270 TIME-VARYING RETURN CORRELATIONS AND PORTFOLIOSfor the last week of the time period, which is 27 December 2004. In this
way it is possible to capture the full extent of the time-varying nature of
these variables as it existed at the time of construction of the portfolio. To be
consistent with the time-varying nature of variances and correlations, the
mean returns for the last four weeks of the sample is used as the expected
mean for each of the stocks.
Using the above procedure, I am able to get the weights of the indi-
vidual stocks in each of the efficient portfolio. Using these weights and
the actual returns of each of the 20 stocks for periods of one-month, three-
months and six-months from the date when the efficient portfolio is created,
ex postreturns of the efficient set of portfolios are calculated for each of the
60 months for which efficient sets are calculated. The performance of effi-
cient portfolios computed using the rolling method and the DCC method
are then compared using the following regression equation:
Rj,t=α+βDummyj,t+εj,t (14.15)whereRj,tis the pooled returns of all eleven efficient portfolios for a period
of sixty months andDummyj,tis a dummy variable, which is 1 if the portfolio
is estimated using the DCC method and 0 if it is estimated using the rolling
method. If the regression coefficientβis significant, then it indicates that
there is difference in theex postperformance of the portfolios estimated using
the two different methods. The value of this variable is also the difference
between theex postreturns of portfolios estimated using the two different
methods.
14.3 RESULTS
The descriptive statistics of weekly returns of the 20 stocks in this study are
given in Table 14.1.
The time period in this study covers the tech bubble of the latter half of the
1990s as well as the dramatic events of 9/11 and the subsequent downturn
in the stockmarkets. The average returns for all the 20 stocks are positive
for the entire period, with Microsoft having the highest and General Motors
the lowest weekly returns. There is also considerable variation in standard
deviationofthereturnsofthese20stocks, withalowof0.030forExxonMobil
and a high of 0.053 for Coca-Cola. Fourteen out of the 20 stocks had negative
skewness, which is an indication that during this period these stocks had
more crashes than booms. Kurtosis measures the heaviness of tails, and
ten of the stocks had a measure greater than three, which is an indication
that these stock returns had fatter tails than that for a normal distribution.
Finally, the Jarque-Bera test strongly rejects the normality assumption for
the returns of all 20 stocks in the sample.