Briefly Speaking, by Victor Niederhoffer
The first blow is half the battle. There is so much drift in stock prices that it's hard to do a good seasonal study, especially since there are numerous possible comparisons and only a small number of years to reep profit. With the best of intentions, I decided to do a proper seasonality study on a going forward basis using prospective information only, which is the only way to do a seasonal study and develop some confidence in it. I decided to handle January in a similar fashion in honor of the mumbo about neural et al since I saw that similarities gave the same results as neural in all cases, but are duplicatable and understandable. This year, January was up 1.4 %. I figured I'd take all the years that had a January of within a 1.5 % range of that and look at the moves in the next three Feb. and the next three January months end to year end. Then I would compute a running total and use that running total to predict the next occurrence. But the best laid plans often go astray. There were only six Januaries with a chance of anything around 1.5% since 1959. The problem is that January is a wild month with many 5 to 10% moves and more. These six Januaries were as follows, with moves the next month and the next 11 appended.
| Year | Jan. Move | Feb. Move | Jan. End - Year End |
| 1968 | 0.5 | -1.8 | -11.5 |
| 1972 | 1.8 | 2.5 | 13.8 |
| 1986 | 0.2 | 7.1 | 7.5 |
| 1993 | 0.7 | 1.0 | 6.1 |
| 1998 | 1.0 | 7.0 | 26.0 |
| 2004 | 1.7 | 1.2 | 7.2 |
| Avg. | 2.8 | 4.3 |
No prospective tests are possible because of the paucity. However, the 2.8 % move in Feb. looks about 5 in 100 by chance, which the artful simulator will vet. tomorrow morning.
Steve Wisdom writes:
Previously, Vic wrote that there were only six Januaries with a change of anything around 1.5% since 1959. The problem is that January is a wild month with many 5% to 10% moves and more. Below displays a stem & leaf of January % changes in SPX, since 1959. As suggested by Chair, there are several moves >10%.
-7 | 72
-6 | 92
-5 | 10
-4 | 64
-3 | 8
-2 | 750
-1 | 8760
-0 | 98
0 | 2457
1 | 0478
2 | 457
3 | 33335
4 | 000129
5 | 8
6 | 13
7 | 148
8 |
9 |
10 |
11 | 8
12 | 3
13 | 2
Alston Mabry adds:
“The problem is that January is a wild month with many 5% to 10% moves and more.”
If you look at each January move (S&P cash, 1959-2007) as a z-score using the mean and sd of the previous 12 months, and then create a histogram with steps of .25, you get a distribution with a somewhat different "balance":
z / frequency
-3.39 1
-3.14 0
-2.89 0
-2.64 0
-2.39 1
-2.14 1
-1.89 1
-1.64 3
-1.39 3
-1.14 2
-0.89 0
-0.64 2
-0.39 2
-0.14 2
+0.11 4
+0.36 5
+0.61 4
+0.86 3
+1.11 4
+1.36 1
+1.61 2
+1.86 4
+2.11 1
+2.36 2
+2.61 0
+2.86 1