THADAVILLIL JITHENDRANATHAN 273correlations are calculated using equation (14.8) and, in a similar fashion
as the standard deviations, by using a rolling window of five years. The
other set of correlations are estimated using the DCC method described in
section 14.2.
As can be seen in this plot, the rolling correlation estimates tend to smooth
out the short-term changes in correlations. There is a dramatic increase in
the correlations after 9/11, which is much more pronounced with the DCC
model than the rolling correlations model. The rolling correlations model
and the DCC model are very similar at the beginning and towards the end of
the period, where the fluctuations in the average correlations are relatively
small. On the other hand for the period after 9/11, the average correlations
estimated using DCC method had much higher variability than the rolling
model.
The plots of efficient set of portfolios estimated using the DCC model is
given in Figure 14.3. This plot contains 36 efficient portfolio sets for each
of the months from January 2002 to December 2004. The purpose of this
graph is to illustrate how the efficient frontier changes with the changes in
expected returns, variances and co-variances.
It is clear from the plots of efficient frontiers that the frontier moved
around quite a bit during the 30 months. In most of the instances, the stan-
dard deviations of the minimum variance portfolios are very close to each
other, but the expected returns are substantially different in most of the cases.
It may also be observed that in some instances entire sets of efficient port-
folios have negative returns. This is due to the fact that I use the four-week
average returns in my portfolio optimization model, and in a few instances
all the stocks in the portfolio has negative returns.
Std. dev.0.010.050.040.0200.02Returns0.040.060.080 0.02 0.03 0.04 0.05 0.06 0.07 0.08Figure 14.3Efficient portfolios for the months January 2003 to
December 2004