CISCO


CISCO Futures
1-303-306-1521 1-800 800 7227 Fax 1-303-306-1598
http://www.cisco-futures.com
dljones@cisco-futures.com



Market Waves are NOT Cycles

Donald L. Jones
Copyright CISCO Futures March 25, 2005

A hope of many technical analysts is that markets have a cyclic component that can be used for predictive purposes. Belief in an underlying periodicity is implicit in moving average smoothing, since the moving average is expected to act as a filter. The same is true of oscillators, where two moving averages of different time frames are subtracted to find differences. The fact that oscillator differences often move smoothly and change fast in highly directional markets is taken as evidence that the resulting curves provide information that can be traded. An underlying but unspoken assumption of virtually all technical analysis is that market data is well conditioned (small errors in the data produce small errors in the result). In fact, as will be shown below, the fundamental assumption of essentially equidistant peaks in a set of market data is incorrect, and thus market data is poorly conditioned for most of technical analysis.

It is theoretically true (Fourier analysis) that several waves of varying amplitudes and periods can be combined to provide a display that looks like market flow (with rises, falls and periods of low amplitude). Unfortunately, it is also true that market flow can and does come from a complex, self-regulating process (aggregate decisions of a large number of traders). This process cannot be described by any known mathematical distribution. Specifically ruled out is the fourier process, the market is not (so far as anyone can tell) a combination of sine waves.

Many elements of normal life are cyclic; the 24 hour day, seasons, weather, ice ages and other natural phemonena. Some economic phenomena such as booms and busts are thought to follow some sort of wave, such as the Kondratieff 30 to 60 year wave. In markets, much has been made of the Elliott five wave up and three wave down proposition. While phemonena such a Elliott waves become apparent after the fact, proponents seem unable to agree on the present. Even if you could tell which leg of an Elliott wave you are in, that knowledge would be hard to use in day-to-day trading where your outlook is rarely more than just a few minutes or days.

Markets always display wave-like motion. Prices move up and down with some regularity, describing local highs and lows. This movement reflects the changes in the way the composite of all traders, their feedback, value the market. While clearer on longer term charts, the local highs and lows describe periods that vary from wave to wave. Prediction of the next high or low cannot be made in any reliable way. Incidentally, prediction is not a requirement of successful trading (see the section on the Market Unit).

The Market Unit

Because the source of market motion cannot be tied to any known distribution, a market surely cannot be described by a set of sine waves or helped in any real analytical sense by smoothing.

Some analysts describe market waves as cycles, imputing a regularity not supported by the data itself. Analyzing market waves to obtain any predictability is not simple and may well be impossible, due to wave irregularity. Some waves can be very short, comprising just a day or two from top to bottom, others may take twenty days to find a bottom. While market waves for predicting the future seem to be impossible to divine, it is possible to look to the past to study the obvious wave motion in past data, with the aim of better understanding markets. We show in figure 1 below how widely the SP market has varied through the years. Figure 1 shows that the wave ranges of the SP have been decreasing since 2002 and helps explain why it is harder to trade the SP profitably today, as compared to the past.

We identify the historical wave motion with a 'seven day' rule--a peak is defined as the highest price reached since the previous low with no higher price within the past seven days. The low is generally defined the same way, but in cases of disagreement, say with a very short wave, the procedure is modified.

In the two short tables below, the SP futures of March 2000 and 2005 show a remarkable variability in period (time from peak to peak) and amplitude (range from peak to trough) is evident. The over-heated markets of 2000 had an average period of 14.5 days (with large variations) and an average amplitude of $25,000. The quieter time of 2005 displays a 25% longer period and an average amplitude 68% less.


SP MAR 00
  DATE     PEAK VALLEY CAL DY MKT DY   Period    Ampl
11/16/991450.00           175    121      12
12/ 1/99       1406.50    190    131            43.50
12/ 3/991470.00           192    133      20
12/ 9/99       1410.50    198    137            59.50
 1/ 3/ 01496.50           223    153       9
 1/ 5/ 0       1387.00    225    155           109.50
 1/14/ 01484.50           234    162      17
 1/31/ 0       1357.00    251    172           127.50
 2/ 9/ 01454.80           260    179    
 2/28/ 0       1327.00    279    191           127.80

Wave periods and amplitudes for the first quarter of 2000. This study at the height of the telecommunications bubble shows the cross market effect on the SP index in the wave amplitudes. A 100.0 range is $25,000. Wave times (periods) averaged 14.5 days. The average range per day is about $1,700; indicating much opportunity for the day trader.


SP MAR 05
  DATE     PEAK VALLEY CAL DY MKT DY   Period    Ampl
11/17/ 41191.50           597    335      30
11/22/ 4       1171.00    602    338            20.50
12/31/ 41219.70           641    365      13
 1/19/ 5       1176.70    660    378            43.00
 1/19/ 51197.20           660    378      20
 1/24/ 5       1166.10    665    381            31.10
 2/16/ 51213.40           688    398      13
 2/22/ 5       1184.00    694    402            29.40
 3/ 7/ 51225.70           707    411    
 3/16/ 5       1185.60    716    418            40.10

Wave periods and amplitudes for the first quarter of 2005. Five years after 2000, in a much cooler market, wave periods average 18.25 days and amplitudes are around 31 (approximately $8,000). Daily opportunity averages about $450. Clearly, from the standpoint of opportunity alone, it is harder to make money trading the SP in 2005.

In neither 2000 or 2005 are the periods of the waves stable. In both cases the variation is a factor of two or more over the approximately sixty days of the study.

The variation of the periods, more than 50%, illustrates how very poorly conditioned these data are for moving average operations, or in any other sort of filtering.

Market Information Available
What can be learned from the two tables above?
1) As traders, we might guess that there was much more opportunity for the day trader in 2000 than 2005. It is clear that market opportunity can show large changes over time.

2) The time-frame variations of the waves in these two three-month periods are such that it is unlikely that standard moving averages or oscillators can be trusted.

3) Amplitudes of the waves, if longer time-frames are examined (tables below), might measure the relative opportunity at various times. It is an observed fact that all markets pass through periods of good tradeability and periods of sluggishness. A trader finds it very difficult to trade profitably if a market is offering little opportunity.

4) We know that (theoretically, at least) it may be possible to locate those markets offering opportunity at a given time. In fact, the CISCO Advice Engine's job is to ferret out those markets with large opportunity.

Advice Engine and Select Table

Select Table runs from 001031 through the current day minus one. Latest day is at the bottom. Starting at the bottom, reading up finds many energy entries.

5) Simply knowing the irregular structure of the market will lead us to disbelieve the stories told by model salesmen. More to the point, such knowledge will lead us to search analytical methodologies that work within the actual, complex market, analysis.

Graphic of SP Wave Amplitudes, 1990 - 2005
In figure 1 below we examine the wave amplitudes for nearly fifteen years of the SP market (emini SP, of course, has the same amplitudes but only one-fifth of the dollar range). Large wave amplitudes are trader friendly because they indicate opportunity. We note that SP went from a quiet, rather dull market (early to mid 1990's), to an extremely active, large amplitude period (1995 to 2002). Now it is cooling down.

                Average Wave Amplitudes for SP 1990 - 2005

     Ampl
     100 - +                                xxx   xxxxx    xx         
                                                 x      x    x             
      90 -                                 x                                 
                                                x        x                  
      80 -                                                                    
                                               x          x   x               
      70 -                               x                                   
                                          x            x                     
      60 -                                                              
                                        x                          x       
      50 -                             x                       x          
                                      x                             x     
      40 -                                                      x x  x    
                                   x                             x        
      30 -                        x xx                                      
          xxxx                   x           
      20 -                               
              xxxxxxxxx   xxxx                                           
      10 -             xxx    xxx                                          
                                                                        
       0 -
          |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |  |  
         90  91  92  93  94  95  96  97  98  99  00  01  02  03  04  05  06
                                       Years

Figure 1. Average trading wave amplitude for SP. Quarterly averages (four per year), provide the average trading opportunity (price range from high to low in a wave). Wave peaks are the highest prices within the previous 7 trading days. The average number of days in a wave, calculated quarterly (not shown on this graphic) varies from a low of 11 (second quarter of 1998) to a high of 43 (fourth quarter of 1998). Wave amplitudes (price range from high to low in a wave, averaged per quarter) were as small as 11.2 (4th Qtr 1993 and 1st Qtr 1995) and as large as 155.5 ($38,875) )(4th Qtr 2000). Ranges above 100 are truncated on this graph.


Wave Table of SP 1990 to 2005
The tabular data for figure 1 provides more detail on the wide, diverse variation in wave highs and lows as well as the number of days in periods. The 'bubble' of 1998, 1999, 2000, 2001 and 2002 shows exceptional variation. Markets are most tradeable if the waves have large amplitude and long wave periods. Large ranges mean that whatever your strategy, you can get aboard at a variety of prices. Your timing does not have to be perfect. Likewise, if the wave period is longer, again your timing constraints are relaxed.

Each market behaves differently, but relative to itself it is easy to use a graphic like figure 1 or the table below, to sort out the good places to trade. Figure 1 shows that the best times started to wane in 2002. Roughly, we believe that wave amplitudes below about 40 ($10,000 for SP, $2,000 for emini) herald more difficult trading. Below about 25 ($6,250 for SP, $1,250 for emini) a trader is well advised to bring other markets, ones with more opportunity, into the trading mix. SP/emini will still offer cases of exceptional potential, but more rarely. Even in the duller periods SP offers some big opportunities, but that may not be enough to keep a day-trader going.

In contrast to the SP, crude oil spends long periods doing little, then a great amount of activity. Crude will be briefly discussed after the SP.

   Del  NRng   Rng-Hi  Rng-Lo  Rng-Av   NPd     Pd-Hi   Pd-Lo   Pd-Av   Pri
DEC 89     6   40.35    4.40   15.86      6      21       7      14     360

MAR 90     2   44.20   15.80   30.00      2      27      26      26     350

JUN 90     2   22.20   12.85   17.53      2      35      18      26     350

SEP 90     4   40.15   19.20   28.86      4      28      16      21     350

DEC 90     3   27.90   12.35   19.57      4      17       8      13     320

MAR 91     3   25.40    9.80   15.47      3      42       8      20     340

JUN 91     4   19.30   12.25   16.54      4      20       9      15     390

SEP 91     4   23.90    7.90   16.71      4      32      12      19     385

DEC 91     4   28.10    6.15   15.38      4      21       9      15     385

MAR 92     4   15.20   11.05   13.40      3      20      11      16     410

JUN 92     3   20.30    9.25   13.68      3      17      13      15     410

SEP 92     3   19.00    8.80   14.87      3      31      14      24     410

DEC 92     2   35.50    7.10   21.30      2      35      25      30     420

MAR 93     3   22.30    6.25   15.08      3      28      14      21     430

JUN 93     4   18.85   10.00   14.00      4      18       8      14     445

SEP 93     4   13.60    7.80   10.75      4      35       7      18     450

DEC 93     4   17.15    7.05   12.48      4      22       8      15     460

MAR 94     5   17.50    3.50    9.95      5      23       8      15     475

JUN 94     3   36.30   13.30   20.98      3      31      11      19     450

SEP 94     4   24.65    5.40   12.88      4      22      11      16     460

DEC 94     4   32.40   14.40   20.21      4      21       8      13     460

MAR 95     3   13.80    7.40   10.93      3      40      18      27     465

JUN 95     2   13.75    9.35   11.55      2      33      13      23     510

SEP 95     5   21.55    9.60   13.91      5      21      12      15     560

DEC 95     3   21.35   13.05   17.17      3      15       7      12     580

MAR 96     3   42.90   18.65   31.32      3      28      13      21     625

JUN 96     2   39.50   27.90   33.70      2      27      19      23     645

SEP 96     3   71.50   24.70   41.97      3      41      26      34     670

DEC 96     1   20.10   20.10   20.10      1      26      26      26     710

MAR 97     4   50.00   33.00   38.23      4      22      14      17     760

JUN 97     2   69.30   41.00   55.15      2      43      10      26     790

SEP 97     3   76.05   22.75   43.52      3      33       9      20     890

DEC 97     5  148.25   26.70   63.97      5      22      11      15     940

MAR 98     1   77.50   77.50   77.50      1      14      14      14     955

JUN 98     5   74.50   37.20   52.78      4      18       8      11    1105

SEP 98     3  176.50   56.70  125.33      3      27      22      24    1130

DEC 98     1  151.40  151.40  151.40      1      43      43      43    1120

MAR 99     3   89.70   61.00   75.23      2      16      14      15    1220

JUN 99     5  104.00   61.10   77.52      5      17      11      14    1340

SEP 99     3  158.00   49.30   96.27      3      29       8      21    1375

DEC 99     3  112.00   46.90   89.33      3      26      12      20    1400

MAR 00     4  126.00   41.30   97.20      4      32       9      19    1440

JUN 00     4  201.10  112.50  142.03      4      14      11      12    1440

SEP 00     3  107.20   41.80   70.33      3      34      11      21    1515

DEC 00     3  157.80  119.50  144.47      3      29      18      23    1440

MAR 01     3  283.40   77.50  166.47      3      38      16      24    1340

JUN 01     2   83.10   28.50   55.80      2      24       3      13    1260

SEP 01     4   76.40   63.00   70.60      4      28      10      16    1230

DEC 01     3  256.50   26.30  111.13      3      30       9      22    1080

MAR 02     5  103.00    6.00   49.08      5      27       7      14    1130

JUN 02     3  130.10   76.70   98.90      3      22      20      21    1080

SEP 02     2  271.90   96.10  184.00      2      46      13      29     930

DEC 02     2  159.50   56.00  107.75      2      39      17      28     900

MAR 03     3  129.00   34.70   83.00      3      28       9      20     840

JUN 03     2   63.50   51.80   57.65      2      14       9      11     840

SEP 03     6   55.10   27.10   39.07      5      47      13      25     980

DEC 03     3   50.10   32.90   40.57      3      21      12      16    1030

MAR 04     2   33.50   24.00   28.75      2      15      13      14    1130

JUN 04     2   74.50   36.30   55.40      3      23      11      17    1130

SEP 04     4   67.50   18.90   48.95      4      33      12      24    1090

DEC 04     2   55.60   26.00   40.80      2      30      13      21    1100

MAR 05     4   43.00   20.50   31.00      3      30      13      21    1200



Headings: 
  Del    = delivery 
  NRng   = number of waves per quarter 
  Rng-Hi = the largest high-low range per quarter  
  Rng-Lo = is the smallest high-low range per quarter  
  Rng-Av = average high-low range
  NPd    = the number of waves in a calculation 
  Pd-Hi  = the largest number of days in a wave 
  Pd-Lo  = the least number of days in a wave  
  Pd-Av  = the arithmetic average number of days in a wave.
  Pri    = approximate average price for the quarter

Grouping the period lengths shows their general distribution:

         # Days     Pd-Hi   Pd-Lo
        40 - 49         7       1
        30 - 39        16       0
        20 - 29        28      11
        10 - 19        11      30
         3 -  9         0      20
Historically, from the time of Welles Wilder's book on technical analysis in 1978, the choice for averaging was fourteen days. For the low periods, that falls in about the middle. However, the median for the high periods is about ten days more or around twenty five days. Again, there is not even a vestige of a median to average around. The consequence is that averaging, as in moving averages and oscillators, is close to dealing with random numbers.

Both the price range and number of days in a wave are highly variable. The days in the average wave tend to be less in the low opportunity regions.

The rough plot of the quarterly average wave amplitudes (figure 1, above), gives one a feel for the wave fluctuations. From 1997 through 2002 the wave amplitudes were extraordinarily high. Lately (2005), the amplitudes seem to be regressing toward the earlier values. First quarter of 2005 at amplitude of 40 is 1/2 to 1/4 the preceeding values of several years. Thus, there is now less opportunity.

SP is not alone in showing long term variations in opportunity. All markets pass through periods of high demand and then regress back to normality. Since the SP, and its small brother the emini, have been the most actively traded markets we have ever seen; traders who began trading in the late 1990's are finding profits more elusive. They may find it advisable to diversify into other markets.

Most traders rely on forms of technical analysis for their trading. When the market is accomodating by offering a lot of opportunity, many sorts of analyses work. In the stock market it is well known that all stock pickers are smart in bull markets. In futures where a trader can do as well in a big bear market as in a bull, the key is opportunity. A market that is shutting down (congesting) displays smaller trading ranges and even these take longer to develop. The trader is advised to constantly seek opportunity. It can be done. Anyone can keep track of the waves, simply from the daily high - low price data. As noted above, another source of daily measures of opportunity is in the CISCO Advice Engine Select Table. A market that starts appearing regularly in the Advice Engine table should be considered.

Crude Oil
We noted above that a long term view of the waves of a market can orient a trader with it's perspective. Whereas SP appears to be fading as a primary market for day-trading, crude seems to be coming to the fore. Lengths of the waves are steady but amplitudes are generally extending since 2000. Crude is becoming a better market to trade. This observation is supported by the frequency of energy appearances in the Advice Engine Select Tables:


Wave Table of Crude Oil 1990 to 2005

Crude Oil

   Del  NRng   Rng-Hi  Rng-Lo  Rng-Av   NPd     Pd-Hi   Pd-Lo   Pd-Av   Pri
MAR 90     5    2.28    0.38    0.99      5      29       9      17      19

JUN 90     3    3.55    0.80    2.15      3      32       8      18      21

SEP 90     3    2.65    0.92    1.73      3      18       7      12      19

DEC 90     4    4.91    0.85    3.17      4      30       8      19      30

MAR 91     6   12.20    2.90    6.79      6      34       5      14      31

JUN 91     3    2.40    0.97    1.76      3      22      11      16      20

SEP 91     4    1.83    0.72    1.11      4      41       8      18      21

DEC 91     3    1.42    0.62    0.96      3      35       9      19      22

MAR 92     3    4.70    0.73    2.47      3      40       9      20      22

JUN 92     2    1.53    0.66    1.10      2      41      17      29      20

SEP 92     3    1.77    0.64    1.03      3      30      21      25      21

DEC 92     2    1.10    0.61    0.86      2      33      24      29      22

MAR 93     4    1.80    0.69    1.49      4      23       7      19      20

JUN 93     3    1.40    0.89    1.21      3      25      21      22      21

SEP 93     2    3.45    1.02    2.24      2      40      19      30      20

DEC 93     3    2.06    0.48    1.11      3      24      11      16      19

MAR 94     3    3.60    1.26    2.31      3      32      20      26      17

JUN 94     2    1.71    0.96    1.34      2      18      14      16      15

SEP 94     4    1.10    0.92    1.02      4      34       8      19      18

DEC 94     4    1.89    0.72    1.65      4      28      14      21      19

MAR 95     3    1.58    0.70    1.15      3      27      13      18      18

JUN 95     2    0.56    0.45    0.51      2      47      20      34      19

SEP 95     3    2.31    0.60    1.37      3      30       4      16      19

DEC 95     5    1.28    0.43    0.75      5      22       8      14      17

MAR 96     3    2.49    0.32    1.07      3      43       8      31      17

JUN 96     3    2.68    1.18    1.85      3      35       9      25      20

SEP 96     3    1.81    1.06    1.43      3      20      17      19      20

DEC 96     3    1.88    0.80    1.29      3      28      17      23      22

MAR 97     4    2.42    1.13    2.01      4      22      11      17      24

JUN 97     2    3.65    3.07    3.36      2      33      17      25      22

SEP 97     3    3.20    0.73    1.96      3      34       8      18      21

DEC 97     3    2.35    0.69    1.52      3      22      10      17      21

MAR 98     2    5.41    0.90    3.16      2      50      14      32      21

JUN 98     2    4.86    2.10    3.40      2      36      18      27      17

SEP 98     5    2.56    1.06    1.73      5      23      10      14      16

DEC 98     4    3.07    0.76    1.55      4      22      11      17      15

MAR 99     3    3.66    1.86    2.52      3      31      14      20      14

JUN 99     2    1.35    1.32    1.34      2      41      25      33      16

SEP 99     3    1.54    0.28    0.95      3      22      10      17      18

DEC 99     2    4.18    1.44    2.81      2      26      18      22      23

MAR 00     3    2.55    1.59    2.16      3      23      15      19      25

JUN 00     1    1.35    1.35    1.35      1      32      32      32      28

SEP 00     5    5.21    1.35    3.90      5      23      10      16      28

DEC 00     5    4.56    1.53    2.90      5      40      10      32      33

MAR 01     3    8.39    0.44    3.29      3      33       5      18      31

JUN 01     3    2.86    1.94    2.39      3      17      13      15      28

SEP 01     5    4.00    0.42    2.83      5      16       5      11      29

DEC 01     5    8.10    0.36    2.46      5      20       8      13      28

MAR 02     3    3.84    2.14    3.23      3      20      15      18      22

JUN 02     2    2.75    1.16    1.96      2      32      26      29      22

SEP 02     4    4.40    1.55    2.65      4      40       9      19      27

DEC 02     4    1.30    0.64    1.02      4      22       4      13      28

MAR 03     1    4.36    4.36    4.36      1      53      53      53      30

JUN 03     4    8.93    2.37    4.43      4      32      12      18      30

SEP 03     3    2.25    2.20    2.22      3      34      20      25      31

DEC 03     2    4.63    1.59    3.11      2      34      10      22      31

MAR 04     3    3.00    2.80    2.92      3      26      15      20      32

JUN 04     3    4.78    1.85    3.23      3      44       4      22      34

SEP 04     4    5.50    1.55    3.11      4      30      11      21      42

DEC 04     2   10.65    6.25    8.45      2      45      19      32      51

MAR 05     2    9.40    5.55    7.48      2      26      13      20      48
                                                                        
JUN 05*    2    3.85    2.91    3.38      2      30       6      18     (55)
                                                                      incomplete


Headings: 
  Del    = delivery 
  NRng   = number of waves per quarter 
  Rng-Hi = the largest high-low range per quarter  
  Rng-Lo = is the smallest high-low range per quarter  
  Rng-Av = average high-low range
  NPd    = the number of waves in a calculation 
  Pd-Hi  = the largest number of days in a wave 
  Pd-Lo  = the least number of days in a wave  
  Pd-Av  = the arithmetic average number of days in a wave.
  Pri    = estimated average price for the quarter


The timeframe MAR 90 through Jun 00 is one of low opportunity and low trading opportunity (a range of 1.0 is $1000). Average wave length for this period is 22 days. From Sep 00 through the present, average wave amplitudes are about double of the earlier ones. Average wave length for the later period is 22 days, same as for the low amplitude region. What the market is doing, is simply offering more opportunity in the same elapsed time.

Advice Engine Select Tables go back only to the 4th quarter of 2000. They select markets with the better trading opportunity, based on a proprietary algorithm. A chart of the annualized opportunity tends to confirm the findings of the wave table, although the dip in opportunity later in 2003 is much sharper. The rebound in 2004 is clear on both representations. It should be kept in mind that Advice Engine data is specifically designed to find trading opportunity, while the waves are more general.
 Data from Advice Engine Select Tables: Trading Opportunity for Crude Oil 2000 - 2005

           Crude Oil  Annualized Opportunity Averages Per Trade
          $   |                                       
              |
          650 |
              |                              X    
          600 |                                  X
              |
          550 |      X                   X 
              |
          500 |
              |
          450 |  
              |
          400 |          X     
              |                      X       
          350 |                                   
              |             
          300 |              X                           
              |
          250 |                  X                   

                01  01  02  02  03  03  04  04  05  05
                                  Years