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
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".
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:
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