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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