19                 0                   1   19              0
     20                 0                   0                   1   20
     21                 0                   0                   0
     22                 0                   0                   0
     23                 0                   0                   2   46
     24                 0                   0                   1   24
     25                 0                   0                   0
     26                 0                   0                   0
     27                 0                   0                   0
     28                 1   28              0                   0
     29                 0                   0                   1   29

     Total             51  377             59  380             51  390
     Ave Day/Event         7.4                 6.4                 7.6
      
     M=> Median            7 dy                5 dy                5 dy

Figure 3. Market Units on three time scales for the DJ in 2004.
A market unit cannot be shorter than 2 days, one for the balance (5, 10 or 15 days) to be reported and one day for the directional move. The very short units of 2 or three days are usually failed breakouts. In the table column 1 is the number of days in the market unit. Column 2 is the number of events found in 2004 for 5 day Overlays extended out for the sum of days in each unit (7 events at 3 days is 21 total days for the 3 day unit). Similarly for the 10 and 15 day columns. At the bottom are the total market units for the year (51 for 5 day Overlays) and the average number of days per unit (7.4 for 5 day Overlays). The Figure M=> locates the median value.

While it is possible to find averages and medians for the market units, the spread is large. For 5 day Overlays, there is approximately the same probablity of occurrence for 3, 4, 5, 6, 7 and 8 days. This confirms the statement in the article Market Waves are NOT Cycles
Market Waves are NOT Cycles
concerning the use of moving averages in market analysis. For instance, the variation in market unit lengths from unit to unit, Feb. 23 to May 16 were 8, 11, 28, 7, 15, 16, and 7 days respectively. It would be hard to make sense of any sort of average for this time period. A long run of 15 or 28 days offers a great deal of opportunity for the day trader and swing trader both. For instance the 28 day run of March 16 through April 8 saw price go from 101620 to 104290 (about $2,500). The day trader would have maintained a generally 'long' mentality for this period while swing traders would look to stay on the long side.

Market Units for emini SP for 2005

Figure 4. 5 Day Overlay Balances for emini SP.
Each box represents a balance period as measured by the 5 day Overlay. The height of the rectangle is the average price range of the balance period and the width is the number of days the balance is maintained. The last balance may have a breakout sometime within the day.

Table of Balance Periods:  emini SP 2005
PD       1       2       3       4       5       6       7       8       9      10
D1    0110    0126    0207    0217    0309    0324    0420    0524    0629    0715
D2    0111    0131    0211    0221    0314    0413    0516    0622    0707    0804
#D       2       4       5       3       4      14      20      22       6      15
OP  119125  117300  120100  120125  120675  117475  115775  119625  120300  123125
CL  118400  118175  120700  120100  121200  117600  116700  112125  120275  123800


PD 11 12 13 14 15 16 17 18 19 20 D1 0810 0819 0829 0913 0926 1011 1104 1115 1129 1221 D2 0815 0823 0830 0919 0928 1101 1109 1116 1212 1222 #D 4 3 2 5 3 16 4 2 11 2 OP 123350 122075 121450 123875 122150 118925 122350 123250 125925 127000 CL 123750 122150 120850 123800 122275 120125 122375 123475 126925 127550


Table 1. Balance Periods: emini SP 2005, 5 Day Balances
The 20 periods of balance are labeled PD. D1 and D2 are the starting and ending dates of a balance. #D is days in balance, including the breakout day if breakout occurs inside the trading period (regular market day). OP is the point of control of the first day of balance, CL is the point of control of the last. (Point of control is the central price of the day from the Meta-Profile or for CBOT cleared volume, the Market Profile.)

The rectangles on Figure 4 depict the variety of times and approximate amplitudes the balance periods can take. This is trader driven and hence is a picture of the vagaries of the collective trader. Although the SP market was generally rising through 2005, there is no apparent general strategy for the year. A trader with a 'long' attitude for the year (say on some fundamental view) would find a number of periods of adversity. Arguably the best strategy is to key off the balances, which are identified by the Overlay Demand Curve (Visual Graphic). You can know the balance and, at the start of any day, the price that will break out of the balance (an alert for start of a trend). This is a key signal, regardless of one's strategy.

The lack of pattern to the changing balance blocks evidences the lack of ability to project or predict the coming market behavior. Everyone would like to project the market successfully for even a few hours. Unfortunately, the tenets of Auction Market Value Theory
Auction Market Value Theory
precludes prediction. It is easy to see why. Think of a market that has just experienced a jump in price. Each trader responds in his own way, in his own time frame. This response also appears to all as a change in market behavior, collectively maybe up, maybe down or maybe no change. Each of us individually cannot know know what is going to happen because those who are effecting the change by trading are just making up their minds. Until they make up their minds, we cannot know which way it will go. That 'time for the market to make up its mind' is called the relaxation time, most typically in the order of 15 to 30 minutes. Steidlmayer (ref 1) thought this 'market relaxation time' was about 30 minutes and so chose that as the time frame for Market Profile (half-hour bars).

References
1. Markets and Market Logic, J.P. Steidlmayer & K. Koy, Porcupine, 1986
2. Overlay Detection of Long Term Market Condition, D. L. Jones, The Profile Report, Vol. 2, Oct 1988
Also, Value Based Power Trading, D.L. Jones, Probus, 1993
3. Estimating the Market Profile Value Area for Intraday Trading, D.L. Jones S&C Sep. 1987
Also, Determining the TPO Value Area, D.L. Jones Mkt Logic Sch. AI Ltr, Apr 13, 1987