Daily Speculations The Web Site of Victor Niederhoffer and Laurel Kenner
 The Chairman Victor Niederhoffer About Victor Niederhoffer
Write to us at:(address is not clickable)

5/27/2005

The alacrity with which the managers are rushing to take the remaining contracts and shares at the 1200 S&P level reminds me of what Art Bisguier always used to say after I got myself into a bad position and then reflected as I tried to get out of it: "Now... you're thinking ?!"

Much more helpful was the approach of Tom Wiswell who would scratch the cap or cane 50 moves before and quietly say "You have a good move". Such can help you build a stately mansion on the "board".

5/27/2005
Up the Ladder, Down the Chute, by Chris Hammond and Charles Pennington

Laszlo Birinyi's firm recently prepared a table that partitioned the time from 1962 through the present into periods of rally and decline for the S&P. Among the questions it suggested, one of the most prominent was "Is this behavior consistent with randomness?" Before we could begin to answer this question, we had to first decide how to reconstruct the data using some algorithm. Using monthly data for the S&P since 1953, we settled on the following procedure:

1. Select a point as being a potential maximum if the price of the S&P at the close of the month is greater than the price at the close of the previous six months as well as the next six months (which means, of course, that one cannot identify such a point until six months after it has occurred). Minima are selected in the same fashion.
2. Order the set of all maxima and minima. If there are several maxima before a minimum, throw away all but the last one. Do likewise for minima. One is left with a set of points partitioning the time from 1953 to 2005.
3. The periods from a minimum to a maximum will be called rallies, and the periods from a maximum to a minimum will be called declines.

The results of performing this procedure to the S&P are shown below. For each period, we take note of its duration in months, and the annualized percent change in price over the period. This provides a reasonable approximation to the Birinyi table. However, it is also a little finer, giving us a larger data set.

In order to address the question posed, we found the percent change over each month, and we stored it in a list. We then simulated the S&P time series by starting at the same initial value and moving to the next month's value by randomly selecting one of the percent changes in our list and using that as the current month's percent change. We sample without replacement, i.e., we use all of the same values but in a random order. We perform our algorithm on each of the simulated time series and keep track of the data. Twenty trials were performed.

We find a significant distinction between the actual S&P data and the simulations. The average duration of a rally in the S&P is 22 months, and there were 17 rallies. For each simulation, there was an average rally duration. Taking the average of these yields 15 months, with 25 rallies on average. The standard deviation is 3.4 months. The actual value for the average rally duration is about 4 standard deviations away from the mean, a significant finding. This indicates that actual rallies tend to last longer than in the simulations.

This could be the result of correlation in returns between successive months, meaning that when you are rising, you tend to continue doing so, making for a longer run. When you remove these correlations, you get choppier time series. However, there are some misgivings regarding this approach. One objection is that "If its not predictive, then it is consistent with randomness," and our study has no predictive value. These are questions that ought to be addressed and which will require significant thought.

```Table 1: Rallies and Declines in the S&P 500 Since 1953, Monthly Data

Duration        Annualized Return
Stage     Start   End      Rally  Decline  Rally Decline
Rally     Aug-53  Jul-56      35            0.29
Decline   Jul-56  Feb-57               7           -0.20
Rally     Feb-57  Jul-57       5            0.28
Decline   Jul-57  Dec-57               5           -0.35
Rally     Dec-57  Jul-59      19            0.30
Decline   Jul-59  Oct-60              15           -0.10
Rally     Oct-60  Dec-61      14            0.29
Decline   Dec-61  Jun-62               6           -0.41
Rally     Jun-62  Jan-66      43            0.16
Decline   Jan-66  Sep-66               8           -0.25
Rally     Sep-66  Sep-67      12            0.26
Decline   Sep-67  Feb-68               5           -0.17
Rally     Feb-68  Nov-68       9            0.29
Decline   Nov-68  Jun-70              19           -0.22
Rally     Jun-70  Apr-71      10            0.54
Decline   Apr-71  Nov-71               7           -0.16
Rally     Nov-71  Dec-72      13            0.23
Decline   Dec-72  Sep-74              21           -0.30
Rally     Sep-74  Jun-75       9            0.71
Decline   Jun-75  Feb-78              32           -0.03
Rally     Feb-78  Aug-78       6            0.41
Decline   Aug-78  Oct-78               2           -0.43
Rally     Oct-78  Nov-80      25            0.22
Decline   Nov-80  Jul-82              20           -0.15
Rally     Jul-82  Jun-83      11            0.63
Decline   Jun-83  May-84              11           -0.11
Rally     May-84  Aug-87      39            0.27
Decline   Aug-87  Nov-87               3           -0.76
Rally     Nov-87  May-90      30            0.20
Decline   May-90  Oct-90               5           -0.34
Rally     Oct-90  Dec-91      14            0.31
Decline   Dec-91  Jun-94              30           -0.02
Rally     Jun-94  Aug-00      74            0.22
Decline   Aug-00  Sep-01              13           -0.29
Rally     Sep-01  Feb-04      29            0.04

Average                     22.1    12.3    0.31   -0.25

Table 2: Results of Simulating the S&P Time Series

Rallies                              Declines
Number Duration  StDev   Annualized  Number Duration  StDev   Annualized
Return                               Return
Average     24.55    14.94  11.80   0.33         24.55    10.40   8.74  -0.23
StDev        2.52     1.68   3.40   0.05          2.40     2.04   3.11   0.03
StErr        0.56     0.38   0.76   0.01          0.54     0.46   0.70   0.01
Actual         17    22.06  17.47   0.31            16    12.29   8.94  -0.25
T-score     -2.99     4.23   1.67  -0.41         -3.57     0.93   0.06  -0.64```