THADAVILLIL JITHENDRANATHAN 271Table 14.1 Descriptive statistics of weekly returns from 9 January 1995 to
27 December 2004
Name Mean Std. dev. Skewness Kurtosis Jarque-Bera
3M Co. 0.00269 0.035925 0.128619 2.899320 183.5649
Alcoa Inc. 0.00234 0.049083 0.092774 1.559698 53.4535
American Express 0.00370 0.046580 −0.689641 4.191052 421.7922
Boeing Co. 0.00178 0.050970 −1.294453 9.671405 2171.8343
Caterpillar Inc. 0.00281 0.046521 0.072897 1.022872 23.1296
E.I. du Pont 0.00165 0.041369 −0.275150 1.255070 40.6906
Exxon Mobil 0.00287 0.029678 −0.363687 2.217943 118.0474
General Electric 0.00320 0.039681 −0.321620 3.536954 280.0157
General Motors 0.00102 0.043620 −0.349797 3.129738 222.8350
Honeywell 0.00176 0.052903 −1.477493 10.179735 2434.4439
IBM 0.00332 0.048704 0.233023 2.151064 104.9592
JP Morgan 0.00231 0.052093 0.007047 1.218793 32.1892
McDonald’s 0.00176 0.040196 −0.096122 1.434563 45.3901
Merck & Co. 0.00162 0.043450 −0.899514 4.107817 435.7310
Microsoft 0.00400 0.050139 −0.229235 1.463085 50.9342
SBC Comm. 0.00134 0.043267 0.175905 2.952786 191.5921
Coca-Cola 0.00239 0.053019 −0.746449 7.363402 1223.0493
P & G 0.00283 0.041425 −3.865948 41.841616 39227.5663
United Technology 0.00390 0.043373 −2.294469 21.525604 10495.5498
Walt Disney 0.00131 0.047635 −0.533730 4.322953 429.5935
The average standard deviations of the 20 stocks estimated using the two
methods for the five-year period from January 2000 to December 2004 is
plotted in Figure 14.1. With the rolling method, the standard deviations
of individual stock returns are calculated using equation (14.7). The first
observation in the plot is the average of standard deviations estimated for
the time period from 9 January 1995 to 27 December 1997 using the weekly
returns. From that point onwards, each observation is for a period that
is moved ahead by one week. For example, the second observation is for
the period from 16 January 1995 to 3 January 2000. In this way weekly
observations are created using the rolling window of five years worth of
weekly data.
The dynamic volatility estimates in the plot also covered the period from
3 January 2000 to 27 December 2000 and are computed using a GARCH(1,1)
model. The difference between the two methods is that the rolling model
uses past data to estimate the standard deviations and the GARCH models
use only the data within the time period to estimate the standard deviations.