266 TIME-VARYING RETURN CORRELATIONS AND PORTFOLIOSwith other securities in the portfolio. Other studies have indicated that the
forecasted returns by the optimization model are highly sensitive to changes
in the expected returns and co-variances (Best and Grauer, 1991; Chopra and
Ziemba, 1993).
Several methods have been suggested to reduce the sensitivity of the
errors of the mean-variance optimization model (Jorion, 1986; Jorion, 1991;
Fletcher and Hiller, 2001). Most of these studies focus on reducing the sensi-
tivity of the optimization model to the input parameters. In this chapter I try
to improve theex postreturns of efficient portfolios by using time-varying
variances and co-variances.
Several studies into the nature of variances and co-variances of asset
returns have indicated that variances and co-variances do change over time
(Goetzmann, Li and Rouwenhorst, 2005; Forbes and Rigbon, 2002). If the
variances and co-variances are time varying, then the next question is which
is the best method of estimating these. The most popular method is to use a
moving average specification in which the correlations are estimated using a
moving window of time. The drawback of this method is that it gives equal
weight to all the observations during the time period used in the moving
average calculations. The other method of estimating the time varying cor-
relations is to use multivariate GARCH models. The first set of models of
this genre is based on the Constant Correlation Coefficient model of Boller-
slev (1990). But the assumption that the correlation coefficient was constant
remained the main weakness of theses models. The second set of GARCH
models are based on the multivariate GARCH models introduced by Kroner
and Ng (1998). Even though these multivariate GARCH models are appeal-
ing from a theoretical standpoint, computationally they suffered from the
problem of estimating too many coefficients at the same time. Engle (2002)
introduced a new class of multivariate GARCH models called “Dynamic
Conditional Correlation Models”, which combined flexibility of the uni-
variate models with the theoretical appeal of time-varying correlations. In
this chapter I use this technique to estimate the time-varying correlations.
The main focus of this chapter is to test whether the efficient portfo-
lios created with variances and co-variance estimates using the multivariate
GARCH models will have superiorex postperformance over the traditional
approach of estimating the same using a moving or rolling window of time.
Two sets of efficient portfolios are created – one using the rolling window of
time and other using the multivariate GARCH models andex postreturns of
these portfolios are calculated for periods of one, three and six months. The
ex postreturns of these two sets of efficient portfolios are then compared to
see if there is any statistically significant difference between the two.
The rest of the chapter is organized as follows. Section 14.2 describes the
empirical methodology and the sources and details of data. The results of the
tests are detailed in section 14.3 and the results are discussed in section 14.4.