EMANUELE BORGONOVO AND MARCO PERCOCO 5919920123455781993 1994 1995 1996 1997Portfolio volatility1998 1999 2000 2001 2002Figure 3.2 Volatility of the portfoliocolumns 1 and 2 are the SA results that would be obtained if an analyst
made use of PDs orErespectively (see Propositions 1 and 2). The difference
in ranking shows that conclusions onσpsensitivity obtained by making use
of PD/Ecannot be extended to TRS other than uniform/proportional ones
respectively.
Let us now discuss how the use of Savage Score correlation coeffi-
cients (SSCC) can enable the analyst to have a quantitative measure of TRS
similarity. We refer the reader to Campolongo and Saltelli (1997) for the
mathematical definition of SSCC’s. For the purposes of this paper, we need
only to recall that a high SSCC between two rankings means that the most
and least influential assets tend to be the same.
Table 3.4 displays the Savage Score correlation matrix for the three
strategies for the portfolio at hand.
The interpretation of Table 3.4 is as follows. Rankings in proportional and
optimal strategy tend to be more correlated than rankings of the uniform
and optimal strategy. This suggests that the optimal strategy is closer to a
proportional rather than a uniform one from an SA viewpoint.
Finally a note on the information that one can infer from the quantification
of the total change in volatility provoked by the three strategies (Table 3.2).
In the case shown in Table 3.2, the TRS imposing uniform changes will result
in a decrease of−7.0 in the volatility and the optimal strategy would reduce