stock market volatility

Yesterday, the S&P 500 traded at a low of 1,270.05 and closed near its high for the day, at 1,338.60. Relative to the opening index value of 1310.41, a 67.95 point intraday move sure feels volatile. Since I have been a fairly serious student of financial markets for the past 20 years or so, I thought that it would be interesting to put this into a larger historical perspective.

To do this, I downloaded daily data on the S&P 500 from Yahoo! Finance for the period January 3, 1950 – January 23, 2008. During this period, there are a total of 14,607 observations. My measure is the ratio of the difference between high and low index values for a given day divided by the value of the index at the open; let’s call this variable PCT_CH_SP500. For example, for January 23, 2008, PCT_CH_SP500 = (1,338.60 – 1,270.05)/1,310.41 = 5.27%. Not surprisingly, I found that in a statistical sense, yesterday’s market action was clearly an “outlier”; only .18%, or 27 of the 14,607 trading days during this more than 57 year time period were more volatile. Here are the descriptive statistics for this data series:

Percentile

PCT_CH_SP500

10%

0.00%

25%

0.49%

50%

1.15%

75%

1.67%

90%

2.16%

95%

2.55%

99%

3.55%

The average value for PCT_CH_SP500 during this period was 1.14%, and the standard deviation was 0.90%. Furthermore, the distribution for PCT_CH_SP500 is highly positively skewed (1.73), and fat-tailed (kurtosis = 23.04).

I sorted the dataset from highest to lowest values for PCT_CH_SP500, and it is interesting to see the volatility implications of various major financial events in history. The financial media has drawn comparisons between what is currently happening with other events such as the 1987 stock market crash, the Asian financial crisis in October 1997, the failure of the Long Term Capital Management (LTCM) hedge fund in 1998, and 9/11. The first day that the markets opened after 9/11 was on September 17, 2001, and the value for PCT_CH_SP500 recorded on that day was less than the value for PCT_CH_SP500 recorded yesterday (specifically 5.04% versus yesterday’s 5.27%, although two days later on September 19, 2001, PCT_CH_SP500 came in at 5.26%). In terms of their volatility effects, the Asian financial crisis and the LTCM debacle were both largely two-day events, with dramatic drops on the first day followed by dramatic rallies the second day. Here’s what happened numerically in those cases:

Asian financial crisis

date

open

high

low

close

PCT_CH_SP500

27-Oct-97

941.64

941.64

876.73

876.99

6.89%

28-Oct-97

876.99

923.09

855.27

921.85

7.73%

Long-Term Capital Management

date

open

high

low

close

PCT_CH_SP500

31-Aug-98

1027.14

1033.47

957.28

957.28

7.42%

1-Sep-98

957.28

1000.71

939.98

994.26

6.34%

The title of “granddaddy of volatility” clearly goes to the 1987 stock market crash. Although October 19, 1987 is famous as “Black Monday” (on this day, PCT_CH_SP500 clocked in at 20.47%, the highest value for all data since January 3, 1950) , the month of October 1987 produced 8 days with higher recorded values for PCT_CH_SP500 than what occurred yesterday:

October 1987

date

open

high

low

close

PCT_CH_SP500

16-Oct-87

298.08

298.92

281.52

282.7

5.84%

19-Oct-87

282.7

282.7

224.83

224.84

20.47%

20-Oct-87

225.06

245.62

216.46

236.83

12.96%

21-Oct-87

236.83

259.27

236.83

258.38

9.48%

22-Oct-87

258.24

258.38

242.99

248.25

5.96%

26-Oct-87

248.2

248.22

227.26

227.67

8.44%

28-Oct-87

233.19

238.58

226.26

233.28

5.28%

29-Oct-87

233.31

246.69

233.28

244.77

5.75%

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