Daily Speculations
The Web Site of Victor Niederhoffer and Laurel Kenner
Dedicated to the scientific method, free markets,ballyhoo deflation, value creation and laughter.
A forum for us to use our meager abilities to make the world of specinvestments a better place.

Home

Write to us at: (address is not clickable)

The Professor
Charles Pennington

6/15/05
Bull and Bear, by Chris Hammond and Charles Pennington

In a study we conducted earlier this year ("Up the Ladder, Down the Chute," May 2005), we broached the naive question that has turned up countless times: Is there any prospective way to identify bull or bear markets? In our ongoing effort to address this issue, we looked at the end-of-month prices for the Dow from January 1949 through December 2004. We defined a six-month high pivot as a month where the price is higher than all of the monthly prices within six month before or after, and a six-month low pivot is defined analogously. A pivot cannot be observed until 6 months after it has occurred, so we have found all six-month pivots and calculated the returns 1, 4, 6, 8, and 12 months after they can be identified in order to make the study prospective.

The first table is a summary of the average changes 1, 4, 6, 8, and 12 months after the pivot is observed. The expected 1 month returns after a high or a low pivot are roughly the same, and they are about 50% larger than the average monthly returns. Over a 4 month holding period, low pivots outperform highs, and the average, by about 50%. They are all comparable over 6 months. Over an 8 month period, returns following a high are substandard, but over the year, they are marginally better. However, by looking at the z-score for the difference between the returns following low pivots and following "normal" months, we see no evidence that they are statistically different. Likewise for returns following high pivots.

Average Returns Following
        High and Low Pivots
           1 Month  4 Months 6 Months 8 Months 1 year
   High    0.010    0.026    0.040    0.034    0.089
    Low    0.011    0.041    0.040    0.054    0.074
    ALL    0.007    0.021    0.035    0.050    0.077

Returns Following Normal Months
1 Month    4 Months 6 Months 8 Months 1 year
Average    0.007    0.021    0.035    0.050   0.077
STD DEV    0.042    0.072    0.095    0.116   0.150
#Trials    659      653      649      644     637

Z-Score for Difference of Returns after
Low Pivots and after "Normal" Months
   1 Month 4 Months 6 Months 8 Months 1 year
   -0.49   -1.23    -0.25    -0.18     0.09

Z-Score for Difference of Returns after
High Pivots and after "Normal" Months
   1 Month 4 Months 6 Months 8 Months 1 year
   -0.27   -0.33    -0.26    0.63     -0.45
   
Returns After a Low Pivot is Observed
  Date     1 Month  4 Months  6 Months  8 Months  1 year
  Oct-52   0.054    0.056    0.021      -0.004    0.024
  Feb-54   0.030    0.132    0.140      0.196     0.398
  Aug-57  -0.058    -0.100   -0.092     -0.059    0.050
  Jun-58   0.052    0.136    0.221      0.262     0.346
  Mar-61   0.003    0.042    0.036      0.066     0.045
  Dec-62   0.047    0.101    0.084      0.118     0.170
  Dec-65   0.015    -0.037   -0.102     -0.187    -0.189
  Mar-67   0.036    0.044    0.070      0.011     -0.029
  Aug-68   0.044    0.053    0.010      0.060     -0.066
  Dec-70   0.035    0.123    0.062      0.071     0.061
  May-72  -0.033    -0.008   0.060      0.040     -0.062
  Mar-75   0.069    0.082    0.033      0.120     0.301
  Aug-78  -0.013    -0.082   -0.078     -0.025    0.012
  Apr-79  -0.038    0.038    -0.046     -0.019    -0.044
  Sep-80  -0.009    0.016    0.077      0.064     -0.088
  Jan-83   0.034    0.116    0.115      0.146     0.135
  Nov-84   0.019    0.065    0.106      0.133     0.238
  Mar-87  -0.008    0.116    0.127      -0.204    -0.137
  May-88   0.054    0.040    0.041      0.153     0.221
  Jul-90   -0.100   -0.119   -0.058     0.003     0.041
  Apr-91   0.048    0.054    0.063      0.097     0.163
  May-92  -0.023    -0.037   -0.027     -0.026    0.038
  Apr-93   0.029    0.065    0.074      0.095     0.074
  Dec-94   0.002    0.127    0.188      0.202     0.335
  Feb-99   0.052    0.179    0.164      0.153     0.088
  Aug-00   -0.050   -0.038   -0.064     -0.043    -0.113
  Mar-02   -0.044   -0.160   -0.270     -0.145    -0.232
  Mar-03   0.061    0.155    0.161      0.224     0.296
  
Average    0.011    0.041    0.04       0.054     0.074
STD DEV    0.043    0.087    0.105      0.118     0.168
#Trials    28       28       28         28        28
STD ERR    0.008    0.016    0.02       0.022     0.032

Returns After a High Pivot is Observed
Date      1 Month  4 Months  6 Months  8 Months  1 year
  Mar-52  -0.044   0.037     0.004     0.053     0.039
  Jun-53  0.027    0.028     0.047     0.098     0.243
  Jan-57  -0.030   0.054     0.061     -0.048    -0.061
  Jan-58  -0.022   0.028     0.118     0.182     0.320
  Jun-60  -0.037   -0.094    -0.039    0.033     0.068
  Jun-62  0.065    0.051     0.162     0.181     0.259
  Jul-66  -0.070   -0.066    0.003     0.022     0.067
  Mar-68  0.085    0.050     0.113     0.172     0.113
  May-69  -0.069   -0.133    -0.134    -0.206    -0.253
  Oct-71  -0.009   0.106     0.137     0.107     0.139
  Jun-73  0.039    0.073     -0.046    -0.035    -0.100
  Apr-74  -0.041   -0.189    -0.205    -0.264    -0.018
  Dec-75  0.144    0.169     0.176     0.142     0.179
  Jun-77  -0.029   -0.107    -0.093    -0.190    -0.106
  Feb-79  0.066    0.041     0.097     0.009     0.067
  Feb-80  -0.090   0.006     0.080     0.071     0.129
  Sep-81  0.003    0.025     -0.032    -0.036    0.054
  May-84  0.025    0.092     0.076     0.165     0.191
  Feb-88  -0.040   0.034     -0.019    0.037     0.090
  Jan-91  0.053    0.106     0.105     0.102     0.178
  Nov-92  -0.001   0.039     0.067     0.071     0.115
  Jul-94  0.040    -0.007    0.021     0.104     0.251
  Jan-98  0.081    0.126     0.124     -0.008    0.184
  Oct-98  0.061    0.083     0.256     0.277     0.249
  Jun-00  0.007    0.050     0.032     0.005     0.005
  Feb-01  -0.059   0.000     -0.052    -0.135    -0.037
  Nov-02  0.017    0.056     0.007     -0.113    -0.097
  Sep-02  0.106    0.061     0.053     0.166     0.222
  
Average   0.010    0.026     0.040     0.034     0.089
STD DEV   0.059    0.080     0.099     0.130     0.137
#Trials   28       28        28        28        28
STD ERR   0.011    0.015     0.019     0.025     0.026