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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
```