Jun

16

A common assumption in finance is that because of panic, declines are bigger or faster than rises. Though through personal experience it certainly feels like it, evaluation of single-day moves does not bear this out.

SPY c-c daily returns were ranked, and for each day found how many standard deviations from mean the individual move was. Then compared big up and down days in terms of their st dev multiple. Here, for example, are top and bottom 10:

Date         ret  #stdev    Date         ret  #stdev
07/24/02 0.060 5.580    10/27/97 -0.072 -6.877
01/07/00 0.058 5.426    08/31/98 -0.071 -6.765
10/28/97 0.058 5.391    04/14/00 -0.057 -5.429
10/15/98 0.054 5.019    09/17/01 -0.052 -4.971
09/08/98 0.054 5.019    08/27/98 -0.047 -4.472
07/29/02 0.049 4.551    03/12/01 -0.043 -4.076
01/03/01 0.048 4.487    02/27/07 -0.039 -3.730 (hi pal!)
10/15/02 0.048 4.486    01/04/00 -0.039 -3.730
10/01/02 0.048 4.482    08/04/98 -0.039 -3.693
03/16/00 0.047 4.361    09/03/02 -0.038 -3.638

Notice that for the biggest three up and down days, the magnitude (of move and st dev) is bigger for drops. But going down the list, paired ups are bigger than downs.

This effect was evaluated further by charting the sum of paired up (positive) st devs and down (negative) st devs.

This shows that for all but the most extreme three pairs, the size of big up days is greater than big downs all the way to 40 pairs. Moving in from the tails beyond 40 pairs reverses the size relationship, but the differences are much smaller.

So it seems that for daily returns extreme up-days are bigger moves than extreme down. 

Alston Mabry comments:

Dr. Zussman's post showed that for SPY, the biggest C-C up moves
over the last 10 years were larger in magnitude than the biggest C-C
down moves. (All moves converted to z scores.)

But just to satisfy perverse curiosity, take the SPY data for the last
10 years and look at not 1-day, but all 3-day moves (overlap allowed).

All 3-day moves:
count: 2511
mean move:  +0.10%
sd: 1.95%
negative moves: 1200
positive moves: 1311

Here are the largest 20 of each paired:

Date / z                      Date / z
31-Aug-98  -6.10      15-Oct-02  +5.07
27-Oct-97  -5.16         8-Aug-02  +4.33
14-Apr-00  -4.95       14-Oct-02  +4.23
22-Jul-02  -4.87        30-Jul-02  +4.17
23-Jul-02  -4.63        17-Mar-00  +3.95
5-Aug-02  -4.20        29-Oct-99  +3.63
19-Sep-01  -3.82      26-Jul-02  +3.57
10-Jul-02  -3.76        17-Mar-03  +3.57
12-Mar-01  -3.64      19-Apr-01  +3.45
19-Jul-02  -3.36        31-Jul-02  +3.28
4-Aug-98  -3.29        27-Mar-01  +3.26
21-Sep-01  -3.21      16-Oct-98  +3.23
1-Oct-98  -3.15         15-Oct-98  +3.02
17-Sep-01  -3.05      29-Jul-02  +3.00
21-Feb-01  -3.01      19-Oct-98  +2.91
19-Sep-02  -3.01      15-Sep-98  +2.84
4-Oct-02  -2.99         16-Mar-00  +2.81
28-Aug-98  -2.92       9-Aug-02  +2.73
13-Mar-01  -2.91       6-Jan-03  +2.69
20-Sep-01  -2.79       1-Jun-00  +2.66

In only one instance in the top 20 does the positive move have a greater magnitude than its paired negative.

And it turns out that if one pairs the top 500 in magnitude of negative
and positive 3-day intervals, the negatives are larger in magnitude
than the positive 498 times.

So, watch out for those drops!


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