EMANUELE BORGONOVO AND MARCO PERCOCO 49asEis not additive, and Limitation 1 would be replaced by the following
(Borgonovo and Apostolakis, 2001a; Borgonovo and Apostolakis, 2001b;
Borgonovo and Peccati, 2004; Borgonovo and Peccati, 2005):
3 utilizingEis equivalent to impose that all the parameters are changed by
the same proportion.These mathematical considerations translate into shortfalls in using PDs
orEfor the evaluation of the impact of weights on trading/reallocation
strategies (TRS):^2 due to Limitations 1 and 3 it is not possible to evaluate
the impact of generic portfolio composition relative changes, and due to
limitation 2, it is not possible to test the impact of simultaneous changes
in groups of weights. In TRS, however, simultaneous changes in more
than one weight are involved and the relative changes are generally not
uniform/proportional.
In this study, we show that the use of an alternative SAtechnique, namely
the Differential Importance Measure (D), leads to overcome the two above
mentioned limitations.Dgeneralizes other local SA techniques, and, in par-
ticular, contains PDs and E as particular cases. D shares two important prop-
erties – (i) additivity and (ii) relative changes consideration. With reference
to TRS analysis, we show that property (i) makes the computation of the sen-
sitivity ofσpon groups of weights straightforward, and property (ii) enables
the analyst to accommodate any relative portfolio composition changes.
The empirical part of this chapter begins with the derivation of the analyt-
ical expression of individual portfolio weightsDfor the SA ofσpestimated
via Generalized Autoregressive Conditional Heteroscedasticity (GARCH)
models.^3 Thanks toDadditivity, we obtain the importance of group of
weights straightforwardly. As a result a method for the SAofσpwith respect
to weight groups (Sectors) is provided.
We apply the approach to a portfolio composed of 30 stocks of the Dow
Jones index. We present numerical results for the impact of weights onσp
in TRS involving uniform, proportional and optimal weight changes.^4 We
show how the utilization of Savage Score Correlation Coefficients (SSCC)
(Campolongo and Saltelli, 1997) can serve as a quantitative measure of
similarity among TRS. We then analyse the portfolio with respect to its sec-
torial composition, examining how the results can be interpreted in terms
of diversification across sectors.
In section 3.2, the definition ofDand some SA background related to the
recent developments in this field are discussed, and in section 3 analytical
considerations on the SA of portfolio models highlighting the limitation of
PDs andEare presented. In section 3.4 results for the SA ofσpestimated via
GARCH models are derived. Section 3.5 presents numerical results focusing
on financial management aspects and their implication in the analysis of
TRS. Section 3.6 offers conclusions and future research perspectives.